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Water and Environmental EngineeringDepartment of Chemical Engineering

Modeling Anaerobic Digestion-Validation and calibration of the Siegrist model

with uncertainty and sensitivity analysis

Master Thesis by

Oscar Lidholm & Elin Ossiansson

November 2008

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Vattenförsörjnings- och AvloppsteknikInstitutionen för Kemiteknik

Lunds Universitet


Lund University, Sweden

Modeling Anaerobic Digestion

Master Thesis number: 2008-12 by

Oscar Lidholm & Elin Ossiansson


Lund University

November 2008

Supervisor: Professor Jes la Cour Jansen

Examiner: Associate Professor Karin Jönsson

Picture on front page:

Figure 26 Examples of scatter plots for the Aalborg household wasteexperiment; gas production vs. TS (left) and gas production vs. kH (right)

from MC analysis on characterization and model parameters respectively(Figure 26).

Postal address: Visiting address: Telephone:

P.O Box 124 Getingevägen 60 +46 46-222 82 85SE-221 00 Lund +46 46-222 00 00Sweden Telefax:

+46 46-222 45 26

Web address:

www.vateknik.lth.se

1

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SummaryAnaerobic digestion is a complex system of biochemical and physical processes. Due to thecomplexity of the process, it has traditionally been treated as a black box system, andoptimization has been based on experience or trial and error methods. As experiments ofanaerobic digestion processes are expensive and time consuming, modeling can provide a

useful tool for process understanding and optimization. Models have potentials for revealingnon-linear behaviors of the system and to quantify the performance of alternative operationalsetups. The aim of this work was to evaluate the uncertainty, sensitivity and applicability of amodel for anaerobic digestion of mixed sludge published by Siegrist et al (2002) on pilot andfull scale processes.

Experimental data from two pilot scale experiments on household waste and one experimenton mixed sludge published in Davidsson (2007) were used for validation of the model. Thehousehold waste experiments were operated at meso- and thermophilic temperaturerespectively, and the sludge experiment was conducted at mesophilic temperature. For thehousehold waste experiments, characterizations of the substrates were available and thehydrolysis dynamics was determined from batch experiments. The results from the validationshowed that the steady state gas production could be predicted in the household wastesimulations, but not to the same extent in the sludge reactor simulation. The ammoniumcorrelated better for the sludge validation than for the household waste experiments, but VFAconcentrations needed to be calibrated for all simulations.

To assess the quality of the simulations, uncertainty analysis is required. The effect ofmeasurement uncertainty on the model predictions was evaluated using Monte Carlo methods.It was concluded that measurement errors could explain some of the discrepancy betweensimulations and data, but that further calibration was needed. It was also concluded that thehousehold waste characterization measurements reduced the prediction uncertaintysubstantially, compared to using a general waste composition. The gas production andammonium proved to be highly affected by the quality of the input data while the alkalinityand VFA were less influenced.

To deepen the understanding of the process, and to find the parameters best suited forcalibration, sensitivity analysis was conducted. The importance of individual input and model

parameters were quantified with a variance-based method with Monte Carlo sampling,measuring the effect of individual parameter variations on the total variance of outputs. Thismethod needed to be supplemented with scatter plots, to enable visual evaluation of thecorrelation between parameters and output. A drawback of the sensitivity analysis was the

lack of reliable distributions for the model parameters, which produced unreliable results. Itwas concluded that better defined distributions would provide a better ground for finding parameters for calibration.

The most important parameters to determine the gas production were the degradability and thehydrolysis rate constant. The VFA and alkalinity, on the other hand, were dependent on themodel parameters connected to propionate degradation and acetoclastic methanogenesis. Tocalibrate the VFA concentrations, the half saturation constants were changed substantially.This implies different mass transfer conditions than suggested in the model implementation

by Siegrist et al. (2002). The precision for ammonium prediction could not be improvedwithout recalibration of the feed protein content. It was therefore concluded that a revision of

the model structure was needed for a successful validation. A slower hydrolysis rate for protein than for e.g. sugar would be required. After calibration, the model precision was

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improved significantly for the mixed sludge, while the precision for the household wastesimulations could not be improved to the same extent.

The full scale operation at Käppala waste water treatment plant on Lidingö was simulated tovalidate the model and evaluate various process designs. Data of flows and VS measurements

were used as input to the model, complemented with literature values for the characterizationof the sludge. The simulation gave predictions of gas production and alkalinity withacceptable accuracy. To evaluate different reactor setups and pretreatment options,simulations were tested and evaluated with respect to gas production, sludge reduction andeconomical viability. The simulations with different scenarios indicated that there areeconomical incitements to operate reactors in series, at thermophilic temperature, and to useenzymatic pretreatment of waste activated sludge.

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SammanfattningAnaerob nedbrytning är ett komplext system av biokemiska och fysiska processer. På grundav systemets komplexitet har det traditionellt blivit betraktat som ett s.k. black box system,och optimering har baserats på erfarenhet och praktiska försök. Eftersom experiment är bådekostsamma och tidsödande kan modellering vara ett användbart verktyg för ökad förståelse

och processoptimering. Modeller har potentialen att exponera olinjärheter i systemet och attkvantifiera prestandan för alternativa utformningar av processer. Målet med det här arbetetvar att utvärdera osäkerheten, känsligheten och användbarheten för en modell av anaerobnedbrytning av blandslam publicerad av Siegrist et al (2002). Modellen applicerades pårötning av hushållsavfall i pilotskala och rötning av blandslam i pilot- och fullskala.

Data från två experiment i pilotskala med hushållsavfall och ett experiment med blandslam, publicerade i Davidsson (2007), användes för validering av modellen. Hushållsavfalletrötades mesofilt och termofilt, och blandslammet rötades vid mesofil temperatur.Karaktäriseringar för hushållsavfallen fanns att tillgå, och hydrolyskonstanten för ett avhushållsavfallen och för blandslammet bestämdes med data från flaskförsök. Resultaten frånvalideringen visade att gasproduktionen vid stabil drift kunde simuleras med godträffsäkerhet, medan träffsäkerheten för simuleringen med blandslam inte var lika god.Mätningar och simuleringar för ammonium korrelerade bättre för valideringen med blandslamän för hushållsavfallen, medan koncentrationen av flyktiga organiska syror (FOS) behövdekalibreras för samtliga fall.

Osäkerhetsanalys fordrades för att bedöma kvaliteten av simuleringarna. Effekten avmätosäkerheter på modellens prediktioner utvärderades med en Monte-Carlo metod.Slutsatsen var att mätosäkerhet kunde förklara en del av skillnaderna mellan simuleringar ochdata, men att kalibrering av parametrar behövdes för att öka korrelationen. Det kunde ävenobserveras att en uppmätt karaktärisering väsentligen kunde minska osäkerheten i utdata

jämför med att använda en generell karaktärisering för hushållsavfall. Gasproduktionen ochammonium visade sig vara mycket påverkade av kvaliteten hos indata, medan alkalinitetenoch FOS var mindre påverkade.

För att öka förståelsen av processen och hitta de parametrar som är bäst lämpade förkalibrering genomfördes en känslighetsanalys. Vikten av inflödes- och modellparametrarnakvantifierades med en variansbaserad metod, och prover renderade med Monte-Carlometoden användes. Denna metod behövde kompletteras med punktdiagram för att visualiserakorrelationen mellan parametrarna och utdata. En nackdel med känslighetsanalysen varavsaknaden av trovärdiga fördelningar för modellparametrarna, vilket ledde till otillförlitligaresultat. Bättre definierade intervall för modellparametrarna skulle möjliggöra en mertillförlitlig känslighetsanalys och därmed ge bättre grund för att hitta lämpliga parametrar attkalibrera.

De viktigaste parametrarna för att bestämma gasproduktionen var nedbrytbarheten ochhydrolyskonstanten. Alkaliniteten och FOS var å andra sidan beroende avmodellparametrarna kopplade till acetogenes av propionsyra och acetoklastisk metanogenes.Halvmättnadskonstanterna för dessa processer ökades avsevärt i kalibreringen, vilket visar påförändrade betingelser för masstransport än vid modellkalibreringen av Siegrist et al.Träffsäkerheten för ammoniumprediktionen kunde inte förbättras utan att kalibrera

proteininnehållet i substratet. Slutsatsen av detta var att en lägre hydrolyshastighet för proteinän för t.ex. kolhydrater skulle krävas för en lyckad validering. Efter kalibreringen ökadekorrelationen avsevärt för simuleringen av blandslam, medan precisionen för simuleringarnamed hushållsavfall inte kunde förbättras i samma utsträckning.

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Fullskaleprocessen på Käppala reningsverk på Lidingö simulerades för att validera modellenoch jämföra olika processdesign. Data för flöden och VS användes som indata i modellen, ochkompletterades med karaktäriseringar av primär och sekundärslam från litteraturen.Simuleringarna gav en godtagbar träffsäkerhet för gasproduktionen och alkaliniteten. Olika

processkonstruktioner simulerades och utvärderades med avseende på gasproduktion, VS-

reduktion och ekonomisk nytta. Simuleringarna av de olika scenarierna påvisade att det finnsekonomiska incitament att införa seriell drift, termofil rötning och att använda enzymer förförbehandling av sekundärslam.

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AcknowledgementsThis Master Thesis project would not have been possible without the valuable assistance fromour supervisors, Jes la Cour Jansen and Michael Recktenwald (Kemira RecyclingCompetence Center). The cooperation has been a pleasure, and owing to your competence wehave gained a lot of insights to the field of anaerobic digestion. Mattias Alveteg has been very

helpful when we accoutered programming and modeling problems. The experimental datareceived from Åsa Davidsson, was used extensively in this dissertation. Many thanks forassisting us also with supplementary information. We would also like to recognize AndreasThunberg for providing us with information on the full scale process at Käppala WWTP.Hansreudi Siegrist helped us with the implementation of the model, something we are verygrateful for. We would also like to thank our competent opponent, Niklas Borg, and the otherfolks at the department for good company at the coffee breaks. Last, but not least, thank youEmma and Fredric for your loving support.

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Abbreviations and symbols

Waste Water Treatment Plant WWTPLong-Chain Fatty Acids LCFAVolatile Fatty Acids VFA

Gas-liquid transfer coefficient k La d-1

Continuously Stirred Tank Reactor CSTRUpflow Anaerobic Sludge Blanket UASBTotal solids TSVolatile solids VSPerson Equivalents p.e.Chemical oxygen demand COD g/m3 Solubilized COD SCOD g/m3 Extracellular Polymeric Substances EPSWaste Activated Sludge WASAnaerobic Digestion Model no. 1 ADM1Sludge Retention Time SRT dHydraulic Retention Time HRT dOrdinary Differential Equations ODEVector of liquid phase state variables x i

Liquid concentrations

ProtonsHydrogenMethaneCarbon dioxideHydrogen carbonate

Ammonium ionsAmmoniaAcetateAcetic acidPropionatePropionic acidDissolved amino acidsDissolved sugarsDissolved long chain fatty acidDissolved inert CODParticulate degradable COD

Amino acid fermentersSugar fermentersLong chain fatty acid degradersPropionate degradersAcetotrophic methanogensHydrogenotrophic methanogensInert particulate matter

Partial pressures in gas bubbles

HydrogenMethaneCarbon dioxide

S H

S H2

S CH4

S CO2

S HCO3

S NH4 S NH3

S ac

S hac

S pro

S hpro

S aa

S su

S fa

S in

X S

X aa X su

X fa

X pro

X ac

X H2

X in

p H2

pCH4

pCO2

mol/m3 mg COD/m3 g COD/m3 mol/m3

g COD/m3

bar

Volumetric flow q m3/dVolume V m3

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Vector of inflow concentrations cin

Vector of outflow concentrations cout

Vector of reaction rates r

Vector of reaction rates includinggas stripping reactions r tot

Vector of gas stripping rates r stripping Stoichiometric matrix T

Stoichiometric coefficient ѵ

Vector of reaction rates for all processes ρ

Hydrolysis rate constant d-1

Maximum growth rate d-1

Half saturation constant for growth g COD/m3 Decay rate d-1

Inhibition of process I Inhibition constant K I Chemical equilibrium rate constant

Acidity constant / Partial pressure p barMolecular weight MG g COD/molGas constant R bar m3 mol-1 K -1 Temperature T Proportional constant K pDifferential Algebraic Equations DAEUncertainty Analysis UAProbability Density Function PDEMonte Carlo MC

Stochastic Differential Equations SDELatin Hypercube Sampling LHS Number of realizations N

Cumulative Distribution Function CDFSensitivity Analysis SAModel coefficient of determination R2

Model value for output parameter θ

Simulated value for output parameter θ

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Contents

1. Introduction ............................................................................................................................ 1

2. Theoretical background to anaerobic digestion ..................................................................... 3

3. Overview of existing models .................................................................................................. 7

4. Mathematical structure of the Siegrist model ........................................................................ 9

5. Numerical aspects ................................................................................................................ 13

6. System identification ............................................................................................................ 15

7. Model validation .................................................................................................................. 17

8. Uncertainty analysis ............................................................................................................. 33

9. Sensitivity analysis ............................................................................................................... 45

10. Sensitivity analysis of the Siegrist model .......................................................................... 4911. Calibration of the model parameters .................................................................................. 59

12. Industrial scale application ................................................................................................. 71

13. Conclusions ........................................................................................................................ 77

14. Suggestions for further research ......................................................................................... 79

References ................................................................................................................................ 81

Appendices ...................................................................................................................................

Article ...........................................................................................................................................

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1. Introduction

1.2. BackgroundIncreasing awareness of global warming and rising energy prices have led to a growinginterest for renewable energy during recent years. Biogas, consisting mainly of methane, is an

energy carrier with many advantages. It can be produced from a variety of substrates, preferably from different types of wastes, in the process of anaerobic digestion. The techniqueis widely used at waste water treatment plants (WWTPs) for reducing the waste volume andstabilizing the sludge produced from waste water treatment. The process can also be appliedto treat e.g. household and agricultural waste, turning them into valuable resources andsolving a waste handling problem. Greenhouse gas reduction is not only attained by thereplacement of fossil fuels, but digesting household waste, sludge and manure prevents directemission of the strong greenhouse gases methane and nitrous oxide to the atmosphere. Theresidues from the digestion process can be used as fertilizer on farmland, and the carbondioxide produced from the methane combustion is thus taken up by plants. Plants which onceagain can be used for biogas production, thus the carbon cycle is closed.

1.3. Why model anaerobic digestion?To increase the biogas production capacity at WWTPs, different alternatives can beconsidered. Serial digestion and thermophilic temperature are possible measures for improved

process efficiency. Another technique is to increase the degradation of the sludge withdifferent methods of sludge pretreatment. At many facilities, the possibilities of includingother wastes than sludge, e.g. household waste is considered as a way to increase the biogas

production. Before implementation of a new process design, it is essential to evaluate thealternatives. Pilot plant and lab scale experiments are important tools, but costly and timeconsuming.

Mathematical models can serve as useful tools to deepen the understanding of complexsystems, and to facilitate operation and design of the process. If the behavior of a system can

be predicted, the production can be optimized and process failure can be prevented. Moreeffective processes could lead to a better competitiveness for biogas as an energy carrier.Despite of these motivations modeling has rarely been applied on anaerobic digestion(Batstone, et al., 2003). The obstacles for introducing modeling to the industry are amongothers that the models of anaerobic digestion are complex and require extensive input data,and that the performance of the models on full scale processes has not yet been tested(Batstone, 2006). It is therefore interesting to perform validations and uncertainty/sensitivityanalysis of the models to gain knowledge that will facilitate model application.

1.4. The aim of this workThe aim of this work was to evaluate the uncertainty, sensitivity and applicability of amathematical model on pilot scale digestion of sludge and household waste. The model foranaerobic digestion of mixed sludge, published by Siegrist et al. (2002) was also used forstudying the potentials of simulating a full scale process with different operational settingsand pretreatments.

Some of the questions that needed to be answered were: What input data is required to use themodel with desirable accuracy? Which model parameters are most influential? Is the modelsuitable for simulating household waste digestion? Can the results from a sensitivity analysis

be used for calibration of model parameters? Can the model predict the operation at a fullscale digester, and how can the model be used to evaluate different process designs?

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Central methods for investigating these questions were uncertainty and sensitivity analysis.

1.5. Outline of the reportAn introduction to anaerobic digestion is given in section 2, and an overview of models can

be found in section 3. A presentation of the Siegrist model (section 4) is then followed by a

discussion on the numerical aspects of the implementation (section 5). In section 6, the readerwill be introduced to system identification of models. The first validation of the model,including description of the data, input parameters, results and reflections is presented insection 7. The uncertainty analysis, section 8, includes introduction, results and reflections. Insection 9, a literature study on sensitivity analysis is provided as in introduction to section 10,where the results from the sensitivity analysis on the studied examples are presented. Theseresults were used in the calibration of parameters (section 11). Examples of application on fullscale digesters, in section 12, give an insight on the practical benefits from model use. Last,

but not least, are the conclusions and proposals for further studies in section 13 and 14. Thelast part of the report includes the appendices and the unpublished article “Application,uncertainty and sensitivity of the anaerobic digestion model by Siegrist et al. (2002) on

household waste digestion”.

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2. Theoretical background to anaerobic digestion

2.1. Biochemical reactionsAnaerobic degradation of organic material to methane and carbon dioxide is a complexsystem of biochemical reactions. The reactions are commonly divided into four groups of

processes; hydrolysis, acidogenesis, acetogenesis and methanogenesis (Figure 1), each stepinvolving a specific group of microorganisms. To obtain a stable and efficient process all fourreaction steps need to function, as the processes are connected.

Figure 1 Overview of the biochemical reactions in anaerobic digestion with flows expressed as percent of

COD (from Siegrist et al 2002 based on Gujer et al 1983)

2.1.1. Hydrolysis

In this context hydrolysis refers to the group of reactions that degrades particulate organicmatter, consisting of complex carbohydrates, proteins and lipids to soluble monomers. Theend products are dissolved amino acids, sugars, long-chain fatty acids (LCFA) and dissolvedinert organic matter. The process can be subdivided into biological, chemical and physical

hydrolysis. Biological hydrolysis occurs when microorganisms excrete enzymes such aslipase, protease and sucrase that attack the substrate. Chemical hydrolysis is often due to weakacids or bases, which can be added to increase the hydrolysis rate. It can also be effective tomechanically facilitate the disintegration of particulate matter by treatment with ultrasound orwith thermal treatment. These processes are examples of physical hydrolysis.

Hydrolysis is often rate limiting when the particulate matter is not readily degradable or insystems with high loading rates (Davidsson, 2007). Even though the dynamics of hydrolysisof some individual substrates are known, the process is often described as a simple first-order

process due to extensive variations in substrate composition (Batstone, 2006).

7) Hydrogenotrophic

methanogenesis6) Acetotrophic

methanogenesis

14%

45%

5%31%

7%

28%67%

20%

3%

9%29%

12%50%

Amino acids ( S aa), Sugars ( S su)

Inert diss. COD S

Long chain fatty acids ( S fa)

Propionate ( S pro)

Acetate ( S ac) Hydrogen ( S H2)

Methane ( S CH4

)

1) Hydrolysis

Fermentation of

2) amino acids

3) sugars

4) Anaerobic oxid. of S a

5) Anaerobic oxid. of S ro

Degradable particulate organic material ( X S )

Proteins Carbohydrates Lipids

30% 17% 5% 48%

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2.1.2. Acidogenesis

Acidogenesis refers to the fermentation of dissolved sugars, amino acids and LCFA to volatilefatty acids (VFA), carbon dioxide and hydrogen. These processes are energetically favorablefor the microorganisms, and are seldom rate limiting.

2.1.3. AcetogenesisThe VFA produced from acidogenesis consist of short chained fatty acids like acetate,

propionate and butyrate. During acetogenesis, a group of strict anaerobe Achaea oxidizesVFA of higher order than acetate to acetate and hydrogen, which can be used to producemethane in the methanogenesis. The energetic yields for these reactions are negative, and themicroorganisms need to co-metabolize with methane producing bacteria in order to make thisdegradation step energetically feasible. Acetogens are easily inhibited by environmentalfactors like pH, NH3, etc., and can thus be rate limiting and a source of instability to the

process. Accumulation of VFA is an indication of process failure. The dissolved hydrogenconcentration is a crucial parameter as it determines the energetic yield from the reactionwhere VFA are degraded to acetate and hydrogen (Nilsson et al, 2007).

2.1.4. Methanogenesis

Methane producing bacteria can be divided into two groups; acetotrophic methanogens andhydrogenotrophic methanogens. Acetotrophic methanogens produces methane and carbondioxide from acetic acid, and hydrogenotrophic methanogens produces methane fromhydrogen and carbon dioxide. Methanogenesis requires neutral pH, otherwise the gas

production is inhibited (Reith, et al., 2003).

2.1.5. Environmental requirements

The microbial processes are dependent on suitable environmental factors when it comes toe.g. pH, temperature, nutrient levels and the levels of toxicants. The processes will be

inhibited if the requirements are not met. The reactor temperature is generally mesophilic(35±5 °C) or thermophilic (55±5°C). These temperature ranges provide optimal conditions fordifferent populations of microorganisms. The reactions in a mesophilic reactor are not as fastas in the thermophilic case, but mesophilic reactors are more stable and not as sensitive toammonia inhibition. Problems with instability are most likely to occur if easily degradablesubstrates are digested in a thermophilic digester (Davidsson, 2007).

2.2. Physicochemical processes

2.2.1. Equilibrium processes

Important equilibrium reactions in anaerobic digestion systems are the acid-base reactions of

VFA, ammonium and the carbonate system. VFA affect the alkalinity and pH of the system,which in turn can have inhibitory effects on the processes. Ammonia inhibition occurs mainlyat high pH, when the deprotonated ammonia is favored.

2.2.2. Gas s tripping

The liquid-gas transfer is a crucial parameter for a bioreactor. A typical anaerobic digesterconsists of a mixture of liquid phase, particles and gas bubbles. In a simplified manner, thetransport of dissolved gas to gas bubbles can be modeled as a two-phase system usingstationary liquid-film theory. All mass transport resistance is then assumed to be in the liquid

phase, and the kinetics is based on the overall transfer coefficient , k La, which includes theliquid-gas film area, the diffusivity of the specimen and the layer thickness. The k La value

also depends e.g. on the degree of stirring and the temperature. The high concentrations ofdissolved gases in anaerobic digesters often led to supersaturation of the liquid. The effect of

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particles that work as catalysts for the gas stripping process is neglected in the two-phasesystem.

2.3. Reactor conf igurationA key parameter for the reactor operation is the loading rate. Anaerobic stabilization ponds

are often used for low rate systems, which are often modeled as continuously stirred tankreactors (CSTR) with liquid inflow and outflow streams and a separate gas collection system.Examples of high-rate reactors are upflow anaerobic sludge blanket (UASB), expandedgranular sludge bed (EGSB) and anaerobic sequencing batch reactor (ASBR). The benefits ofthese high rate reactors are for example less space requirements and odor problems, and amore effective process (Batstone, 2006). The effectiveness of the reactors can be enhanced byincreasing the plug flow characteristics and by increasing the biomass retention. Two-stepdigestion where the fermentation and methanogenesis occur in different reactors can also beapplied. The aim for this configuration is to make the process more stable, since the processvariables can be adapted for the fermenters and methanogens respectively. The first step isusually thermophilic and the second step mesophilic (Blumensaat F, 2005). Thus, the

concentration of inhibitory ammonia can be kept lower in the second reactor where the bacteria are more sensitive (Davidsson, 2007).

2.4. Substrate characterizationTotal solids (TS ), volatile solids (VS ), total and solubilized chemical oxygen demand (COD,

SCOD) are common parameters to measure in the incoming substrate at digestion facilities. Ifthe fractions of fat, protein and carbohydrates are known, the theoretical methane yield can bedetermined using the Buswell formula (eq. 2.1) (Buswell, et al., 1930).

(2.1)

The methane production capacity can thus be expressed as

mole per mole

organic compound, . If combining the Buswell formula with the oxygen demand ofthe organic substance, the theoretical methane production potential per unit of COD can bedetermined. The oxygen demand can be expressed as (eq. 2.2).

mol O2 per mole organic substance (2.2)

The average elemental compositions of the organic compounds used in this project are presented in Table 1. These compositions were calculated for household waste samples inHøjlund Christensen et al. (2003). Fat is a beneficial substrate with a much higher biogas

potential than both sugars and proteins; furthermore it gives a higher methane ratio. Highamounts of protein can on the other hand cause disturbances in the process due to a higherammonia concentration (Davidsson, 2007).

Table 1 Average composition of organic compounds (Højlund Christensen, et al., 2003)

Compound Elemental compositionFatProteinCarbohydrates

C57H104O6

C5H7 NO2

C6H10O5

The theoretical methane yield can be used as an indicator of the quality of the substrate, but

digestion tests needs to be carried out to determine the practical biogas potential. The ratio ofdegradable COD to total COD (inert + degradable) will in this text be denoted as the

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degradability of the substrate. The inert fraction can consist of complex structures of thementioned organics, fibers, extracellular polymeric substances (EPS) etc.

The processes covered in this project include digestion of sludge from wastewater treatment plants and household waste. The sewage sludge from a waste water plant can be subdivided

into primary, secondary and tertiary sludge. Primary sludge is the residue after the mechanicaltreatment stage at the plant, often including a chemical precipitation process. The secondarysludge, or waste activated sludge (WAS) usually contains more inert organic material fromdead bacteria and is more difficult to degrade than the primary sludge (Davidsson, 2007).High sludge age at the activated sludge process leads to more inert material and hence lowerdegradation potential in the anaerobic digestion process. Household waste has a large

potential for anaerobic digestion. With improved collection systems, urban waste could beadded to the existing digesters at the wastewater plants, and increase the methane production.Other commonly used substrates are grease trap waste, manure, food processing residuals orcrops (Davidsson, 2007).

2.5. Sludge pre-treatmentPre-treatment can be applied to increase the degradability and dewatering properties of theWAS. This can be done by physical treatments like thermal treatment or ultrasonication orwith chemical treatment, e.g. by acid or base addition or addition of enzymes (Davidsson,2007). During these treatments, the flocs are disintegrated and both intracellular andextracellular materials are extracted (Eskicioglu C, 2006). After thermal pre-treatmentexperiments carried out by Eskicioglu (2006) the soluble COD increased with over 350 %,and the digestibility with over 450 %. The rate of the digestion was however lower than forthe control sample, possibly due to denaturation of enzymes during the pre-treatment(Wawrzynczyk, 2007). It has been shown that thermal treatment in combination with enzymeaddition gives a high methane yield (Davidsson, 2007).

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3. Overview of modelsAnaerobic digestion has traditionally been treated as a black box system due to thecomplexity of the process. To facilitate design, system analysis, operational analysis andcontrol, a mathematical model describing the processes is required (Batstone, 2006). Thedifferent purposes require different ranges of accuracy and model complexity. A complex,

non-linear model with focus on the biochemical reactions is well suited when theunderstanding of the process is important, e.g. for operational analysis or for research

purposes. These models can facilitate optimization of operational stability and efficiency.When implementing model-based control on a system, a linear and well parameterized modelis needed with measurable key parameters as input signals. For design purposes, the modelshould focus on hydraulics and particle structure (Batstone, 2006). An example of such amodel is presented in Elmitwalli et al. (2003).

3.1. ADM1Researchers have strived for a standardization of model structure and parameterization overthe last couple of years (Batstone, 2006). The most widely used model for anaerobic digestionis the Anaerobic Digestion Model no. 1 (ADM1), developed by a task group for theInternational Water Association (IWA) and published in 2002 (Batstone, et al., 2002). Thismodel has often been used as a framework model enabling researchers to focus onmodifications for specific purposes. The model includes kinetics for disintegration ofhomogenous particles to carbohydrates, proteins and lipids, and hydrolysis of these particlesto sugars, amino acids and LCFA. The disintegration process is often rate limiting, andmodeled with first order kinetics with respect to the concentration of particulate matter.Acidogenesis and acetogenesis are also accounted for, including the dynamics of the VFAacetate, propionate, valerate and butyrate. Methanogenesis from acetate and hydrogen/CO2 to

biogas is included. Inhibition functions of the metabolic activity by ammonia, pH, acetate and

hydrogen, and nitrogen limitation are included. The model also describes gas-liquid transferand ion association and -dissociation. Implemented as a system of differential equations, thereare 32 dynamic concentration state variables, and as a set of differential and algebraicequations, 26 state variables and 8 implicit algebraic equations are used (Batstone, et al.,2002). Examples of known excluded processes in ADM1 are lactate formation, sulphatereduction, nitrate reduction, LCFA inhibition, competitive uptake of H2 and CO2 and chemicaland biological precipitation (Blumensaat F, 2005).

The benefits from using a model to evaluate and optimize anaerobic processes are not fullyrecognized by the industry. ADM1 is not widely used due to the lack of implementation in acommercial program, and due to the low number of case studies (Batstone, et al., 2003). In

Batstone, et al. (2003), two examples of ADM1 application were demonstrated to clarify theadvantages from modeling. Process modifications in the industry were evaluated, and themodel predictions were considered to be of high accuracy.

3.2. The Siegrist model

3.2.1. Comparison with ADM1

The ADM1 model has been regarded as too complex for practical applications (Batstone, etal., 2003). In parallel to the ADM1 model, Siegrist, et al., (2002) published a slightly moresimplified model oriented towards mixed sludge treatment. The main differences are theexclusion of valerate and butyrate as state variables. The hydrolysis rate is modeled as a

single step process with first order kinetics with respect to the concentration of particulatematter, furthermore, the uptake and decay rates are higher than in the ADM1 model. The two

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models were constructed with different approaches, the Siegrist model parameters are basedon experiments, whereas the ADM1 uses review consensus (Batstone, 2006). The Siegristmodel was calibrated with lab scale experiments and validated with full-scale experiments.The incoming sewage sludge used to calibrate the Siegrist model was a mixture of primary,secondary and tertiary sludge from a municipal treatment plant (Siegrist, et al., 2002). The

particulate matter, which is lumped together in the Siegrist model, is divided in sugars, fattyacids, proteins and inert material with different hydrolysis constants in ADM1. The particulate substrate composition can however be defined in the stoichiometry of thehydrolysis.

3.2.2. Model assumptions and limitations of the Siegrist model

Anaerobic digestion is a complex process, and could not be modeled without manysimplifications and without neglecting many processes. Apart from the assumptions regardingthe processes already mentioned in 3.2.1, there are several others to declare, some of them arestated below:

• The fixed stoichiometry in the microbial processes is problematic, especially the

fermentation of sugars (Batstone, et al., 2006). Increased temperature can increase

maintenance and thus alter the stoichiometry.

• According to the liquid film theory, mass transfer resistance is assumed to lie only on

the liquid side (Nielsen, et al., 2004). The k La value is only dependent on temperature

in the model, but in reality it is affected by several other parameters.

• Although the mass has been reduced in the digestion, the liquid phase is considered to

be dilute and the volume is assumed to be constant. This assumption is however

widely used (Batstone, 2006).

• The reactor is assumed to be completely mixed and the sludge retention time (SRT) is

equal to the hydraulic retention time (HRT).

Due to the many assumptions in the model, there are limitations to what can be modeled,some of them are:

• A rapid change in reactor temperature from mesophilic to thermophilic cannot be

predicted due to the change in the microbial population (Siegrist, et al., 2002).

• Since all parameters are calibrated for sewage sludge digestion, a change in substrate

may not be modeled well. The particle size of the substrate is not included in the

model.

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4. Mathematical structure of the Siegrist modelIn this section the mathematical structure of the model is presented, as it was implemented inMatlab. For further reading, see Siegrist et al. (2002).

4.1. Model structure

The model is based on a system of ordinary differential equations (ODE) for the vector ofstate variables x , (eq. 4.1).

, (4.1)

The state variables ( x i) of the system are presented in Table 2. The model includes 23 statevariables of liquid phase concentrations (with units g COD/m3, mol/m3 and g N/m3), and threestate variables describing the pressures of gases in the rising gas bubbles (measured in bar).

Table 2 State variables of the system

State variable Notation Unit

Liquid concentrations

1. Protons2. Hydrogen3. Methane4. Carbon dioxide5. Hydrogen carbonate6. Ammonium ions7. Ammonia8. Acetate9. Acetic acid10. Propionate

11. Propionic acid12. Dissolved amino acids13. Dissolved sugars14. Dissolved long chain fatty acid15. Dissolved inert COD16. Particulate degradable COD17. Amino acid fermenters18. Sugar fermenters19. Long chain fatty acid degraders20. Propionate degraders21. Acetotrophic methanogens22. Hydrogenotrophic methanogens

23. Inert particulate matter Partial pressures in gas bubbles

24. Hydrogen25. Methane26. Carbon dioxide

S H

S H2

S CH4

S CO2

S HCO3

S NH4

S NH3

S ac

S hac

S pro

S hproS aa

S su

S fa

S in

X S

X aa

X su

X fa

X pro

X ac

X H2

X in

p H2

pCH4

pCO2

mol/m3

mg COD/m3

g COD/m3

mol/m3

mol/m3

mol/m3

mol/m3

g COD/m3

g COD/m3

g COD/m3

g COD/m

3

g COD/m3

g COD/m3

g COD/m3

g COD/m3

g COD/m3

g COD/m3

g COD/m3

g COD/m3

g COD/m3

g COD/m3

g COD/m3

g COD/m3

bar

bar bar

4.2. Liquid phase differentialsThe liquid phase differentials are expressed as for a CSTR (eq. 4.2). In the case of a pulse-feddigester, the digester is modeled as batch reactor with instant feeding and withdrawal.

(4.2)

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The liquid phase system includes 17 reactions j (gas stripping not included) with individualreaction rates ρ j. The processes and related state variables are listed in Table 3 (compare withFigure 1). The kinetics will be presented in the following sections.

Table 3 Liquid phase processes included in the model with process number ( j ) and reactants (i )

j Process i 1234567891011

121314151617

HydrolysisFermentation of amino acidsFermentation of sugarsAnaerobic oxidation of LCFAPropionate oxidationAcetotrophic methanogenesisHydrogenotrophic methanogenesisDecay of amino acid fermentersDecay of sugar fermentersDecay of LCFA oxidizersDecay of propionate oxidizers

Decay of acetotrophic methanogensDecay of hydrogenotrophic methanogensEquilibrium of CO2/HCO3

Equilibrium of NH3/NH4 Equilibrium of Ac/HAcEquilibrium of Pro/HPro

X S

S aa

S su

S fa

S pro

S ac

S H2

X aa

X su

X fa

X pro

X ac X H2

S CO2, S HCO2 S NH3, S NH4 S ac, S hac S pro, S hpro

The stoichiometric coefficients ѵ j,i of the reactions j with respect to the state variables i aresorted as rows in a stoichiometric matrix, T , (see Appendix I). The stoichiometry is based onthe conservation of COD, nitrogen and electrons, and that the N/COD ratio in e.g. proteinsshould remain unchanged (Appendix I). The 23 columns in T each represent one of the liquid

phase state variables ( xi). The state variable reaction rates r reaction for the liquid phase reactionscould thus be written as in equation 4.3.

· (4.3)

In equation 4.3 r reaction is a column vector expressing the reaction rates of the 23 statevariables, and ρ is a vector with the reaction rates for all processes.

For the stripping of the dissolved gases H2, CO2 and CH4 (state variables 2-4), the rates(r stripping ) were calculated separately (section 4.3.) and added to the vector r reaction to get thetotal reaction rate r tot .

The concentration in the feed was expressed by the vector cin and the outflow concentrationvector cout also represented the state variables.

4.2.1. Kinetics of microbial reactions

The hydrolysis rate is described with a first order expression with respect to the concentrationof particulate organic matter (eq. 4.4).

(4.4)

Processes 2-7 (Table 3) are functions of the reactants, inhibitory substances and model

parameters. These processes are modeled with first order kinetics with respect to the biomass

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concentration X i (state variables 17-22 in Table 2) and with Monod kinetics with respect tothe substrate concentration (eq. 4.5).

,

,, (4.5)

The inhibition factors, modeled with Monod kinetics, are described with equation 4.6.

, ,,,, (4.6)

x is here the inhibiting variables pH, acetate, ammonia or hydrogen. z is 2 for pH and NH3 inhibition but otherwise 1. All processes calculated from (eq. 4.5) are slowed down by low pHvalues. The anaerobic oxidation of LCFA and propionate are the most sensitive processes,inhibited by high acetate and hydrogen concentrations and by low pH values. Propionateoxidation is also inhibited by a high ammonia concentration, as is the acetotrophicmethanogenesis. The hydrogen inhibition of the hydrogen producing processes is due to the

thermodynamics of the reactions.

The biomass decay (Table 3) is modeled as first order reactions with respect to the biomassconcentrations (eq. 4.7). 80 % of the decayed biomass is assumed to become X S and the rest

X in.

, (4.7)

4.2.2. Protonation- deprotonation

The equilibriums of CO2/HCO3 and NH4/NH3 and protonations of acetate and propionatewere modeled as pseudo-equilibrium processes as in eq. 4.7-4.10. To achieve a more stable

model, the ammonia and VFA were protonated with CO2 instead of a proton (Siegrist, et al.,2002).

/ (4.7) /// (4.8) /// (4.9) /// (4.10)

4.3. Gas-stripping modelThe kinetics of the mass transfer of dissolved gases from liquid to gas phase was based onstationary film theory (eq. 4.11). These reaction rates were added to the liquid reaction ratevector r (eq. 4.3).

, (4.11)

The interfacial concentration S S,i was expressed with Henry’s law (eq. 4.12).

, (4.12)

To calculate the pressure differentials in the gas bubbles leaving the liquid, the common gaslaw was used. As the molecules leave the liquid phase a pressure is induced in the gas

bubbles. The outflow of gas from the bubbles was modeled with a pressure control loop,which kept the pressure close to the ambient pressure using the proportional constant K p. The

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differentials for the pressures in the bubbles were calculated with equation 4.13. It isimportant that K p is high enough to keep the pressure offset low and at the same time not toohigh to avoid numerical instability (Siegrist, et al., 2002).

(4.13)

The biogas flow for 25 °C and atmospheric pressure for the whole reactor was calculated withequation 4.15.

(4.14)

4.4. Temperature dependencyThe temperature dependencies of all constants were described with exponential expressionslike in equation 4.15.

(4.15)

All constants were listed as values at standard temperature (T 0 = 35°C), and then multipliedwith the factor from equation 4.15 to get the actual values. θ are constants determined fromexperiments with varying temperature.

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5. Numerical aspects

5.1. Modeling methods for avoiding numerical problemsADM1 is a very stiff model, with time constants varying from seconds to months (Rosen C,2006). The pH calculations are the fastest processes, e.g. the protonation/deprotonation of

VFA and equilibrium of CO2/HCO3 and NH3/NH4. The problem of stiffness in the model can be reduced if the fastest processes are assumed to be at equilibrium, (dx/dt =0). This meansthat a system of Differential Algebraic Equations (DAE) has been created, a system which isreadily solved with a DAE solver, e.g. ode15s in Matlab. Rosen C, (2006) showed that thedifferences between the results from the ODE system and the DAE system were minor.

Another benchmarking made by (Blumensaat F, 2005) proved that the ODE solvers inAquasim (ASIM) and Matlab (ode15s) gave very similar results for their adapted ADM1model. The results from the implementation of Siegrist model in Matlab made in this reportand the same model implemented in ASIM are therefore not expected to differ significantly.

In the model by Siegrist et al, the problem of stiffness has been addressed differently from theDAE system; the fastest processes have been slowed down instead. The reaction rateconstants of the equilibrium processes are chosen to be large enough to make the processesfaster than the other reactions, but they are very slow compared to the real process rates. Thehydrogen conversions are also very fast and the retention time is lower than for the othersubstrates, which leads to a very low concentration of hydrogen. To avoid long simulationtimes, the hydrogen concentration is artificially increased 1000 times, thus slowing down theresponse time. The authors claim that this does not affect the result, since the response timestill is much shorter than for the other state variables. Another trick that has been used toincrease model stability and create a fast interaction between the acids and bases is to assumethat NH3 is protonated with CO2.

5.2. Numerical methods in the Matlab implementationSince the model is stiff, the preferred integration method is ode15s which is the stiff ODE-solver in Matlab. Numerical problems are not to be expected when performing the simulationand the solver is usually fast. When a pulse-fed reactor is fed at several times, the simulationtime is slower, but still within seconds and not minutes.

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6. System identificationThe goal of system identifiability analysis is to check that the model structure and

parameterization is adequate from a mathematical point of view. For nonlinear models,system identification is complicated, and an analysis lies beyond the scope of this work.

Nonetheless, it is important to be aware of the problems that non-identifiable parameters may

cause when calibrating the model and conducting sensitivity analysis.

6.1. Parameter identifiabilityIf a parameter is identifiable, it can be uniquely determined. If a parameter is globallyidentifiable only one unique solution exists for the parameter value, whereas an infinitenumber of solutions exist for an unidentifiable parameter. A model with unidentifiable

parameters can produce the exact same result with many combinations of parameters, e.g. canthe product of two unidentifiable parameters be identifiable. Calibrating the parameter valuesfrom measurements is not possible for a model with unidentifiable parameters (Jeppsson,1996). Practical identifiability, on the other hand, depends on the quality of the measureddata. Measurements from similar conditions produce many different parameter results which

gives a poor parameter precision. Practical identifiability can be assessed by studying the joint probability distributions with Monte Carlo analysis (see 8.1.1). Functional relationships mayexist between starting values of dynamical variables and parameters, or between model

parameters.

6.2. Examples of identifiability analysisIdentifiability analysis for dynamic models of anaerobic digestion was carried out by Müller,et al., (2002). Two mathematical models were tested, one with simple Monod structure, andone with inhibition and decay coefficients included. For nonlinear models, there are not manyavailable techniques for structural identifiability analysis; Taylor series expansion and adifferential-algebraic method are among the few. The problem is that the methods work wellfor simpler models, but for more complex model they tend to fail. Even a simple Monodmodel could not be evaluated with the methods, so the authors developed a new method basedon the covariance matrix of the probability distributions. If there is a functional relationship

between some of the parameters, the joint probability distributions have a correlation and thecovariance matrix will not be of full rank. This method assumes a white noise, which may notalways be the case. These methods will however not be employed in this report.

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7. Model validationTo enable model validation and calibration of the Siegrist model, data from pilot-scaleexperiments and a full-scale process were collected. The aim was to evaluate the usability ofthe model for different applications, e.g. simulation of the full-scale operation at a WWTP or

pilot plant reactors with varying substrates and temperatures.

The input parameters that needed to be determined before running the simulations wereoperational settings, such as the times of feeding, feed volumes, temperature of the reactorand the properties of the feed. The constituents of the feed needed to be transformed into unitsused in the model (mainly based on COD), and the characteristics of the particulatedegradable organic matter ( X S ) needed to be determined. As the available data differed for thedata sets, the methods for computing these calculations varied. Where data was missing,values from the literature or standard values from the implementation by Siegrist, et al.,(2002) were used instead.

7.1. Process descrip tions

7.1.1. Methods for pilot and lab scale experiments

Pilot and lab scale data was collected from experiments where the biogas potentials ofhousehold wastes were studied. The experiments were carried out by Åsa Davidsson withinthe frame of a Danish-Swedish project (Højlund Christensen, et al., 2003) and a project forthe city of Malmö (la Cour Jansen, et al., 2004). Two sets of continuous data fromexperiments on household wastes were used for validation, with waste from Aalborg,Denmark, and from the city district Västra Hamnen in Malmö. Continuous data from a pilotscale reactor fed with a mixture of primary sludge and WAS from Sjölunda WWTP in Malmöwas used as well. For the experiments on the Sjölunda sludge and on the household wastefrom Västra Hamnen, lab scale batch tests were also available. Here a short description

follows of the continuous and batch experiments, for more detailed information, seeDavidsson, 2007.

The continuous experiments were performed in stirred and heated 35 liter reactors (20 literseffective volume) with a connected gas collection tank of 77 liters. The reactors were operatedat mesophilic conditions (Sjölunda sludge, Västra Hamnen household waste) or thermophilicconditions (Aalborg household waste). The experiments were running over 2-3 months andthe operation was divided into three phases, start-up, continuous operation and post digestion.During the start-up phase 10 liters of inoculum was added to the reactor and the volume wasgradually increased by increasing the daily feeding until a volume of 20 liters was reached.Then the continuous phase followed, where the reactors were operated with daily feeding andeffluent withdrawal at constant HRT (15 days for household waste and 13.3 days for sludge).After achieving a stable process, the feeding and effluent withdrawals were eventuallystopped and the post-digestion phase started. For the Sjölunda sludge process no start-up

phase was needed, since the inoculum was collected at a full scale digester fed with the samesludge. No post digestion phase data was available for the reactor with household waste fromVästra Hamnen.

The lab analyses of the continuous processes consisted of daily measurements of the gas production, methane content, temperature and pH. Weekly analyses of the residue wereHCO3, VFA, TS, VS, COD, N-tot and NH4-N. For the household waste experiments, thesubstrate was stored as frozen samples, and was considered to have constant composition. Forthe Sjölunda sludge experiment, the same batch of substrate was used for 4-20 days, and anew analysis of TS and VS was made for each batch. Characterization of the household

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wastes was conducted within the projects, and included data of TS, VS, fat, protein, fiber,sugar, ash and ammonium content. Calculations were needed for these values to be convertedto input parameters for the model, and these will be presented separately for each substrate.For the Sjölunda sludge, there was no feed characterization made specifically for theexperiment.

The batch experiments were conducted in 2 liter glass bottles filled to about 30 % with amixture of inoculum and substrate (Davidsson, 2007). No withdrawal of liquid was conductedduring the test period, but gas was collected and analyzed for methane content a few times perweek. The bottles were stored for 30-50 days in 35°C to assure that the maximum totalmethane production for the waste was reached. The resulting methane potentials, however,varied more than acceptable for double samples, and were not used in the validation. Theuncertainty can be due to difficulties in taking homogenous samples, described in (la CourJansen, et al., 2004), or insecurities in the lab method.

7.1.2. The process at Käppala WWTP

Käppala WWTP in Lidingö receives 500 000 person equivalents (p.e.) and has two treatmentlines, one old and one new. The old line has chemical phosphorus removal while the new lineis equipped with biological phosphorus removal. Both lines include an activated sludge

process with a sludge age of 8-10 days. The amount of primary sludge is stable throughout theyear, but the WAS volume increases during the winter due to low temperature which leads toslow degradation. After the primary sludge is dewatered, it flows into the first digester, calledR100. This digester is mesophilic (35 °C) and the HRT is kept at 15 d. The outflow fromR100 is further digested in R200, together with the dewatered WAS. R200 is also mesophilic,

but with a HRT of only 10 days (Figure 2). Both reactors are stirred, but there are problemswith clogging of the impellers and the stirring speed is only about 5-6 rpm.

Figure 2 The digestion process at Käppala WWTP

7.2. Determination of the hydrolysis constantsThe hydrolysis constants for the household waste from Västra Hamnen and the Sjölundasludge were calibrated from the batch experiments described in 7.1.1. The dynamics of the

biogas production during these batch tests was used to determine the hydrolysis constants. Itwas assumed that the hydrolysis step was rate limiting, and that there were no inhibitioneffects on the microbial reactions. Under this assumption, a first order differential model for

the hydrolysis could be set up. After transferring the values to logarithm scale and applyinglinear regression, k H was represented by the first order derivative. k H was determined to 0.33

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d-1 for the Sjölunda sludge and 0.20 d-1 for the Västra Hamnen household waste (Figure 3). Asno batch experiment was conducted for the Aalborg household waste, the hydrolysis constantfrom Västra Hamnen household waste was used.

Figure 3 Calibration of k H with batch experiment with Sjölunda sludge (left) and household waste from Västra

Hamnen household waste (right)

7.3. Household waste experiment 1 - Aalborg household wasteThe Aalborg household waste substrate originated from source sorted household waste fromthe city of Aalborg in Denmark. The waste had been pretreated with a waste separator prior tothe experiments (Højlund Christensen, et al., 2003). To be able to use the data for modelvalidation, the experimental data needed to be translated into units used in the model. Manualcalibration was made for the initial value of ammonium and VFA, as no data was available ofthe inoculum used in the experiment. The hydrolysis constant was given from the batchexperiments (see 7.2.), but for the other model parameters default values from Siegrist et al.(2002) was used.

7.3.1. Feed composi tion

The feed properties used as inputs to the model were the concentrations of particulate organicmaterial ( X S and X in), dissolved organics (S su, S fa, S aa , S in) and other dissolved components (S H ,S NH4, S HCO3, etc).

The composition of the particulate organic matter was also calculated. The degradable particulate organic material, X S , degrades into fractions of dissolved amino acids, sugars, fattyacids and inert material during the hydrolysis process. The reaction also produces smallamounts of dissolved CO2 and consumes small amounts of dissolved HCO3. The reaction withstoichiometric coefficients can be written as in equation 7.1, and the default stoichiometriccoefficients from (Siegrist, et al., 2002) are presented in Appendix I (T -matrix).

ѵ, ѵ, ѵ, ѵ, ѵ, ѵ, 0 (7.1)

Omitting the production of CO2 and consumption of HCO3 and introducing new notationresulted in the simplified hydrolysis reaction described by equation 7.2.

ѵ ѵ ѵ ѵ (7.2)

0 10 20 30 40-1

0

1

2

3

4

5

Time , [Days]

G a s p r o d u c t i o n ,

[ N m l / D a y ]

Duplicate 1

Duplicate 2

kh=0.33

0 10 20 30 40 50-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Time , [Days]

G a s p r o d u c t i o n ,

[ N m l / D a y ]

Triplicate 1

Triplicate 2

Triplicate 3

kh=0.2

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The content of sugar, fat and proteins in X S could hence be described with the stoichiometriccoefficients ѵ i for the hydrolysis process. All species were given in COD-fractions, and due tothe conservation of COD, the hydrolysis could be written as in equation 7.3.

ѵ su + ѵ aa + ѵ fa + ѵ in = 1 (7.3)

Characterization data for fat, protein, fiber, sugar, starch, VFA and ammonium content for thewaste is presented in Table 4 as percentages of TS. The soluble and particulate fractions of TSwere determined by centrifugation (Højlund Christensen, et al., 2003).

Table 4 Crude data used for validation of the Aalborg household waste experiment (Højlund Christensen, et al., 2003)

Characterization parameter Value Unit

TSProteinSugarStarch

FatFibersAmmoniumVFASoluble TS

517718

18110.320.1423

%

% of TS

% of TS

% of TS

% of TS% of TS

% of TS

% of TS

% of TS

To convert the data into units used in the model (g COD/m3, g N/m3) the Buswell formulawas used (eq.2.2). The average chemical compositions were needed (Table 1), for fibers itwas assumed to be C5H10O5.

To enable validation to the VFA levels in the reactor, some processing of the data were

needed. The analysis method used measured the total VFA level expressed as acetate. Underthe assumption that the measured VFA consisted of 2/3 acetate and 1/3 propionate on a COD basis, the input variables, S ac and S pro, could be calculated from the data.

The degradable organics were assumed to be the sum of protein, fat, sugar, starch and fibers(cellulose). The sugar, starch and fibers were lumped into a sugar fraction to comply with themodel structure. 23 % of the degradable organics X S were dissolved components (S su, S fa, S aa,S in) with the same distribution as X S . The stoichiometric coefficients for the hydrolysis werecalculated as ratios of protein, sugar and fat to the total COD in X S (ѵ in was set to zero). Theseratios were also assumed to determine the composition of the soluble degradable organics inthe feed. For remaining input parameters, standard values from Siegrist et al. (2002) were

used. The calculated input parameters are presented in Table 5.Table 5 Input values from the feed characterization for the Aalborg household waste simulation

Characterization parameter Notation Value Unit

Total degradable organic matter S aa+ S su+ S a+ Xs 58 193 g COD/m3

Degradable particulate organic matter Xs 45 071 g COD/m3

Protein fraction X S ѵ aa0.21 -

Sugar fraction X S ѵ su0.35 -

Fat fraction X S ѵ a 0.45 -

Inert fraction of hydrolyzed X S ѵ in 0 -

Ammonium S NH4 160 g N/m3

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7.3.2. Initial state variables

The inoculum was collected from a digester at a WWTP in Kalmar. As there were no analysisdata for the inoculum, standard values were applied for the first simulation. Then comparingwith data, it became evident that the concentrations of ammonium and VFA were higher thanfirst assumed, and these levels were iteratively increased to fit to data. The concentration of

ammonium in the inoculum was set to 3500 g N/m3 and the VFA content to 720 g COD/m3.

7.3.3. Resul ts

The simulation of the experiment included all feeding and withdrawals, simulated as newinitial states for the ODE-solver on these occasions. The feeding was hence made in pulses,which was closer to reality than if the reactor would be modeled as a continuous reactor. Thefrequent oscillations of some outputs were due to this fed-batch mode of operation. Themeasured biogas was considered to be dry since it was measured at around 10 °C, whichcorresponded to a partial pressure of less than 15 mbar for water.

The simulated gas production (Figure 4) was overestimated compared to the measurements

during the first 50 days, but correlated better during the stable period and the post-digestion phase. The sharp decrease in biogas production after 10 days was due to lower feedingvolumes; it was seen during the experiment that the pH dropped (Figure 6), and the feedingrate was therefore decreased to prevent overload. The methane content was also overestimatedduring the first part of the time series, and the drop in methane fraction when the feeding wasstopped can not be seen in the simulation (Figure 4). For the steady state phase, the simulatedresult was well correlated to data.

Figure 4 Measured and simulated biogas production (left) and methane content (right) from continuous experiment

with Aalborg household waste

The totals VFA, however, were undervalued in the simulation and are 300-400 gCOD/m3

below the measured values (Figure 5). The fluctuations in the measured values of HCO3 werenot captured in the simulated result, but the predictions were in the same range as themeasurements (Figure 5).

0 20 40 60 800

0.01

0.02

0.03

0.04

0.05

Time [days]

P r o d u c t i o n r a t e [ m 3 / d a y ]

Simu lated dry biogas pr oduction

Measured biogas production

0 20 40 60 800

20

40

60

80

100

Time [days]

P e r c e n t [ % ]

Simulated CH4

Measu red CH4

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Figure 5 Measured and simulated VFA (left) and HCO3 concentrations (right) from continuous experiment with

Aalborg household waste

The high initial ammonium content was washed out during the start-up of the reactor, butseemed to reach a stable concentration during the steady state phase (Figure 6). It wasobserved that the model estimation of the final value was poor, while the dynamics of the startup phase is reflected in the simulation. The measured pH was fluctuating (Figure 6), anddiffered from the more stable simulated values. The values were however in the same range.

Figure 6 Measured and simulated ammonium concentration and pH from continuous experiment with Aalborg

household waste

7.3.4. DiscussionThe inoculum used in the experiment was taken from a full scale sludge fed digester. Thus,the microorganisms were not used to degrading food waste, and all processes could beassumed to be slower in the beginning of the experiment. As the state of the biomass is not astate variable in the model, the start-up phase can probably not be modeled very well withconstant parameters during the whole experiment. It would however be possible to lower thehydrolysis constant during the start-up phase to improve the validation. The problem withsuch measures is that the value of k H would need calibration to data and that the theoretical

background is not fully clear.

Another explanation for the poor correlation to the measured results can be that inhibition

from the high ammonium concentration in the reactor was underestimated in the model. Ahigher inhibition would cause accumulation of VFA, due to reduced methanogenesis rate and

0 20 40 60 800

200

400

600

800

1000

1200

1400

1600

Time [days]

C o n c e n t r a t i o n [ g C O D / m 3 ]

Simulated VFAs

Measured VFAs

0 20 40 60 800

10

20

30

40

50

60

70

Time [days]

C o n c e n t r a i o n [ m o l / m 3 ]

Simu lated HCO3

Measu re d HCO3

0 20 40 60 800

500

1000

1500

2000

2500

3000

3500

Time [days]

C o n c e n t r a t i o n [ g N / m 3 ]

Simulated NH4 mo delled

Measu red NH4

0 20 40 60 800

1

2

3

4

5

6

7

8

Time [days]

p H

Simu lated pH

Measured pH

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a drop in pH. These trends could be seen in the data, as well as a lower methane fraction ofthe biogas. The model parameters were not calibrated for household waste, thus it is likelythat the validation would be more successful with recalibrated parameters. Calibration of themodel parameters is the subject of section 11.

7.4. Household waste experiment 2 – Västra Hamnen household wasteThe operation of the pilot scale experiment on substrate from Västra Hamnen was similar tothe previously described experiment. In this case the reactor was kept at mesophilicconditions, and batch experiments were also available. At the 20 th and 21st day of theexperiment, 50 g of HCO3 was added to the reactor to increase pH; this is also done for thesimulated reactor.


The same methodology as for the Aalborg household waste characterization was applied. Theavailable data is presented in Table 6, and the calculated input values in

Table 7. Values for the soluble fraction of TS and the VFA concentration of the feed were notavailable, so the same values were used as in the Aalborg household waste simulation.

Table 6 Crude data used for validation of the Västra Hamnen household waste experiment (Højlund Christensen, et

al., 2003)

Characterization parameter Value Unit

TSProteinSugarStarchFatFibersAmmonium

5174.3711.6140.027

%

% of TS

% of TS

% of TS

% of TS

% of TS

% of TS

Table 7 Input values from the feed characterization for the Västra Hamnen household waste simulation


Total degradable organic matter S aa+ S su+ S fat + Xs 42 248 g COD/m3

Degradable particulate organic matter Xs 32 721 g COD/m3

Protein fraction of X S ѵ aa 0.28 -

Sugar fraction of X S ѵ su 0.32 -

Fat fraction of X S ѵ fat 0.40 -

Inert fraction of hydrolyzed X S ѵ in 0 -

Ammonium S NH4 13.5 g N/m3


The same methodology as for the Aalborg household waste simulation was used, the initialammonium concentration was set to 835 g N/m3 and the total VFA to 300 g COD/m3.

7.4.3. Resul ts

Both the simulated biogas production and the simulated methane content follow theexperimental values more closely during the start up phase than for the Aalborg householdwaste experiments (Figure 7). After day 15 there is a major drop in methane content from 60to 40 %, and a rise in VFA concentration (Figure 8). The measured alkalinity was decliningduring this period, but increased after the addition of HCO3 after 20 days (Figure 8). The

model simulation did not predict this minor reactor breakdown, and even though the VFAconcentration increased, the methane content in the gas, alkalinity and pH remained

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practically unchanged. The measured ammonium concentration was declining during thewhole experiment, while the simulated ammonium remained fairly constant (Figure 9).


with Västra Hamnen household waste

Figure 8 Measured and simulated VFA (left) and HCO3 concentrations (right) from continuous experiment with

Västra Hamnen household waste

Figure 9 Measured and simulated ammonium concentration (left) and pH (right) from continuous experiment withVästra Hamnen household waste

0 10 20 30 40 500

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Time [days]


Simulated dry biogas pro duction


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P e r c e n t [ % ]

Simulated CH4

Measu red CH4

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Time [days]

V F A s a s a c e

t a t e e q u i v a l e n t s [ g C O D / m 3 ]

Simulated VFAs

Measured VFAs

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20

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Time [days]

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n c e n t r a i o n [ m o l / m 3 ]

Simu lated HCO3

Measured HCO3

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Time [days]

C o n c e n t r a t i o n [ g N / m

3 ]

Simulated NH4 mod elled

Measur ed NH4

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8

Time [days]

p H

Simulated p H

Measured pH

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7.4.6. Discussion

The validation of the gas production was acceptable, whereas the validations of the other parameters were less successful. One of the purposes of modeling is to be able to preventreactor failures, and it can be concluded that the result was poor in this case. The experimentwas designed to keep the feed characteristics constant by freezing daily portions from the

same batch of feed, so it is unlikely that the problems in the reactor around day 20 was caused by changes in the input. It is possible that the reason was a too high loading rate during thestart up phase, which led to consumption of alkalinity in the fermentation. The poorcorrelation for ammonium indicates that the characterization of the waste might not bereliable; the protein content or the hydrolysis rate seems to have been overestimated which ledto a higher ammonium concentration in the simulated result than for the measurements. VFAwere quickly produced and consumed, which gave large daily variations and made it difficultto measure and validate the model. For the inhibition constants and reaction rate of themethanogenesis, it is important that the VFA are in the right range. Methods for calibratingthe VFA concentration will be developed in the following sections.

7.5. Sludge experiment: Sjölunda mixed sludgeThe model was originally calibrated with a mixture of primary and secondary sludge bySiegrist et al. (2002). Hence, default values from the original implementation were assumed toapply for this experiment when no better guess could be made.


The feeding of the Sjölunda sludge reactor was made from batches of sludge that were usedup after 4-15 days. These batches were analyzed for TS and VS but no analyses for protein,fat or carbohydrate content were made. Therefore, the alterative characterization method

proposed by Siegrist et al. (2002) was used. The only parameters needed for the

characterization was the ammonium concentration in the reactor at steady state, the CODreduction and the ratio of CH4 to CO2 in the produced biogas. The degraded particulateorganic matter, X S,red , was calculated from the experimental values for influent VS and meaneffluent VS at steady state (29 g/l and 14 g/l respectively). To calculate the COD content ofthe degraded VS, the default characterization from Siegrist et al. (2002) was used, and theresulting conversion factor was calculated to 1.9 g COD/g VS.

The mean ammonium concentration in the digester (S NH4 = 860 g N/m3) was used forcalculating the stoichiometric coefficient for protein in the hydrolysis (ѵ aa) with equation 7.4.The N-content of protein, i NH4, was given the value 0.1 (Siegrist, et al., 2002), for results fromthe characterization, see Table 8.

,

(7.4)

The fat content (ѵ fa) was calculated from the relation between the real methane fraction in the biogas and the theoretical methane content rendered from fat, protein and sugar (eq. 7.5). Thereal methane fraction in the biogas at steady state ( xCH4,XS = 0.65), could be calculated fromthe known CO2 pressure and HCO3 concentration in the reactor with the equations in thecarbonate system (see Appendix II). The fractions of methane from anaerobic digestion ofsugar, protein and fat ( xCH4,su = 0.5, xCH4,aa = 0.68 and xCH4,fa = 0.7) were found in VAV(1981).

ѵ, ѵ, 1 ѵ ѵ, , (7.5)

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The stoichiometric parameter for sugar, (ѵ su) was calculated from the COD balance, inequation 7.6. A standard value of 0.05 for the inert fraction (ѵ in) was used. The results of thecharacterization (Table 8) does not differ substantially from the characterization by Siegrist, etal., (2002) shown in Figure 1.

ѵ 1 ѵ – ѵ – ѵ (7.6)

The total COD in the inflow was determined using the COD/VS ratio calculated from thecharacterization and the Buswell formula (equation 2.2). The batch experiments resulted in adegradability of 23 % and 54 %, indicating an unreliable method. The degradability based ondata for the continuous process, varied between 40-55 %, the ultimate degradability, however,was assumed to be 60 % in the simulation. The soluble part of incoming COD was assumed to

be 30 %, and the fractions of the dissolved components were assumed to be the same as forthe hydrolysis stoichiometry. The ammonium concentration was suggested by theexperimenter, Åsa Davidsson, (2008).

Table 8 Input values from characterization of the Sjölunda sludge


Total degradable organic matter (mean value) S aa+ S su+ S fa+ Xs 30 785 g COD/m3

Degradable particulate organic matter (mean value) Xs 21 549 g COD/m3

Protein fraction of X S ѵ aa 0.34 -

Sugar fraction of X S ѵ su 0.16 -

Fat fraction of X S ѵ fa 0.45 -

Inert fraction of X S ѵ in 0.05 -

Ammonium S NH4 45 g N/m3


The inoculum was collected from a full scale continuous reactor, fed with the sludge used forthe experiment. Steady state values after running the model could hence be used as initialvalues.

7.5.3. Resul ts

There was no start up phase as for the household waste experiments, since the inoculum wastaken from a reactor with the same feed and with similar operational settings. This resulted ina gas production that was rather stable during the whole experimental period, both for themeasurements and simulation. The variations of the measured gas production were howevermore pronounced than for the simulation, and the simulated values were also significantlylower than the measurements. The modeled methane content in the gas seemed to be slightlyoverrated (Figure 10). Both the measured and simulated VFA concentrations vary over a widerange, but the measured values were generally higher (Figure 11). The validation of alkalinityand ammonium were more successful (Figure 11 and Figure 12), while the simulated valuesof pH were slightly higher than the measured values (Figure 12).

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with Sjölunda sludge

Figure 11 Measured and simulated VFA (left) and HCO 3 concentrations (right) from continuous experiment with

Sjölunda sludge

Figure 12 Measured and simulated ammonium concentration (left) and pH (right) from continuous experiment on

Sjölunda sludge

7.5.4. Discussion

The degradability of the Sjölunda sludge used for the simulation was higher than measured,and the hydrolysis constant was calibrated from the batch experiment. Despite this, the gas

0 20 40 60 800

0.01

0.02

0.03

0.04

0.05

Time [days]




0 20 40 60 800

20

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100

Time [days]

P e r c e n t

[ % ]

Simulated CH4

Measu re d CH4

0 20 40 60 80 1000

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400

Time [days]

V

F A s a s a c e t a t e e q u i v a l e n t s [ g C O D / m 3 ]

Sim ulated VFAs

Measured VFAs

0 20 40 60 80 1000

10

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Time [days]


Simu lated HCO3

Measured HCO3

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Time [days]



Measu red NH4

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8

Time [days]

p H

Simulated p H

Measured pH

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production was lower for the simulation than for the measured data. It is possible that theassumption of a non-inhibitory condition during the batch test was wrong. In that case, thehydrolysis constant, k H, should have been higher for the simulation, which would have led tomore biogas and probably lower methane content in the gas. Another important parameter isthe ultimate degradability, which could have been higher than assumed. The uncertainty of the

characterization is higher for this simulation than for the household wastes since it is not based on direct measurements. It would have been interesting to compare the results from thecharacterization with measured data to evaluate the credibility of the method. On the otherhand, the default model parameters are probably more suitable for this validation than for thehousehold wastes given that they are calibrated for a similar substrate.

7.6. Full scale digester at Käppala WWTP (Lidingö)Validation of the model to a full scale digester was made with data kindly provided byKemira Recycling Competence Center (Helsingborg) to evaluate the practical applicability ofthe model. The time-scale is different from the pilot and lab scale experiments, and thus the

initial values are of less interest. The reactors were modeled as CSTRs and the stiffness of themodel was reduced compared to the previous simulations of pulse-fed reactors. For the modelvalidation, data for R100 and R200 from January to June 2006, and from October 2006 toDecember 2007 was used. For each week, data of mean values for flows and biogas

production were available, as well as measurements of pH, VFA and VS/TS. The reactorswere modeled with weekly variations of inflow parameters, as well as of flows and reactorvolumes. Typical values for sludge variables can be found in Table 9. The meanconcentrations for each week from the simulation of R100 were used as input values to R200.This method does not fully reflect the dynamics of R100, and the mass balance is not fullyclosed but the accuracy of the simulation is still considered to be good enough considering thequality of input data. A simulation with new input values at each time step would be very time

consuming, and it was seen in the simulations for R100 that the changes in concentration foreach week appeared to be linear.

Table 9 Typical values for sludge variables at Käppala WWTP

Variables Unit Primary sludge

Digested primary sludge

WAS Digested primary sludge and WAS

TS % 4.5-6.5 2-2.5 4-6 2.5-3 VS % of TS 80-85 65-70 65-70 2.5-3

pH - 7.1 - 7.2 VFA mg/l - 50-80 - 80-120

Alkalinity mg CaCO3 /l - 3000 - 3500-4500 7.6.1 Feed composi tion

Since no measurements of the protein, fat and carbohydrate content in the sludge was made,typical values were therefore sought after in the literature. A well defined characterization fora primary sludge from the Netherlands which was published by Miron et al. (2000) waschosen for input values to the model. The fractions expressed as percentages of VS (Table 10)gave all inflow characteristics when converted into g COD/m3 (with the Buswell formula,equation 2.2) or g N/m3 (Table 11). Alkalinity and pH were set to 5 mol/m3 and 7respectively. The measured degradability in R100 was 60-70 % with a fairly high HRT, hencethe degradable fraction in the inflow was assumed to be 70 %.

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No data on the properties of the WAS was available from Käppala, thus a characterizationfrom the literature (Chen, et al., 2007) was used for the substrate for R200. Thischaracterization was obtained from a waste water treatment plant in Shanghai with a sludgeage of 7 days (Table 10) and was converted to g COD/m3 as for the primary sludge (Table11). The ammonium concentration in the inflow was assumed to be the same as for the

Sjölunda sludge, and the VFA concentration were assumed to be low (100 g/m3

) with adistribution of 2/3 acetate and 1/3 propionate on a COD basis. The alkalinity was set to 5mol/m3, which is the value proposed in Siegrist et al. (2002), and the pH of the sludge wasfound in Chen et al. (2007) (Table 11).

Table 10 Characterization of primary sludge and WAS

Characterization parameter Primary sludge WAS UnitVS (mean value)COD to VS ratioProteinAmino acids

SugarDissolved carbohydratesFatLCFA

4.71.64181.7

450.652113

3.51.24830

1501.30

% g COD/g VS% of COD % of COD

% of COD % of COD % of COD % of COD

Table 11 Input parameters for primary sludge and WAS

Characterization parameter Notation R100 R200 Unit

Mean total degradable organic matter S aa+ S su+ S fa+ Xs 52 000 21 000 g COD/m3

Mean degradable particulate organic matter Xs 45 000 70 g COD/m3

Protein fraction of X S ѵ aa 0.22 0.83 -

Sugar fraction of X S ѵ su 0.54 0.15 -

Fat fraction of X S ѵ fa 0.25 0.013 -Inert fraction of hydrolyzed X S ѵ in 0 0 -

Mean ammonium S NH4 410 45 g N/m3

VFA S hac+S hpro 5000 100 g COD/m3

HCO3 pH

S HCO3 -log(S H )

107

56.8

mol/m3

7.6.3. Hydrolysis constant

A hydrolysis constant of 0.4 d-1 for primary sludge was found in a review by Vavilin et al.(2008). A lower value of 0.15 d-1 was assumed for the WAS. Only primary sludge ishydrolyzed in R100, and in R200 it was assumed that only the WAS was hydrolyzed.


Owing to the long time scale for the simulation, the initial values for R100 were of littleimportance for this simulation, and were therefore set to steady state values to avoid stiffnessin the simulation. The initial values for R100 were also used for R200.

7.6.5. Resul ts

The biogas production was integrated for each time step and divided with the time differenceto enable a comparison with the measured data. The result from the simulation of the biogas

production in R100 shows that the correlation is fair, except for some outliers (Figure 13).The variations in the modeled gas production are due to changes in TS and flow rate, and it

seems that these variations can explain the variations in measured values to some extent. Theresidual analysis of the gas production in R100 in Figure 13 shows that the model

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underestimates the gas production in the beginning of the time series. It is also shown in thenormal probability plot that the residuals seem to be normal distributed with a mean slightlylower than 0.

Figure 13 Simulated and measured biogas production for R100 and R200 (left) with residuals and normal probability

plot for R100 (right)

The simulation results of R200 depend on the effluent from R100 and the quality of thecharacterization of the WAS. Despite the underestimation of biogas production in R100, the

biogas production in R200 correlates well during the last part of the time series (Figure 13)while it is underestimated during the first part. As for the biogas production in R100, thetrends and variations seem to be reflected in the modeled results for R200. The simulatedVFA are underestimated in the simulations, but are in the same order of magnitude as themeasured values (Figure 14). It has been observed previously in validations of ADM1 that the

VFA correlate worse than the other parameters (Tartakovsky et al. (2008), Jeong et al.(2005)). The simulated alkalinity, on the other hand, correlates well with the measured values(Figure 14). The pH is stable around 7.1 for both the simulation and the measured values,while the ammonium is variable and higher in R200 (Figure 15).

Figure 14 Simulated and measured VFA (left) and HCO3 (right) for R100 and R200

0 100 200 300 400 5000

0.5

1

1.5

2

x 104

Time [days]

W e t b i o g a s p r o d u c t i o n [ m 3 / d a y ]

Simu lated , R100

Measur ed, R100

Simu lated , R200

Measur ed, R200

0 200 400 600 800-2

-1

01

x 104

Time [days]

[ m 3 / d a y ]

-10000 -5000 0 5000

0.10

0.25

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0.75

Data

P r o b a b i l i t y

Nor m al Prob ability Plot

0 200 400 6000

50

100

150

200

250

Time [days] T o t a l V F A s a s a c e t a t e e q u i v a

l e n t s , [ g

C O D / m 3 ]

Measured, R100

Simu lated , R100

Measured, R200

Simu lated , R200

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100

Time [days]

C o n c e n t r a t i o n [ m o l / m 3 ]

Simu lated HCO3

Mes ur ed HCO3

Sim ulated HCO3R200

Measu re d HCO3

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Figure 15 Simulated and measured pH (left) and ammonium (right) for R100 and R200

7.6.6. Discussion

Although the characterization was obtained from the literature and not from directmeasurements, the simulations correlated fairly well with the experimental data. A major

problem with the validation is the lack of data for ammonium in the reactor, which means thatthe real inhibitory effect of free ammonia is unknown. It is possible that the VFAconcentration in R200 was underestimated in the simulation due to the underestimation ofammonia, which led to a higher rate of acetotrophic methanogenesis and thus a lower acetateconcentration.

The fluctuations in the biogas production could not be entirely explained by the model. Thiswas not expected, however, since the model did not include the daily and seasonal variationsin sludge composition. These variations are due to changes in the waste water treatment

processes and to variability in the inflow to the WWTP. Despite this lack of information, themodel could predict some of the observed trends. The result could hopefully be improved if a

better characterization and more data were available. The model parameters were calibratedfor a mixed sludge reactor, and the microbial population in the reactor may be different for thereactors with digestion of household waste. Therefore, a recalibration of the model parameterscould possibly improve the model fit.

0 100 200 300 400 500 600 7000

1

2

3

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5

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8

Time [days]

p H

Simu lated , R100

Measur ed, R100

Simu lated , R200

Measur ed, R200

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Sim ulated NH4, R100

Sim ulated NH4 R200

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8. Uncertainty analysisIn this section, uncertainty analysis (UA) of the model is conducted to enable evaluation ofthe accuracy and credibility of the model output. The uncertainty of the model is evaluatedusing Monte Carlo methods, with known or assumed distributions of the input parameters tothe model.

In section 7, measured values were used as inputs for the simulations. A good fit to themeasured output values were considered as a successful validation, and if the correlation was

poor the validation was considered to be a failure. In this section, the measurement errors will be taken into consideration, to evaluate the quality of the model predictions. If the uncertaintyof the model output is high, then better analysis methods may be required to produce asatisfying fit to data.

Another topic that will be addressed in this section is the benefit from extensivecharacterization of household waste. The variabilities of 40 different household wastes wereused to describe a general characterization. The quality of model predictions with or without

measurements could then be compared, in order to evaluate the importance of a detailedcharacterization.

8.1. Introduction to uncertainty analysisA complex natural system like anaerobic digestion is impossible to perfectly predict, thus theuncertainty is an important measure of the reliability of the prediction. The predictionuncertainty will depend on the uncertainty of the model structure, parameters andmeasurements and on the mathematical uncertainty as in Figure 16. The mathematicaluncertainty arises from the processes where the equations are solved numerically. Modelstructure uncertainty can have different sources, e.g. excluded processes or a falserepresentation of the system. Uncertainty from model structure can change with time if the

excluded processes change with time. An example in the anaerobic digestion model is theinhibition from H2S, which most likely varies with time but is excluded in the model (Kops,et al., 1996). The model structure can be mathematically verified only if the parameters can beidentified (see section 6). The model structure is assumed to be valid for this case, even ifsystem identification is not likely to be successful. Indications of the lack of identifiable

parameters for the model were discussed in section 6.2.

Figure 16 Correlation between uncertainties (adapted from Kops et al, 1996)

RealPredictionUncertainty

ModelUncertainty

ParameterUncertainty

MathematicalUncertainty

DeterminedPredictionUncertainty

MeasurementUncertainty

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The parameter and measurement uncertainties are in focus in this analysis. Uncertainty ininput parameters propagates through the model and affects the model output. The statistical

probability of parameters and measurements can often be described with probability densityfunctions (PDEs), with e.g. normal, uniform, or triangular distribution. To be able todetermine the uncertainty in the model prediction, the PDEs are used as input in the Monte

Carlo analysis.

8.1.1 Monte Carlo analysis

If the PDEs of the parameters are known, it is possible to generate random numbers fromthese and use as input to the model. The procedure where a set of generated random numbersare used as input to a model is called Monte Carlo (MC) analysis. The distribution of theoutput from a MC analysis can be used to quantify the uncertainty of the prediction. Thismethod has many benefits and is widely used; one of the most important advantages is that itcan be applied for non-linear models. The method enables analysis of the model for a span ofinput parameters, i.e. global sensitivity analysis, which will be discussed in section 9.

The sampling of input values is commonly made from the entire spectrum of the PDEsindependently for each input variable, called simple random sampling, or brute forcesampling. If an infinite number of samples are generated, the resulting set of outputs will givethe PDE of the model output. In reality, however, a number of runs are chosen that is largeenough to ensure that the result is not changed notably by increasing the number of runs. Thissampling method is commonly used, since it is relatively easy to conduct and to understand.One drawback with the method is that a large number of simulations often are required, whichcan be very time consuming.

The ordinary MC method does not include variation of the parameters with time, which is adisadvantage (Kops, et al., 1996). In wastewater treatment plants, input parameters are known

to vary with time, for example flow rates and concentrations of phosphorous and nitrogen. Analternative to MC simulation is therefore produce stochastic MC input variables at each timestep, a method called MC with stochastic parameters. Another method is the stochasticdifferential equations method (SDE) where a noise term is added to the ODE system whichads the uncertainty for each time step (Kops, et al., 1996). These methods are rarely used, theyhave the drawback of being slower than MC and they require further assumptions regardingthe quantity of the noise.

8.1.2. Latin Hypercube Sampling (LHS)

To reduce the number of simulations needed in the MC analysis, Latin hypercube sampling(LHS) can be applied. This method divides each parameter PDE into equiprobable intervals,

and combinations of input values are chosen from these intervals so that as much as possibleof the parameter space is covered (Figure 17). An underlying assumption in this method isthat all parameters are independent and could be paired as such, but in real life it is fairlycommon with correlated parameters. If the parameters are correlated the LHS sampling can

produce unlikely input combinations.

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0

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Probability X 2

P r o b a b i l i t y X

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C u m u l a t i v e P r o b a b i l i t y

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-2 -1 0 1 2

X 1

C u m u l a t i v e P r o b a b i l i t y

Figure 17 Visualization of the LHS sampling method (Minasny, 2004)

When generating the MC samples, it is important to verify that the number of realizations, N ,is large enough not to affect to result. If the total mean or variance of the output is changedwhen increasing N , it is not sufficiently large. To evaluate the benefits of the LHS samplingmethods, a comparison between the simple random method and LHS sampling was conducted(Figure 18 and Figure 19). The LHS method produced results converged faster to the finalvalue, and fluctuated less. This method was hence chosen for the analyses in this work. The

choice of N is a trade-off between desired accuracy of the result and the time available for thesimulations. N was chosen to be 5000 for all simulations, a value large enough to producesufficiently consistent results but still low enough to keep the required simulation time withinhours and not days.

Figure 18 Mean (left) and variance (right) for steady state gas production as a function of N for a continuous process

when using simple random MC sampling

0 2000 4000 6000 8000 100000.0494

0.0495

0.0496

0.0497

0.0498

0.0499

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Num ber o f run s (N)

M e a n g a s p

r o d u c t i o n

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2.4

2.6

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3x 10

-3

N

S t a n d a r d d

e v i a t i o n

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Figure 19 Mean (left) and variance (right) for steady state gas production as a function of N for a continuous process

when using LHS sampling

8.2 Measurement uncertainty of the household waste simulations

8.2.1. Methods for the uncertainty analysis

The uncertainties of the simulations of household waste experiments from section 7 wereanalyzed with MC method. The uncertainty from the model structure and parameters is hardto quantify as stated in 6.1., and was omitted in this work. Focus of the analysis was insteadon the impact of the measurement quality on the model predictions. The standard deviationsof the measurements for the characterization of the waste were found in the literature, and are

presented in Table 12. The measurement errors were assumed to be normally distributed.Values for some parameters were not found, either because they were measured withunknown instruments, as in the case of pH and pressure, or because they were impossible to

measure, as in the case of HCO3. For these cases, high values for uncertainty were assumed.

Table 12 Standard deviations for measurements of input parameters

Input parameter Aalborghousehold waste

Västra Hamnenhousehold waste

Unit σ (%)

TSSoluble CODProteinFatStarchSugar

Fibers pH NH4-NAcetatePropionateTemperaturePressureFeed flow rate

5.0231718187

117.40.3248.734.353.31.021.33

5.023 N

171274

147.20.02748.7 N

34.3 N 35.41.031.33

% % % of TS % of TS % of TS % of TS

% of TS % of TS

g COD/m3

g COD/m3

°C bar l/d

2.5S 20U

0.97J

3.5 J 3.4 J 18 J

4.7

J

2U

3 L 10 U 10 U 2 U 2 U 2 U

N No available data, the same values as for Aalborg household waste were used in the simulations,UEstimated value, S (SIS, 1981), J (la Cour Jansen, et al., 2004) , L(Dr Lange®)

The uncertainty of the measurements for the target output parameters gas production, VFA,alkalinity and ammonium are presented in Table 13. The gas production was the key

parameter of interest and the measurements were considered to be very reliable (a relativestandard deviation of 2 % was estimated for the measurements). Measurement variability for

0 2000 4000 6000 8000 100000.0494

0.0495

0.0496

0.0497

0.0498

0.0499

0.05

Num ber o f run s (N)

M e a n g a s p r o d u c t i o n

0 2000 4000 6000 8000 100002

2.2

2.4

2.6

2.8

3x 10

-3

N

S t a n d a r d d e v

i a t i o n

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VFA was unknown, and the method for determination was considered less unreliable.Uncertainties for the ammonium and alkalinity measurements were found in laboratorydocumentation.

Table 13 Standard deviations for measurements of output parameters

Output parameter σ (%)

Gas productionVFA

NH4-NHCO3

2U

10U

3 L

3.5S2

UEstimated value , L(Dr Lange®),S2 (SIS, 1994)

The experiments were modeled as pulse-fed reactors in section 7, but the stiffness of thesesimulations led to long simulation times. MC simulations of these models would be very timeconsuming for a sufficient number of realizations. Instead the reactors are approximated toCSTRs with flows and volumes as in the steady state phase (see section 7.1.1.). One drawbackfor this method is that the results from the uncertainty analysis cannot be fully compared with

the experimental data. The advantage is, apart from the short simulation time, that the resultswill be more useful for real processes which are fed with shorter intervals. To ensure that thesamples are well distributed, the LHS sampling technique was used in Matlab (Minasny,2004). With normally distributed samples, it was possible to get negative values for theconcentrations; in that case they were set to 0.

8.2.2. Results of the measurement uncertainty analysis

The resulting distributions of the model outputs from the MC analysis on the Aalborghousehold waste simulation are presented as cumulative distribution functions (CDFs) inFigure 20. The median for the simulated output is found on the x axis for F(x)=0.5, and the95% confidence interval between F(x)=0.025 and F(x)=0.975. Although the inputs to themodel are normally distributed, it can be seen that the output are not, since the CFDs are notfully symmetrical. Especially for the alkalinity, where it can be seen that the higher outputvalues are more spread out than the lower values (F(x)=0.5 is not in the middle of the curve).The biogas production, however seem to be normally distributed.

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Figure 20 CDF of the model outputs for the Aalborg household waste simulation, gas production (upper left), VFA(upper right), NH4-N (lower left) and HCO3 (lower right)

Intervals of the modeled outputs from the Aalborg household waste simulation with aconfidence level of 95% are presented in Figure 21. These are results from Monte Carlosimulations, and are compared to data with measurement errors also presented withconfidence intervals. The confidence intervals for the gas production and alkalinity are the

broadest, which means that the measurement errors are most influential on these parameters.When the confidence intervals overlap, the validation error can be explained by measurementerror. If not, the explanation for the lack of fit is to be found elsewhere since it is highlyunlikely that measurement error is the cause. Most of the data points for the gas production

are within the interval, except for the first time period. The alkalinity has a broad interval andall data points overlap the simulated confidence intervals. For the VFA and the ammonium;none of the measurements are included in the interval.

0.035 0.04 0.045 0.050

0.2

0.4

0.6

0.8

1

x

F ( x )

Em pir ical CDF

100 150 200 2500

0.2

0.4

0.6

0.8

1

x

F ( x )

Em pir ical CDF

900 950 10000

0.2

0.4

0.6

0.8

1

x

F ( x )

Em pir ical CDF

50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

x

F ( x )

Em pir ical CDF

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Figure 21 Plots of the confidence intervals of the model outputs ammonium and alkalinity with respect to

measurement errors for the Aalborg household waste simulation

The same method for uncertainty analysis was applied on the Västra Hamnen householdwaste simulation from section 7.4., and the results from the simulations are presented inFigure 22. There are many measurements for the gas production which are far from theconfidence interval, while the VFA measurements are all within the interval. The lack of fitfor ammonium and alkalinity cannot be explained by measurement error.

40 45 50 55 60 65 700

0.01

0.02

0.03

0.04

0.05

0.06

Time [days]


Biogas production m odelled

95 % confid ence in ter val


Biogas production measured

40 45 50 55 60 65 700

200

400

600

800

1000

1200

Time [days]


VFAs modelled

95 % confi dence i nter val


VFAs measured

40 45 50 55 60 65 700

500

1000

1500

Time [days]


NH4 m ode lled



NH4 m easur ed

40 45 50 55 60 65 700

20

40

60

80

100

Time [days]


HCO3 model led



HCO3 m easur ed

30 35 40 45 500

0.01

0.02

0.03

0.04

0.05

0.06

Time [days]


Biogas production modelled




30 35 40 45 500

200

400

600

800

1000

1200

Time [days]


VFAs m odelled



VFAs m easured

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Figure 22 Plots of the confidence intervals of the model outputs with respect to measurement errors for the Västra

Hamnen household waste simulation

8.2.3. DiscussionA considerable measurement uncertainty is naturally not desirable since it means that themodel cannot predict the parameters better than the confidence interval, even if the model

parameters were improved by calibration. The only way to reduce measurement uncertainlyis, of course, to improve the analytical method for determination of these inputs. If the

parameters that influence the uncertainty the most are determined, the measurements that needimprovement can be found. Even so, there is also the uncertainty of sampling, which is harderto quantify but further broadens the confidence interval of the result. It can seem unpromisingthat so many measurements are outside of the confidence interval for the household wastesimulations, but it is in fact promising in one way; it allows the correlation to be improved bycalibration of the model parameters. Sensitivity analysis and model calibration is discussed insection 9 and 10.

8.3. Variability of feed composition

8.3.1 Method

To enable comparison of the prediction accuracy when using the characterization frommeasurements and when using a general composition of household waste, the variation ofdata from 40 samples was analyzed. The general characterization was calculated from theliterature and based on household waste collected in Danish cities (Table 14). This comparison is interesting since measurements of proteins, fibers, fat and otherconstituents in the substrate are costly and thus seldom carried out. If the uncertainty of the

model results mainly depends on accurate measurement of these parameters, it means thatthese measurements are needed for a satisfactory simulation. The 40 measurements wereregarded as normally distributed, which was a well-grounded assumption e.g. for the fatcontent (compare with Figure 23). The standard deviations of the parameters can be found inTable 14. It is worth noting that the fractions of the different constituents are assumed not to

be correlated, although it is likely that they are correlated in reality. The total amount of theconstituents makes up the degradable part of TS.

30 35 40 45 500

500

1000

1500

Time [days]

C o n c e n t r a t i o n

[ g N / m 3 ]

NH4 m ode lled



NH4 m easur ed

30 35 40 45 500

50

100

150

200

Time [days]

C o n c e n t r a i o n

[ m o l / m 3 ]

HCO3 m ode lled



HCO3 m easur ed

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Table 14 Means and standard deviations for household waste

Characterization parameter

Generalhouseholdwaste values

Unit σ (%of TS)

Rel std (%)

TSProteinSugarStarchFatFibersSoluble COD

26.4

A

14.96M

15M

13.818.513.9

% % of TS % of TS % of TS % of TS % of TS %

6.51.37351.653.698.3

24.6

B

9.2H 50 H 33.3H 12.0 H 20.0 H 59.7B

ABefore dilution, uncertainty is equal to measurement uncertainty after dilution, MMean values from (Hansen, etal., 2007) and σ from assuming that 95 % of measurements are within the range of 2σ, B (Højlund Christensen, etal., 2003), H (Hansen, et al., 2007)

Figure 23 Normal probability plot and histogram for fat fractions in data from (Hansen, et al., 2007)

8.3.2. Results and discussion

The uncertainties of the model predictions when using the general characterization instead ofmeasurements were determined for the Aalborg and Västra Hamnen household wastesimulations. This analysis was conducted simply by changing the means and distributions ofthe characterizations from 8.2. to the values inTable 14. A comparison between the resulting variances and the variances due tomeasurement errors is presented in Table 15. This table shows that the variance increases

almost 10-fold when it comes to gas production and ammonium. The predictions of VFA andHCO3 are not as influenced of the quality of the input data.

Table 15 Variance of model predictions from analysis with varying characterization parameters

Parameter Unit Aalborghousehold wastewith measuredcharacterization

Aalborghousehold wastewith generalcharacterization

VästraHamnenhousehold wastewith measuredcharacterization

VästraHamnenhousehold wastewith generalcharacterization

Gas productionVFA NH4 HCO3

m3 /d gCOD/m3 gN/m3 mol/m3

4.1x10-6

42242852.9

2.3x10-5

5065.8x103

82

1.2x10-6 22.449359.5

1.5x10-5 13.36.1x103 92.7

11 12 13 14 15 16 17

0.010.020.050.10

0.25

0.50

0.75

0.900.95

0.980.99

P r o b a b i l i t y

10 12 14 16 180

5

10

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The confidence intervals of the model outputs presented in Figure 24 and Figure 25, show thatthe confidence interval for biogas production is significantly broader when the variability ofthe characterization parameters are used instead of the measurement uncertainty. This impliesthat the measurements of the substrate are important to reduce the uncertainty of the resultsfor household waste. One can hence expect that the difference in gas production from

different household wastes can be significant if the fractions of the feed are non-correlated.

Figure 24 and Figure 25 also show that the levels of ammonium and alkalinity in the reactorare affected by the content in the waste, while the VFA seem to be largely unaffected in thesame range. Measurements of the specific household waste would therefore not be expectedto improve the correlation of the simulation for VFA.

The confidence intervals for the general composition also reveal that there are values thatcannot be explained by varying the waste composition. This implies that the model

parameterization or structure needs to be revised. To be able to calibrate the model, theinfluence of individual parameter on outputs needs to be investigated. This is the subject of

section 9 and 10.

Figure 24 Aalborg household waste simulation with general waste composition

40 45 50 55 60 65 700

0.01

0.02

0.03

0.04

0.05

Time [days]



95 % confid ence int erval

95 % confid ence int erval


40 45 50 55 60 65 700

200

400

600

800

1000

1200

Time [days]

C o

n c e n t r a t i o n [ g C O D / m 3 ]

VFAs m odelled

95 % confid ence inter val


VFAs measured

40 45 50 55 60 65 700

500

1000

1500

Time [days]


NH4 mode lled



NH4 m easur ed

40 45 50 55 60 65 700

20

40

60

80

100

Time [days]


HCO3 mo del led

95 % confid ence int er val

95 % confid ence int er val

HCO3 measured

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Figure 25 Västra Hamnen household waste simulation with general waste composition

30 35 40 45 500

0.01

0.02

0.03

0.04

0.05

0.06

Time [days]

P r o d u c t i o n r a t e

[ m 3 / d a y ]





30 35 40 45 500

200

400

600

800

1000

1200

Time [days]

C o n c e n t r a t i o n [

g C O D / m 3 ]

VFAs m odelled



VFAs measured

30 35 40 45 500

500

1000

1500

Time [days]


NH4 mode lled



NH4 m easur ed

30 35 40 45 500

50

100

150

200

Time [days]


HCO3 mode lled



HCO3 measured

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9. Sensitivity analysisIn the uncertainty analysis from the previous section the overall uncertainty of the modeloutput due to uncertainties in input was studied. In this section the sources of the variations inoutput is investigated to find the input parameters which the model is sensitive to. Sensitivityanalysis (SA) can be conducted to find the input parameters that are most important to

measure to minimize the prediction uncertainty. SA can also be used to test the modelstability and to find the model parameters that are most suitable for model calibration. If a

parameter has a negligible impact on the output, then the efforts to determine that parametermight be reconsidered. For some applications, like control, it is desirable to simplify themodel as much as possible, and if the result is insensitive to a parameter, it can be excludedfrom the model. The parameter for which the output is most sensitive to is probably the bestcontrol signal. Another obvious purpose of SA is to improve the understanding of the system.Large ODE systems are not easily understood, and the SA can help to quantify thecontribution of different parts of the system to the output result and give hints on what parts ofthe process that needs special consideration. A specific goal of the SA in this case was to findkey parameters that could be used to calibrate the pilot scale simulations from section 7.

First, a general presentation of different methods for sensitivity analysis is made, in section9.1. and 9.2., then previous SA on anaerobic digestion models from the literature are

presented in 9.3. The sensitivity analysis on the pilot scale simulations from section 7 arefound in section 10.

9.1. Local SA methodsLocal methods evaluate linear perturbations for the output for a specific set of parameters.Thus, the result applies for this set of parameters, but may not be applicable for other values.For linear models without correlation between parameters, these methods are useful.

9.1.1. Sensitivity functions

A common SA method is to study the partial derivative of an output variable with respect to acertain input parameter. This derivative is called the sensitivity function δ, and can beinterpreted as the linear change in output due to the change in the input parameter. Thesensitivity function can be computed continuously during the simulation time, to study thedynamics of the sensitivity of the output to the parameter. The absolute change in an inputvariable x per unit change in the parameter θ is presented in (eq. 9.1) (Jeppsson, 1996).

(9.1)

The definition in equation 9.1 gives a result that strongly depends on the units of the parameter, and often the relative change in parameter is more interesting to compute (eq. 9.2).The derivative of the variable x with respect to the parameter θ is here multiplied with the

parameter value. Here the sensitivity function depends on the parameter on a relative basis,and sensitivity functions for different parameters can easily be compared.

θ (9.2)

When analyzing the sensitivity functions for different parameters dependencies between parameters can be detected. If parameters have similar but inverse sensitivity functions they

can be non-identifiable, i.e. a change in one parameter can be compensated by a change inanother. The best identifiability is achieved when sensitivity functions have different behavior

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and when they differ significantly from zero. As sensitivity functions give a linear sensitivityanalysis they are valid only locally for the specific parameter values that were used.

9.2. Global methods

Models of complex systems such as the anaerobic digestion process are usually nonlinear.Using local SA methods to analyze these models can be questionable, since the results onlyare valid for the set of parameters that were analyzed. For other parameter values, thesensitivity analysis may not be accurate. For nonlinear models, global methods are preferred,that evaluate the sensitivity for a broader spectrum of input parameters. This analysis will not

be as straightforward as the linear methods, though. Here three examples of useful methodsfor nonlinear SA are presented.

9.2.1. Scatter plots

A natural first step when analyzing a model is to study plots of outputs vs. input for aqualitative analysis of the model behavior. Dependencies and nonlinearities can be detected,

and the understanding of the system can be improved. A MC generated sample of inputs andthe corresponding outputs can be used for this analysis. Figure 26 shows an example of howscatter plots can be used for SA.

Figure 26 Examples of scatter plots for the Aalborg household waste experiment; gas production vs. TS (left) and gas

production vs. k H (right) from MC analysis on characterization and model parameters respectively

The qualitative sensitivity analysis from these plots indicates that the TS content in the feedhas an impact on the biogas flow from the reactor, and a nonlinear correlation between k H andgas production was detected.

9.2.2. Standardized regression coeffic ients

Another common SA method is to use the output from a set of MC sampled parameters forlinear regression with respect to the different parameters. The standardized regressioncoefficients are a measure of the sensitivity of the output to the specific parameters. Themodel coefficient of determination, R2, can be used to determine the precision of the model.For R2 values close to 1, the regression model is valid and the regression coefficients are agood measure of the sensitivity. If R 2 is low, on the other hand, it indicates a nonlinear model,

with a poor correlation to the linear regression. In these cases, a nonlinear approach to SA is

0.044 0.046 0.048 0.05 0.052 0.054 0.0560

0.01

0.02

0.03

0.04

0.05

0.06

TS [%]

G a s p r o d u c t i o n r a t e [ m 3 / d ]

0.1 0.15 0.2 0.25 0.30

0.01

0.02

0.03

0.04

0.05

0.06

kH [d -1]

G a s p r o d u c t i o n r a t e [ m

3 / d ]

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preferred. This analysis hence can quantify the degree of nonlinearity, and if the linear behavior is dominant, give a measure of the degree of sensitivity.

9.2.3. Variance-based methods

Scatter plots represent a qualitative method, and is a very useful for revealing nonlinearities

and finding correlations between inputs and outputs. To be able to quantify the sensitivity ofinput parameters, and to compare sensitivities for different parameters, more sophisticatedmethods are required. The method that was chosen for the main part of the SA in this projectis based on the correlation between the variance of input parameters and the variance ofoutputs for steady state simulations. The variance in the parameters will lead to a variance inoutput, and an important parameter will have a bigger impact on the output variance than a

parameter that the model is less sensitive to.

If, for example, the inputs are generated with MC methods from PDEs as in section 8.2., theoutputs will be determined with a total variance. This is the same variance that was used fordetermining the uncertainties of the predictions. In the case of sensitivity analysis, the source

of the variance is of interest. The variance that each parameter adds to the total outputvariance is the measure of sensitivity that is sought. For a linear model, without correlationeffects, the total uncertainty could be decomposed into fractions of variances assigned to each

parameter. The contributions of variance for one parameter at a time could simply becalculated, and the total output variance would be the sum of these. For a nonlinear model, thetotal variance cannot be decomposed in this simple manner due to correlation effects. Instead,the difference between the total output variance and the output variance when one parameterwas held constant was chosen as an estimator of the correlation between variance in input andoutput. This value also represents the possible reduction in uncertainty that would be gained ifa parameter would be determined without uncertainty.

9.3. Sensit ivity analysis of anaerobic digestion models in the literatureLinear sensitivity analysis is the most commonly used method for analyzing the parametersensitivity in anaerobic digestion models, in fact no examples of SA based on MC simulationswere found in the literature. Tartakovsky et al. (2008) developed a distributed version ofADM1 for simulation of an UASB reactor and performed a sensitivity analysis on the model

parameters. They used sensitivity functions to find the most sensitive parameters, which wereused to calibrate the model. The sensitivity analysis showed that specific uptake rates and halfsaturation constants for acetate and propionate and butyrate/valerate had the strongest impacton reactor COD concentration, acetate and propionate, while k La affected the methane

percentage. The measurements had high variability, but model correlation with “reasonableaccuracy” was achieved. COD predictions were better than VFA predictions; the authorssuggested that the model underestimated inhibition of fermentation from free acid, thusoverestimating the VFA.

Another method for SA was used by Jeong et al (2005) as they analyzed the sensitivity ofADM1 using bottle tests with glucose and acetate as substrate. ADM1 was simplified as thedecay processes for microorganisms, inhibition from pH and free ammonia and the gas-liquidtransfer for methane were ignored. The sensitivity analysis was carried out by varying one

parameter at a time over a chosen interval, and then calculating the mean of the absolutedifferences between the standard parameter setting result and the model result with altered

parameter value for each time step. The benefit from this method compared to sensitivityfunctions was that different intervals of variance could be chosen for the parameters, and thatthe non-linearity of the output could be revealed in that range. Yield of product on substrateand Monod maximum specific uptake rates proved to be significant parameters, while yield of

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biomass on substrate were less important. Correlation with the model for methaneconcentration was good after calibration, but worse for acetate which the authors explain withadsorption and storage by the microorganisms. The question which arose from the results ofthis SA was whether the chosen intervals of variance are reasonable, for example the yield of

product on substrate varied with 30 %, a figure which was not supported in the article.

An example of SA for the purpose of parameter reduction can be found in Noykova (2000)where an SA is made on an older and simpler model than ADM1. The only output in the SAwas the biogas flow, and logarithmic or relative sensitivity functions were used (eq. 9.3)

(9.3)

The analytical equation to calculate T ij could not be adapted for non-linear systems, thereforesimulation results were required. µmax for methanogens proved to be the most significant

parameter, as were the yield coefficient for methane and inhibition coefficient formethanogens. Decay rates, on the other hand, had little impact on the results and could beneglected. The simplified model with four optimized parameters had a reasonable fit. Whenreducing a model, it is important to be aware that the conditions under which the model could

be used become narrower. The process needed to be very stable for the reduced model to beuseful.

9.4. DiscussionIf a model prediction is sensitive to a specific parameter, this parameter will also contributemore to the uncertainty of the prediction. Uncertainty and sensitivity analysis therefore gohand in hand.

All sensitivity analyses on anaerobic digestion found in the literature were based on localmethods. These analyses were easy to perform and to grasp. Sensitivity functions, forexample, give a general sensitivity analysis in the sense that the parameters are alwayschanged 100 %. The result should however be treated with caution. Some parameters are notat all likely to vary as much as 100 %, while others could vary more than that. The non-linear

behavior and correlation effects of the model are also excluded using this method. It is knownthat both ADM1 and the Siegrist model are non-linear and it is doubtable whether sensitivityfunctions are a suitable method.

All sensitivity analyses found in the literature only included model parameters and not inflow parameters, although they are interesting as well. It is for example not useful to put mucheffort info calibrating the model parameters if the level of detail is not supported by the data.Furthermore, it could be interesting to compare the relative importance of input parametersfor various operational settings. Increase knowledge of the model sensitivity for all

parameters would enhance model application and ensure that measurements are made for themost influential input parameters.

Global MC methods are preferred over local methods when it comes to analyzing nonlinearmodels. It is however important to stress that sensitivity or uncertainty analysis using MCmethods are performed for a certain case, with chosen ranges for the parameters, and that theresults only are valid for that particular parameter space. The analysis will not be reliable ifthe probability density functions of the parameters are chosen poorly. One of the drawbacks

of MC-based methods is of course the extensive computational force that is required.

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10. Sensitivity analysis of the Siegrist modelAs discussed in chapter 9, a global and variance-based method was considered most suitablefor SA of the validation simulations of section 7. The chosen method quantified the reductionof variance in output when one parameter was kept constant compared to when all parameterswere varying. The background to the sampling method and distributions for characterization

parameters can be found in chapter 8. The sensitivity analysis was conducted by firstrendering a LHS sample of 5000 parameter sets. Steady state simulations were run for theLHS sample, giving the total variance, and also for the same parameter sets but where one

parameter at a time was kept at a constant value (at the mean value). The sensitivity measurefor each parameter was expressed as the relation between the variance when the parameterwas held constant to the total variance. A low value for this relative sensitivity means that theoutput is very sensitive to the parameter.

SA was conducted for the validation simulations of the pilot scale experiments presented insection 7. Each of these experiments were now simulated as steady state simulations, andanalyzed for three different categories of parameters. One of the purposes of the SA was tofind the parameters that were important to measure in order to reduce the output uncertainty.This was achieved by calculating the sensitivity to the measured parameters, using known andestimated measurement errors as parameter distributions. Another aim for the SA was to findthe parameters that would be most suitable for calibration. In this case, the sensitivity to themodel parameters was studied, using rectangular distributions for these parameters with arange of 50 % to 150 % of the default values. This means that all values in this interval wereassumed to be equally probable. This use of general intervals was applied due to the lack ofinformation, and does not always reveal what parameters that was best suited for calibration.The reason for this was partly that some parameters are more variable by nature than others,and may be changed to a higher extent. The sensitivity measure for some parameters could

also be explained with a high rate of unstable simulations, due to e.g. washout. These parameters will not always be good for calibration purposes. The SA therefore needed to besupplemented with scatter plots to study relationships between parameter value and outputmore closely.

The sensitivity of the measured parameters and model parameters were also studied when allinput and model parameters were allowed to vary simultaneously. This could display therelative importance of the measured parameters compared with the model parameter.

The values used in the model were given for 35°C, and recalculated for the actual reactortemperature with the equations for temperature dependency (see equation 4.16).

10.1. Aalborg household waste experimentFor this first example, all results are presented in the text, but for the other cases only the mostinteresting results are shown, and the rest are found in Appendix III.

10.1.1. Sensitivity of input parameters

The first step of the sensitivity analysis for this thermophilic digester was to findmeasurement uncertainties for the input parameters, described as standard deviations. Thestandard deviations and rank of the uncertainties were presented in Table 16. The resultingrelative sensitivity for each parameter with respect to different output parameters is also

presented here. Rank 1 is given to the parameter that lowers output variance the most whenkept at a constant value.

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Table 16 Results of SA, UA and variability of measured parameters for the Aalborg household waste simulation

Parameter Mean Unit Uncertainty

rank σ (%)

Sensitivity(Gas)

rank relative

Sensitivity(VFA)

rank relative

Sensitivity(NH4-N)

rank relative

Sensitivity(HCO3)

rank relativeTSSoluble TSProteinFatSugarStarchFibers pHHCO3 NH4-NAcetatePropionateTemperatureFlowPressure

0.050.230.170.180.070.180.117.41016048.734.355.31.331.02

kg/kg

g/TS g/TS

g/TS

g/TS

g/TS

mol/m3

gN/m3 gCOD/m3

gCOD/m3

°C

l/d

bar

122149310813111441366

2.5S

20U

0.97J

3.5J

18J

3.4J

4.7J

2U 100 U 3L

10 U 10 U 2 U 2 U 2 U

181064791411131512532

0.740.981.000.950.880.970.991.001.001.001.001.000.900.870.78

437115810142915131126

0.950.950.991.000.981.001.001.000.591.001.001.000.491.000.98

132679111445131512810

0.420.930.840.970.970.991.001.000.930.951.001.001.000.981.00

324851371111291015614

0.970.950.991.001.001.001.001.000.0801.001.001.001.001.001.00

S (SIS, 1981), U (Unknown), J (la Cour Jansen, et al., 2004), L(Dr Lange®), B (Højlund Christensen, et al., 2003), H (Hansen, et al., 2007)

The results from the sensitivity analysis show that the gas production is most sensitive to theTS and flow of the feed and to the pressure in the reactor. The temperature and starch contentare also influential (rank 5 and 4), but the other parameters seem to be measured well enoughor have an insignificant effect on the variability for the gas production. The alkalinity, whichwas given the highest uncertainty, is still irrelevant for the gas production. It can also beconcluded that the hydrolysis is not limiting, since the solubility of the waste also isinsignificant for the variance in gas production. The VFA, on the other hand, are very muchaffected by the temperature and by the unknown inflow of carbonate alkalinity.

The measurement uncertainty for protein that was used in this analysis was very low. Thisresulted in a higher contribution of the TS in the feed to the variance of the ammonium levelsin the reactor than for the protein content (compare 0.42 and 0.84). The carbonate alkalinity inthe reactor was mainly affected by the inflow concentration of HCO3, and not by the otherconstituents of the feed.

10.1.2. Model parameter sensiti vity

The results from the sensitivity analysis on model parameters are presented in Table 17. In thefirst column the parameters are listed. The sensitivity analysis did not include the chemicalequilibrium constants, since these were considered to be well defined. The parametersincluded maximum growth rate constants for the processes ( µmax,j), death rate constants (k d,j),half saturation constants ( K Si), inhibition constants ( KI ac), k La for CO2 (which decides the k La

for H2 and CH4 as well) and hydrolysis constant (k H ).

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Table 17 Results of SA of model parameters for the Aalborg household waste simulation

Parameterat 35 °C

Mean Unit Sensitivity(Gas)rank relative

Sensitivity(VFA)rank relative

Sensitivity(NH4-N)rank relative

Sensitivity(HCO3)rank relative

µmax3 µmax4

µmax5 µmax6 µmax7 µmax8

k d9 k d10 k d11 k d12 k d13 k d14

K Saa K Ssu K Sfa

K Spro K Sac K SH2

KI ac56 KI H2,5 KI H2,6 KI H,34 KI H,58 KI NH3,6 KI NH3,7

k LaCO2 k H

44

0.60.60.3720.80.80.060.060.050.350501000

204011500310.015e-425172000.2

d -1

d -1

d -1

d -1

d -1

d -1

d -1

d -1

d -1

d -1

d -1

d -1

gCOD/m3

gCOD/m3

gCOD/m3

gCOD/m3

gCOD/m3 mgCOD/m3

gCOD/m3

mgCOD/m3

mgCOD/m3

mol/m3

mol/m3 gN/m3 gN/m3

d -1

d

-1

1416

224751718413231115213

22682510121992726201

1.001.00

0.991.001.001.001.001.001.001.001.001.001.001.000.99

1.001.001.001.001.001.001.001.001.001.001.000.019

2717

241462322263813211816

15119142051910272512

1.011.00

1.000.350.720.801.001.001.000.640.860.961.001.001.00

0.980.950.900.981.000.801.000.910.470.851.000.96

221

175861127101237132226

202515182414231649191

0.991.00

0.990.990.990.991.001.000.991.000.990.991.001.001.00

1.001.001.001.001.001.001.001.000.990.991.000.051

1922

163282025277613182317

15101214219241145261

1.001.00

1.000.800.750.931.001.001.000.880.880.991.001.001.00

0.990.960.970.991.000.941.000.960.850.861.000.57

The gas production seemed to be virtually insensitive to all model parameters except thehydrolysis constant, which indicates that the hydrolysis could get rate-limiting for certainvalues of k H (Table 17). The non-linear correlation between k H and gas production isillustrated in Figure 26 (in section 9.2.1).

It can be noted that the hydrolysis was irrelevant for the VFA concentrations, as were the ratesof fermentation (processes 3, 4 and 5). The VFA were instead linked to the constants for

propionate degradation (process 6; rank 1, 2 and 3) and the acetoclastic methanogenesis(process 7, rank 4). The high sensitivity for the maximum growth rates could be explainedwith a high rate of washout of propionate degraders when the parameters reached criticalvalues. Figure 27 shows an example where reactor instability can be detected for low valuesfor µmax6 . These parameters would not be suited for calibration, since it would result inunstable reactors. Instead the half saturation constants for processes that determine the VFAlevels should be considered for calibration of VFA. This result could not be found in thesensitivity analysis, and a better approach for the SA would hence have been to either userealistic variations for the parameters, or to sort out values when bacteria were washed out.This analysis was not performed in this project due to lack of time.

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Figure 27 Scatter plot with VFA levels as function of µmax6

The ammonium is primarily produced in the fermentation of proteins, a process which is fast

and limited by the rate of the hydrolysis. Therefore, the hydrolysis constant was far moreimportant for the ammonium concentration than the other model parameters.

The carbonate alkalinity is mostly produced in the methanogenesis (process 7 and 8),consequently the maximum rates of these reactions proved to be important. The mostsignificant parameter, however, was the hydrolysis constant. It affects alkalinity byconsumption in the hydrolysis, but moreover it decides the rates of the other processes, ofwhich many include uptake or production of alkalinity.

A relative sensitivity higher than 1 is unlikely, but it can be seen for the VFA and µmax3. It canhappen if more extreme values are produced for the run where one variable is kept constant

than for the run where all parameters vary. If the distributions for the model parameters wereknown and the number of runs was increased, this problem would probably not occur to thesame extent.

It could be shown that TS contributed to a great deal to the uncertainty for the gas production,although it was measured with a standard deviation of 2.5 %. k H stands out as an important

parameter for gas production, ammonium and alkalinity when it varies between 0.1 and 0.3. Itis possible that the real variability is even higher which makes it clear that k H is essential tomeasure or approximate with sufficient accuracy. This is also practical; k H is easier tomeasure than many of the other constants. The uncertainty of the biogas production cannamely be reduced by measuring three easy variables: k H , TS and the gas pressure. Moreover,

measuring the TS and pressure is inexpensive and already implemented at many plants.Reducing the uncertainty for the alkalinity is more complicated; the most significant variableHCO3 in the feed is immeasurable. Numerical calibration of the feed alkalinity is thereforerequired to find a suitable inflow concentration (section 11).

10.2. Västra Hamnen household waste experimentThis reactor was run with the same operational settings as for the Aalborg household wasteexperiment, but with mesophilic temperature instead of thermophilic. The SA could hencereveal if the importance of certain parameters change with the temperature.


The results from the SA on measured parameters are presented in Table 18. It was shown thatthe sensitive parameters for the biogas production rate were similar to the Aalborg household

0.2 0.4 0.6 0.8 10

1000

2000

3000

4000

5000

max6


[ g C O D / m 3 ]

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waste simulation, while the results for the VFA were more interesting. In this case, thecarbonate alkalinity was the most important parameter, followed by the TS and solubilisationof TS. The temperature, which was the most important parameter for the Aalborg householdwaste reactor was rather unimportant for the mesophilic reactor. This is probably due to theexponential expressions for temperature dependence (compare eq. 4.15), which cause the

parameters to change more in the thermophilic interval than in the mesophilic. It is clear thatthese nonlinearities in the model were exposed by the SA. The sensitivities for ammoniumand carbonate alkalinity are virtually the same as for the thermophilic reactor.

Table 18 Results of SA, UA and variability of measured parameters for the Västra Hamnen household waste

simulation

Parameterat 35 °C

Mean Unit Uncertainty

rank σ (%)

Sensitivity(Gas)

rank relative

Sensitivity(VFA)

rank relative

Sensitivity(NH4-N)

rank relative

Sensitivity(HCO3)

rank relativeTSSoluble TSProteinFat

SugarStarchFibers pHHCO3 NH4-NAcetatePropionateTemperatureFlowPressure

0.050.230.170.12

0.040.070.147.211013.548.734.335.41.331.03

kg/kg

g/TS

g/TS

g/TS g/TS g/TS

mol/m3 gN/m3

gCOD/m3

gCOD/m3 °C

l/d

bar

122149

310813111441366

2.5S

20U

0.97J

3.5J

18J

3.4J

4.7J

2U 100 U 3L

10 U 10 U 2 U 2 U 2 U

15107

4961215131411832

0.690.931.000.95

0.900.990.951.001.001.001.001.000.990.870.79

32610

7119141121513485

0.880.880.971.00

0.981.000.991.000.291.001.001.000.930.990.96

1236

79813151012144511

0.460.760.860.98

0.981.000.991.001.001.001.001.000.970.971.00

32413

7148111121096515

0.970.950.991.00

1.001.001.001.000.0741.001.001.001.001.001.00



The most influential parameters from the SA with model parameters for the Västra Hamnenhousehold waste simulation are presented in Table 19. The sensitivity for the gas productionwas different for mesophilic conditions; k H is still the most influential parameter, but therewere also other parameters that affected the output variance. The maximum growth rate of theacetoclastic methanogens (ranked 2) and the inhibition of the same process (rank 3) wereranked higher for this reactor. This was probably due to the fact that this process was slowerunder mesophilic conditions, and washout of biomass occurred for more parameter settings.The maximum growth rate of the acetoclastic methanogens was therefore ranked high for theVFA and carbonate concentrations, which was not the case in the thermophilic reactor. Theacetoclastic methanogenesis is important for the reactor stability; these results thereforeindicate that the stability for the mesophilic Västra Hamnen household waste digester should

be lower than for the thermophilic Aalborg household waste digester. However, this findingcould not be reasonable since the opposite is known by experience. The drawback of thismethod for a poor precision of the parameter distributions is exposed again, and it is clear thatthe results need to be evaluated before conclusions are drawn.

Table 19 Results from SA of model parameters for the Västra Hamnen household waste simulation

Parameterat 35 °C





µmax7 KI H,58 KI NH3,7

k LaCO2 k H

0.375e-417

2000.2

d -1

mol/m3 gN/m

3

d -1

d -1

243

171

0.780.860.78

1.000.21

132

206

0.090.520.14

1.000.88

253

241

0.980.990.98

1.000.024

152

213

0.410.810.47

1.000.65

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10.3. Sjölunda sludge experiment


For the Sjölunda sludge, the uncertainty of the feed characterization method was unknown,and instead guessed standard deviations of 20 % were used (Table 20). The results from thisSA were in other words less reliable than for the household wastes.

Table 20 Results of SA, UA and variability of measured parameters for the Sjölunda sludge simulation

Parameterat 35 °C


rank σ (%)

Variability

rank σ (%)

Sensitivity(Gas)

rank relative

Sensitivity(VFA)

rank relative

Sensitivity(NH4-N)

rank relative

Sensitivity(HCO3)

rank relativeTSVSSoluble TSProteinFatInert

pHHCO3 NH4-NTemperatureFlowPressureDegradability

0.0390.750.30.340.450.05

7.131245341.51.020.6

kg/kg g/TS

gCOD/gX S gCOD/gX S gCOD/gX S

mol/m3 gN/m3

°C

l/dbar

gCOD/gCOD

8132222

9179992

2.5S

0.53J 20U 20 U 20 U 20 U

2 U 100 U 3L 2 U 2 U 2 U

20 U

1210----

---0.600.9-

41082133

115129671

0.991.001.000.971.010.98

1.000.991.001.000.990.990.13

5812146

1039131172

0.991.001.000.460.970.99

1.000.901.001.001.001.000.48

35611312

114810792

0.991.001.000.431.001.00

1.001.001.001.001.001.000.60

7125246

9110118133

1.001.000.990.780.981.00

1.000.691.001.001.001.000.81


The most influential input parameters for the sludge simulation were the degradability and protein content (Table 20), which indicated that ammonia inhibition became important forhigh protein levels, and that the degradability of the substrate is fundamental to measure. Thecomposition of the waste did not affect the gas flow as much as the degradability, which

indicated that the characterization was less important to measure. The VFA are affected by thedegradability, which could not be seen for the household wastes, probably because of the broadened intervals for the inputs.


The results of interest from the model parameter SA are presented in Table 21. The gas production was mostly dependent on the rate of the acetoclastic methanogenesis whichimplied that it was the rate-limiting process. One could suspect that the lower bound for thegrowth rate was too low and that this led to washout of bacteria. The degradability was so lowthat the biogas production could not be increased much by a faster hydrolysis in this range.For shorter HRT or higher degradability, the hydrolysis rate would be rate limiting and k H

would have contributed more to the uncertainty of the result. The instability of the reactor ledto a high sensitivity for all outputs to KI NH3,7 and µmax7 , parameters determining the ammoniainhibition and growth rate of acetoclastic methanogens. The scatter plot in Figure 28 showsthat the frequency of reactor failure was higher for low values on µmax,7 .

Table 21 Results of SA of model parameters for the Sjölunda sludge simulation

Parameterat 35 °C





µmax7 KI NH3,7 k H

0.37170.2

d -1

gN/m3 d -1

126

0.190.530.94

1226

0.250.541.03

132

0.380.600.60

1227

0.240.511.03

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Figure 28 Gas production rate vs. µmax from MC simulation with varying model parameters

10.4. Aalborg household waste experiment w ith general characterizationIn this case the same reactor settings were used as for the previous simulation on Aalborghousehold waste, but with the general feed characterization from section 8.3. The distributionsfor the characterization variables hence reflect the variability of the parameters whencollected from different sites. The previous SA investigated the relative decrease in outputuncertainty that would be achieved if the characterization variables were determined withoutmeasurement errors. In this case, the SA is conducted to analyze the output uncertainties if nocharacterization measurements were made at all. The SA methodology is the same as in

previous sections, but with other means and standard deviations for the characterization. Itshould be noted that the variability of the fractions are caused both by real variability in thewaste, but also by measurement errors.


The results from the SA with varying input parameters are presented in Table 22. Whenthrowing a glance at the results, it may first seem like the starch was a more importantfraction of the substrate than the other constituents. But it can also be seen that the starchcontent in the waste had a high variability, and consequently the high values for starch wouldincrease the degradability of the waste. This was a consequence of the determination ofdegradable fraction from the sum of protein, carbohydrates, fibers and fat. The increaseduncertainty for the biogas production seen in 8.3. for the unmeasured substrate can in fact beexplained by the varying degradability of the waste. When plotting the gas production as afunction of degradablility, this relationship is clearly shown (Figure 29). The protein content

of the feed was not very variable and does not affect the biogas production as much, but hadan impact on the concentrations of VFA, ammonium and alkalinity, three parameters that areof major importance for the reactor stability.

0.2 0.3 0.4 0.50

0.005

0.01

0.015

0.02

max7

[d -1]

G a s p r o d u c t i o n

r a t e [ m

3 / d ]

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Table 22 Results of SA, UA and variability of measured parameters for the general thermophilic household waste

simulation

Parameterat 35 °C


rank σ (%)

Variability

rank σ (%)

Sensitivity(Gas)

rank relative

Sensitivity(VFA)

rank relative

Sensitivity(NH4-N)

rank relative

Sensitivity(HCO3)

rank relativeTS

Soluble TSProteinFatSugarStarchFibers pHHCO3 NH4-NAcetatePropionateTemperatureFlowPressure

0.05

0.140.150.140.060.150.197.41016048.734.355.31.331.02

kg/kg

g/TS g/TS

g/TS

g/TS

g/TS

mol/m3

gN/m3

gCOD/m3 gCOD/m3

°C

l/d

bar

5

------61422666

2.5S

------2U 100 U 3L

10 U 10 U 2 U 2 U 2 U

-

176324--------

-

59.7B

9.2H

12.0H

33.3H

50H

20.0H

------

--

5

10743121411131512986

0.96

1.000.980.920.850.550.831.001.001.001.001.000.990.980.97

8

51106471431115132129

0.98

0.950.601.000.960.880.961.000.771.001.001.000.661.000.99

2

71543612108111315914

0.96

0.990.130.990.980.960.991.001.001.001.001.001.001.001.00

4

32865711113121015914

0.98

0.940.701.000.990.990.991.000.391.001.001.001.001.001.00


Figure 29 The gas production vs. the degradability of the substrate from the simulation of the Aalborg household

waste with general characterization


k H is still the highest ranked model parameter, and in general it seems that the broadeneddistributions of the feed fractions has no significant impact on the sensitivity for the

parameters (Table 23). It could be expected that the broader span for the protein couldincrease the importance of the ammonia inhibition constants for the VFA, but this was not thecase. Instead, the decay rate for the propionate degraders turned out to be more important. Theamount of propionate depends on the amount of sugars and proteins; fat does not lead to

propionate production in the model. When the span of sugars and proteins are broadened, the propionate production is increased, and the slow process of propionate degradation becomeseven more important for the total VFA concentration than it already was for the measuredcharacterization. Another interesting difference is the increased sensitivity for KI H2,6 (the halfsaturation concentration for H2 inhibition of propionate degradation) which means that thethermodynamics of the process is affected by the variable substrate. The hydrogenotrophicmethanogenesis (process 8) is affected if the fat content is too high and the hydrogen level isincreased, or if the growth rate of the bacteria is too low. This can also be seen in the SA, as

the sensitivity for µmax8 and KI H,58 are increased as well.

0 0.1 0.2 0.3 0.4 0.5 0.60

0.01

0.02

0.03

0.04

0.05

0.06

Non-degradable frac tion of TS

G a s p r o d u c t i o n [ m 3 / d ]

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Table 23 Results of SA of model parameters for the general thermophilic household waste simulation

Parameterat 35 °C





µmax3 µmax5

µmax6 µmax7 KI H2,6 k H

40.6

0.60.3710.34

d -1

d -1

d -1

d -1

mgCOD/m3 d -1

192

4891

1.000.98

0.980.980.980.04

2616

16514

1.011.00

0.340.680.650.98

217

912141

0.981.00

0.991.001.000.08

1614

3281

0.990.98

0.780.720.880.58

10.5. Västra Hamnen household waste experiment with generalcharacterization


This SA was conducted using the same characterization as in the previous example, but withoperational settings as in the Västra Hamnen household waste simulation (mesophilic). Theresults (Table 24) show that the ranking of the parameters remains mainly unchangedcompared to the Aalborg household waste reactor. The same pattern can be observed for thegas production, but the sensitivity for the VFA is slightly altered and the importance for the

protein is higher than in the thermophilic reactor.

Table 24 Results of SA, UA and variability of measured parameters for the general mesophilic household waste

simulation


rank σ (%)

Variability

rank σ (%)

Sensitivity(Gas)

rank relative

Sensitivity(VFA)

rank relative

Sensitivity(NH4-N)

rank relative

Sensitivity(HCO3)

rank relativeTSSoluble TS

ProteinFatSugarStarchFibers pHHCO3 NH4-NAcetatePropionateTemperatureFlowPressure

0.050.14

0.150.140.060.150.117.21013.548.734.335.41.331.03

kg/kg

g/TS g/TS g/TS

g/TS

g/TS

mol/m3

gN/m3

gCOD/m3 gCOD/m3

°C

l/d

bar

5-

-----61422666

2.5S

-

-----2U 100 U 3L

10 U 10 U 2 U 2 U 2 U

-1

65324-----8-7

-59.7B

9.2H

12.0H

33.3H

50H

20.0H

-----1.4A -1.6A

59

7431214111315121086

0.960.99

0.980.920.840.540.831.001.001.001.001.001.000.980.97

84

1116371521214135910

0.960.90

0.381.000.940.810.941.000.701.001.001.000.910.981.00

35

1742612151011139814

0.960.98

0.170.980.980.940.981.001.001.001.001.001.001.001.00

53

2864712113141110915

0.990.93

0.721.000.990.980.991.000.391.001.001.001.001.001.00


10.5.1. Model parametersAs for most other cases, k H stands out as the first parameter to be calibrated (Table 25). Thiscan be seen by the much lowered variances in the gas production, ammonium and alkalinity.If k H is varying, the VFA will have more extreme values than if it is kept constant (relativesensitivity >1), the same applies for the K Sac. The reason for these odd values could be theextreme values for VFA that are produced by some combinations. It is also possible that theVFA have not converged to the steady state values during the simulation time.

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Table 25 Results of SA of model parameters for the general mesophilic household waste simulation

Parameter Mean Unit Sensitivity(Gas)rank relative




µmax7 k d13

KI H,58 KI NH3,7 k H

0.370.05

5e-4170.34

d -1

d -1

mol/m3

gN/m3 d-1

43

251

0.870.87

0.860.870.19

14

2326

0.440.52

0.450.521.12

32

541

0.980.97

0.980.980.06

25

341

0.720.77

0.760.760.52

10.5. Discussion on SAAs discussed earlier, using spans of ± 50 % when varying model parameters producesmisleading results. The ranges of variability for the model parameters were not available, anda realistic uncertainty or sensitivity analysis was not feasible to conduct within this project.Although the quality of the SA results may be disputable, it could still give interestinginformation on the system. For example: even if the relation between the importance of inputand model parameters may be incorrect, the difference in this relationship can still be

compared for different modes of operation, for example mesophilic and thermophilicconditions. In the results from the uncertainty analysis it was revealed that the outputs wereaffected differently by the changes in input data. The SA could provide some clues on whatone should measure to reduce uncertainty but also give a deeper understanding of the processand of the mathematics of the model. Nonetheless, it was clear that the method was useful tofind interesting parameters but it needed to be supplemented with scatter plots to avoid falseconclusions from the results.

10.6. Summary of the SAThe most important findings from the SA were:

•

The hydrolysis rate constant k H and the degradability are important input parametersfor the biogas production for the household waste digesters.

• In the Sjölunda sludge digester, the degradability of the substrate was so low that thehydrolysis constant was unimportant for the studied HRT.

• The VFA concentration is much more affected by the model parameters linked to propionate degradation and acetoclastic methanogenesis than by the input parameters.

• The sensitivities for the parameters differ between a mesophilic and thermophilicdigester; the model parameters are more important for the gas production in amesophilic digester.

•

If the protein content in a household waste is not measured, this contributes to theuncertainty for the ammonium, VFA and alkalinity.

• The SA method can give some information on which parameters are suitable forcalibration, but it is important to consider reasonable distributions of the model

parameters and to study scatter plots before performing a calibration based in the SAresults.

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11. Calibration of the model parametersIn this part of the thesis, some parameters are calibrated to improve the fit of model

predictions to data. The calibration is made for the pilot scale simulations for whichsensitivity analysis was conducted in the previous section. The results from the SA will beused for choosing suitable parameters for calibration of different output variables. As far as

possible, changes in the parameterization are motivated with a physical explanation.

11.1. Method for calibrationMost of the calibrations were conducted by minimizing the sum of absolute errors for model

predictions, θ i, compared to measured data (eq. 11.1). The sums of absolute errors weresimply plotted as functions of the calibration variable, and the calibration value for which theerror function was minimized was chosen. Compared to using optimizers in Matlab such as

fmincon and fminsearch this method has lower precision, but it is faster, and gives a graphical presentation of the error which makes it easier to avoid local minimums as solutions. Themagnitude of the error and non linear behaviors are also revealed with this method. The start-up phases of the pilot scale reactors on household waste were not stable, and were therefore

excluded when performing the calibration.

∑ , , (11.1)

The first step in the calibration procedure for the Västra Hamnen household waste andSjölunda sludge simulations was to calibrate the alkalinity of the feed. This was done first ofall, because the sensitivity analysis showed that the reactor alkalinity was sensitive to this

parameter, and because it is immeasurable in these types of wastes. Many processes in thedigestion involve uptake and production of alkalinity, and it would not be desirable that thelack of calibration for inflow alkalinity affected the calibration of other parameters. For the

Aalborg household waste, this method could not be applied since the dependency between thealkalinity and the VFA needed to be considered. The VFA were sensitive to the inflowalkalinity while the alkalinity in the digester was sensitive to the parameters in propionatedegradation and acetoclastic methanogenesis which are important for the VFA concentration.It was thus impossible to calibrate the parameters apart from each other; a numerical methodfor minimizing the errors for several parameters at a time was required here. An optimizationwith fminsearch was therefore conducted. The same relation existed for the Västra Hamnenhousehold waste simulation but in that case it did not cause a problem in the calibration

because the alkalinity in the reactor was much too high compared to the measured values. Ifthe calibrations were conducted simultaneously, the alkalinity in the inflow would still need to

be reduced substantially.

The other model parameters to be calibrated differed from case to case, but for all cases the biogas production was an interesting output parameter to include in the calibration process,e.g. for calibration of k H . In the sensitivity analysis, it was concluded that the VFAconcentration mostly depended on the parameters connected to the propionate degradationand the acetoclastic methanogenesis. These parameters were calibrated to minimize the sumof errors for VFA predictions.

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11.2. Aalborg household waste experiment

11.2.1. Hydro lysis constant kH

The SA showed that k H was more important for determining the gas production, alkalinity andammonium concentration than any of the other model parameters. It was not calibrated from

batch experiment, but assumed to be the same as for the Västra Hamnen household waste andwas therefore an interesting candidate for calibration. Due to the high relative error forammonium, it would have had a major impact on the optimization if it was included in theobjective function for the calibration. A trial to calibrate k H from the ammoniummeasurements only revealed that the k H would have to be so low that the hydrolysis almoststopped to lower the error for ammonium. It was therefore concluded that the relative error forammonium cannot be reduced by calibration of k H . The gas production, on the other hand, themost economically important output, could probably be used successfully to calibrate k H . Itwas therefore chosen as output for the calibration. The result (Table 26) showed that theformer value which was determined by experiments should be reduced slightly to improve themodel fit to the data.

11.2.2. Protein content

The deviation from the measured values for the simulation of ammonium is problematic sinceammonia is important for inhibition of propionate degradation and acetotrophicmethanogenesis. k H could not be used in the calibration, since it was calibrated from the gas

production rate, although it was the most important parameter for the ammoniumconcentration. This means that either the protein measurement was unsuccessful, or thehydrolysis model could not describe the degradation of protein properly. For the ammoniumto correlate with the measured values, the protein content in the feed would have to be 9 % ona weight basis instead of the measured value 17 % (Table 26). It is unlikely that themeasurement of protein would deviate so much from the real value. A more plausible

explanation is that the protein was hydrolyzed slower than the other fractions in the substrate, but to include this in the model, an alteration of the hydrolysis model would be required.Throughout this work, however, a fixed model structure was used, and in the furthercalibration the calibrated value for protein content was used instead. This was used because itis important to have reasonable values of ammonium to calibrate the processes that areaffected by ammonia inhibition. To compensate for the error in inflow COD as the proteincontent is reduced, the weight was added to the sugar content in order to retain the biogas

production.

11.2.3. Parameters for propionate degradation, acetotrophic methanogenesis

and inflow alkalinity

Both the VFA and the alkalinity were sensitive to µmax7 , µmax6 (growth rates of propionatedegraders and acetotrophic methanogens) and K INH3,6 , (inhibition constant for propionatedegradation). The SA thus indicated that these parameters could be used for calibration ofthese outputs. However, as discussed in 10.1.2 the high sensitivity to these parameters wasmainly due to a frequent washout of bacteria when these parameters reached extreme levels.When trying to calibrate the VFA using growth rates, the result showed that the fit to themeasured values only could be improved slightly, and that instability occurred when changingthe values further. A better result was achieved when calibration with half saturation constantsinstead, which were calibrated by Siegrist et al. by measuring propionate and acetate fordifferent HRTs in a mixed sludge digester. The fit to data could be improved more in this

case, but the changes in parameter values were high for optimal fit. In Figure 30, acomparison between a calibration of VFA with µmax7 and K S,ac is shown. When increasing the

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half saturation constant, the Monod kinetics produces the same reaction rate at a highersubstrate concentration. Thus, the gas production should not be affected from the calibration,which made the calibration process less complicated.

Figure 30 Example of calibration of VFA using µmax7 (left) and KS,ac (right)

VFA needed most calibration for the household waste experiments. It is possible that theaccessibility of the substrate for the propionate degraders and acetotrophic methanogens waslower for the household waste digester, which could give a physical explanation forcalibrating K S,pro and K S,ac.

For the Aalborg household waste simulation both parameters were first calibratedindependently with the graphical method, and it was seen that they should be increased manytimes to lower the error for the VFA, to 220 and 240 g COD/m3 respectively. The shape of thecurve for the total VFA was more similar to the measured values for the calibration of K S,ac than for K S,pro, which means that K S,ac probably is altered more than K S,pro for the substrate. Itwas thus decided that K S,pro should be set to 100 g COD/m3 and that calibration of K S,ac shouldaccount for the rest of the output error. As was discussed in 11.1., the inflow alkalinity andVFA are correlated and must be calibrated simultaneously. With the start guesses 180 g COD/m3 for K S,ac and 30 mol/m3for S HCO3, the optimizer fminsearch converged well, but the results(Table 26) differed much from the values suggested by Siegrist et al. (2002). The halfsaturation concentration for acetate would have to be increased more than six fold tominimize the error. On the other hand, it has been seen in calibration of ADM1 that the halfsaturation constants for propionate and acetate uptake were 297 and 582 g/m3 respectively

(Jeong, et al., 2005). The suggested values in ADM, 100 and 150 (Jeong, et al., 2005) werealso much higher than the values in the Siegrist model. The substrate uptake rate in ADM1,which is equivalent to the maximum growth rate parameter in the Siegrist model has beenshown to be important and was calibrated to much lower values by Tartakovsky et al. ( 2008).This indicates that the uptake rate of VFA is variable, Tartakovsky, et al., (2008) suggestedthat the content of intert material in the substrate could affect the the mass transfer. Theresulting VFA levels after calibration (Figure 32) shows that the steady state concentrationcould be modeled, but that the fit to data in the start-up phase was poor.

0 0.1 0.2 0.3 0.4 0.5 0.6

0

1000

2000

3000

4000

5000

6000

7000

max7

S u m o f a b s o l u t e e r r o r s

0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000

S u m o f a b s o l u t e e r r o r s

KSac

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Table 26 Values for former and calibrated parameters for the Aalborg household waste simulation

Parameter Unit Former

value

Calibrated

value

Output θ

k H d -1 0.20 0.15 Dry gas production

Protein content g/g TS 0.17 0.09 Ammonium in reactor

K S,pro for 35 °C g COD/m3 20 100* VFA in reactor

K S,ac for 35 °C g COD/m3 40 260 VFA in reactor+ Reactor alkalinity

Inflow S HCO3 mol/m3 5 42 VFA in reactor+ Reactor alkalinity

*Assumed value

An important issue when calibrating the model was the problem with parameter identifiabilitywhich was discussed in section 6. There are many combinations of for example µmax6 , k d,12,

K S,pro and K INH3,6 that give the same reaction rate for the propionate degradation which meansthat a correct calibration is impossible. This problem could easily be dealt with by using one

parameter at a time for the calibration, and that strategy was employed in this work. The

alternatives would have been to make guesses for parameter combinations or simply to avoidcalibrating these parameters.

11.2.4. Simulation results with calibrated parameters

The gas production and methane content were not changed notably after the calibration(compare Figure 31 with Figure 4), and the start up phase was still not correlating well.Considering that the calibration was performed for the steady state phase, this was notsurprising. The lower biogas production rate in the start-up phase was probably due to that themicroorganisms were not adapted to the substrate, and lacked specific enzymes for thehydrolysis. When modeling a slower hydrolysis in the beginning, the measured gas

production correlated better to measurements. An example of how this could be modeled

iteratively is shown in Figure 34. The VFA were over predicted during the start-up withcalibrated parameters, and the correlation for alkalinity was poorer (Figure 32). Thecalibration improved the correlation for ammonium and pH (Figure 33).


with Aalborg household waste after model calibration

0 20 40 60 800

0.01

0.02

0.03

0.04

0.05

0.06

Time [days]




0 20 40 60 800

20

40

60

80

100

Time [days]

P e r

c e n t [ % ]

CH4 mo delled

CH4 measur ed

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Aalborg household waste after model calibration


household waste after model calibration

Figure 34 Measured and simulated biogas production (left) with k H increased stepwise as in the figure to the right

0 20 40 60 800

500

1000

1500

2000

2500

3000

3500

Time [days]


VFAs m odelled

VFAs measured

0 20 40 60 800

10

20

30

40

50

60

70

80

Time [days]

C o n c e n t r a i o n

[ m o l / m 3 ]

HCO3 m ode lled

HCO3 m easur ed

0 20 40 60 800

500

1000

1500

2000

2500

3000

3500

Time [days]


NH4 mod elle d

NH4 m easur ed

0 20 40 60 800

1

2

3

4

5

6

7

8

Time [days]

p H

pH mo delled

pH me asured

0 20 40 60 800

0.01

0.02

0.03

0.04

0.05

0.06

Time [days]

P r o d u c t i o n

r a t e [ m 3 / d a y ]



0 20 40 60 800

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Time [days]

k H

[ d - 1 ]

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11.3. Västra Hamnen household waste experiment

11.3.1. Inflow alkalinity

As seen in section 7.4.3., the simulated alkalinity during the steady state operation was toohigh. The calibration of inflow alkalinity showed that it should be as low as possible, but even

if it was set to zero, large errors remained. The calibration was hence not successful, and other possible calibration parameters were examined. The calibration of the reactor alkalinity washowever considered good enough since the deviations were small enough to have only minorimpact on the result. It was clear that the variations in alkalinity could not be modeled verywell; the UA showed that the uncertainty of alkalinity is high which means that detailedcalibration is impossible.

11.3.2. Hydro lysis constant kH

It was revealed in the SA that k H had a significant impact on both the gas production and onthe ammonium concentration in the reactor. Only the error in gas production was used for thecalibration, however, since this parameter was prioritized because of the stronger correlation

to the other processes in the system. If both the gas production and ammonium levels in thereactor were to be calibrated, the model would have to be expanded to include an individualhydrolysis constant for particulate protein, as discussed for the calibration of the Aalborghousehold waste simulation. It turned out that the value used previously in the simulationsgave the best fit to data (Table 27), which showed that the batch experiment produced areasonable value. The value for the hydrolysis rate constant when calibrating the ammoniumlevels was low (k H = 0.02), which indicated that the degradation of the protein fraction of the

particles was ten times slower than the other constituents.

11.3.3. Protein content of feed

The ammonium concentration in the reactor was also dependent on the protein content of the

feed, and could be calibrated with this value. The value for protein content that gave theoptimal fit to data was 10 % instead of 17 % of TS (Table 27). The measurements are notexpected to be this poor for protein, thus indicating that it rather is the hydrolysis of proteinthat is slower. The result, however, had the same effect on the amount of degraded protein inthe reactor, and hence the ammonia inhibition will be better modeled with this new value. Theseven percent of particles that was withdrawn from the total degradable TS was added to thesugar fraction to compensate for the loss of degradable matter.

11.3.4. Half saturation constant for acetotrophic methanogenesis, KS,ac

For calibration the VFA in the reactor, the sensitivity analysis indicated that the growth rate ofaceticlastic methanogens and the inhibition of this process were suitable as calibration

parameters. The high sensitivity could however be explained by the high rate of washout of bacteria, as discussed in the previous section. Using the half saturation constant K s,ac turnedout to be more successful, and is easier to motivate from a biological point of view, see11.2.3. The required value for best fit to data K S,ac=190 (Table 27), was lower than the valuecalibrated for the Aalborg household waste. It could probably have been useful to calibratemore parameters than only one in this case, but this was not prioritized.

11.3.5. Simulation results with calibrated values

The resulting simulation results are shown in Figure 35 - Figure 37. Compared to the firstcrude validation in 8.4., the gas production was more stable but otherwise not much changed.The correlation for ammonium was much better after the calibration of the protein content,

but it can also be noted that the initial value probably was higher than the average in theSjölunda sludge digester. The modeled VFA were variable, but the range of variation was

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now closer to the measured values. It seemed that the drop in methane content in the gascould and pH not be reflected in the results after calibration.

Table 27 Values for former and calibrated parameters for the Västra Hamnen household waste simulation

Parameter Unit Former value Calibrated value Output θ

Inflow S HCO3 mol/m3 10 0 Reactor alkalinity

k H d -1 0.20 0.20 Dry gas production

Protein content of feed g/g TS 0.17 0.10 Ammonium in reactor

K s,ac d -1 40 190 VFA in reactor


with Västra Hamnen household waste after model calibration


Västra Hamnen household waste after model calibration

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

Time [days]


Sim ulated dry biogas pr oduction


0 10 20 30 40 500

20

40

60

80

100

Time [days]

P e r c e n t [ % ]

Simulated CH4

Measur ed CH4

0 10 20 30 40 500

50

100

150

200

250

300

350

400

Time [days]

V F A s a

s a c e t a t e e q u i v a l e n t s [ g C O D / m 3 ]

Sim ulated VFAs

Measured VFAs

0 10 20 30 40 500

20

40

60

80

100

120

Concentr ation o f HCO3

Time [days]


Simu lated HCO3Measured HCO3

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Figure 37 Measured and simulated ammonium concentration and pH from continuous experiment with Västra

Hamnen household waste after model calibration

11.4. Sjölunda sludge

11.4.1. Inflow alkalinity

The inflow alkalinity was calibrated with the graphical method, and it was shown that thecalibrated value was the same as the former used assumed value (Table 28).

11.4.2. Degradability

In the sensitivity analysis, it was concluded that the gas production was more sensitive to thedegradability of the substrate than to the model parameters connected to the acetoclasticmethanogenesis and propionate degradation. Furthermore, the model parameters had already

been calibrated while the ultimate degradability of the sludge was more or less assumed. It

was thus decided to use the gas production to calibrate the degradability of the substrate. Theresult, (Table 28) is reasonable for mixed sludge. As seen in section 8, the measurementuncertainty of VFA is low, but the sampling uncertainty is probably more significant. Thecorrelation for VFA concentration (Figure 39) was therefore considered to be good enoughafter the calibration of degradability; no further calibrations were needed for the parameters in

propionate degradation and acetate methanogenesis.

Table 28 Values for former and calibrated parameters for the Aalborg household waste simulation

Parameter Unit Former value Calibrated

value

Output θ

Inflow S HCO3 mol/m

3

10 10 Reactor alkalinityDegradability gCOD/gCOD 0.60 0.72 Dry gas production

0 10 20 30 40 500

200

400

600

800

1000

Time [days]


[ g N / m 3 ]

Simul ated NH4 mod elled

Measu red NH4

0 10 20 30 40 506

6.5

7

7.5

8pH

Time [days]

p H

Sim ulated pH

Measured pH

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11.4.3. Simulation results calibrated parameters

The resulting simulation results from the calibration of the Sjölunda sludge experiments are presented in Figure 38 - Figure 40. It can be seen that the calibration of degradabilitysignificantly improved the correlation for the gas production. Overall, the quality of the

predictions is higher for the sludge than for the household wastes, which further emphasize

the importance of parameter calibration for household wastes. For mixed sludge, however,these simulation results show that results with high accuracy can be achieved with only minorcalibration if the characterization method of Siegrist, et al., (2002) is used.


with Sjölunda sludge digestion after model calibration


Aalborg household waste after model calibration

0 20 40 60 800

0.01

0.02

0.03

0.04

0.05

Time [days]




0 20 40 60 800

20

40

60

80

100

Time [days]

P

e r c e n t [ % ]

Simulated CH4

Measu red CH4

0 20 40 60 80 1000

100

200

300

400

500

Time [days]

V F A s a s a c e t a t e e q u i v a l e n t s [ g C O

D / m 3 ]

Simulated VFAs

Measur ed VFAs

0 20 40 60 800

20

40

60

80

100

Time [days]


Simu lated HCO3

Measu red HCO3

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household waste after model calibration

11.5. Discussion on the calibrationFrom the SA in section 10 it was concluded that the most important output variable, the gas production rate, could be used to calibrate k H . In section 11, it was shown that the values of k H which were calibrated from batch experiments were good approximations. It was howeverimpossible to get a good fit to data in the start-up phase for the Aalborg household wastesimulation with a constant k H , indicating that the hydrolysis was slower before themicroorganisms had adapted to the new substrate.

When it came to the ammonium levels in the reactor, however, the only way to improve the fitto data with a fixed k H was to drastically change the protein content in the feed. It is unlikelythat the measurements would be of such low quality. Furthermore, the mean protein content in

the tested household wasted was 15 % (Table 22 in 10.4.), which is much higher than thevalues that were needed to achieve an acceptable correlation to the measurement. If the modelis to be used successfully for household waste digestion, it is essential to calibrate the proteincontent with the ammonium concentration in the reactor or to extend the hydrolysis model.Both methods produce reasonable results, but the second option has a theoretical backgroundand is therefore preferable. The hydrolysis description applied in ADM1 (Batstone, et al.,2002) includes different hydrolysis rate for all constituents, and could be used in furtherstudies. The hydrolysis rate for protein would in that case be approximately ten times slowerthat the average particular organic component.

For the Sjölunda sludge, the correlation of modeled ammonium to data was much better, but

this was not surprising since the protein was calculated from the ammonium in the digester. Itis possible that the real protein content in the mixed sludge was higher, which would meanthat the hydrolysis of protein is slower in this case as well. A measurement of the protein inthe Sjölunda sludge would confirm if this theory is likely. Another option is that thehydrolysis description in the model is less suitable for household waste than for mixed sludge.Household waste includes meat and other components with high protein content and may inother words be less available for hydrolysis than the protein in the mixed sludge. This candepend on the particle size which is affected by the pretreatment method, and on the proteincharacteristics. Protein in the primary sludge is readily available, and the protein in the WAS

becomes available after cell lysis, together with the other substrates.

As suspected in the first validation of the model (7.4.6. and 7.6.6.), the model parameters forthe household wastes needed to be recalibrated to improve the correlation for VFA. The lack

0 20 40 60 800

500

1000

1500

Time [days]


[ g N / m 3 ]


Measu red NH4

0 20 40 60 800

1

2

3

4

5

6

7

8

Time [days]

p H

Simulated p H

Measured pH

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of identifiability and the correlation between the parameters were however problematic forcalibration of model and inflow parameters. It was concluded that the SA did not give the bestcalibration values, but that the half saturation constants was better suited for calibration

purposes. As discussed in 11.2.3., half saturation constants of VFA seem to vary considerablyfor different substrates and it was not surprising that these parameters needed recalibration for

household wastes. The VFA are thus less likely to be successfully modeled withoutcalibration than other outputs, which was also indicated in the crude validation (7.3.3. and7.4.3.). Since the sampling uncertainty is suspected to be high for VFA, it is also possible thatthe model results are more credible than the measurements if the measurements are slightlylower than the simulated values. However, as long as simulated VFA levels do not exceedlevels that are inhibitory to the methanogenesis, the correlation for biogas will still beacceptable.

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12. Industrial scale applicationIn this section, the model will be used for evaluation of a full scale process at KäppalaWWTP; various process designs will be assessed and discussed. A simple economicalanalysis is made to compare the economical benefits for the process designs.

12.1. Example with Käppala digestersKäppala WWTP which receives 500 000 p.e. has two mesophilic digestion chambers, R100and R200 (Figure 2, section 7.2.1.). The primary sludge is digested separately in R100 toavoid filamentous bacteria clogging the upper part of the digester and causing reactoroverflow. The digested primary sludge is mixed with the WAS in R200, for typicalcharacteristics of the inflow and validation to data, see section 7.2.1. With the current setupthe biogas production from R200 is low and it could possibly be improved with thermophilictemperature, different process design or pretreatment of the WAS. Experimental trials tocompare different solutions would be both expensive and time consuming. Nonetheless,different alternatives for reactor setup and process variables can be tested on the full scale

process, which has been done on some occasions. The drawback of such full scale

experiments is that they are can be costly e.g. if the VS reduction is poor or if practical problems arise. Simulating different alternatives for process setups can be a useful tool fordiscovering possibilities and problems quickly and inexpensively. Several possibilities for the

process are explored in this section, including thermophilic digestion and pretreatment of theWAS. Some parameters are not included in the model, like the dewaterability of the sludge,which will raise the costs for handling of the remaining sludge, or the amount of filamentous

bacteria. The results can however be used to evaluate the potentials of the different setups.

12.1.1. Simulated cases

A) Original design described in 7.1.2., mesophi lic (35 °C)

The retention time for the primary sludge is very long for this design, 15+10 dayswhile the WAS has a shorter retention time of 10 days.

B) Original setup, thermophi lic (55 °C)

The degradability in thermophilic digestion has proved to increase with 7.6 %compared to mesophilic digestion (Song, et al., 2004). A representative retention timefor mesophilic digestion is 25 days, while it is about 15 days for thermophilicdigestion. Consequently, the temperature dependency of k H (see 4.4) resulted in anincrease for the WAS k H from 0.15 to 0.24 d-1, and 0.4 to 0.65 d-1 for the primarysludge k H . The digester volumes and thus retention times were kept constant.

C) The digesters in series, mesophi lic (35 °C)

For this case, the sludge is mixed and flows first into R100 and then R200 (Figure 41).The total retention time for the primary sludge is reduced in this case, from 25 to 20days total but it is increased for the WAS from 10 to 20 days total.

D) The digesters in series, thermophilic (55 °C)

The same reactor design as in case C is used, but with thermophilic temperature 55 °C.The degradability and k H are the same as for case B.

E) The digesters in series, enzyme addit ion mesophil ic (35 °C)

Sludge pretreatments have been proved to increase the gas production significantly asdiscussed in section 2.5. Many treatment methods require expensive investments in

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form of vessels, heat exchangers, pumps etc. Enzymatic treatment has the advantageof low investment costs; the enzymes are simply poured into the digester. Thesolubilisation and degradability of the primary sludge are not notably improved byenzyme addition; the substrate is already highly degradable and hydrolysable. TheWAS, on the other hand, is not readily degradable unless the EPS are degraded

(Recktenwald, 2008). Solubilisation of WAS with a dose of 60 mg/g TS increased to0.41 g SCOD/g TS (Wawrzynczyk, 2007); recalculated for the characterization of theWAS this means a solubilisation of 49 % on a COD basis. The degradability of WASwith enzyme pretreatment was calculated from the increased methane production from

batch tests, which increased with 60 % (Wawrzynczyk, 2007). It should be noted thatthe enzymatic dose of 60 mg/L in the laboratory scale tests is significantly higher thanthe dose of 0.25 mg/L which is used for full scale processes (Recktenwald, 2008). Thelaboratory scale data was used due to lack of known input variables for full scaledigesters with enzymatic pretreatment.

F) One reactor with the volume V R100+ V R200

In many WWTPs, there is only one digester in which both the primary sludge andWAS are digested (Figure 42). The total retention time is 20 days for both flows, thesame as for case D.

Figure 41 Reactors in series, cases C, D and E

R100+R200

Primary sludge

Waste activated sludge

To dewatering

Figure 42 The digester in case F

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12.1.2. Method

Data from 2007 for flows and VS content of the primary sludge and WAS were used. Allinitial values and parameters for case A can be found in section 7.6. The allocation forcalculating the characterization of the substrate and k H was made on a basis of mass VS of

primary sludge and WAS into the reactor.


With thermophilic temperature, (cases B and D) the methane content in the gas is 3 percentage points lower than for the mesophilic cases (A and C), but it can also be seen thatthe methane production is increased with 9 percentage points compared to mesophilicdigestion (Table 29). Enzyme addition is also an effective measure to improve the methane

production, an increase of 11 % was reached compared to the first case. The methane production in the single digester (case F) is the lowest; 5 % lower than for case A.

The increase of ammonium for the thermophilic digesters compared to the mesophilic issmall, only 100 and 200 g COD/m3 for case B-A and D-C (Table 30). The risk for ammonia

inhibition, however, increases more compared to the mesophilic cases and it was seen that theinhibition was more important in case D than case C.

The alkalinity was mainly unaffected by the temperature (compare case A-B and C-D) butvaried for different process designs (compare A-B and C-D). The enzymatic treatment in caseE increased solubilization which led to a fast acidogenesis and high concentration of VFA(Table 30). Although the concentration reached over 3000 g COD/m3, the gas production wasstill high, this indicated that VFA inhibition was not a substantial problem for the gas

production (Table 29). Furthermore, it is worth noting that the VFA concentrations for casesA and B are similar in R100 and R200, while the VFA level is higher in R100 when thedigesters are run in series (cases C and D). The thermophilic cases B and D showed higher

VFA concentration than the mesophilic cases A and C.

The total COD reduction could be increased 3 percentage points compared to case A byrunning the process in series, and 7 percentage points by introducing thermophilic digestion(Table 30). Enzymatic treatment and thermophilic digestion in series give the highest VSreduction, 0.64 and 0.65 respectively.

Table 29 Biogas production for R100 and R200 with different process designs for 2007

Case Totaldry gasR100

[106

m3

]

Totaldry gasR200

[106

m3

]

TotalmethaneR100

[106

m3

]

TotalmethaneR200

[106

m3

]

Meanmethanecontentin dry gas

Total dry gas production inR100 andR200

[106

m3

]

Totalmethane production

[106

m3

]

Relativechange intotalmethane

productionOriginal setup, A 5.1 1.1 3.2 0.79 0.64 6.3 4.0 0 %B, 55 °C 5.9 1.3 3.5 0.83 0.61 7.2 4.3 9%C, series mesophilic 5.6 1.6 3.2 0.97 0.58 7.2 4.2 5%D, series thermophilic 6.8 1.4 3.7 0.78 0.55 8.2 4.5 14 %E, Enzyme treatment, series 5.9 1.8 3.3 1.1 0.57 7.7 4.4 11 %F, one digester 6.6 - 3.8 - 0.58 6.6 3.8 -5%

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Table 30 Process variables for R100 and R200 with different process designs Case Mean

NH4-NR100

[g N/m3]

Mean NH4-NR200

[g N/m3]

MeanHCO3R100

[mol/m3]

MeanHCO3R200

[mol/m3]

Mean VFAR100

[g COD/m3]

Mean VFAR200

[g COD/m3]

TotalCODreductionafterR100

TotalCODreductionafterR200

Original setup, A 1100 1300 68 87 66 49 0.30 0.56B, 55 °C 1200 1400 71 88 200 220 0.38 0.63C, series mesophilic 1400 1600 80 110 780 170 0.45 0.59D, series thermophilic 1600 1800 92 110 870 330 0.54 0.65E, Enzyme treatment, series 1600 1800 8 200 3500 1800 0.50 0.64F, one digester 1500 - 94 - 580 - 0.53 -

It is common in WWTPs to run the digesters in parallel instead of series to facilitate thecontrol of the process, but it can be seen that this is not the best process design if increasedgas production, VS degradation and stabilization is the goal (Table 29 and Table 30).Apparently, the process rates are increased with serial digestion. This is due to higherconcentrations of the substrates in R100 than in a single digester where the feed is more

diluted. The substrates are more easily available for the biomass, and the substrate uptake rateis increased. Although the retention time for R100 in the case of serial operation (C) is half ofthe retention time with one big digester (F), it can be seen in Table 29 that the biogas

production in R100 for case C is much higher than half than for case F. It is understandablethat many WWTP prefer parallel digestion, but it could be preferable to implement serialdigestion with improved process control.

Enzyme addition was beneficial for increasing the VS degradation and methane production, but resulted in a high VFA concentration which could lead to inhibition of themethanogenesis and propionate degradation (case E). The VFA increased during the winterdue to the higher production of WAS, and the total effect from the enzyme addition became

more pronounced. Problems with high VFA levels could be avoided if the dose of enzymeswas adapted to the amount of WAS, or if the active volume was increased. However, the doseof enzymes used in the simulation was, as mentioned, too high to be economically defendable.If enzyme addition was introduced, the dose would be significantly lower and the VFAconcentrations would not reach the levels shown in (Table 30). The drawback of a lower dosecould be that the methane production would not be increased as much as the 11 % for case E.The effect from enzyme dosing is also dependent on the sludge characteristics, e.g. ratiomunicipal/industrial waste water, sludge genesis, season and sludge age. In order to evaluatethe process with enzyme dosing with less uncertainty, experimental results of the sludge fromKäppala would be needed. The literature values used for case E in this simulation produceresults that are less credible than for the other cases.

12.2. Economical evaluation

12.2.1. Method

A simple economical analysis of the results from section 12.1. was conducted for thequantification of the economical benefits for the process designs. The cost for investmentsand running costs for the processes would be dependent on the individual factors for theWWTPs and were not included here. A switch from mesophilic to thermophilic digestion mayfor example require new heat exchangers in some cases, and the cost depends on the reactorconfiguration. The fee for the handling of the dewatered sludge and the income from sellingthe methane gas are similar for all WWTP in Sweden and were therefore included in the

economical analysis.

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The fee for handling of the sludge is 300 SEK per m3, and considering the amounts of sludge produced each year this is a significant cost for the WWTPs. After dewatering, the TS contentis stable at around 25 % and the total amount sludge can therefore be calculated from the massof TS out from digester R200. In this case the VS reduction is assumed to be equal to theCOD reduction shown in (Table 30), and the outgoing VS is simply calculated from the total

influent mass of VS. Total amount of ashes out from digester R200 during the year iscalculated from the data of TS and VS in incoming flows (equation 12.1), and summarizedwith outgoing VS for each case. The total outgoing TS is transformed to a volume assumingthat the densities of the dewatered sludge and water are 1 ton/m3. The WWTP sells themethane gas for 5 SEK /m3 in these calculations.

∑ ∑ 1.61 · 10 1.25 · 10 3.58 · 10

(12.1)


For cases B-E, it is possible to earn and save money if the yearly costs for investments andcontinuous expenses compared to case A are lower than the total change shown in the outmostright column (Table 31). For case F, it is only possible if the expenses are lower than the totalchange compared to case A. It is less expensive to run a single digester with the doublevolume, but it is also associated with poorer mixing and heating due to the upscaling. Formost WWTPs, it would probably be economically favorable to choose serial digestion. If theWWTP is equipped with several digesters run in parallel, it is both simple and inexpensive toconvert the process. The economical benefit would be around 3 million SEK per year for aWWTP similar to Käppala (compare case C and case F).

At Käppala WWTP, the problems with filamentous bacteria means that case A is choseninstead of case C. With improved control of the activated sludge process, Käppala could haveapplied serial digestion and saved 1.5 million SEK 2007 from reduced fees and increased

income from biogas. The cost for changing from case A to C is practically zero.

The most economically favorable option is thermophilic digestion in series, which would havespared Käppala 4 million SEK 2007, enzymatic treatment is next with 3.4 million SEK. Acomparison between these measures would require a detailed analysis of the process atKäppala and of the costs for investments and maintenance. As mentioned before, the effect ofenzyme addition on the Käppala sludge would need to be studied closer, the degradability andsolubilization could be both lower and higher than the literature values. A lower enzyme dosewould mean less effect, but the sludge at Käppala could be more or less suitable for enzymatictreatment than the sludge studied in the literature. It is however likely that the investmentcosts for enzymatic treatment are lower than for conversion to thermophilic digestion; theequipment for enzyme dosing is about 50 000 - 100 000 SEK depending on the reactorconfiguration (Recktenwald, 2008). Improved heat exchangers, revetment of the reactor andnew pumps which could have been required for thermophilic digestion are expensive.Furthermore, thermophilic digestion has the drawback of being less stable than mesophilicdigestion, which means that the risk for expensive process failures is higher.

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Table 31 Change in cost for sludge handling and income from methane production for the cases Case Outgoing

mass of TS

[106 kg /yr]

Outgoingvolume ofsludge

[103 m3/yr]

Fee forsludgehandlingcompared tocase A

[106 SEK /yr]

Income frommethane productioncompared tocase A

[106 SEK /yr]

Total changecompared tocase A

[106 SEK /yr]

A Original setup, 9.09 36 0 0 0B, 55 °C 8.22 33 1.1 1.8 2.9C, series mesophilic 8.72 35 0.45 1.0 1.5D, series thermophilic 7.97 32 1.4 2.7 4.0E, Enzyme treatment, series 8.09 32 1.2 2.2 3.4F, one digester 9.47 38 -0.45 -1.1 -1.5

The increase in income from selling the methane gas is higher than the savings from thesludge handling fee for all cases. The price for the gas is however variable and less

predictable compared to the sludge handling fee which could make it hazardous to introduce

expensive equipment with high continuous costs. Political decisions and public awareness ofclimate change are important to make the methane gas competitive compared to otheralternatives and to enhance investments to increase biogas production.

The economical analysis showed that there are many options for process design that could beeconomically beneficial if the investment and maintenance costs do not exceed the profit fromdecreased sludge handling fees and increased income. The model can be a useful tool toevaluate different process designs and choose interesting options for further investigations. Itis of course still essential to perform pilot plant experiments, but the number of experimentscould be reduced if the least appealing alternatives are sorted out after simulations. The

process variables VFA and alkalinity give indications on the stability of the processes and a

comparison between those can be useful when assessing the stability of the process.Unwanted side-effects of a process configuration can thus be found by simulations and not byexpensive pilot plant experiments.

Important variables, like the formation of mercaptans which causes odor problem and thedewaterability of the remaining sludge, are not included in the model. These neglectedfactors, and the problem with filamentous bacteria described above, could be affected by thealterations of the process. This needs to be taken into account when evaluating the simulationresults.

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13. ConclusionsThe first part of this dissertation was aimed at giving the reader a background of the processof anaerobic digestion, and to summarize the prior research in the field of modeling anaerobicdigestion. It was stated that models have not been widely used in this field, and due to thecomplex microbiologic and physiochemical processes, they are difficult to parameterize and

impossible to identify mathematically.

For household waste experiments, it was possible to get accurate predictions of steady stategas production, but the correlation for ammonia was less satisfying. Simulations of the sludgeexperiment produced the opposite result. VFA concentrations were difficult to model in allthree cases. In the household waste experiments, the inoculums were not adapted to thesubstrates. The startup phase before adaptation proved to be difficult to simulate with thecurrent model structure. Validation of the model to the full scale process at Käppala proved to

be successful, considering the lack of data for the feed characterization.

It was shown in the uncertainty analysis that measurement errors could not be used to explain

the discrepancy between the simulations and data. The output uncertainties when using ageneral characterization of household waste were significantly higher than when conductingmeasurements for gas production and ammonia, while VFA and alkalinity were less affected

by input data.

The global, variance based method chosen for the sensitivity analysis was useful for theinflow variables, but as the distributions of model parameters were unknown, the analysisneeded to be supplemented with scatter plots to study the correlations between parameters andoutput. The results from the sensitivity analysis indicated that to determine the gas production,information of degradability and hydrolysis rate of the sludge were needed, in addition to theactual flows and sludge concentrations. The batch experiments used for determination of the

hydrolysis rate constant proved to give reasonable values. For better precision for VFA predictions, the parameters connected to propionate degradation and acetoclasticmethanogenesis were essential.

A revision of the model structure is needed for a successful calibration of ammonium. In themodel by Siegrist, particulate organic matter is lumped. To be able to calibrate theexperiments on household waste digestion, a slower degradation of particulate protein would

be required. To calibrate the VFA concentrations, the half saturation constants were changedsubstantially. This implies different mass transfer conditions than suggested in the modelimplementation by Siegrist et al.

The model proved to be a promising tool for testing different process designs for a full scale process. The productivity could be improved by running the reactors in series, at thermophilictemperature and by implementing enzymatic pretreatment.

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14. Suggestions for further researchIt was concluded that the degradability and hydrolysis rate are more important to measurethan the individual constituents of a substrate, when it comes to prediction of biogas

production rate. This could be due to the relative stability of the simulated systems, withoutsignificant problems with inhibited processes. It would be interesting to validate the model at

more critical states, to evaluate the ability of the model to simulate reactor instability.

The Siegrist model was primarily developed for modeling mixed sludge digestion. In thisdissertation the model was applied on household waste digestion, but not withoutcomplications. A changed hydrolysis model would be required for this task, as in the morecomplex model ADM1. Further research is however needed to determine the hydrolysiskinetics and other process parameters for different wastes, as there is scarce informationavailable in the literature.

It was seen in the validation and SA of the household wastes that the precision for VFAcorrelation was poor and that a calibration of parameters connected to propionate degradation

and acetoclastic methanogenesis was necessary to improve the model fit. It would be beneficial to increase the knowledge about the uptake rates for VFA; is it dependent of thefraction of inert material or particle size in the reactor or is it a related to the microbialspecies? If the relations between the parameters µmax, K S , and K I for propionate degradationand acetoclastic methanogenesis could be expressed as functions of the substratecharacteristics, this would allow application of the model to various substrates withoutrecalibration of these parameters. More research about the theoretical background for these

parameters could therefore be valuable.

It was shown in 11.2.4. that an upstart phase cannot be modeled well with the Siegrist model.Siegrist, et al., (2002) also stressed that a simulation of a transition between mesophilic and

thermophilic digestion could not be performed with accuracy. An inclusion of a state variabledescribing the physiological state of the biomass may solve this problem. More research onthis subject would be interesting, although it must be admitted that such a variable would bedifficult and expensive to verify with measurements.

More studies are required to specify the distributions of the model parameters. This wouldenable a more useful SA and it would be possible to get a better ground for allocation ofresources to determine model parameters, and to deepen the understanding of the processes.In some cases, it could be used for simplification of the model if several parameters are

proven to be irrelevant.

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71.

Batstone, D. J., Keller, J., Angelidaki, I., Kalyuzhnyi, S. V., Pavlostathis, S. G., Rozzi, A., et al.(2002). The IWA Anaerobic Digestion Model No 1 (ADM1). 45, 65-73.

Batstone, D., & Keller, J. (2003). Industrial applications of the IWA anaerobic digestion model No. 1(ADM1). Water science and technology , 47, 199-206 .

Batstone, J., Keller, J., & Steyer, J. P. (2006). A review of ADM1 extensions, applications, andanalysis: 2002-2005. Water Science and Technology , 54, 1-10.

Bernard, O., Polit, M., Hadj-Sadok, Z., Pengov, M., Dochain, D., & Estaben, M. (2001). Advancedmonitoring and control of anaerobic wastewater treatment plants: software sensors and controllers foran anaerobic digester. Water Science and Technology , 43(7), 175-182.

Blumensaat F, K. J. (2005). Modelling of two-stage anaerobic digestion using the IWA AnaerobicDigestion Model No. 1 (ADM1). Water Research , 39, 171–183.

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Davidsson, Å. (2007). Increase of biogas production at wastewater treatment plants. DoctoralDisseration, ISBN 978-91-7422-143-5, Lund University.

Elmitwalli, T., Sayed, S., Groendijk, L., van Lier, J., Zeeman, G., & Lettinga, G. (2003). Decentralisedtreatment of concentrated sewage at low temperature in a two-step anaerobic system: two upflow-hybrid septic tanks. Water Science and Technology , 48(6), 219-226 .

Eskicioglu C, K. J. (2006). Characerization of soluble organic matter of wast activated sludge beforeand after thermal pretreatment . 40 (3725-3736).

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Hansen, T. L., la Cour Jansen, J., Spliid, H., Davidsson, Å., & Christensen, T. H. (2007). Compositionof source-sorted municipal organic waste collected in Danish cities. Waste Management , 27; 510–

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og biogaspotentiale i organisk dagrenovation. Miljøstyrelsen (Danish Environmental Board).

Højlund Christensen, T., la Cour Jansen, J., Kjems Toudal, J., & Gruvberger, C. (2003). Basisdokumentation for biogaspotentialet i organisk dagrenovation. Miljøprojekt Nr. 815,Miljøstyrelsen (Danish Environmental Board).

Jeong, H.-S., Suh, C.-W., Lim, J.-L., Lee, S.-H., & Shin, H.-S. (2005). Analysis and application ofADM1 for anaerobic methane production. Bioprocess Biosyst Eng , 27; 81–89.

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Kops, S. G., & Vanrolleghem, P. A. (1996). An evaluation of Methodologies for uncertainty analysisin biological waste water treatment. Unknown publisher .

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la Cour Jansen, J., Spliid, H., Lund Hansen, T., & Svärd, Å. (2004). Assessment of sampling andchemical analysis of source-separated organic household waste. Waste Management , 24; 541-549.

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Miron, Y., Zeeman, G., van Lier, J. B., & Lettinga, G. (2000). The role of sludge retention time in thehydrolysis and acidification of lipids, carbohydrates and protein during digestion of primary sludge inCSTR systems. Water Reserch , 34:5 1705-1713.

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Vavilin, V. A., Fernandez, B., Palatsi, J., & Flotats, X. (2008). Hydrolysis kinetics in anaerobicdegradation of particulate organic material: An overwiev. Waste Management , 28; 939-951.

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91-628-7246-5, Lund University.

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Appendix I

Matrix of stoichiometric coefficients T (with default values for ѵ j,i):

State variable (see table 2)

SH SH2 SCH4 SCO2 SHCO3 S NH4 S NH3 Sac Shac S ro Shpro Saa Ssu Sfa Sin Xs X

P r o c e s s n u m b e r

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 171 0 0 0 0.0004 -0.0005 0 0 0 0 0 0 0.3 0.2 0.45 0.05 -1 0 2 0 0.96 0 0.043 -0.022 0.587 0 3.29 0 1.42 0 -6.67 0 0 0 0 1 3 0 0.96 0 0.91 -0.07 -0.08 0 3.29 0 1.42 0 0 -6.67 0 0 0 0 4 0 6.7 0 0.199 -0.202 -0.08 0 14.3 0 0 0 0 0 -22 0 0 0 5 0 8.2 0 0.162 0.004 -0.08 0 10.8 0 -20 0 0 0 0 0 0 0 6 0 0 0 -0.006 0.618 -0.08 0 -40 0 0 0 0 0 0 0 0 0 7 0 -22 39 -0.353 -0.006 -0.08 0 0 0 0 0 0 0 0 0 0 0 8 0 0 21 0 0.003 0.045 0 0 0 0 0 0 0 0 0 0.8 -19 0 0 0 0 0.003 0.045 0 0 0 0 0 0 0 0 0 0.8 0 10 0 0 0 0 0.003 0.045 0 0 0 0 0 0 0 0 0 0.8 0 11 0 0 0 0 0.003 0.045 0 0 0 0 0 0 0 0 0 0.8 0

12 0 0 0 0 0.003 0.045 0 0 0 0 0 0 0 0 0 0.8 0 13 0 0 0 0 0.003 0.045 0 0 0 0 0 0 0 0 0 0.8 0 14 -1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 -1 1 14 -14 0 0 0 0 0 0 0 0 0 0 16 0 0 0 -1 1 0 0 -64 64 0 0 0 0 0 0 0 0 17 0 0 0 -1 1 0 0 0 0 -112 112 0 0 0 0 0 0

Conservation matrix with respect to mass conservation of theoretical COD (1), conservation of N/COD ratCOD, N or mol (3) and mol of C/g of COD or mol:

State variable

SH SH2 SCH4 SCO2 SHCO3 S NH4 S NH3 Sac Shac S pro Shpro Saa Ssu Sfa Sin

c x z x c z

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 2 0 0 0 0 0 1 1 0 0 0 0 0.1 0 0 0.02 3 1 0 0 0 -1 -1/14 0 -1/64 0 -1/112 0 0 0 -0.0012 0 4 0 0 0.0156 1 1 0 0 0.0313 0 0.0268 0 0.029 0.031 0.0216 0.03

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III

Appendix II

Calculation of the Sjölunda sludge characterization

%cal cul at i ng t he amount of CO2 i n t he carbonate syst empH=7. 14;H=10 -̂ pH; %kmol / m3HCO3m=4000/ 61000; %kmol / m3, t he mean val ue i n t he di gest er at st abl eoper at i on T=35+273; %KkHCO3=10̂ ( 6. 53- 2906/ T- 0. 0238*T) ; %equi l i br i um const ant CO2 t o HCO3kH2CO3=10̂ ( 14. 82- 3401/ T- 0. 0327*T) ; %equi l i br i um const ant HCO3 t o H2CO3kH=10̂ ( - 12. 59+2198/ T+0. 0126*T) ; %henry' s const ant f or CO2pCH4=0. 65; %bar , measured i n r eact orpCO2=1- pCH4;

H2CO3=kH*pCO2HCO3=kH2CO3*kH*pCO2/ %The measur ed and cal cul at ed val ues f orHCO3 ar e al i keCO3=HCO3*kHCO3/ H

mol es_ i n_l i qui d=1. 5*( H2CO3+HCO3+CO3) %mol es of car bon i n t hecar bonate syst eml eavi ng t he r eact or 1. 5 i s t he out t ake vol umemol es_i n_gas=( 21. 8e- 3*pCO2) / ( 0. 082e- 3*( 273+18)) %mol es l eavi ng as gas,cal ucl ated f r ommean f l ow of gas and general gas l awCO2t ot=mol es_i n_gas+mol es_i n_l i qui d %mol es l eavi ng as gas andl i qui dCH4=( 21. 8e- 3*pCH4) / ( 0. 082e- 3*( 273+18)) %mol es l eavi ng as gas,cal ucl ated f r ommean f l ow of gas and general gas l aw

par t _i n_l i qui d=mol es_i n_l i qui d/ ( mol es_i n_l i qui d+mol es_i n_gas)

r eal CO2f r act i on=CO2t ot / ( CH4+CO2t ot ) % The f r act i on of CO2pr oduced by the bi omass f r omt he subst r ater eal CH4f r act i on=CH4/ ( CH4+CO2t ot ) % The f r act i on of CH4pr oduced by the bi omass f r omt he subst r ate

%Cal cul at i on of t her or et i cal pr ot ei n f r act i on f r om hansr eudi met hodi N=0. 1; %g N/ g COD t aken f r om t he st oi chi omet r i c mat r i xSNH4=834; %mean val ue i n r eact or f or st abl e operat i on

%COD- r educt i onds. VSr ed=ds. i ndat a. ch. VS*0. 45; %45 % r educt i onds. CODr ed=1e6*ds. VSred*1. 9; % amount of COD r educed, 1. 9 gCOD/ g VS and1e6 t o get g/ m3

XST=mean( ds. CODr ed) ; % mean val ue f or r educed CODvaa=SNH4/ ( i N*XST) % cal cul at i on of pr ot ei n cont ent i n f eed

%val ues f r omRoedi ger et al . 1967 f r omt he book by VAV are used f or t he%met hane f r act i on f r om di f f er ent subst r at es.pr oCH4_f r act i on=0. 68;f at CH4_f r act i on=0. 7;suCH4_f r act i on=0. 5;

%cal cul at i on of f at cont entvf a=( - vaa*proCH4_f r act i on+suCH4_f r act i on*vaa-suCH4_f r act i on+( pCH4/ 1) ) / ( f at CH4_f r act i on- suCH4_f r act i on)

vsu=1- vf a- vaa

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Appendix III

Results from the sensitivity analysis

Aalborg household waste

Table III, 1 Results of SA, UA and variability on measured parameters for the Aalborg household waste simulation


rank σ (%)

Variability

rank σ (%)

Sensitivity(Gas)

rank relative

Sensitivity(VFAs)

rank relative

Sensitivity(NH4-N)

rank relative

Sensitivity(HCO3)

rank relativeTSSoluble TSProteinFatSugarStarchFibers pHHCO3 NH4-NAcetatePropionateTemperatureFlowPressure

0.050.230.170.180.070.180.117.41016048.734.355.31.331.02

kg/kg

g/TSg/TSg/TSg/TSg/TS

mol/m3 gN/m3 gCOD/m3 gCOD/m3 °Cl/d bar

122149310813111441366

2.5S

20U

0.97J

3.5J

18J

3.4J

4.7J

2U 100 U 3L

10 U 10 U 2 U 2 U 2 U

5176324-----9-8

24.6B

59.7B

9.2H

12.0H

33.3H

50H

20.0H

-----1.4A -1.6A

181064791411131512532

0.740.981.000.950.880.970.991.001.001.001.001.000.900.870.78

437115810142915131126

0.950.950.991.000.981.001.001.000.591.001.001.000.491.000.98

132679111445131512810

0.420.930.840.970.970.991.001.000.930.951.001.001.000.981.00

324851371111291015614

0.970.950.991.001.001.001.001.000.0801.001.001.001.001.001.00

S (SIS, 1981), U (Unknown), J (la Cour Jansen, et al., 2004), L(Dr Lange®), B (Höjlund Christensen, et al., 2003), H (Hansen, et al., 2007)

Table III, 2 Results from SA on model parameters for the Aalborg household waste simulation


Sensitivity(VFAs)rank relative



µmax3

µmax4 µmax5 µmax6 µmax7 µmax8 k d9 k d10

k d11 k d12 k d13 k d14 K Saa K Ssu K Sfa

K Spro K Sac K SH2 KI ac56 KI H2,5 KI H2,6

KI H,34 KI H,58 KI NH3,6 KI NH3,7 k LaCO2 k H

4

40.60.60.3720.80.80.060.060.050.350501000204011500310.015e-425172000.2

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 mgCOD/m3 gCOD/m3 mgCOD/m3 mgCOD/m3 mol/m3 mol/m3 gN/m3 gN/m3 d-1 d-1

14

1622475171841323111521322682510121992726201

1.00

1.000.991.001.001.001.001.001.001.001.001.001.001.000.991.001.001.001.001.001.001.001.001.001.001.000.019

27

1724146232226381321181615119142051910272512

1.01

1.001.000.350.720.801.001.001.000.640.860.961.001.001.000.980.950.900.981.000.801.000.910.470.851.000.96

2

21175861127101237132226202515182414231649191

0.99

1.000.990.990.990.991.001.000.991.000.990.991.001.001.001.001.001.001.001.001.001.001.000.990.991.000.051

19

2216328202527761318231715101214219241145261

1.00

1.001.000.800.750.931.001.001.000.880.880.991.001.001.000.990.960.970.991.000.941.000.960.850.861.000.57

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VI

Table III, 3 Results of SA of all parameters for the Aalborg household waste simulation





TS

Soluble TSProteinFatSugarStarchFibers pHHCO3 NH4-NAcetatePropionateTemperatureFlow

Pressure µmax3 µmax4 µmax5 µmax6 µmax7

µmax8 k d9 k d10 k d11 k d12 k d13 k d14

K Saa K Ssu K Sfa K Spro K Sac K SH2

KI ac56 KI H2,5 KI H2,6 KI H,34 KI H,58 KI NH3,6

KI NH3,7

k LaCO2 k H

0.05

0.230.170.180.070.180.117.41016048.734.355.31.33

1.02440.60.60.3720.80.80.060.060.050.3

50501000204011500310.015e-42517

2000.2

kg/kg


mol/m3 gN/m3 gCOD/m3 gCOD/m3 °Cl/d

bard-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

gCOD/m3

gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 mgCOD/m3 gCOD/m3 mgCOD/m3 mgCOD/m3 mol/m3 mol/m3 gN/m3 gN/m3

d-1 d-1

2

2224204152336931303465

339402117148323829131610

3735262518114227123371941

281

0.88

0.990.990.980.910.970.991.000.971.001.001.000.960.93

0.901.001.000.980.970.970.971.001.001.000.970.970.97

1.001.000.990.990.980.971.011.000.971.000.970.981.00

1.000.52

15

4020291418253172728302342

174135191453936383812

37342116131126226321029

2433

0.97

1.010.991.000.950.981.001.000.821.001.001.000.991.02

0.981.011.000.980.330.690.781.001.001.000.660.830.91

1.001.000.990.970.920.881.000.990.801.000.880.430.85

0.991.00

2

438142629395637403331

249342510131217421918715

23364132282127352038221116

301

0.86

0.980.970.990.991.001.001.000.980.991.001.001.001.00

1.000.991.001.000.990.990.991.001.001.001.000.990.99

1.001.001.001.001.001.001.001.001.001.001.000.990.99

1.000.30

9

318321720263513430332441

222738195483140426714

39372129161325231036121115

282

0.98

0.960.991.000.991.001.001.000.241.001.001.001.001.00

1.001.001.001.000.970.960.981.001.001.000.970.980.99

1.001.001.001.000.990.991.001.000.981.000.990.980.99

1.000.93

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VII

Västra Hamnen household waste

Table III, 4 Results of SA, UA and variability on measured parameters for the Västra Hamnen household waste

simulation


rank σ (%)

Variability

rank σ (%)

Sensitivity(Gas)

rank relative

Sensitivity(VFAs)

rank relative

Sensitivity(NH4-N)

rank relative

Sensitivity(HCO3)

rank relativeTSSoluble TSProteinFatSugarStarchFibers pHHCO3 NH4-NAcetatePropionate

TemperatureFlowPressure

0.050.230.170.120.040.070.147.211013.548.734.3

35.41.331.03

kg/kg


mol/m3 gN/m3 gCOD/m3 gCOD/m3

°Cl/d bar

12214931081311144

1366

2.5S

20U

0.97J

3.5J

18J

3.4J

4.7J

2U 100 U 3L

10 U 10 U

2 U

2 U 2 U

5176324-----

9-8

24.6B

59.7B

9.2H

12.0H

33.3H

50H

20.0H

-----

1.4A

-1.6A

151074961215131411

832

0.690.931.000.950.900.990.951.001.001.001.001.00

0.990.870.79

326107119141121513

485

0.880.880.971.000.981.000.991.000.291.001.001.00

0.930.990.96

12367981315101214

4511

0.460.760.860.980.981.000.991.001.001.001.001.00

0.970.971.00

32413714811112109

6515

0.970.950.991.001.001.001.001.000.0741.001.001.00

1.001.001.00


Table III, 5 Results of SA on model parameters for the Västra Hamnen household waste simulation





µmax3 µmax4 µmax5

µmax6 µmax7

µmax8 k d9 k d10 k d11

k d12 k d13

k d14 K Saa K Ssu K Sfa

K Spro K

Sac

K SH2 KI ac56 KI H2,5 KI H2,6

KI H,34 KI H,58

KI NH3,6 KI NH3,7 k LaCO2 k H

440.60.60.3720.80.80.060.060.050.350501000204011500310.015e-425172000.2

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1


121926722324216105221816915201127138254143171

1.001.001.020.980.781.011.011.000.980.990.911.001.001.000.990.991.001.001.021.001.001.010.861.000.781.000.21

261527511292411144172122161819132523873102206

1.020.981.090.840.090.950.951.000.950.970.700.991.001.000.991.001.000.951.021.000.930.900.520.950.141.000.88

626782139271012421161923202522151714185113241

1.001.001.001.000.981.001.001.001.001.000.991.001.001.001.001.001.001.001.001.001.001.000.991.000.981.000.024

191427611222248104231716131825926207155112213

1.001.001.020.960.410.991.001.000.990.990.781.001.001.000.991.001.010.991.021.000.971.000.810.990.471.000.65

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VIII

Table III, 6 Results of SA on all parameters for the Västra Hamnen household waste simulation





TS






KI NH3,7

k LaCO2 k H

0.05

0.230.170.120.040.070.147.211013.548.734.335.41.33

1.03440.60.60.3720.80.80.060.060.050.3

50501000204011500310.015e-42517

2000.34

kg/kg



bard-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

gCOD/m3


d-1 d-1

6

113514917122942272528107

83334401322137361541530

242620231819382216394323

311

0.94

0.981.000.990.960.990.981.001.031.001.001.000.970.95

0.951.001.001.000.990.831.001.001.000.991.000.921.00

1.001.001.001.000.991.001.001.000.991.000.911.000.83

1.000.45

39

2027251533233140283230714

24371942511118291316422

3634172621124138983102

356

1.01

0.991.001.000.981.000.991.001.011.001.001.000.910.97

1.001.010.981.100.810.100.950.981.000.960.980.690.99

1.001.000.981.000.990.961.041.010.940.940.580.950.16

1.000.87

2

34917402734132233351124

311039121651528422021738

262937324125193023148186

361

0.92

0.960.981.001.001.001.001.001.001.001.001.001.001.00

1.001.001.001.001.000.981.001.001.001.001.000.991.00

1.001.001.001.001.001.001.001.001.001.000.991.000.98

1.000.19

8

71238142219321312527915

203728421021339401718521

342923352616413311306243

364

0.98

0.970.991.001.001.001.001.000.421.001.001.000.981.00

1.001.001.001.010.990.800.991.001.001.001.000.911.00

1.001.001.001.001.001.001.011.000.991.000.931.000.82

1.000.89

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IX

Sjölunda sludge

Table III, 7 Results of SA, UA and variability on measured parameters for the sludge simulation


rank σ (%)

Sensitivity(Gas)

rank relative

Sensitivity(VFAs)

rank relative

Sensitivity(NH4-N)

rankrelative

Sensitivity(HCO3)

rank relative

TSVSSoluble TSProteinFatSugarInert pHHCO3 NH4-NTemperatureFlowPressure

0.0390.750.30.340.450.160.057.131245341.51.02

kg/kgg/TS

gCOD/gXS

gCOD/gXS

gCOD/gXS

gCOD/gXS

mol/m3 gN/m3 °Cl/d bar

81322222917999

2.5S

0.53J 20U 20 U 20 U 20 U 20 U 2 U 100 U 3L 2 U 2 U 2 U

41082133115129671

0.991.001.000.971.010.981.000.991.001.000.990.990.13

58121461039131172

0.991.001.000.460.970.991.000.901.001.001.001.000.48

35611312114810792

0.991.001.000.431.001.001.001.001.001.001.001.000.60

71252469110118133

1.001.000.990.780.981.001.000.691.001.001.001.000.81

S

(SIS, 1981),

U

(Unknown),

J

(la Cour Jansen, et al., 2004),

L

(Dr Lange®), B (Höjlund Christensen, et al., 2003),

H

(Hansen, et al., 2007)

Table III, 8 Results of SA on model parameters for the sludge simulation





Zerogas- prod.


µmax6 µmax7 µmax8 k

d9

k d10 k d11 k d12

k d13 k d14 K Saa K Ssu K Sfa K Spro

K Sac K SH2 KI ac56

KI H2,5 KI H2,6 KI H,34

KI H,58 KI NH3,6 KI NH3,7 k LaCO2 k H

440.60.60.3720.80.80.060.060.050.350501000204011500

310.015e-425172000.2

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 mgCOD/m3 gCOD/m3

mgCOD/m

3

mgCOD/m3 mol/m3 mol/m3 gN/m3 gN/m3 d-1 d-1

25235171726241410492119161813128

1511223272206

1.001.000.911.000.190.961.001.000.990.980.680.971.001.001.001.000.990.990.97

0.990.981.000.631.000.531.000.94

241227516132515114923201718142110

228163721926

1.010.961.030.850.250.910.981.020.990.960.790.951.001.001.001.000.991.000.96

1.000.950.990.740.940.541.001.03

72762511326814125182316172110199

1124224153202

0.951.090.951.010.381.001.040.971.001.000.651.001.001.001.001.000.991.000.99

0.991.011.000.621.000.601.000.60

221826516251621104820231924111312

177153921427

1.001.001.010.960.240.971.011.001.000.990.800.991.001.001.001.000.991.000.99

1.000.981.000.800.990.511.001.03

2027212302223212322122221222222212121

232221112292221(23)

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X

Table III, 9 Results of SA of all parameters for the sludge simulation





TS

VSSoluble TSProteinFatSugarInert pHHCO3 NH4-NTemperatureFlowPressure µmax3

µmax4 µmax5 µmax6 µmax7 µmax8 k d9

k d10 k d11 k d12 k d13 k d14 K Saa K Ssu

K Sfa K Spro K Sac K SH2 KI ac56 KI H2,5

KI H2,6 KI H,34 KI H,58 KI NH3,6 KI NH3,7 k LaCO2

k H

0.039

0.750.30.340.450.160.057.131245341.51.024

40.60.60.3720.80.80.060.060.050.35050

1000204011500310.015e-425172000.34

kg/kg

g/TS

gCOD/gXSgCOD/gXSgCOD/gXSgCOD/gXS

mol/m3gN/m3°Cl/d bard-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

gCOD/m3 gCOD/m3

gCOD/m3

gCOD/m3 gCOD/m3 mgCOD/m3 gCOD/m3 mgCOD/m3 mgCOD/m3 mol/m3 mol/m3 gN/m3 gN/m3 d-1 d-1

19

3323381135631242021128

30716210392712229133432

363815141725263744052918

0.99

1.000.990.880.940.981.000.921.001.000.990.990.481.00

1.000.930.980.790.961.001.000.980.990.960.981.001.00

1.001.000.980.980.991.001.001.000.901.010.901.000.99

24

3414291327628262223133

173910315323712257311830

36293819212016115843540

1.00

1.000.990.670.980.991.000.901.001.001.001.000.661.00

0.991.010.980.720.991.001.000.981.000.961.000.991.00

1.001.001.001.001.001.000.990.980.890.970.821.001.01

12

33341142932635232437217

40111038391826207133830

31361522162521195274289

0.99

1.001.000.461.001.001.000.981.001.001.001.000.601.00

1.000.990.990.960.991.001.001.001.000.990.991.001.00

1.001.001.001.001.001.001.001.000.981.000.981.000.99

22

3616461433135191824529

37101729342620158113830

283112132125233274032739

1.00

1.000.990.860.910.991.000.771.001.000.991.000.881.00

1.000.980.990.770.981.001.001.000.990.960.991.001.00

1.001.000.990.991.001.001.001.000.921.020.851.001.00

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XI

Aalborg household waste wi th general characterization

Table III, 10 Results of SA, UA and variability on measured parameters for the general thermophilic household waste

simulation


rank σ (%)

Variability

rank σ (%)

Sensitivity(Gas)

rank relative

Sensitivity(VFAs)

rank relative

Sensitivity(NH4-N)

rank relative

Sensitivity(HCO3)

rank relativeTSSoluble TSProteinFatSugarStarchFibers pHHCO3 NH4-NAcetatePropionate

TemperatureFlowPressure

0.050.140.150.140.060.150.197.41016048.734.3

55.31.331.02

kg/kg


mol/m3 gN/m3 gCOD/m3 gCOD/m3

°Cl/d bar

5------61422

666

2.5S

------2U 100 U 3L

10 U 10 U

2 U

2 U 2 U

5176324-----

9-8

24.6B

59.7B

9.2H

12.0H

33.3H

50H

20.0H

-----

1.4A

-1.6A

510743121411131512

986

0.961.000.980.920.850.550.831.001.001.001.001.00

0.990.980.97

85110647143111513

2129

0.980.950.601.000.960.880.961.000.771.001.001.00

0.661.000.99

2715436121081113

15914

0.960.990.130.990.980.960.991.001.001.001.001.00

1.001.001.00

4328657111131210

15914

0.980.940.701.000.990.990.991.000.391.001.001.00

1.001.001.00


Table III, 11 Results of SA on model parameters for the general thermophilic household waste simulation






µmax6 µmax7

µmax8 k d9 k d10 k d11

k d12 k d13

k d14 K Saa K Ssu K Sfa

K Spro K

Sac

K SH2 KI ac56 KI H2,5 KI H2,6

KI H,34 KI H,58

KI NH3,6 KI NH3,7 k LaCO2 k H

440.60.60.3720.80.80.060.060.050.350501000204011500310.015e-425172000.34

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1


192524832123155136202412181410271692271126171

1.001.000.980.980.980.981.001.000.990.980.990.981.001.000.991.000.990.991.031.000.981.000.980.991.001.000.04

262216164252423291020211713128271851973111514

1.011.001.000.340.680.581.001.001.000.530.800.821.001.001.000.960.920.771.011.000.651.000.760.540.910.990.98

223179124627710358242619201321221425151116181

0.981.001.000.991.000.990.991.000.990.990.990.990.991.001.001.001.001.001.001.001.001.001.000.991.001.000.08

162514325192622471218241715131127208239610211

0.991.000.980.780.720.851.001.001.000.840.860.931.001.000.990.990.930.911.011.000.881.000.900.850.911.000.58

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XII

Table III, 12 Results of SA of all parameters for the general household waste simulation for thermophilic conditions





TS






KI NH3,7

k LaCO2 k H

0.05

0.140.150.140.060.150.197.41016048.734.355.31.33

1.02440.60.60.3720.80.80.060.060.050.3

50501000204011500310.015e-42517

2000.34

kg/kg



bard-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

gCOD/m3


d-1 d-1

6

20953123442333031148

7384122112510273226131812

36292428401921351639171523

374

0.97

1.000.980.930.860.580.841.001.001.001.001.000.990.98

0.971.001.001.000.981.000.981.001.001.000.980.990.98

1.001.001.001.001.000.991.001.000.991.000.990.991.00

1.000.92

17

2011222791334162928332341

212618391124314036375

32303819251014356248215

3742

0.93

0.970.800.991.000.750.831.000.931.001.001.001.001.01

0.981.000.961.010.260.830.511.001.011.000.470.730.63

1.001.001.000.971.000.760.851.000.690.990.730.460.90

1.001.04

3

8156473317932343918

28152531141216264241201019

38294027372224362135301311

232

0.96

0.990.220.990.990.970.991.001.001.001.001.001.001.00

1.001.001.001.001.001.001.001.001.001.001.001.001.00

1.001.001.001.001.001.001.001.001.001.001.001.001.00

1.000.93

9

3219147132913431273322

37233220816635363851510

39282140181725261230114142

244

0.99

0.950.731.000.990.990.991.000.431.001.001.001.001.00

1.001.001.001.000.990.990.981.001.001.000.980.990.99

1.001.001.001.001.001.001.001.000.991.000.991.001.01

1.000.98

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XIII

Västra Hamnen household waste with general characterization

Table III, 13 Results of SA, UA and variability on measured parameters for the general thermophilic household waste

simulation


rank σ (%)

Variability

rank σ (%)

Sensitivity

(Gas)

rank relative

Sensitivity

(VFAs)

rank relative

Sensitivity

(NH4-N)

rank relative

Sensitivity

(HCO3)

rank relativeTSSoluble TSProteinFatSugarStarchFibers pHHCO3 NH4-NAcetatePropionateTemperature

FlowPressure

0.050.140.150.140.060.150.117.21013.548.734.335.4

1.331.03

kg/kg


mol/m3 gN/m3 gCOD/m3 gCOD/m3 °C

l/d bar

5------614226

66

2.5S

------2U 100 U 3L

10 U 10 U 2 U

2 U

2 U

5176324-----9

-8

24.6B

59.7B

9.2H

12.0H

33.3H

50H

20.0H

-----1.4A

-1.6A

5974312141113151210

86

0.960.990.980.920.840.540.831.001.001.001.001.001.00

0.980.97

841116371521214135

910

0.960.900.381.000.940.810.941.000.701.001.001.000.91

0.981.00

351742612151011139

814

0.960.980.170.980.980.940.981.001.001.001.001.001.00

1.001.00

532864712113141110

915

0.990.930.721.000.990.980.991.000.391.001.001.001.00

1.001.00S (SIS, 1981), U (Unknown), J (la Cour Jansen, et al., 2004), L(Dr Lange®), B (Höjlund Christensen, et al., 2003), H (Hansen, et al., 2007)

Table III, 14 Results of SA on model parameters for the general thermophilic household waste simulation






µmax6

µmax7 µmax8 k d9 k d10 k d11 k d12

k d13 k d14 K Saa K Ssu K Sfa K Spro

K Sac

K SH2 KI ac56 KI H2,5 KI H2,6 KI H,34

KI H,58 KI NH3,6 KI NH3,7 k LaCO2 k H

440.60.6

0.3720.80.80.060.060.050.3505010002040

11500310.015e-425172000.34

d-1

d-1

d-1

d-1

d

-1

d-1

d-1

d-1

d-1

d-1

d-1

d-1

gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3

mgCOD/m3

gCOD/m3 mgCOD/m3 mgCOD/m3 mol/m3 mol/m3 gN/m3 gN/m3 d-1 d-1

191768

47162224253271418121126

9231020212135151

1.001.000.980.99

0.870.981.001.011.021.020.871.061.001.001.001.001.04

1.001.021.001.001.000.861.000.871.000.19

1522175

16241123104251821191427

816127132932026

0.981.020.990.53

0.440.561.030.951.020.930.521.100.991.001.000.981.23

0.820.980.960.700.980.450.920.521.001.12

7261014

311986232131518252019

17272412225164211

0.991.001.001.00

0.981.001.001.000.991.000.971.001.001.001.001.001.00

1.001.001.001.001.000.981.000.981.000.06

1622116

27212325145271720151226

924138193104181

1.001.000.980.84

0.720.851.001.001.031.000.771.061.001.001.000.991.03

0.931.020.990.901.000.760.970.761.000.52

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XIV

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1

Appl ication, uncertainty and sensit iv ity analysis of the anaerobic digestionmodel by Siegrist et al. (2002) on household waste digestion

E. Ossiansson* and O. Lidholm** Water and Environmental Engineering, Department of Chemical EngineeringE-mail: * [email protected], ** [email protected]

Abstract In this paper the anaerobic digestion model published by Siegrist et al. (2002) is applied on household waste digestion. Datafrom two pilot scale experiments with measured characterizations were used, one with mesophilic and one with thermophilictemperature. Validation simulations with focus on the gas production rate, ammonium and VFA were first performed, usingdefault values for model parameters. The steady state gas production could be predicted with acceptable accuracy, while thesimulated ammonium and VFA concentrations were overestimated by the model. An uncertainty analysis was conducted toanalyze the quality of the predictions with respect to measurements of input data. The measurement errors influenced the gas production the most, but that the VFA and ammonia predictions could not be improved with more accurate measurements. Tofind suitable parameters for calibration of model parameters, a Monte Carlo based sensitivity analysis was conducted,supplemented with scatter plots. The sensitivity analysis showed that the hydrolysis constant was the most important parameter to determine for both ammonium and gas production. This was problematic for the calibration, as the particulateorganic matter is lumped and calibrating the ammonium from the hydrolysis constant therefore led to unrealistically low gas production. To model the protein degradation accurately, without changing the overall hydrolysis constant or the modelstructure, the protein content in the substrate was calibrated instead. The Siegrist model was hence not suitable for simulation

of characterized household waste, unless a hydrolysis model with slower protein hydrolysis was introduced or thestoichiometry for the hydrolysis was calibrated. The VFA concentrations in the reactor were dependent on model parametersrelated to the aceticlastic methanogenesis and the propionate degradation. Calibration of half saturation constants for these processes was successful, but the values were increased considerably. A possible explanation for the considerable change inthese parameter values could be that the mass transfer of substrate was more limiting than for the default Siegrist model.

Keywords anaerobic digestion, model, household waste, uncertainty analysis, sensitivity analysis, calibration, Monte Carlo,hydrolysis constant

Introduction

Anaerobic digestion is a complex system of biochemical and physical processes. Due to thecomplexity of the process, it has traditionally beentreated as a black box system, and optimization has been based on experience or trial and errormethods. As experiments of anaerobic digestion processes are expensive and time consuming,modeling can provide a useful tool for processunderstanding and optimization. Models have potentials for revealing non-linear behaviors of thesystem and to quantify the performance ofalternative operational setups.

The aim of this report is to evaluate theapplicability of a model for anaerobic digestion published by Siegrist, et al (2002), here referred to

as the Siegrist model. The model was primarilydeveloped for simulating the digestion of mixedsludge, but in this report the applicability for themodel on household waste is studied. Compared tothe more commonly used model by theInternational Water Association (IWA), calledAnaerobic Digestion Model no 1 (ADM1), theSiegrist model is less complex, with a lumpedhydrolysis constant and fewer Volatile Fatty Acids(VFA) included. The two models were constructedwith different approaches, the Siegrist model parameters are based on experiments, whereas theADM1 uses review consensus (Batstone, 2006).

ADM1 has been validated in the literature withvarying success (Parker, 2005; Batstone, et al.,2003; Tartakovsky, et al., 2008). The Siegrist

model is less utilized, but interesting because of thesimpler structure with fewer input variables.The aim of the report is also to evaluate the

required quality of input parameters, and to find themost important parameters to measure whenmodeling household waste digestion. Furthermore,the model parameters most suitable for calibrationare evaluated and results with calibrated parametersare shown.

Materials & Methods

The model was implemented in Matlab as a systemof differential equations with 23 liquid phase statevariables and 3 state variables describing gaseouscompounds. The stiff ODE-solver ode15s was usedfor the numerical integration. The hydrolysis ratewas described with first order kinetics with respectto the degradable particulate organic matter X S(process 1 in Figure 1). Monod kinetics, incombination with inhibition expressions withrespect to ammonia, pH, acetate and dissolvedhydrogen, were used to simulate the microbial processes (process 2-7 in Figure 1). The model alsoincluded stripping of the gases methane, carbondioxide and hydrogen from the liquid with a pressure control loop (Siegrist, et al., 2002).

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2

Figure 1 Overview of the biochemical reactions in anaerobic digestion

with flows expressed as percent of COD (from Siegrist et al 2002

based on Gujer et al 1983)

Data from one mesophilic (35°C) and one

thermophilic (55°C) pilot scale experiment wasused for validation and model analysis (Davidsson,et al. 2007). The household waste used in themesophilic experiment was collected in the citydistrict of Västra Hamnen in Malmö, Sweden, andthe thermophilic digester was fed with householdwaste from Aalborg, Denmark. Characterizationdata for fat, protein, fiber, sugar, starch, VFA andammonium content as fractions of TS was found inHøjlund Christensen, et al. (2003). Themeasurement errors of the characterization datawere found in an evaluation of the analysis methods by la Cour Jansen, et al. (2004). Relative standarddeviation for the ammonium measurements were provided by the analysis instrument manufacturer(3.5 %, Dr Lange®). The relative standarddeviation for VFA was assumed to be 10 %, and2.5 % for gas production measurements.

The experiments were divided into three phases;startup, steady state and post digestion. As theinoculums were collected from digesters fed withsludge, the startup phase was needed for themicroorganisms to get accustomed to the new typeof feed. Post digestion data was not available forthe mesophilic digestion experiment.

Validation simulationsBefore the pilot scale experiments could besimulated, some processing of data was needed,including unit conversions and calculation ofstoichiometry and the rate constant for thehydrolysis process. The elemental compositions for protein, fat etc. were found in Davidsson, et al.(2007) and converted to the unit gCOD/gTS withthe Buswell formula (Buswell, et al., 1930). Thedefault stoichiometry of mixed sludge hydrolysis inFigure 1 was hence updated to apply for thehousehold wastes.

Data from batch experiments on the waste from

Västra Hamnen was used to determine the firstorder hydrolysis constant for degradation of

particulate degradable organic matter, X S . It wasassumed that the hydrolysis step was rate limitingand that there were no inhibition effects on themicrobial reactions. The hydrolysis constant, k H ,was determined to 0.20 d-1 (Figure 2).

Figure 2 Calibration of k H from batch experiment on household waste

from the mesophilic digestion

Except for the hydrolysis constant and thecomposition of the waste, default values for model parameters were used for the validationsimulations. The results show that the steady stategas production rate could be predicted fairly wellfor both household wastes, while the correlationduring the start-up phase was poorer (Figure a and4a). The modeled gas production rate during thestartup phase was higher than measured, indicatinga slower degradation before adaptation to thesubstrate. The fit to data for steady state ammoniumconcentrations were unsatisfactory for both

simulations, especially for the mesophilic case(Figure 3b and 4b). The good fit to data for thestartup of the thermophilic experiment was mainlydue to a washout effect. The VFA concentrationswere underestimated in the model predictions,especially for the thermophilic household wastedigestion (Figure 3c and 4c).

Uncertainty analysis

The characterizations were based on measurementswith inherent measurement errors. A Monte Carlomethod with Latin Hypercube Sampling (LHS) wasused to study the effects of these measurement

errors on prediction uncertainty. The distributionsof the measurement errors were assumed to bedescribed by Gaussian functions, and thedistributions of outputs from 5000 simulations werestudied.

In Figure 5 the uncertainty of simulated outputs presented as 95 % confidence intervals can becompared with measurement uncertainties ofvalidation data (vertical intervals) for thethermophilic household waste simulation. When theconfidence intervals overlap, the lack of fit could beexplained by measurement error. Figure 5a showsthat measurement errors can explain some of the

discrepancy between simulations and data for the

0 10 20 30 40 50-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Time, [Days]

G a s p r o d u c t i o n , [ N m l / D a y ]

Triplicate 1

Triplicate 2

Triplicate 3

kh=0.2

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3

Figure 3a Modeled and measured biogas production Figure 3b Modeled and measured ammonia Figure 3c Modeled and measured VFA

for the thermophilic experiment for the thermophilic experiment for the thermophilic experiment

Figure 4a Modeled and measured biogas production Figure 4b Modeled and measured ammonia Figure 4c Modeled and measured VFA

for the mesophilic experiment for the mesophilic experiment for the mesophilic experiment

gas production rate, but that further calibration wasneeded for ammonia and VFA (Figure 5b and 5c).The confidence intervals are broader for the gas production than the ammonia and VFA, indicatingthat the gas production is affected more by thequality of input data than the other two outputs.

Sensitivity analysisSensitivity analysis was conducted with two main purposes; to determine the importance of measuringspecific input parameters and to find model parameters suited for calibration. Sensitivityanalyses of ADM1 found in the literature usedsensitivity functions or other local analysis methods(Tartakovsky et al. 2008, Jeong et al. 2005, etc.). Inthis report, a global sensitivity analysis method wasemployed instead, to include the non-linear behavior of the system.The sensitivity analysis wascarried out with the same methodology as in the

uncertainty analysis, e.g. Monte Carlo with LHS.This time, however, instead of varying all parameters, one parameter at a time was kept at aconstant value. The relative decrease in outputvariance when keeping a parameter constant,compared to if all parameters varied, was used as ameasure of the sensitivity for this parameter.

This variance-based method needed to besupplemented with scatters plots to enable visualevaluation of the correlation between parametersand output.

The analysis of measured input parameters was based on the same parameter distributions as in theuncertainty analysis. As no information of realisticdistributions for model parameters was found, themodel parameters were assumed to be uniformlydistributed between ± 50 percent of the defaultvalues.

Figure 5a Confidence intervals of the gas production Figure 5b Confidence intervals of the ammonium Figure 5c Confidence intervals of the VFA

for the thermophilic experiment for the thermophilic experiment for the thermophilic experiment

0 20 40 60 800

0.01

0.02

0.03

0.04

0.05

Time [days]

P r o d

u c t i o n r a t e [ m 3 / d a y ]



0 20 40 60 800

500

1000

1500

2000

2500

3000

3500

Time [days]

C o n

c e n t r a t i o n [ g N / m 3 ]

Simulated NH4 modelle d

Measured NH4

0 20 40 60 800

200

400

600

800

1000

1200

1400

1600

Time [days]

C o n c

e n t r a t i o n [ g C O D / m 3 ]

Simulated VFAs

Measured VFAs

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

Time [days]

P

r o d u c t i o n r a t e [ m 3 / d a y ]

Simulated dry biogas prod uction


0 10 20 30 40 50 600

200

400

600

800

1000

Time [days]


Simulated NH4 modelled

Measured NH4

0 10 20 30 40 50 600

50

100

150

200

250

300

350

Time [days]

V F A s a s a c e t a t e e q u i v a l e n t s [ g C O D / m 3 ]

Simulated VFAs

Measured VFAs

40 45 50 55 60 65 700

0.01

0.02

0.03

0.04

0.05

0.06

Time [days]



95 % confidence inter val

95 % confidence inter val


40 45 50 55 60 65 700

500

1000

1500

Time [days]


NH4 mo delled

95 % confidence interval


NH4 measured

40 45 50 55 60 65 700

200

400

600

800

1000

1200

Time [days]


VFAs mo delled



VFAs measured

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4

Table 1 Results from sensitivity analysis of measured input parameters

Parameter Mean Unit Sensitivity

(Gas)

Sensitivity

(VFA)

Sensitivity

(NH4-N)

Thermophilicdigestion

rank relative

Mesophilicdigestion

rank relative


Rank relative

Mesophilicdigestion

rank relative


rank relative

Mesophilicdigestion

rank relativeTS

Soluble TSProteinHCO3

0.05

0.230.1710

kg/kg

g/TSmol/m3

1

51015

0.69

0.931.001.00

3

261

0.88

0.880.970.29

4

372

0.95

0.950.990.59

3

261

0.88

0.880.970.29

1

324

0.42

0.930.840.93

1

2315

0.46

0.760.861.00

The sensitivity analysis of measured input parameters showed that the variance for predictionof gas production rate decreased the most if the TSmeasurements were made without errors (Table 1).Reliable measurements for TS are thus important.The most significant sources of uncertainty for theammonium predictions were the TS, solubilized TSand protein content of the feed (Table 1). For VFA,the uncertainty from distributed input parameterswas not significant, but the HCO3 of the feed wasmost influential (Table 1).

With the aid of scatter plots, the correlations between the measured input parameters and outputcould be visualized. From this analysis, thecorrelation between the degradable fraction of TScould be pointed out as more important for the gas production rate than the total measured TS (Figure6 and 7). The linear correlation to the gas production is more pronounced for the degradableTS and the output values are less dispersed. Thisresult is no surprise, however, since it is thedegradable fraction of TS that is used for gas production. This result emphasizes the importanceof measuring the degradability of the substrate.

Figure 6 Gas production vs. total TS for the thermophilic experiment

Figure 7 Gas production vs. degradable TS for the thermophilic

experiment

The results from the variance-based sensitivityanalysis of model parameters showed that thehydrolysis constant k H is the most important parameter both for determining the gas productionrate and the ammonium levels in the reactor (Table2). This indicates that the hydrolysis step is ratelimiting, and that the hydrolysis constant can becalibrated from either the gas production rate or theammonia level in the reactors. Figure 8 shows thenon-linear correlation between the hydrolysisconstant and the gas production.

Figure 8 Gas production vs. k H for the thermophilic experiment

VFA levels in the reactor were sensitive to parameters related to the acetotrophicmethanogenesis and the anaerobic degradation of propionate (Table 2). The scatter plot analysis ofthe correlations revealed that the high sensitivity tothese parameters was partly due to that bacteriawere washed out when these constants reachedextreme values. Figure 9 shows an example of afrequent washout of bacteria for low maximum

growth rates for the aceticlastic methanogens.

Figure 9 Gas production vs. maximum growth rate of aceticlastic

methanogens

0.045 0.05 0.0550

0.01

0.02

0.03

0.04

0.05

0.06


3 / d ]

TS [kg/kg]

0.03 0.032 0.034 0.036 0.038 0.040

0.01

0.02

0.03

0.04

0.05

0.06


3 / d ]

TS [kg/kg]

0.1 0.15 0.2 0.25 0.30

0.01

0.02

0.03

0.04

0.05

0.06

kH [d -1]


3 / d ]

0.2 0.3 0.4 0.5 0.60

0.005

0.01

0.015

0.02

0.025

0.03

max6


3 / d ]

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Table 2 Results from sensitivity analysis of model parameters

Calibration

In the sensitivity analysis, the most influentialmodel parameters for each output were ranked. Thisresult could then be used for calibration purposes,where the most influential parameters were chosen,and used to increase the fit to data. The calibrationwas conducted by varying parameters so that thesum of absolute errors for model predictionscompared to data during the steady state phasecould be minimized.

Calibration of the hydrolysis constant to the gas production measurements resulted in an unchangedvalue for the mesophilic experiment, while the bestfit to data for the thermophilic experiment wasslightly decreased (from 0.2 to 0.15). This indicateda successful determination of k H from batchexperiment for the household waste from VästraHamnen. To enable calibration during the startup phase, the hydrolysis constant was iterativelyincreased until a good fit to data was achieved. Theresults from the calibration of the hydrolysisconstant to the gas production errors are presentedin Figure 10a.

The hydrolysis constant was also the mostinfluential parameter when it came to determiningthe ammonia levels in the reactor. When calibratingthe hydrolysis constant with the ammoniameasurements, the resulting hydrolysis constantswere lower, indicating slower degradation of protein than other particulate constituents. The factthat the particulate organics were lumped into onestate variable, X S , complicated the calibration process. As the hydrolysis constant determined boththe protein degradation and the gas production rate,only one of the two processes could be calibrated atthe same time. The model structure hence needed to

be revised, to include a separate process of

hydrolysis of particulate protein. The modelstructure was however not changed in this project, but is suggested for further studies. The problemwas instead solved by decreasing the stoichiometriccoefficient of protein in the degradation of X S . Theresult from this calibration is presented in Figure10b.

The sensitivity analysis showed that themaximum growth rate constants for the acetoclasticmethanogenesis and the propionate degradation

were most important for the VFA concentration. Asdiscussed in the sensitivity analysis section, thisresult was partly due to the high rate of washout forextreme values of these parameters. This indicatedthat they may not be suited for calibration purposes.When calibrating with these values, the fit to dataonly improved slightly, and when changing thevalue further, the errors increased rapidly. Anexample when calibrating the maximum growthrate constant for the aceticlastic methanogens is presented in Figure 11.

Figure 10 Sum of absolute errors for VFA for the thermophilic

simulation when varying maximum growth rate constant for the

aceticlastic methanogenesis

Figure 11a Biogas production for the thermophilic Figure 11b Ammonium concentration for the Figure 11c VFA concentration for the

experiment after calibration thermophilic experiment after calibration thermophilic experiment after calibration

0 0.1 0.2 0.3 0.4 0.5 0.60

1000

2000

3000

4000

5000

6000

7000

max7

S u m

o f a b s o l u t e e r r o r s

0 20 40 60 800

0.01

0.02

0.03

0.04

0.05

0.06

Time [days]




0 20 40 60 800

500

1000

1500

2000

2500

3000

3500

Time [days]


NH4 modelled

NH4 measured

0 20 40 60 800

500

1000

1500

2000

2500

3000

3500

Time [days]


VFAs modelled

VFAs measured

Parameter Mean Unit Sensitivity

(Gas)

Sensitivity

(VFA)

Sensitivity

(NH4-N)


rank relative

Mesophilicdigestion

rank relative


Rank relative

Mesophilicdigestion

rank relative


rank relative

Mesophilicdigestion

rank relative µmax6

µmax7 k H

0.6

0.370.2

d -1

d -1d -1

24

71

1.00

1.000.019

7

21

0.98

0.780.21

1

412

0.35

0.720.96

5

16

0.84

0.090.88

5

81

0.99

0.990.051

2

81

0.98

1.000.024

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Better calibration results were instead achievedwhen using half saturation constants. A better fit todata was obtained, and the process was stable for awide range of values (Figure 12). The minimumerror was acquired for a K S of 100 g COD/m3for propionate degradation and 260 g COD/m3 in the

thermophilic digester (compare with the defaultvalues 20 and 40 g COD/m3 respectively). Formesophilic digestion, only K S for acetoclasticmethanogenesis was calibrated, to 190 g COD/m3.The physical explanation for changing the halfsaturation constants could be that the mass transferconditions was different than suggested in theimplementation by Siegrist et al. The resultingsimulation after calibration is showed in Figure 10c.

Figure 12 Sum of absolute errors for VFA for the thermophilic

simulation when varying half saturation constant for the aceticlastic

methanogenesis

Conclusions

Applying the Siegrist model on household waste

experiments gave acceptable predictions of thesteady state gas production. The simulation of thestartup phase, i.e. before the inoculum was adaptedto the substrate, was less successful. The correlationof ammonia and VFA predictions to data was notsatisfying for simulations without calibrated values.

The uncertainty analysis showed thatmeasurement errors could explain some of thediscrepancy for gas production predictions to data

method for determining the hydrolysis constantcould thus be used in this case.

The ammonium concentration in the reactor wasdetermined from the degradation of protein. As the particulate organics are lumped in the Siegristmodel, the individual hydrolysis of particulate

protein could not be modeled. This was problematic, since the protein degradation wasmuch slower in the simulated experiments. It wastherefore concluded that a hydrolysis model withseparate hydrolysis rates as in ADM1 is preferablewhen modeling household waste degradation. Thisapplies particularly when characterizationmeasurements of the substrate are used; otherwisecalibrations of the stoichiometric coefficients areneeded.

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treating domestic [Journal] // Reviews in Environmental Scienceand Bio/Technology. - 2006. - pp. 5, 57–71.

Batstone D.J. and Keller J. Industrial applications of the IWA

anaerobic digestion model No. 1 (ADM1) [Article] // Waterscience and technology. - 2003. - Vols. 47, 199-206.

Buswell E G and Neave S L Laboratory studies of sludgedigestion [Article] // Illinois Division of State Water Survey. -1930. - Vol. Bulletin no. 30.

Davidsson Åsa [et al.] Methane yield in source-sorted organic fraction of municipal solid waste [Article] // WasteManagement. - 2007. - Vols. 27, p.406-414 .

Gujer W and Zehnder A J B Conversion processes in anaerobicdigestion [Article] // Water Science and Technology. - 1983. -Vols. 15 (8/9); 127-167.

Højlund Christensen T, la Cour Jansen J and Jörgensen O Datarapport om sammensætning og biogaspotentiale i organiskdagrenovation [Report]. - [s.l.] : Danska Miljöstyrelsen, 2003.

Jeong Hyeong-Seok [et al.] Analysis and application of ADM1

for anaerobic methane production [Article] // BioprocessBiosyst Eng 2005 Vols 27; 81 89

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