Kinetic Modeling of Cellulosic Biomass Processing ... · Conversion Prediction, E = 10.5 U/g Prediction, E = 20 U/g Data, E = 10.5 U/g Data, E = 20 U/g Prediction vs. experimental

Kinetic Modeling of Cellulosic Biomass Processing Featuring Enzymatic Hydrolysis with Anticipation of

Incorporation into a CFD Framework (Revised title)

* Corresponding Author

Funding from grant No. 60NANB1D0064 from the National Institute of Standards and Technology

Xiongjun Shao, Zhiliang Fan, Colin HebertLee R. Lynd*, Charles E. Wyman*

Thayer School of EngineeringDartmouth College

André BakkerFluent Inc.

Presented at the 2003 AIChE Annual MeetingSan Francisco, CA

Nov 21, 2003

Project RationaleBiological Conversion of cellulose biomass to commodity products

� Sustainable resource supply� Energy security� Rural economic development

Desirable because of potential benefits with respect to

Cost of overcoming the recalcitrance of cellulosic biomass

� Most costly process step� Least technically mature� Enzyme, microbially-based processes have outstanding potential

Scale-up

� No experience with full-scale facilities� Limited fundamental understanding

� Computational fluid dynamics (CFD) is powerful tool for scale up analysis� A collaborative project with FLUENT inc. recently initiated

Bottlenecks

01

System definition

Cellulose Cellobiose Glucose EthanolCellulase β-Glucosidase Yeast

Experimental data

� Pretreated wood, peptone yeast extract growth media, 37 ºC� Genencor CL cellulase supplemented with Novozyme 188 β- glucosidase� Yeast (Saccharomyces cerevisiae), strain D5A� 1 L working volume

Simultaneous Saccharification & Fermentation

02

South et al. (1995), batch & continuous feeding

� As above except paper sludge (Fraser Papers Mill, Gorham, NH) wasprocessed in a lean medium containing 0.15% (v/v) corn steep liquor and 0.25mM MgSO4.

This study, intermittent feeding

� All three features deviate from classical kinetics for soluble substrates� While various mathematical forms can be used to describe these phenomena, all

three must be addressed for any broadly applicable model

Essential features of enzymatic hydrolysis models (South et al)

1) Rate saturation with respect to either substrate or enzyme(e.g. using Langmuir adsorption, but not Michaelis-Menten kinetics)

2) Declining reaction rate per adsorbed enzyme with increasing conversion

3) Particle reactivity changes with concentration & conversionParticle population model (For a well-mixed, fully continuous steady state reactor)

RTD

CPDM (Loescher et al)

dttExx t∫ ×=∞0

),()( τ )exp(1),( τττttE −×=

dxxnxn

x ∫ ××=1

00

)(ˆ1 dxxnn ∫=

1

00)(ˆ

03

+−=

s

S

dx

rd

r

xn

dx

xnd

τ0ˆ

ˆ)(ˆ)(ˆ

cmxkxk +−×′= )1()(

Outline of South et al. model (perfect mixing assumed)

Rate equations

Cellulose:

Cellobiose:

Glucose:

Cells:

Ethanol:

PSKPPSK

CSKCBCSK

S

CEcmxkSr

/][/

/

/][))1((+

×+

××+−×′−=σ

][)][

1(

][][056.1

/

CBK

GK

BCBKrr

GC

m

CSCB

++×

××−×−=

)][

1(][

][][

/

max

PXG

C

K

P

KG

GXrXc −×+

××=

µ

GXY

rrrr XcCBSG

/

053.1)056.1( −×−×−=

GX

GP

Y

Yrr XcP

/

/×=

Conservation equations

Cellulose:

Lignin:

Cellulase:

S

CESS f σ

][][][ +=

L

LELL f σ

][][][ +=

][][][][ LECEEET ++=

Material balance

Batch:

Continuous:

ir

dt

id =][

])[]([1][

0 iiir

dt

id −×+=τ

i = Cellulose, Cellobiose, Cells, Glucose, Ethanol

04

Batch SSF

□: 5 U/go: 10 U/g∆: 15 U/g◊: 20 U/g

Enzyme loading

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (days)

Con

vers

ion

SubstrateDilute acid-pretreatedwood

Curves generated using best-fit parameters to

cmxkxk +−×′= )1()(

k’ = 2.8625 /hm = 5.30c = 0.18125 /h

05

Continuous SSF (steady state)

• Predictions based on parameter values obtained by fitting batch data without adjustment

• Consideration of changing reactivity over the time a particle spends in the reactor is absolutelyrequired to get agreement with experimental data for the continuous system

- Experimental data - CSTR prediction

Range of CSTR data, runs 1 through 7

Feeding concentrations: 12.9-foldEnzyme loadings: 2.1-fold

Residence time: 5.6-fold

06

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

# 1 # 2 # 3 # 4 # 5 # 6 # 7

Solution Algorithm of South et al model

� Set derivatives = 0 (assumed steady state)

� Simultaneous solution of 5 non-linear algebraic equations using multiple iterative loops

Limitations

General� Not readily adapted to intermittent feeding� Perfect mixing assumed (not readily adjusted to imperfect mixing)

Specific to CFD (limited to solving ~50 dynamic equations per element per time step)

� Particles modeled as ~100,000 discrete populations� Extensive iterations (~30)� Excessive computational requirements when implemented on a

distributed basis in a CFD framework (~10,000 computational elements)

07

In light of these limitations, the solution of South et al. has to be modifiedto be compatible with CFD analysis

Modifications to Kinetic model

Change Equilibrium Enzyme Adsorption to Dynamic Enzyme Adsorption

08

Accommodate Intermittent Feeding

Dynamic enzyme adsorption

Equilibrium enzyme adsorption

Model prediction: Batch SSF (enzyme loading = 10 U/g)

Accommodate Discrete feeding

Particle conversion, xp(i)

)]([

)]([)(

1)]([

)(0

0

iS

iSiR

iSi

px

×=

−

[S0(i)] = g cellulose/L, population i, fed to the reactor [S(i)] = g cellulose/L, population i, in the reactor @ t

)(iR Fraction of particles of population iremain in the reactor

=

xp changes due to reaction only

][

)]([[

0

1]0

S

iSSx

n

i∑−

= =

Reactor conversion

Define particle conversion

[S0] = g cellulose/L, fed to the reactor [S(i)] = g cellulose/L, population i, in the reactor @ t

Changes due to

1. Reaction2. Exit of substrate

x

cmxkxk ipip +−×′= )1()( )()(

xp(i) rather than , is appropriate to use for the conversion dependent rate constantx

09

Accommodate Discrete feeding (continued)

� Particles fed at a given time are modeled as a discrete population (i)

� Total enzyme = Free enzyme + sum (enzyme bound to each population)

� Track particle populations until they are highly converted

10

, )]([

]))(1([S

mp

iCEcixkir σ

×+−×=)]([

)]([)(

1)]([

0

0

)(iS

iSiR

iS

x ip

×=

−

Hydrolysis rate

]/[))]([([ 01

]0 SiSSxn

i∑−==

Reactor conversion

Material balancefor component J )]([

)()]([

)()]([0 iJf

tOiJ

f

tIirdt

iJd ×−×+=

=0

1)(tI

t = t0 (original feeding)

i: index of individual particle population

n: total number of particle populationsf : feedings/residence time

R(i): remaining fraction of particle pop i

=0

1)(tO

removal time (feeding time)

at all other times at all other times

J = Substrate, enzyme, lignin, cellobiose, glucose, cells, ethanol

Comparison of predicted CSTR conversion using the South Solution Algorithm and the Discrete Solution Algorithm

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

# 1 # 2 # 3 # 4 # 5 # 6 # 7

- Experimental data - CSTR prediction - Discrete model prediction ( f = 200)

11

f (feedings/residence time)

Fully continuousResults( f= )∞

Tau = 96 hrs, Enzyme loading = 10 U/g

Discrete SSF, Steady State (end of cycle) cellulose conversionvs. feeding frequency (enzyme loading = 10 U/g, = 4 days )τ

Batch SSF, t = 4 days

12

10

Experiments in this region

Experimental system

13

Paper sludge as substrate

0.85

0.86

0.87

0.88

0.89

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

1 2 3 4 5 6 7 8 9 10 11

Feeding frequency, f

Con

vers

ion

Prediction, E = 10.5 U/g Prediction, E = 20 U/g

Data, E = 10.5 U/g Data, E = 20 U/g

Prediction vs. experimental data for Paper sludge

� Lowering f allows conversion to remain constant while reducing enzyme loading� Model predictions based on parameter values for pretreated wood� Experimental data obtained with paper sludge

14

Anticipated trends:Lower enzyme cost Lower cost for mixing, heat transfer

CFD analysis of continuous systems requires that the number of equation solved per element (N) be limited (Current limit: 50 equations)

Number of equations (N)

Equations for n discrete particle population

Additional equations

• Cellulose concentration, i th population, [S(i)]• Cellulose-enzyme complex concentration, i th population, [CE(i)]

• Lignin concentration, [L]• Lignin-enzyme concentration, [LE]• Cellulase enzyme concentration, [E1]• Cellobiose concentration, [CB]• Cell concentration, [Xc]• Ethanol concentration, [P]• Glucose concentration, [G]• Carbon dioxide concentration, [CD]

2n + 8

2n

8

15

ε(n) = 1 -Quasi-steady state reactor conversion with n particle populations tracked

Quasi-steady state reactor conversion with >> n particle populations tracked

Fractional error

N depends on the degree of accuracy required

16

2482810401687.23%20

14318522788.73%8

919112293.63%2

4

48205825783577.10%20

2482810361478.36%8

12214316482.74%2

2

NnNnNn

ε(n) = 2.0%ε(n) = 1.0%ε(n) = 0.2%f(days)

Enzyme loading = 15 U/g

τ x

Equations limit: ~50

For many scenarios, N falls within the practical range for CFD

Status of Modeling Work in Relation to Complexity

17

Not likely to be practical w/ CFDmanyImperfectContinuousN (staged)10

SolvablefewImperfectIntermittent15

Solvable

In progress

In progress

Not likely to be practical w/ CFD

Done

Done (South)

Done*

Done (South)

Status/Solution expected

fewImperfectIntermittentN (staged)9

fewPerfectIntermittentN (staged)8

manyPerfectContinuousN (staged)7

manyImperfectContinuous16

fewPerfectIntermittent14

manyPerfectContinuous13

1ImperfectBatch12

1PerfectBatch11

PopulationMixingFeeding# of reactorsScenario

Intermittent feeding is advantageous in terms of both application and computational feasibility

* Presented at 25th Symposium on Biotechnology for Fuels and Chemicals

Summary

18

• Combining kinetic and CFD models for biocommodity processesis a promising approach for scale-up analysis that has received little prior attention previously

• SSF model of South et al. has been reformulated to be compatiblewith requirements for analysis via CFD, reducing the number of particle populations tracked from 100,000 to < 30 with little error

• Model results indicate that reduced feeding frequency allows high conversion to be realized at ~ 2-fold lower enzyme loading

• Experimental results with paper sludge confirm predicted trend

• Good agreement between experimental and predicted data is obtainedalthough parameter values obtained for a different substrate

• Continued development and application of combined kinetic and CFD models is underway