Model Based Prognostic Maintenance as Applied to Small Scale PVRO Systems for Remote Communities by Leah C. Kelley Bachelor of Fine Arts, Dance The Boston Conservatory, 1998 Bachelor of Engineering, Mechanical Engineering City College of New York, 2009 Master of Science, Mechanical Engineering Massachusetts Institute of Technology, 2011 Submitted to the Department of Mechanical Engineering in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2015 L.te 2\50 0 2015 Massachusetts Institute of Technology All rights reserved Signature of Author: ....................................................... Certified by: .................................................................. ARCHIVES MASSACHUSF-TTS 1NTIT[TE OF TECHNOLOLGY JUL 302015 LIBRARIES Signature redacted Department of Mechanical Engineering Mayt2 Signature redacted Steven Djbowsky Professor of Aeronautics and Astronautics & Mechanical Engineering Thesis Supervisor Signature redacted Accep ted by : ........................................................ .. ....... ----------------------------- David E. Hardt Professor of Mechanical Engineering Chairman, Committee on Graduate Studies
152
Embed
Model based prognostic maintenance as applied to small scale ...
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Model Based Prognostic Maintenance as Applied to Small ScalePVRO Systems for Remote Communities
by
Leah C. Kelley
Bachelor of Fine Arts, DanceThe Boston Conservatory, 1998
Bachelor of Engineering, Mechanical EngineeringCity College of New York, 2009
Master of Science, Mechanical EngineeringMassachusetts Institute of Technology, 2011
Submitted to the Department of Mechanical Engineeringin Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May 2015 L.te 2\50
0 2015 Massachusetts Institute of TechnologyAll rights reserved
Signature of Author: .......................................................
Signature redactedDepartment of Mechanical Engineering
Mayt2
Signature redactedSteven Djbowsky
Professor of Aeronautics and Astronautics & Mechanical EngineeringThesis Supervisor
Signature redactedA ccep ted b y : ........................................................ .. .. ..... -----------------------------
David E. HardtProfessor of Mechanical Engineering
Chairman, Committee on Graduate Studies
Model Based Prognostic Maintenance as Applied to Small Scale PVROSystems for Remote Communities
by
Leah C. Kelley
Submitted to the Department of Mechanical EngineeringMay 26, 2015 in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy inMechanical Engineering
ABSTRACT
Many systems degrade as functions of their operation and require maintenance to extendtheir productivity. When operating under steady conditions, prescheduled maintenance can beused to ensure such systems meet their required levels of productivity at lowest cost. However,using pre-scheduled maintenance on systems that degrade as functions of their operation underuncertain, varying conditions will not guarantee that they meet their productivity at lowest cost.They require maintenance schedules that accommodate changes in their operating conditions anddegradation. This research develops a prognostic maintenance methodology that ensures asystem degrading with its operation under variable, uncertain operating conditions meets itsdesired productivity at the lowest cost.
An example of a degrading system under variable, uncertain operating conditions is aphotovoltaic-powered reverse osmosis (PVRO) desalination system. PVRO desalination canprovide drinking water to remote communities in sunny areas with saline water sources. Suchsystems produce clean water and degrade as functions of their operating conditions, includingsolar radiation, water chemistry and community demand. These conditions are not constant, butvary stochastically. Maintenance (system flushing and cleaning) will extend a PVRO system'sproductivity, but requires time, chemicals and use of the clean product water. Hence, it has asubstantial impact on the total cost of water production and should be adjusted in response tovariations in operation. The community members who generally operate and maintain PVROsystems do not have the training or experience to determine the best type and timing ofmaintenance to ensure their water demand is met at lowest cost, and require a method to do so.
Here, prognostic maintenance methodology is developed and applied to community-scalePVRO desalination. Degradation (fouling) and remediation (cleaning) of the RO membranehave the largest impact on the system productivity and water cost, and hence are the focus of thisstudy. Fouling and cleaning are complex functions of water chemistry and system operation.Physics-based mathematical models of fouling and cleaning rely on two critical unknownparameters: fouling rate and cleaning effectiveness. They can be determined using systemidentification methods in real time, using measurements of the PVRO feed water pressure andclean water production rates. The identified fouling and cleaning models are combined with
3
statistical models of the expected future PV power and community water demand to predict thetype and timing of future maintenance procedures. The maintenance protocols are adjusted inreal time in response to changes in identified fouling. The prognostic algorithm developed hereis suitable for implementation on a PVRO system's embedded microcontroller.
Case studies presented here show that the prognostic maintenance methodology providesnon-expert operators with near optimal maintenance protocols when compared with conventionalperiodic scheduling, especially under varying degradation, solar radiation and demand. In thisexample study, annual maintenance happens to be nearly optimal, so the prognostic maintenancealgorithm produces a nearly annual cleaning schedule that minimizes maintenance costs. Sincethe statistical nature of this example prevents demand from being met 100% of the time, theprognostic maintenance method is used to minimize cost and water loss. On average, followingthe prognostic maintenance protocol results in less than 4% loss of water over a 5-year period atlowest cost.
Although developed in the domain of PVRO, the prognostic maintenance methodologydeveloped here is anticipated to be applicable to other systems that degrade as functions of theiroperation, including machine systems, vehicle fleets and transportation networks.
Thesis Supervisor: Steven DubowskyTitle: Professor of Aeronautics and Astronautics & Mechanical Engineering
4
ACKNOWLEDGEMENTS
I thank my advisor, Steven Dubowsky, for his guidance, support, advice and patience over thepast six years. I also thank my committee members, Professors Kamal Youcef-Toumi andOlivier L. de Weck, for their guidance, advice and encouragement.
I especially thank Amy Bilton and Huda Elasaad for their friendship, technical help and advice,ranging from developing the Matlab code for clear-sky solar radiation calculations to discussionsof physical process modeling and water quality requirements, their willingness to listen to ideasand their boundless generosity. It has been my great pleasure to assist them and ProfessorDubowsky with the implementation of the community-size PVRO system in La Mancalona,Mexico, in spite of all the insects and frogs we encountered while there. I also thank the manyother members of the Field and Space Robotics Laboratory over the past six years for theirfriendship and support, and especially our administrative assistant, Irina Gaziyeva. I thank themany friends I've made at MIT for their support and encouragement, including NevanHanumara, Folkers Rojas and others in the Precision Engineering Research Group, friends andfaculty in the Department of Mechanical Engineering, and friends from the MIT Ballroom DanceTeam and community.
I thank the Department of Defense SMART Scholarship for Service Program for its financialsupport of my PhD studies. I also acknowledge my sponsoring facility, SPAWAR SystemsCenter Pacific. I thank the W.K. Kellogg Foundation and the Fondo Para la Paz for theirfinancial support of the PVRO system installed in La Mancalona, Mexico.
Finally, I thank my family for their love, support and encouragement.
A CK N O W LED G EM ENTS ...................................................................................................... 5
CO N TEN TS................................................................................................................................... 7
FIG U R ES..................................................................................................................................... 11
TA BLES....................................................................................................................................... 13
N O M EN CLA TU RE.................................................................................................................... 15
1. IN TR O D U CTIO N ................................................................................................................... 19
1.1 M OTIVATION ................................................................................................................. 19
1.1.1 System D egradation.................................................................................................. 191.1.2 Photovoltaic Pow ered Reverse O sm osis............................................................... 22
1.2 PROBLEM STATEMENT AND A PPROACH ..................................................................... 27
2.3.1.1 Concentration Polarization and M ineral Scaling ........................................... 432.3.1.2 Colloidal Fouling .......................................................................................... 452.3.1.3 Biofouling ...................................................................................................... 462.3.1.4 Effects of Fouling on RO W ater Production.................................................. 48
2.3.2 M odels of RO Fouling in the Literature ............................................................... 482.3.3 Fouling M itigation ................................................................................................. 50
2.3.3.1 Pretreatm ent.................................................................................................... 512.3.3.2 M echanical Cleaning ..................................................................................... 522.3.3.3 Chem ical Cleaning ........................................................................................ 542.3.3.4 RO M em brane M aintenance .......................................................................... 57
3. PVRO PERFORMANCE, DEGRADATION AND REMEDIATION MODELING ... 65
3.1 RO W ATER PRODUCTION ............................................................................................ 65
7
3.2 RO D EGRADATION ..................................................................................................... 703.3 RO M EM BRANE REMEDIATION................................................................................... 71
3.3.1 System Flushing........................................................................................................ 723.3.2 Chem ical Cleaning.................................................................................................. 73
3.4 REPRESENTATIVE DEGRADATION AND REMEDIATION EXAMPLE ................................ 74
3.5 SUM M ARY...................................................................................................................... 78
4. DETERMINISTIC MAINTENANCE STUDY ............................................................... 81
4.1 PROBLEM STATEMENT ................................................................................................ 81
4.1.1 W ater Production w ith M aintenance ...................................................................... 82
4.1.2 The Optim ization ................................................................................................... 82
4.2 REPRESENTATIVE PV RO SYSTEM M ODEL.................................................................. 84
4.3 RESULTS ........................................................................................................................ 864.3.1 N om inal Case............................................................................................................ 864.3.2 Sensitivity Study ................................................................................................... 88
4.4 SUM M ARY...................................................................................................................... 90
5. PARAMETER IDENTIFICATION AND FORECASTING ............................................. 93
6.4.3 Fixed Fouling Rate Parameter, Varying Water Demand Results ........................... 1266.4.4 Varying Fouling Rate Parameter and Varying Water Demand Results ................. 129
6 .5 S U M M A R Y.................................................................................................................... 132
7. SUMMARY AND CONCLUSIONS................................................................................... 135
7 .1 S U M M A R Y .................................................................................................................... 13 5
7.2 SUGGESTIONS FOR FUTURE WORK............................................................................... 136
7.2.1 Future R efinem ents................................................................................................. 1367.2.2 Applications to Other Domains .............................................................................. 138
APPENDIX A: RELATING SOLAR POWER TO FEED WATER PRESSURE............. 149
9
10
FIGURES
Figure 1.1: Pre-scheduled preventative maintenance: an open-loop system ............................. 19
Figure 1.2: Condition-based maintenance: a type of feedback system...................................... 21
Figure 1.3: Populations using improved drinking water sources............................................... 23
Figure 1.4: Areas with high water stress and over-exploitation of local water sources ........... 24
Figure 1.5: Annual average daily clear sky solar insolation at ground level............................ 24
Figure 1.6: A representative PVRO system ............................................................................... 25
Figure 1.7: Block diagram representation of prognostic maintenance strategy........................ 28
Figure 2.1: Cross-section of RO spiral-wound membrane; axial feed and brine flow into the page........................................................................................................................................... 3 9
Figure 2.2: Detailed view from Figure 2.1, rotated so feed flows from left to right ................ 39
Figure 2.4: Mineral scaling on a reverse osmosis membrane .................................................... 44
Figure 2.5: Colloidal fouling on an RO membrane surface...................................................... 46
Figure 2.6: Biofouling on an RO membrane surface............................................................... 47
Figure 2.7: Loosely deposited particles removed by system flushing ...................................... 53
Figure 3.1: Clean water desalination through an RO membrane............................................... 66
Figure 3.2: Short term permeate flow rate with and without system flushing........................... 75
Figure 3.3: Longer term permeate flow rate with and without system flushing........................ 76
Figure 3.4: Longer term permeate flow rate with and without chemical cleaning .................... 76
Figure 3.5: Permeate flow rate decline with and without maintenance .................................... 77
Figure 4.1: M aintenance optim ization structure ........................................................................ 83
Figure 4.2: Daily water production under optimized maintenance, compared with productionunder no maintenance and under daily flushing alone.................................................. 87
Figure 4.3: Daily water production under lower fouling rate ................................................... 89
Figure 4.4: Daily water production under high fouling rate ...................................................... 90
Figure 5.1: Measured, identified and predicted RO membrane permeability (left) and % error inpredicted permeability (right) from the brackish water RO pilot plant in Brownsville, TX........................................................................................................................................... 9 7
Figure 5.2: Measured, identified and predicted RO permeate flow rate (left), and % errorbetween predicted and measured permeate flow rates (right), for the Brownsville ROp lan t................................................................................................................................... 9 8
11
Figure 5.3: Measured and predicted RO permeate flow rate (left), and % error between predictedand measured permeate flow rates after identification (right), for La Verne, CA, RO plant......................................................................................................................................... 10 0
Figure 5.4: Solar radiation scale factor as a function of cloud fraction...................................... 103
Figure 5.5: Forecasting water production and RO membrane degradation using cloud statistics......................................................................................................................................... 1 0 4
Figure 5.6: Average monthly salinity in Mediterranean Sea near Limassol, Cyprus................. 105
Figure 6.4: Histograms of water loss percentage with optimal fixed maintenance (A) andseasonal m aintenance (B ) ............................................................................................... 122
Figure 6.5: Histograms of water loss percentage with aggressive (C) and sparse maintenance (D)......................................................................................................................................... 12 2
Figure 6.6: Histograms of water loss percentage with adjusted prognostic (E) and sparsemaintenance (F) under varying fouling rate parameter and fixed demand..................... 126
Figure 6.7: Histograms of water loss percentage with prognostic (G) and seasonally adjustedprognostic maintenance (H), under fixed fouling rate parameter and varying demand. 127
Figure 6.8: Histogram of water loss percentage with sparse maintenance (I)............................ 128
Figure 6.9: Histograms of water loss percentage with adjusted prognostic (J) and sparsemaintenance (K), under varying fouling rate parameter and varying water demand ..... 131
Figure A. 1: RO pressure vessel as a fluid resistance network.................................................... 150
12
TABLES
Table 3.1: RO fouling and remediation example parameters ................................................... 74
Table 4.1: Representative 1,000 L/day brackish water PVRO system parameters .................. 84
Table 4.2: System flushing and chemical cleaning parameters ................................................. 86
Table 4.3: Sensitivity study maintenance optimization results.................................................. 88
Table 5.1: Measurements available from pilot RO plant in Brownsville, TX........................... 96
Table 5.2: Measurements from the Metropolitan Water District pilot RO plant....................... 99
Table 5.3: Estimated cleaning effectiveness from measured data.............................................. 101
Table 5.4: Cloud cover conditional probabilities for La Mancalona, Mexico............................ 103
Table 6.1: Representative brackish water PVRO system parameters......................................... 111
Table 6.2: Chemical and water requirements for a single chemical cleaning ............................ 112
Table 6.3: RO m em brane and chem ical costs............................................................................. 112
Table 6.4: M aintenance process param eters ............................................................................... 113
colloids), 4) microorganisms and 5) metallic oxides. They recommend that the chemical
cleaning process be structured such that it prioritizes removal of foulants according to the
hierarchy. Cleaning guidelines available from membrane manufacturers now follow the cleaning
process order presented in [86].
The cleaning effectiveness studies cited above investigate single instances of cleaning
and do not address the long-term effects of cleaning over time. The effects of long-term cleaning
(e.g., on RO membrane useful life) have not been thoroughly studied. Chemical cleaning cannot
perfectly restore the RO membrane to its original condition. Though all of the foulants may be
removed during the chemical cleaning, the foulants also cause irreversible damage, such as
surface abrasions. One optimal design study on seawater reverse osmosis systems presents a
model to capture the decline in the RO membrane permeabilities to water and salt, considering
imperfect cleaning and RO membrane replacement [88]. In this model, membrane permeability
decays exponentially. Chemical cleaning partially restores permeability; permeability is only
fully restored when the membrane is replaced. Similarly to other models in the literature, the
model presented in [88] depends on experimentally determined parameters.
After several years of operation, an RO membrane wears out due to compaction from the
high pressure feed water, from irreversible fouling, and from general deterioration. Membrane
life depends on the feed water chemistry, with lifetimes of 2-5 years typically given in the
literature, based on operator experience [28].
Chapter 2. Background and Literature Review 56Chapter 2. Background and Literature Review 56
2.3.3.4 RO Membrane Maintenance
Historically, RO plants have been maintained using conventional periodic maintenance
[11, 28, 89]. System pretreatment and maintenance procedures, including the specifics of
flushing and chemical cleaning flow rates, durations, frequencies and chemicals, are determined
by analyzing the feed water chemistry at the intended plant site during several times of the year,
prior to plant construction. The water chemistry analysis includes details of the chemical species
present and the type of biological content. The concentrations of chemical species, such as
calcium, soluble silica, barium and strontium, can be used to determine whether or not mineral
scaling is likely. The likelihood of mineral scaling can also be determined by calculating the
Langlier Saturation Index (LSI) or the Stiff-Davis Saturation Index (SDSI) of the water [28].
Both indices uses the pH and temperature of the water in addition to the concentration of total
dissolved solids (TDS), calcium hardness and alkalinity to quantify the scaling and corrosive
tendencies of the water. A positive LSI or SDSI indicates calcium carbonate scaling is likely. A
negative LSI indicates the water is corrosive and may dissolve scale. An LSI of 0 indicates the
water is chemically balanced. The LSI is used for water with TDS of up to 4,000 ppm, and is
only appropriate for low-level brackish water. The SDSI is used for water with higher TDS
concentration, including seawater.
The concentrations of metals, including iron, manganese and aluminum, along with
concentrations of hydrogen sulfide and total organic carbon (TOC), can be used to estimate
colloidal and organic fouling potentials [28]. Color, measured in color units, and water turbidity,
measured in Nephelometric Turbidity Units (NTU), are additional indicators of the fouling
potential of feed water. Industry guidelines recommend feed water have color less than 3 APHA
and turbidity less than 1 NTU. Particulate fouling potential is also measured using the Silt
Density Index (SDI). The SDI is calculated from a standardized test in which the water being
Chapter 2. Background and Literature Review 57
analyzed flows through a 0.45 micron filter pad at 30 psi. The time it takes for 500 ml of water
to flow through the filter pad is recorded initially. After 15 minutes of flow through the pad at
30 psi, an additional 500 ml of water is collected and its time is recorded. The SDI is calculated
from these measurements. An SDI above 3 indicates higher fouling potential. The SDI test can
also be performed once the RO plant has been constructed and the pretreatment system is in
place. The Modified Fouling Index (MFI) is an extension of the SDI and is also used to
determine fouling potential [90].
Additional indices for fouling potential have been developed [11, 91-94]. Estimates of
fouling potential based on RO system performance data are defined in [91, 92]. One method
tracks the change in RO membrane permeability over time and plots the volumetric clean water
production versus the ratio of current membrane permeability to starting membrane permeability
[91]. This method can be used to determine how much the system water production is affected
by the types of foulants, but doesn't provide information on how fast the ratio declines. Another
method defines a filtration coefficient that is essentially a lumped parameter of the bulk
membrane permeability of the entire RO plant, and calculates its value [92]. By calculating this
value over time, the level of fouling is determined. Molar species have also been used to
develop water fouling classifications [93, 94].
Assimilable organic carbon (AOC) measures the growth potential of microorganisms in a
water sample [28]. This can be used as an indication of the likelihood of biofouling before plant
operation. Analysis of the concentrate (brine) water stream in an RO plant can be used to
determine whether or not biofouling has occurred. Typical analysis methods are growing
cultures from the reject stream, or obtaining a total bacterial count (TBC) from a filter through
which the RO concentrate flows.
Chapter 2. Background and Literature Review 58
The above indices are measured before plant operation takes place. Although such
indices can be used to determine the types of chemicals needed for cleaning the RO membranes,
cleaning frequency and duration will need to be adjusted during plant operation.
In addition to water quality testing, a pilot plant may be constructed and operated for
several months to a year before construction of a large RO plant begins [28]. During pilot plant
operation, flushing and chemical cleaning processes determined from water quality testing can
be refined and optimized empirically. RO membranes from the pilot plant can also be autopsied
to determine the types of fouling present in the pilot system. For a large-scale RO project,
incurring such costs may be considered trivial. However, pilot plant construction and testing is
prohibitively expensive and impractical for small, community-size projects.
Optimization of periodic maintenance has been performed for RO plants during the
design stage, assuming that fouling is exponential and that regeneration is perfect after
maintenance [95-97]. Optimization of an RO system fluid network is performed in terms of total
cost and maintenance schedule, assuming perfect regeneration, in [95]. Flexible fluid RO
networks able to accommodate a given range of feed water and system performance variations
are optimized in terms of lowest annual cost, considering fouling and maintenance, in [96].
Optimization of the operation of an RO plant with a given set of membranes in terms of
minimizing its specific energy consumption and annual operating cost is performed in [97].
These studies are applied to large RO plants and do not assume large variations in operating
conditions.
Condition-based maintenance is also used in RO plants [28]. The performance metrics
for RO are the permeate flow rate and pressure drop from feed inlet to brine outlet.
Measurements are normalized to account for temperature, pressure and salinity variations, and
Chapter 2. Background and Literature Review 59
are compared with normalized plant measurements taken at either plant startup or when new RO
membranes are installed. RO process experts and manufacturer maintenance guidelines
consistently recommend that RO membranes be cleaned when the normalized permeate flow rate
drops by 10%, or when the normalized pressure drop along the RO pressure vessel increases by
15% [28, 29, 81]. Maintenance chemical suppliers and RO membrane manufacturers sell
software-based condition monitoring systems that perform the normalization calculations from
plant operating data, and that notify operators when chemical cleaning is needed. CBM is a
reasonable method of maintaining a large RO plant with staff available on hand to perform
maintenance as required, but is not suitable for remote, community-size PVRO plants. Small
PVRO plants will not have the expert staff available to perform maintenance quickly. Also,
simply defining suitable CBM metrics for a PVRO plant that operates over wide pressure and
flow ranges is challenging. It is not appropriate to use the normalized pressure drop and water
production rates, since the variability in operation may trigger maintenance when it is not yet
required.
Prognostic maintenance has been applied to RO plants. Neural network approaches have
been used to develop short-term forecasting models of RO performance [98, 99]. An approach
using radial basis functions has been used to predict performance over a two hour period based
on "transmembrane pressure, ionic strength, solution pH, particle size and elapsed filtration time
[98]." Note that this is a very short period with respect to RO membrane fouling. A neural
network approach for predicting the short term performance (i.e. the next 24 hours) of an RO
plant subject to fouling has been developed from experimental data [99]. Risk modeling and
model predictive control have been combined to determine RO plant operation that will
minimize risks [100]. The model predictive controller determines the timing of risk-mitigating
Chapter 2. Background and Literature Review 60
actions. This method has been tested in simulation. Fault detection and isolation (FDI) and fault
tolerant control (FTC) have been applied to a high recovery RO plant in simulation [101]. In this
work, the redundancy in the structure of the RO plant permits multiple flow pathways, which is
necessary for FTC. Fault tolerant control has been applied to a small-scale laboratory RO
system; however, this system treats municipal tap water, so faults resulting from fouling/scaling
are not addressed [102]. This small laboratory system also includes a reconfigurable network of
reverse osmosis pressure vessels and membranes. Implementing redundancy in community-
sized PVRO plants adds capital costs and may not be economically viable, so such an approach
is not necessarily applicable. A prognostic maintenance method for PVRO systems that will
ensure they meet their community demands at lowest cost has yet to be developed. The
development of a prognostic maintenance method is the focus of this thesis.
2.4 Summary
Prognostic health monitoring (PHM) and maintenance is an active area of research. Early
research in diagnostics of machine health led to the development of condition-based maintenance
(CBM), which has now been widely adopted in industry. CBM improves on pre-determined
periodic maintenance so that preventative maintenance is not performed when it isn't needed.
Efforts to improve CBM so that preventative maintenance can be scheduled in advance have led
to predictive condition-based maintenance and prognostic maintenance (PHM). The methods
described in the literature predict the remaining useful life of components and schedule the next
immediate maintenance action, but do not produce sequences of maintenance actions and
determine the time between them. Though sufficient for applications in which dedicated, onsite
operators with specialized knowledge are present, a prognostic method that provides non-expert
Chapter 2. Background and Literature Review 61Chapter 2. Background and Literature Review 61
operators with a sequence of maintenance actions and their timing while accounting for highly
variable and uncertain operating conditions and degradation has yet to be developed.
PVRO desalination is a representative application requiring model-based prognostic
maintenance. An RO membrane's degradation is caused by fouling, which is a complex function
of RO system operation. It is dependent on water chemistry, operating pressure and water flow
rates. When part of a PVRO system, water desalination through the RO membrane becomes a
complex function of the solar energy driving the RO process, so its degradation is even more
complex and uncertain. A PVRO system is also operated by community members who do not
have the expert knowledge to determine the maintenance strategy that will ensure community
water demand is met at the lowest cost. Following recommended maintenance guidelines from
RO membrane manufacturers will not necessarily guarantee PVRO systems meet their demand,
or may not ensure that demand is met at the lowest cost. Similarly, CBM for PVRO may also
not ensure demand is met at the lowest cost, and is also difficult to implement for PVRO systems
operating over wide power ranges.
In this research, a model-based prognostic maintenance algorithm for community sized
PVRO systems, subject to highly varying, uncertain and stochastic operating conditions is
developed. It uses probabilistic methods to handle uncertainties in future inputs, such as
incoming solar radiation and water demand. Prognostic maintenance also requires models of RO
membrane fouling and remediation. The physics of various types of RO membrane fouling have
been studied and mathematical models that describe the effects of fouling over time have been
developed. The models range from simple empirically derived models that describe the decline
in water flow, to extensive two and three dimensional models that require intensive computation.
Simple empirical models are valid for the systems from which their underlying data was sourced.
Chapter 2. Background and Literature Review 62
Even the extensive models rely on empirically derived parameters. A simple, yet valid, physics-
based model of RO fouling that can be used for prognostics is needed, and is developed here.
Chapter 2. Background and Literature Review 63Chapter 2. Background and Literature Review 63
Chapter 2. Background and Literature Review 64
CHAPTER
3PVRO PERFORMANCE, DEGRADATION AND
REMEDIATION MODELING
The development of a prognostic maintenance algorithm requires an understanding of the
physics of system degradation and remediation. The previous chapter presents the physics of RO
water production and membrane fouling, including mineral scaling, colloidal fouling and
biofouling. In this chapter, mathematical models that describe the clean water production,
degradation (fouling) and remediation of the RO membrane are presented. The degradation
model is a simplification of the cake growth model found in [72]. The simple remediation
models presented here are unique to this work. These models will be used to predict PVRO
system performance when subject to fouling.
3.1 RO Water Production
The reverse osmosis process is a function of the RO membrane permeability, osmotic
pressure and the feed water pressure. A schematic showing the flow of clean water across an RO
membrane is shown in Figure 3.1. The well-known solution-diffusion model describes the clean
water (permeate) flow rate through the RO membrane, q, (t), (L/s), [103, 104]:
e(3.1)
where-
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 65
P (t) is the average hydraulic pressure (bar)
i (t) is the average osmotic pressure (bar)
K (t) is the membrane permeability to water (L/m2/bar/s)
A,, is the area of the membrane (m2).
RO Membrane AM,K(t)
Feed Feed (Permeate
qf, p, Cf (Clean water)
Concentrate q,, p,,C
(Brine)
q b Pb , Cb
Figure 3.1: Clean water desalination through an RO membrane
The water produced by the RO system over a period of time, Q,, is found by integrating
Equation Error! Reference source not found.:
tF tF
QP = qP(t~dt = Am f K (t)[(t t- 17(t})dtis is (3.2)
where ts and tF are the starting and ending times of the period, respectively. Equation (3.2) can
be solved if the permeability and pressures are known functions of time.
The RO membrane permeability increases with temperature. Membrane manufacturers
provide temperature correction factors in tabular form for use when normalizing flow rates for
CBM [105, 106]. Permeate flow is typically normalized to 25 'C. RO membrane permeability
can also be normalized using the temperature correction factor:
K,t Q) = TFC (T. ) K (t) (33
where
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 66
TFC is the temperature correction factor,
T, is the water temperature inside the RO pressure vessel ('C) and
K, (t) is the normalized membrane permeability at time t.
The average hydraulic pressure is a function of the feed water pressure at the RO inlet,
axial pressure drop along the RO membrane from the feed water inlet to the brine water outlet,
and the pressure of the permeate water on the opposite side of the membrane. The upper limit on
the pressure drop for a single RO membrane element is 1 bar, according to RO membrane
manufacturer data [107]. Since the community-sized PVRO systems considered in this work are
assumed to consist of pressure vessels containing one or two RO membranes each, the average
pressure on the feed water side of the RO membranes can be calculated using:
p- -t ()+ b=t -p(W2 (3.4)
where
pf (t) is the feed water pressure at the RO inlet (bar),
Pb (t) is the pressure of the concentrate (brine) water (bar), and
p, (t) is the pressure of the permeate (clean) water (bar).
These parameters are shown in Figure 3.1. The pressure drop over a single membrane element in
a small PVRO system was measured and found to be on the order of 0.1 bar [25]. For very small
RO systems, such as those containing a single RO membrane in a single vessel, it can be
assumed that the permeate water exits the RO pressure vessel at approximately atmospheric
pressure. Also, the average water pressure on the feed water side of the single RO membrane
can be assumed to be the feed water inlet pressure, p1 (t).
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 67
The osmotic pressure of water depends on its composition and temperature. An
approximate empirical relationship for osmotic pressure of saline water, r,, as a function of the
concentration of total dissolved solids and temperature is [103]:
/7 (2.654 x 10-) C, (T, +273.15)
1000 - / (3.5)
where
C, is the concentration of total dissolved solids (TDS) in ppm and
T, is the water temperature ('C).
Note that the constants in Equation (3.5) have units that are not shown.
The average osmotic pressure will depend on the concentrations of salt in the feed,
concentrate and permeate, as well as the effect of concentration polarization at the RO membrane
surface. The following equation can be used for a single RO membrane element [103]:
C~f (t)jgC( = ,z ( C~t)W]Pf (3.6)
where
/ 7f (t) is the osmotic pressure of the feed water (bar),
Cf (t) is the arithmetic average of the feed and concentrate salt concentrations (ppm),
Cf (t) is the feed salt concentration (ppm),
7t, (t) is the osmotic pressure of the permeate water (bar), and
pf is the concentration polarization factor (dimensionless).
The concentration polarization for a single RO element can be found using an empirical
relationship [103]:
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 68
pf = exp 0.7 qP (t)q (t)) (3.7)
where q, (t) is feed water flow rate (L/s). The ratio of permeate flow to feed water flow is
called the recovery ratio.
In a PVRO system, the feed water pressure at the RO pressure vessel inlet will depend on
the amount of sunlight that is converted to electrical energy by the solar panels. The electricity
produced by the solar panel, P,,,,, for a given level of solar radiation can be calculated using
[108]:
Peec (t) = qI(t)A ., (3.8)
where
I(t) is the instantaneous solar radiation (W/m 2),
A,, is the area of the solar panels (M2), and
q is the solar to electrical conversion efficiency of the solar panels. This efficiency is
temperature dependent. Improving the efficiencyof a community-size PVRO system by cooling
the solar panels with the incoming feed water has been studied [108, 109].
The RO inlet pressure also depends on the efficiency of the maximum power point
tracker, if included, the efficiencies of the pumps, fluid inertia, the hydraulic resistances of the
pretreatment components, and the hydraulic resistance of the concentrate exit of the pressure
vessel. The topology of a PVRO system must be known in order to correctly model the
individual motors, pumps, filters, etc. Steady-state, physics-based models of the individual
components of a PVRO system, including the different types of motors, pumps, and energy
recovery devices, have been developed and presented in [26]. Components such as electrical
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 69
motors have extremely fast dynamics relative to the RO fouling process, so steady-state models
of such components can be used when predicting long-term RO performance and fouling. Once
a PVRO system topology is established, the appropriate physics-based models and numerical
values for their parameters can be incorporated into a full system description. Measurements of
the PVRO system and component performance may need to be recorded in order to calibrate the
system models. For example, the initial RO membrane permeability can be determined from
pressure, flow, salinity and temperature measurements.
3.2 RO Degradation
As discussed in Chapter 2, RO membranes may be fouled by colloids, mineral scales and
biological colonies (biofilms). The underlying physical method of both colloidal fouling and
mineral scaling is accumulation of material on the RO membrane surface through deposition of
particles or minerals by the transmembrane flow. Even though the axial fluid velocity sweeps
some of the particles away from the RO membrane surface, there is a net deposition of particles
over time. This layer of foulant decreases the flow of clean water through the membrane. In
general, this fouling layer is not uniform. In small RO systems consisting of one or two RO
membranes within a pressure vessel, it is assumed that the variations in the fouling layer are
small, so a lumped parameter approach is justified. Using this idea, the decrease in RO
membrane permeability, dK ) , is assumed to be proportional to the transmembrane velocitydt
through it:
dK(t) = m q(3dt A, (3.9)
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 70
where y is a fouling rate that represents the net deposition of particles and minerals (one/bar/s).
This approach is motivated by the modeling methods in [72, 92], where membrane resistance and
the filtration coefficient are proportional to the cake layer growth. Note that the fouling rate is
not necessarily assumed constant. It will depend on the water chemistry and on the
hydrodynamics.
Substituting Equations (3.1) and (3.3) into (3.9) describes the change in membrane
permeability as a function of the current membrane state and water pressure:
dK, (t) -dt (3.10)
Biofouling physics are more complex than those of colloidal fouling and mineral scaling,
since, in addition to deposition, bacteria grow into colonies and occasionally detach from the
membrane surface to form new colonies downstream. This can cause a time-dependent fouling
rate y(t). However, for the PVRO application here, it is assumed that UV disinfection
pretreatment effectively eliminates the biofouling risk. Hence, biofouling is considered
negligible here. For other RO applications where the risk of biofouling is higher, a more
complex fouling model that includes the growth and detachment effects can be developed and
incorporated into the prognostic model formulation.
3.3 RO Membrane Remediation
The decrease in RO membrane permeability with fouling in an RO system with
pretreatment happens slowly, on the order of weeks or months, depending on the water
chemistry. Maintenance processes occur much more quickly - on the order of minutes or hours.
When considering system performance over a membrane lifetime, maintenance processes can be
approximated using delta functions [110]. System flushing and chemical cleaning are two
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 71
maintenance procedures that are likely to be used to maintain a PVRO system, and they are
modeled below.
3.3.1 System Flushing
As discussed in Chapter 2, system flushing takes place on the order of minutes and
requires approximately 7% of the total permeate water produced during a day [80]. The increase
in membrane permeability due to flushing will depend on the flushing water flow rate. A simple
model describes this change during flushing:
dK,(t)
dt (3.11)
where
g, is a proportionality constant (one/bar/m2/s), and
q, is the flushing water flow rate (L/s).
Since flushing happens on the order of minutes, Equation (3.11) can be written as:
dK" ( gfqfAtf (t -tf Gg t -t [,(dt (3.12)
where
At, is the duration of the flushing cycle, and
Gf is the increase in RO membrane permeability due to one flushing cycle (L/bar/m 2/s 2).
Again, this will be system-dependent. It will also not be known a priori, and will need to be
identified during system operation.
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 72
3.3.2 Chemical Cleaning
Chemical cleaning is a much more complex process than simple flushing, and takes
several hours. This is still a rapid process compared with the rate of change in RO membrane
permeability due to fouling. Again, a delta function is used to describe the increase in RO
membrane permeability due to a chemical cleaning process:
dK, (t)
dt ((3.13)
where G, is the increase in RO membrane permeability due to a chemical cleaning cycle. This
proportionality constant will depend on the specifics of the chemical cleaning cycle, such as the
duration, flow rates during recirculation and flushing, order of chemical application, types of
foulants, etc. This parameter may also depend on the number of cleaning cycles. As with the
increase in RO membrane permeability with system flushing, G,,, the increase in RO membrane
permeability due to cleaning will also need to be identified from the system performance during
its operation.
Neither the system flush nor the chemical cleaning will result in total restoration of the
RO membrane permeability. In general, chemical cleaning will provide greater increases in
permeability, since it can remove more types of foulants. Both models rely on proportionality
constants that will not be known prior to performing maintenance. As a rough estimate,
experimental results from the literature suggest chemical cleaning followed by system flushing
can restore up to 97% of the RO membrane's permeability [80]. Though the same group of
experiments found that flushing alone can restore the RO membrane permeability by 90%, this
was limited to short-term colloidal fouling. These percentages will vary by system.
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 73
3.4 Representative Degradation and Remediation Example
A representative example presents the behaviors of the above models. The operating and
initial conditions are presented in Table 3.1. It is assumed that the RO system operates for 12
hours per day and must produce 1,000 Liters each day.
Table 3.1: RO fouling and remediation example parameters [11, 71]Parameter Value
Feed pressure pf 18 bar
Feed salinity C/ 20,000 ppm
Feed temperature Tf 25 OC
Osmotic pressure ii> 11.64 bar
Initial RO membrane permeability K 4.62 x 10-4 L/bar/m 2/s
Active Area A, 7.2406 m 2
Fouling rate y 3.4614 x 10-9 one/bar/s
Minimum permeate flow rate 0.0231 L/s
System flush flow rate g, 0.57 L/s
Flushing duration Az> 5 minutes
Membrane improvement after flushing G 1 x 10- L/bar/m 2/s
Chemical cleaning water demand 7,000 L
Membrane improvement after flushing Gc( ( 4 x 10-4 L/bar/m 2/s
Table 3.1 also gives the assumed system flushing and chemical cleaning process
parameters. These values are based on experimental results from [80]. Maintenance cannot
increase the RO membrane permeability beyond its initial permeability. Therefore, in this
example, if the membrane has not degraded much and maintenance is applied, it is assumed to
restore the membrane permeability to its initial value.
RO performance under constant degradation was calculated over three years of operation
using Equations (3.1), (3.10), (3.12) and (3.13). Four cases are considered: no maintenance,
daily system flushing, monthly chemical cleaning, and daily system flushing combined with
monthly chemical cleaning.
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 74
RO permeate volumetric flow rate over the first 11 days is plotted in Figure 3.2 to
compare the short-term effects of system flushing with doing no maintenance. The small
increases in RO membrane permeability from the flushing are visible in the increases in
permeate flow rate immediately following flushing. Though not huge, the daily restoration from
daily flushing results in a slower net permeate flow rate decline.
0.0615
0.061 -With daily system flushing
. 0.0605
Cz 0.06-
0 0.0595
S0.059-
S Without system flushing
0.0580.058- -
0.05750 2 4 6 8 10 12
Operating time (days)
Figure 3.2: Short term permeate flow rate with and without system flushing
Figure 3.3 shows the permeate flow rate with and without system flushing over a longer
operating period. For this representative case, the permeate flow rate drops to 30% of its initial
value after 200 days of operation without any system flushing. After approximately 180 days,
this system can no longer maintain the required 0.0231 L/s flow rate to meet the required daily
water demand. With daily system flushing, permeate production drops to 60% of its initial value
after 200 days. From the long-term perspective, one can say that the net fouling rate is reduced
by daily flushing.
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 75
(U
40a)C)
0.07
0.06
0.05
0.04
0.03
0.02
0.0110 50 100 150 200 250
Operating time (days)
Figure 3.3: Longer term permeate flow rate with and without system flushing
Figure 3.4 compares longer term permeate flow rate with and without chemical cleaning.
In this example, the permeate flow rate drops to about 70% of its initial value after 200 operating
days when only chemical cleaning is performed monthly.
p..
U,
Figur 3.4:
0.07
0.06
0.05
0.04
0.03
0.02
I.I1I0 50 100 150 200
Operating time (days)
Longer term permeate flow rate with and without
250
chemical cleaning
Chapter 3. PVRO Performance, Degradation and Remediation Modeling
With daily system flushing
- Without maintenance
Minimum flow rate to meet demand
With monthly chemical cleaning
Without maintenance
Minimum flow rate to meet demand
76
Figure 3.5 shows the effectiveness of cleaning over three years. It is known that repeated
chemical cleaning can cause damage to the membrane surface, and that as the membrane ages
chemical cleaning becomes less effective [88]. In this example, membrane damage is not
considered, though cleaning effectiveness is limited.
0.07
0.06With daily system flushing and
0.05 - ' monthly chemical cleaning
0.04-
0.03 - Without maintenance
E0.02Minimum flow rate to meet demand
A- 0.01 -
01-0 200 400 600 800 1000 1200
Operating time (days)
Figure 3.5: Permeate flow rate decline with and without maintenance
In this simulation, the RO membrane becomes so fouled that after two years, clean water
barely flows through it. This makes sense physically for the following reasons. As the
membrane fouls, the concentration of salts at the membrane surface increases, driving the local
osmotic pressure up. To maintain permeate water flow at the pre-fouled rate, one would have to
increase the feed water pressure. Also, the increased concentration of sparingly soluble salts
increases the likelihood of salt precipitation and mineral scaling. Although a decrease in
permeate flow implies higher axial feed velocity if the feed volumetric flow remains the same,
the higher feed velocity may dislodge part of a colloidal layer but will not remove hard mineral
scale. A single element for small systems typically has a maximum permissible recovery ratio
between 12 and 15%, depending on the type of water being desalinated [111], so the increase in
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 77
feed water axial velocity may not be large. When completely fouled, little to no permeate water
will flow through the RO membrane, even if water still flows axially through the pressure vessel.
3.5 Summary
This chapter presents simple mathematical models that describe clean water flow rate
through an RO membrane, RO membrane water permeability decrease with fouling, and RO
membrane permeability increases with system flushing and chemical cleaning. Clean water flow
through the RO membrane is described using the well-known solution diffusion model. The
colloidal fouling and mineral scaling model assumes that the change in membrane permeability
is proportional to the transmembrane flow, and is thus a function of the RO membrane
permeability and applied water pressure. The fouling rate y encapsulates effects of water
chemistry and axial hydrodynamics, and so it will not necessarily be constant.
Maintenance processes are very fast with respect to membrane fouling, so are modeled
using delta functions that describe an impulse in foulant removal. This corresponds to a step-
change increase in RO membrane permeability. The magnitudes of the delta functions for each
type of maintenance are limited so that the membrane permeability after remediation cannot
exceed its permeability when new.
Also presented are simple models of the solar to electrical conversion of energy in a solar
panel, equations for osmotic pressure, concentration polarization, and average water pressure
within an RO pressure vessel.
The models are used to calculate the performance of an RO membrane under constant
pressure over three years under four scenarios: no maintenance, daily flushing, monthly chemical
cleaning, and combined daily flushing and monthly cleaning. The trends displayed in the
simulation results are similar to trends found in the literature for constant pressure systems [71,
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 78
74]. Daily system flushing essentially reduces the long term net fouling rate. Chemical cleaning
becomes less effective over time. The next chapter demonstrates how these models are
incorporated into a deterministic maintenance optimization.
Chapter 3. PVRO Performance, Degradation and Remediation Modeling 79
80Chapter 3. PVRO Performance, Degradation and Remediation Modeling
CHAPTER
4DETERMINISTIC MAINTENANCE STUDY
The models presented in Chapter 3 can be used in a prognostic maintenance algorithm. If
the solar radiation, water chemistry, temperature, water demand, etc., over an operating period
are known, determining the maintenance protocol that maximizes water production can be
formulated as a deterministic optimization problem. This optimization is the precursor to the
prognostic maintenance algorithm for systems with substantial variation and uncertainty in their
operating conditions, such as PVRO systems.
4.1 Problem Statement
The maintenance schedule that maximizes the clean water production over the lifetime of
a typical RO membrane for a community-sized PVRO plant under fixed demand is to be
determined. It is assumed that batteries for electrical energy storage are not included in the
example system, so it will operate at varying power levels as a function of the incident solar
radiation on the photovoltaic panels. Feed water pressure, water flow rates and fouling will vary
each day. Maintenance processes include system flushing and chemical cleaning. An automatic
system flushing loop can be incorporated into the PVRO topology. The community members are
assumed to be able to chemically clean the RO membranes with proper training. Also, since the
community members are not continuously monitoring their system, a periodic maintenance
Chapter 4. Deterministic Maintenance Study 81Chapter 4. Deterministic Maintenance Study 81
schedule is desired. In this case, only the chemical cleaning interval needs to be optimized, since
the optimization results show that daily system flushing is always required.
4.1.1 Water Production with Maintenance
The total water produced over a period of interest can be calculated using Equation (3.2).
However, both the system flushing and chemical cleaning processes require the use of some of
the product water. The net water produced by the system including the water used for cleaning
and the time the system is shut off can be calculated using:
Qnet = Am f K (t)[P(t)- rt)dt- NQf - MQ,,=1 (4.1)
where
Y is the number of periods of water production between maintenance processes,
(, is the starting time of the yth water production period,
tF,y is the ending time of the yth water production period,
N is the number of system flushes over the total time of interest,
Qf is the amount of permeate water used during a flushing process (L),
M is the number of chemical cleanings over the total time of interest, and
Q , is the amount of permeate water used during a chemical cleaning process (L).
Equation (4.1) accounts for the loss of productivity during cleaning and system flushing since it
adds the water production only when the RO system is operating.
4.1.2 The Optimization
The maintenance optimization problem can be stated:
Chapter 4. Deterministic Maintenance Study 82
Maximize QeN,M
subject to: Qd,,, QD, Equations (3.1),(3.3) --(3.8),(3.10),(3.12),(3.13) (4.2)
where
Qda, is the volume of permeate water produced in a day, and
QD is the daily volume of water needed by the community.
Figure 4.1 shows the structure of the optimization in block diagram form. A
meteorological model describing the solar radiation as a function of location and day of the year
is used to generate the daily clear-sky solar radiation.profile. The radiation profile and the water
chemistry are used to calculate water production and fouling over time using Equations (3.1),
(3.3) - (3.8), (3.10), (3.12) and (3.13), (the Fouling and Water Production Models in Figure 4.1),
along with a system dependent model that describes feed water pressure as a function of solar-
generated electrical power. These calculations are used by the maintenance optimizer to
determine the schedule which maximizes the total water production. In this study, the optimizer
performs exhaustive search by computing the total water production under every frequency and
selecting the maintenance frequency that results in the maximum water production.
SolarRadiation
Meteorological RoTime ti l Solar Radiation Fouling and Calculated
Model Water Production -- Production
Water Chemistry o Models and Fouling
Maintenance MaintenanceOptimizer Schedule
Figure 4.1: Maintenance optimization structure
Chapter 4. Deterministic Maintenance Study 83Chapter 4. Deterministic Maintenance Study 83
4.2 Representative PVRO System Model
An optimal maintenance protocol is to be determined for a small system in the Yucatan
Peninsula, Mexico. The PVRO system is assumed to have UV disinfection pre- and post-
treatment to eliminate biofouling on the membrane and in the product water tank. It is sized to
produce 1,000 liters of fresh water per day from brackish groundwater. The system's assumed
location and relevant system and operating parameters are presented in Table 4.1.
Table 4.1: Representative 1,000 L/day brackish water PVRO system parametersParameter Value
Latitude 18.50560 N
Longitude 89.3972"W
Feed Water Osmotic Pressure 1.1721 bar
Feed Water Temperature T. 200C
Number of RO Membranes IMembrane Diameter 0.1016 m
Membrane Length 1.016 m
Membrane Area Am 7.246 m 2
Initial Membrane Permeability Ko 4.62 x 10-4 L/bar/m 2/s
Number of PV Panels 2
Solar Panel Summer Tilt Horizontal (00)
Solar Panel Winter Tilt 18.50
Solar Panel Area AP 1.244 m2
Solar Panel Conversion Efficiency q 17.9%
Fouling Parameter y 4.1537 x 10-9 one/bar/s
Operating Period 3 years
The incident sunlight on the solar panels is calculated using the clear sky model from [26,
112]. The calculations account for the seasonal variations in solar radiation, but do not include
variations in solar radiation from cloud cover. Using Equation (3.8) and the following
empirically derived relationship, the RO pressure can be calculated as:
p (t)= (5.09 x10-P5)p +0.056P, -0.2197
Chapter 4. Deterministic Maintenance Study 84Chapter 4. Deterministic Maintenance Study 84
This empirical relationship was derived from operating data from a small-scale experimental
seawater PVRO system and scaled appropriately for a brackish water system [25].
Other assumptions are made for this example study. The solar panels are assumed to be
adjusted for the summer and winter seasons to increase the amount of solar energy collected.
The solar-to-electrical conversion efficiency is chosen based on the performance of a 215 Watt
solar panel manufactured by Suntech Power [113]. The feed water is assumed to be well water
at a constant temperature of 20'C and constant salinity, with an osmotic pressure of 1.17 bar.
The fouling rate is assumed constant, and is chosen such that if the PVRO system were operated
constantly at 80% power, its flow rate would decay exponentially with a time constant of
approximately 200 days. The community water demand is assumed constant at 1,000 L/day.
The storage of water is not accounted for. Here, it is assumed that there is a clean water storage
tank that holds the water needed for chemical cleaning and system flushing. The PVRO system
is also assumed to produce water for the entire duration of each day, and so it continues to
produce water after the daily demand is satisfied. In actual operation, one would likely turn the
system off once the water storage tank is full so as not to waste water.
The following maintenance processes are assumed. System flushing takes place for 3
minutes at a flow rate of 0.57 L/s. Chemical cleaning consists of an acid clean to remove the
calcium carbonate scale, followed by an alkaline cleaning. Table 4.2 lists the values of the
cleaning parameters. As in the constant pressure degradation example in Chapter 3, the increase
in permeability after system flushing is limited such that the post-system flush permeability is no
greater than the initial "clean membrane" permeability. The increase in membrane permeability
after chemical cleaning is limited to 97% of its original permeability to capture the effects of
Chapter 4. Deterministic Maintenance Study 85Chapter 4. Deterministic Maintenance Study 85
imperfect cleaning. Chemical cleaning effectiveness is limited since it does partially damage the
RO membrane [28].
Table 4.2: System flushing and chemical cleaning parametersParameter Value
System flushing permeability increase G 5.0 x 10 L/bar/m2/s
Permeate water flow rate during system flush qgf 0.57 L/s
System flush duration Ats 3 minutes
Chemical cleaning permeability increase Gc 4.009 x 10-' L/bar/m 2/s
Permeate water used for chemical cleaning Q, 5,000 L
Chemical cleaning duration 4 hours
To determine the optimal pre-scheduled maintenance, Equation (4.1) is solved using
exhaustive search. This method is applicable due to the small number of combinations of system
flushing and chemical cleaning frequencies considered. The number of days between chemical
cleanings ranges from 365 to 3 in single day increments. The time between system flushes
ranges from 3 hours to once per day, and then from one day to 7 days in single day increments.
Water production for cases with only system flushing, with only chemical cleaning and with no
maintenance are also calculated. Operation for all cases starts on January 1st. The sensitivity of
the optimization to changes in the fouling rate was also studied.
4.3 Results
4.3.1 Nominal Case
The optimal system flushing frequency is once per day, at the end of the day, when there
is no chemical cleaning as part of the maintenance protocol. System flushing is done at the end
of the day, when there is low solar energy and low water production so the loss of water
production penalty is small. The optimal chemical cleaning frequency, when system flushing is
not part of the cleaning protocol, is once every 62 days. The chemical cleaning takes several
Chapter 4. Deterministic Maintenance Study 86
hours and is assumed to be at the beginning of the day. The optimal combination of system
flushing and chemical cleanings is found to be daily system flushing with chemical cleaning
every 146 days.
The simulated daily average water production for the PVRO system for these four cases
is compared in Figure 4.2. The seasonal effects on daily water production are evident in all four
cases. Without maintenance, the daily water production declines more rapidly when the duration
of sunlight is shorter, during the winter. During the spring as the sunlight duration becomes
longer, the fouling rate is such that the daily water production remains nearly constant. In the
cases including maintenance, the daily water production increases as the sunlight duration
becomes longer, hits a local maximum during the summer, and decreases as the sunlight duration
becomes shorter.
1600Daily flushing, chemical
1400- cleaning every 146 days
1200
1000
800 -Daily flushing, no
600 .chemical cleaning
Expected demand400-
200- No maintenance
20
0 200 400 600 800 1000Operating time (days)
Figure 4.2: Daily water production under optimized maintenance, compared
with production under no maintenance and under daily flushing alone
Chapter 4. Deterministic Maintenance Study 87
Figure 4.2 shows daily system flushing with chemical cleaning every 146 days will
maximize water production. In all other cases, the daily demand is not met at some point during
the simulation period. On the days chemical cleaning is performed, the average daily water
production decreases due to the lost production time of the cleaning process. The seasonal
effects on water production are also visible in the figure. Daily water production increases with
increasing daily duration of sunlight. Note that this simulation does not show the required water
storage for the system. It is assumed that sufficient permeate water is available for chemical
cleaning at the appropriate times.
4.3.2 Sensitivity Study
Since the fouling rate parameter is not well known in advance, its sensitivity effects on
the optimal cleaning schedule is studied. The fouling rate is varied by 20% and 30%. The
revised maintenance schedule optimization results are presented in Table 4.3. They clearly show
that the fouling rate value has a significant effect on the optimal cleaning schedule.
Table 4.3: Sensitivity study maintenance optimization resultsFouling Rate Optimal Chemical Cleaning Period
Nominal Case y = 146 days
20% decrease y = 0.8 v, 185 days
30% decrease y = 0.7v, No chemical cleaning
20% increase y = 1.27, 127 days
30% increase y = 1.3y 103 days
In all cases in Table 4.3, daily system flushing, whether alone or combined with the
optimal cleaning chemical frequency, results in maximized water production. This implies that
in general, one would want to incorporate daily system flushing into the maintenance protocol
Chapter 4. Deterministic Maintenance Study 88
for PVRO. This can be automated using controllable valves and an appropriate piping network.
When operating commercial RO plants, it is typical to perform a system flush just after stopping
water production for any reason [28].
Figure 4.3 compares the daily water production when the fouling rate is reduced by 30%
for the following cases: 1) no maintenance, 2) daily system flushing and 3) daily system flushing
and chemical cleaning every 146 days - the schedule generated using the nominal fouling rate.
Under these conditions, there is no need to chemically clean the RO membrane, as it has no
benefit.
1600Daily flushing, no chemical cleaning
1400
1200
1000 \Daily flushing, chemical800 cleaning every 146 days
"06 600
Expected demand3 400 .No maintenance.
200-
0 200 400 600 800 1000Operating time (days)
Figure 4.3: Daily water production under lower fouling rate
Figure 4.4 compares the daily water production when the fouling rate is increased by
30% for the following cases: 1) no maintenance, 2) previous schedule using daily flushing and
chemical cleaning every 146 days, and 3) daily flushing and chemical cleaning every 103 days,
which maximizes water production. Using the schedule generated under the nominal fouling rate
89Chapter 4. Deterministic Maintenance Study
is clearly no longer optimal, since the system fails to meet the daily demand after about a year in
operation. This result demonstrates that a prognostic maintenance schedule needs to be based on
a reasonably accurate value of the fouling rate, and will need to adapt if the fouling rate changes
during the system's operation. Since the fouling rate will not be known in advance, it must be
identified from the PVRO system operation.
1600Daily flushing, chemical
1400- cleaning every 103 days
1200
10 20 40 000 10
800-Daily flushing, chemical
600O- cleaning every 146 days -Expected demand
(U 400 - -
200-No maintenance
"' 200 400 600 800 1000Operating time (days)
Figure 4.4: Daily water production under high fouling rate
4.4 Summary
A deterministic study demonstrates the use of the system models in an optimization that
finds the periodic maintenance schedule which meets the daily water demand. Results from this
optimization show that under the assumptions given, flushing the RO system daily is a
requirement for maximizing water production over the operating period. Generally, the fouling
rate will not be known before system operation starts, so it must be identified from PVRO
performance measurements over time. The optimization is sensitive to changes in the fouling
Chapter 4. Deterministic Maintenance Study 90
rate, particularly with respect to chemical cleaning, as expected, and so the maintenance
algorithm will need to be updated in response to such changes.
Chapter 4. Deterministic Maintenance Study 91Chapter 4. Deterministic Maintenance Study 91
Chapter 4. Deterministic Maintenance Study 92
CHAPTER
5
PARAMETER IDENTIFICATION AND FORECASTING
Process models often depend on parameters that cannot be calculated before operating a
system, and that change slowly over time. Such is the case with the fouling rate y in the RO
membrane fouling model presented in Chapter 3. The system operating history can be used to
identify these parameters to forecast future system performance. In this chapter, linear recursive
least squares estimation with forgetting [114] is used to identify the RO fouling rate from RO
plant performance data from the literature.
In addition to the identified unknown model parameters, forecasting requires estimates of
future system inputs, which may be both highly variable and uncertain. For example, the solar
radiation that powers a PVRO process varies both seasonally and with passing clouds.
Probabilistic descriptions of future input conditions can be generated from past data, such as
from past solar radiation and cloud histories. These descriptions are used to forecast the most
likely system performance. This chapter describes how the probabilistic descriptions of solar
radiation, including cloud cover, and of water demand are formed from available data. It also
describes how the forecasting algorithm combines the identified fouling rate and probabilistic
models to estimate future PVRO system performance.
Chapter 5: Parameter Identification and Forecasting 93Chapter 5: Parameter Identification and Forecasting 93
5.1 Parameter Identification
In Chapter 2, the review of the literature on RO membrane fouling shows that it is a
complex function of the water chemistry, transmembrane water flow, and the additional
hydrodynamics in the RO feed channels. All the models presented in the literature, whether
simple or complex, depend on system-specific parameters that are not known in advance. The
fouling model developed in Chapter 3 relies on a fouling rate that cannot be determined prior to
system operation. This parameter captures the net deposition of matter on the membrane surface,
so it is expected to change with the changes in salinity, water flow rates and hydrodynamics,
albeit slowly. The deterministic study in Chapter 4 shows that the optimal frequency-based
maintenance schedule is sensitive to changes in the fouling rate, so the prognostic algorithm
needs to respond to changes in it. The fouling rate must be identified from the system's
operation as a function of time.
Similarly, the system flushing and chemical cleaning models depend on the type of
foulant layer on the RO membrane. Loosely deposited particles can be swept away, but hard
scale layers will remain. Also, cleaning effectiveness depends on the types of chemicals used,
their order of application, the chemical-foulant interactions, flow rates, temperature, and other
factors. Hence, their net cleaning effects will not be known in advance and also must be
identified.
5.1.1 Fouling Rate Identification
During system operation, the salinities, pressures, temperatures and volumetric flow rates
of the feed, permeate and concentrate streams can be measured. The instantaneous RO
membrane permeability at a given time is calculated using the pressure, salinity, flow and
temperature measurements in Equations (3.1) and (3.3). The change in RO membrane
Chapter 5: Parameter Identification and Forecasting 94
permeability with time can be estimated using a difference equation, assuming measurements are
sampled at high frequency and properly calibrated. For PVRO degradation, sampling at 67
millihertz is reasonable, since RO membrane fouling occurs over several days, weeks or months.
In Equation (3.10), the fouling rate is linear with respect to the system measurements and
is in the form:
y =bu
(5.1)
dK(t )In Equation (3.10), the change in RO membrane permeability, , is output y , the fouling
dt
rate y is the unknown parameter b, and the product of the current membrane state and pressure,
-K (t)(p - Z) are the system measurements u. This structure permits the use of recursive
linear least-squares parameter estimation [114]. A forgetting factor, a , is incorporated so that
more weight is given to recent measurements and large initialization errors will be minimized.
The estimation algorithm is [114]:
R(t -1)u(t)b(t)= b(t -1)+ \2 Hy(o- b (t - 1) u(t))a + R (t -1)(u(t)) (5.2)
1 (R (t -1)u (t))2
a a + R (t -1)(u(t)) (5.3)
where R (t) is defined as:
R= Lu(tju(tt=1 (5.4)
Equation (5.3) permits the update of R without needing to store all measurements. When
initializing the recursive least squares algorithm, R0 is constrained to be positive definite.
The forgetting factor a is constrained such that
Chapter 5: Parameter Identification and Forecasting 95
0<a 1(5.5)
The closer the forgetting factor is to zero, the more weight is given to the most recent
measurement. For a slow process such as RO membrane fouling, using a forgetting factor close
to 1 will suppress errors in the initial value chosen for 70, yet retain much of the system history.
Recursive least-squares parameter identification is applied to operating data found in the
literature for a pilot-scale brackish water desalination plant in Brownsville, Texas [115]. The
feed water is sourced from 20 local wells with salinities ranging from 2700 and 3400 ppm TDS.
The RO plant contains six pressure vessels arranged in a two-stage configuration. The first stage
consists of two parallel flow paths, each containing two vessels in series. The second stage
contains a single train of two vessels in series, each containing four RO membranes
manufactured by Dow Chemical. The feed water is pre-filtered using ultrafiltration before being
desalinated, and the RO system is flushed at the end of each operating day. No chemical
cleaning is performed. The pilot plant is operated at constant product water flow for 8 hours per
day, 6 days per week, for one month. Full details of the RO plant are available [115].
Fouling parameter identification is performed using data from the second stage, only.
The following measurements are recorded at 16.7 millihertz (once per hour):
Table 5.1: Measurements available from pilot RO plant in Brownsville, TX [115]Measurement RangeSecond stage feed water pressure 13.9-19.5 barSecond stage permeate water pressure 1.3-1.7 barConcentrate water pressure 12.0-17.7 barFeed conductivity 4240-5270 pS/cmConcentrate conductivity 14950-17900 pS/cmPermeate conductivity 32.14-92.96 pS/cmPermeate water flow rate 1.95-2.34 L/sFeed water temperature 26.5-29.1 CPermeate water temperature 27-300CConcentrate water temperature 19.4-30.20 C
Chapter 5: Parameter Identification and Forecasting 96
The temperature measurements and the temperature correlation table from Dow Chemical
are used to normalize the permeate flow data [105]. The RO membrane permeability is
calculated using the normalized permeate flow, salinity and pressure in Equations (3.1) and (3.3)
- (3.5). The change in RO membrane permeability is approximated using a difference equation.
Recursive least squares with a forgetting factor of 0.998 is applied to the data for the first 110
measurements. Here, a fouling rate of 4.6382 x 10~8 (one/bar/s) is identified. The identified
fouling rate is used to calculate an estimate of the membrane permeability and a prediction of the
RO membrane permeability over the next 70 operating hours. Figure 5.1 shows that the
predicted permeability captures the overall decline in permeability occurring during the
prediction period. Although the membrane permeability derived from the measurements is not
reproduced, possibly due to measurement noise, the identified fouling rate is acceptable for
estimating the longer-term fouling behavior. Error between measured and predicted permeability
is within 6%.
7 X 10-4 ,,,6Measured 4-
6.5 permeability + + *
+ +
6 Identification - +* .
stopped Predicted U. + + .5. permeability + + . +
0, -2- +* + * +
++ ++
Identified - ++ .
4.5 permeability +
40L 10 16 80 50 100 150 200 -POO 120 140 160 180
Operating time (hours) Operating time (hours)
Figure 5.1: Measured, identified and predicted RO membrane permeability (left) and % error in
predicted permeability (right) from the brackish water RO pilot plant in Brownsville, TX [115]
The identified fouling rate parameter, pressure, temperature and salinity measurements
are used in Equations (3.1), (3.3) - (3.5), and (3.10) to calculate RO clean water flow rate during
97Chapter 5: Parameter Identification and Forecasting
operating hours 111-180. The left graph in Figure 5.2 shows the calculated and measured clean
water flow rate. The right graph shows the percent error between the measured and calculated
clean (permeate) water flow rate, defined as
e = q''"' -' qx100q,,?, (5.6)
where subscripts m and c refer to measured and calculated flow rates, respectively. The error
between calculated and measured flow rates is within 5%.
2.5 10
Identification Predicted 5
Measured Identified stopped flow rate
1.5 flow rate flow rate A
o-50.5
00 50 100 150 10 120 130 140 150 160 170 180
Operating time (hours) Operating time (hours)
Figure 5.2: Measured, identified and predicted RO permeate flow rate (left), and % error
between predicted and measured permeate flow rates (right), for the Brownsville RO plant
Parameter identification was also applied to data from a pilot plant in California
desalinating a blend of 60% brackish Colorado River water and 40% California Southern Water
Project water in La Verne, California, at the Metropolitan Water District [116]. This
combination of feed water has a TDS of 452 ppm. The feed water is filtered prior to entering the
RO unit using microfiltration, and is also dosed with Permatreat 191 antiscalant and sulfuric acid
to minimize scaling on the RO membranes. This plant is operated at constant permeate water
flow rate and product water recovery ratio, so the pressure is adjusted accordingly by the system
98Chapter 5: Parameter Identification and Forecasting
operators. The RO plant consists of three RO arrays. Data from the second RO array is used for
identification. This array consists of two pressure vessels in series, each with three 4-inch
diameter, 40-inch long RO membranes, manufactured by Koch Industries, Inc. Full details on
the plant setup and operation are available [116]. Over the first 1,000 operating hours, the plant
operators adjusted the pressure twice to increase the RO plant recovery ratio from 85 % to 90%.
It is assumed that no chemical cleaning is performed on array two during this period, since none
was documented. Table 5.2 shows the measurements used for fouling rate identification. The
net driving pressure and osmotic pressure were provided in the data [116].
Table 5.2: Measurements from the Metropolitan Water District pilot RO plant [116]Measurement RangeFeed water pressure 4.55-7.38 barPermeate water flow rate 0.22-0.34 L/ sNet driving pressure (calculated by study authors) 2.68-4.34 barOsmotic pressure (calculated by study authors) 0.37-1.46 barWater temperature 17-270 C
The data set used here is extremely sparse, with measurements recorded once per
operating day. The elapsed time between measurements is also inconsistent, so no data filtering
or smoothing is applied. Identification is performed using data from the first 1,200 operating
hours, consisting of a total of 50 data points. Data from the next 750 hours (the next 32 data
points) is used for validation. Here, the permeate flow rate was not normalized to eliminate
temperature effects. A forgetting factor of 0.99 was used.
The graph in Figure 5.3, left side, shows the measured clean (permeate) water flow rate,
the calculated flow rate using the identified fouling rate parameter during the same period, and
the permeate flow rate predicted using the identified fouling parameter, measured net driving
pressure, and Equations (3.1), (3.3) - (3.5), and (3.10). Even with extremely sparse data and no
Chapter 5: Parameter Identification and Forecasting 99Chapter 5: Parameter Identification and Forecasting 99
temperature normalization, the predicted clean water flow rate is within 5% of the measured
New RO Membrane 1.080011 x 10-'1 1.04761 x 10-32 1.01618 x 10-3
3 9.857 x 10-44 9.5613 x 10-4
5 9.2744 x 10-4
6 8.9962x 10-4
7 8.7263 x 10-48 8.4645 x 10-49 8.2106 x 10-4
The economic data presented in Table 6.3 and Table 6.4 shows that the cost of replacing
an RO membrane is slightly higher than the cost of six cleaning cycles. RO membrane
replacement is not included in the optimization performed here. Chemical cleaning frequencies
that result in fewer than six cleaning cycles over the 5-year period and still meet water demand
are less expensive to implement than changing the RO membrane once during the same period.
Table 6.6 lists the 5-year chemical and labor costs for select cleaning frequencies that are less
expensive than RO membrane replacement. If the cleaning frequency that ensures demand is
met at lowest cost is shorter than 261 days, one would need to include RO membrane
replacement in the optimization.
Table 6.6: Chemical and labor costs for select cleaning frequenciesCleaning frequency range Number of cleanings in 5 years 5-year cleaning cost (pesos)366-456 days 4 1,696.16305-365 days 5 2,120.20261-304 days 6 2,544.24
6.3 Case Study Details
The prognostic algorithm performance is simulated under the following scenarios: 1)
Cleaning Schedule Average Number of Cleanings Average Cost (MEX)
Adjusted Prognostic Maintenance 5.35 2,268.50
Sparse Maintenance 5 2,120.20
Chapter 6. Prognostic Maintenance Case Studies 131131Chapter 6. Prognostic Maintenance Case Studies
Once again, one can argue that simply following an annual cleaning schedule will result
in reasonable performance without relying on prognostic maintenance. However, the fouling
rates for other PVRO systems in other locations may differ substantially, and so annual
maintenance may result in higher water loss. Also, since the causes of the bimodal histogram in
Figure 6.9 (K) and not well understood, and since the mode of Figure 6.9 (K) is higher than its
average, following an annual schedule may result in more water loss than implied by the
average. The prognostic maintenance approach can be used to find a lowest cost maintenance
program that minimizes water loss percentage.
6.5 Summary
The prognostic maintenance algorithm is applied to a simulated PVRO system sized to
produce 1,000 L/day from brackish water under four scenarios: 1) fixed, unknown fouling rate,
2) slowly varying unknown fouling rate, 3) fixed, unknown fouling rate with varying water
demand, and 4) slowly varying, unknown fouling rate and varying water demand. The
variability in solar radiation from cloud cover is accounted for in all scenarios, as described in
Chapter 5. In this study, the water demand is not always met 100% of the time. Preliminary
results indicate that the prognostic approach ensures demand is met the majority of the time at
minimal maintenance cost under both constant fouling rate estimates and when adjusted in
response to changes in the fouling rate estimate, both with and without accounting for variations
in community water demand.
The method proposed here is intended to be general and can be applied to a broad class of
systems that degrade with operation that are stochastic in nature. Here it is applied to a solar
powered water purification system. For illustrative purposes the methodology is applied to a
representative, also though not typical, PVRO system and location as discussed in this section.
Chapter 6. Prognostic Maintenance Case Studies 132
The results are rational and in some cases somewhat counter intuitive. For example, in this
study, adjusting the maintenance schedule seasonally does not ensure demand is met at minimal
cost. This is likely due to the timing of maintenance cleanings selected by the prognostic
scheduler under the simulated conditions. The time between cleanings is between 305 and 365
days. Under these circumstances, it does not make sense to change frequencies with seasons.
Under different conditions, seasonal adjustments to the prognostic schedule may ensure demand
is met even more of the time, with minimal increases to maintenance costs.
The prognostic maintenance methodology can ensure the community water demand is
met at minimal cost by accounting for variable, stochastic operating conditions, RO membrane
degradation and cleaning effectiveness. Refinements to the prognostic scheduling optimization
algorithm, such as optimization of the threshold at which the prognostic maintenance schedule is
adjusted, can improve its performance under varying fouling and community water demand.
Chapter 6. Prognostic Maintenance Case Studies 133Chapter 6. Prognostic Maintenance Case Studies 133
Chapter 6. Prognostic Maintenance Case Studies 134
CHAPTER
7SUMMARY AND CONCLUSIONS
7.1 Summary
In this thesis, a methodology for developing a model-based prognostic maintenance
algorithm for systems degrading as complex functions of their operation, under varying,
uncertain conditions has been developed and applied to a community-sized, brackish water
PVRO desalination system in simulation. The methodology combines physics-based modeling,
system identification based on operation history and statistical models of future system inputs to
predict system performance and to optimize maintenance scheduling in terms of maintaining its
desired performance at the lowest cost.
The methodology is applied to a remote, community-scale PVRO system assumed to
operate without the benefit of energy storage. A physics-based model describing the long-term
effects of RO membrane degradation due to colloidal fouling and mineral scaling is formulated.
System flushing and chemical cleaning models are also formulated and are justified based on the
relative timescales of fouling versus flushing and cleaning. Given a system location and design,
the prognostic algorithm identifies the RO membrane permeability and fouling rate from water
pressure, flow and salinity measurements. It uses the identified fouling rate and estimated state
of the RO membrane, combined with a clear-sky solar-radiation model and historical weather
data, to project future performance and degradation. It is able to predict when the system will
fail to meet community demand. It is also able to predict the costs of applying maintenance
135Chapter 7. Summary and Conclusions
actions at different times to compare alternatives. By setting up a constrained optimization
problem using the identified fouling rate, anticipated environmental conditions, predicted
performance and costs, production time lost and product water required, a maintenance schedule
that ensures community water demand is met the majority of the time at lowest cost is generated.
Example results show that the prognostic maintenance approach can minimize the water loss
percentage at minimal cost, subject to variable operating conditions and degradation. An
optimized maintenance schedule is needed by PVRO system operators, who do not have the
expertise to determine the type and timing of the maintenance that will assure community water
demand is met at lowest cost, and the prognostic maintenance methodology can fill this need.
7.2 Suggestions for Future Work
Several directions are available for extension of this work. Refinements can be made to
the prognostic maintenance algorithm as applied to PVRO systems, both with and without
batteries. The prognostic maintenance methodology can also be applied to other degrading
systems subject to variable and uncertain operating conditions.
7.2.1 Future Refinements
Many future refinements to the prognostic maintenance algorithm as applied to PVRO
exist. The set of case studies presented in this work determine the chemical cleaning schedule
for a 5-year period. This length of time was chosen based on RO plant operator and
manufacturer experience. However, the prognostic maintenance algorithm for PVRO can be
extended so that membrane replacement can be incorporated. In the example study, the increase
in RO memhrane permeability after chemical cleaning is limited to 97/of its nrevisy11Q1r cleaned
value. After 8 cleanings, the RO membrane permeability cannot be increased enough to meet the
Chapter 7. Summary and Conclusions 136
daily water demand on a clear day, and so the RO membrane should be replaced. In general, the
limit on the number of cleanings will depend on the cleaning effectiveness and type of fouling.
Though assumptions are made for the example study, the cleaning effectiveness of a real PVRO
system can be estimated from system performance history. Limits on the number of chemical
cleanings can be calculated once the cleaning effectiveness is identified.
Biofouling is assumed negligible in the community-sized PVRO systems considered
here, since UV disinfection is assumed to effectively prevent it. Extensions of this work as
applied to reverse osmosis systems can include the modeling, identification and remediation of
biofouling.
In this work, the prognostic maintenance schedule was constrained to evenly spaced
waiting periods between chemical cleanings under the assumption that an even schedule is the
easiest for non-expert operators to follow. The operators are also assumed to follow the schedule
perfectly. These constraints can be relaxed. Permitting the days between chemical cleanings to
vary may result in a cleaning schedule that ensures community water demand is met 100% of the
time. Effectively communicating the cleaning schedule to the system operators can also be
considered.
The case studies in this work assume that battery banks are not used for energy storage,
and that the PVRO pumps operate variably as the incident sunlight fluctuates. In a PVRO
system that incorporates batteries, the RO motor/pumps run at constant power, and the batteries
mitigate the fluctuations in solar power. Battery charging and discharging, and hence its
degradation, will fluctuate with solar radiation. The prognostic algorithm will still need to
identify the RO fouling rate and determine chemical cleaning schedules. However, it will also
need to forecast battery charging, discharging and degradation. The same methodology applied
137Chapter 7. Summary and Conclusions
to a PVRO system without batteries can be applied. A suitable model of the battery bank
charging and discharging can either be found in the literature or can be developed. Unknown
parameters in such models may need to be identified, in which case parameter estimation
methods, such as recursive least squares or others [114], can be used along with measurements of
battery current, voltage and temperature. Identification methods will depend on model structure.
The solar radiation model incorporating the cloud statistics presented here can be used as an
input to the battery degradation model, and thus its degradation can be forecasted, and its
replacement schedule can be determined.
The PVRO prognostic algorithm has not yet been applied to a physical PVRO system.
This is needed to validate the prognostic maintenance approach. Field experiments will enable
further refinement of appropriate RO fouling models and their validation, refinement of demand
models, refinement of climate statistical models, and refinement of the prognostic algorithm
itself. Additionally, operators claim that cleaning an RO membrane becomes less effective over
time, based on their experiences. However, this has yet to be been studied. Such experimental
studies obviously will take years to perform, and are difficult to perform in the actual settings.
7.2.2 Applications to Other Domains
The prognostic maintenance methodology can be applied to other systems that degrade
with operation and are subject to varying, uncertain conditions, such as vehicle fleets. For
example, a fleet of military vehicles will be subject to many different road conditions,
temperatures, levels of dust, etc. Maintaining fleets of vehicles is expensive. Instead of
performing reactive or condition-based maintenance, prognostic maintenance can potentially
lower costs and facilitate better scheduling of vehicle deployment.
Chapter 7. Summary and Conclusions 138Chapter 7. Summary and Conclusions 138
Prognostic maintenance can also be applied to other solar-powered or renewable energy-
powered systems, such as systems powered by wind turbines. These may include RO processes
or other processes driven by variable, uncertain power sources, and may or may not include
energy storage. Applying this methodology can ensure such systems maintain their desired
productivity without excessive maintenance.
Chapter 7. Summary and Conclusions 139
Chapter 7. Summary and Conclusions 139
Chapter 7. Summary and Conclusions 140
REFERENCES
[1] A. Sharma, G. S. Yadava, and S. G. Deshmukh, "A literature review and future perspectives onmaintenance optimization," in Journal of Quality in Maintenance Engineering. vol. 17 Bradford: EmeraldGroup Publishing, Limited, 2011, pp. 5-25.
[2] R. Kothamasu, S. Huang, and W. VerDuin, "System health monitoring and prognostics - a review ofcurrent paradigms and practices," The International Journal ofAdvanced Manufacturing Technology, vol.28, pp. 1012-1024, 2006.
[3] A. Chen and G. S. Wu, "Real-time health prognosis and dynamic preventive maintenance policy forequipment under aging Markovian deterioration," International Journal ofProduction Research, vol. 45,pp. 3351-3379, 2007.
[4] H. P. Bloch and A. R. Budris, "Improvements Leading to Pump Mechanical Maintenance Cost Reduction,"in Pump User's Handbook: Life Extension: Fairmont Press, 2004.
[5] D. Yellamati, E. Arthur, S. James, G. Morris, T. Heydt, and E. Graf, "Predictive Reliability Models forvariable frequency drives based on application profiles," in Reliability and Maintainability Symposium(RAMS), 2013 Proceedings - Annual, 2013, pp. 1-6.
[6] "Tactical Water Purification," Knoxville, TN: Aqua-Chem, Inc., 2015. Available http://aqua-chem.com/node/22.
[7] Y. Peng, M. Dong, and M. Zuo, "Current status of machine prognostics in condition-based maintenance: areview," The International Journal ofAdvanced Manufacturing Technology, vol. 50, pp. 297-3 13, 2010.
[8] R. C. M. Yam, P. W. Tse, L. Li, and P. Tu, "Intelligent Predictive Decision Support System for Condition-Based Maintenance," The International Journal ofAdvanced Manufacturing Technology, vol. 17, pp. 383-391, 2001.
[9] W. Wang, P. A. Scarf, and M. A. J. Smith, "On the Application of a Model of Condition-BasedMaintenance," The Journal of the Operational Research Society, vol. 51, pp. 1218-1227, 2000.
[10] D. B. Durocher and G. R. Feldmeier, "Predictive versus preventive maintenance," Industry ApplicationsMagazine, IEEE, vol. 10, pp. 12-21, 2004.
[11] A. S. Bhujle, "Autonomous Control and Membrane Maintenance Optimization of Photovoltaic ReverseOsmosis Systems," SM Thesis. Cambridge, MA: Massachusetts Institute of Technology, 2013.
[12] S. R. McCormick, K. Hur, S. Santoso, A. Maitra, and A. Sundaram, "Capacitor bank predictivemaintenance and problem identification using conventional power quality monitoring systems," in PowerEngineering Society General Meeting, 2004. IEEE, 2004, pp. 1846-1850 Vol.2.
[13] V. Venkatasubramanian, "Prognostic and diagnostic monitoring of complex systems for product lifecyclemanagement: Challenges and opportunities," Computers & Chemical Engineering, vol. 29, pp. 1253-1263,2005.
[14] H.-E. Kim, A. C. C. Tan, J. Mathew, and B.-K. Choi, "Bearing fault prognosis based on health stateprobability estimation," Expert Systems with Applications, vol. 39, pp. 5200-5213, 2012.
[15] H. Lu, W. J. Kolarik, and S. S. Lu, "Real-time performance reliability prediction," Reliability, IEEETransactions on, vol. 50, pp. 353-357, 2001.
[16] H. T. Pham and B.-S. Yang, "Estimation and forecasting of machine health condition usingARMA/GARCH model," Mechanical Systems and Signal Processing, vol. 24, pp. 546-558, 2010.
[17] C. S. Byington, M. Watson, D. Edwards, and P. Stoelting, "A model-based approach to prognostics andhealth management for flight control actuators," in Aerospace Conference, 2004. Proceedings. 2004 IEEE,2004, pp. 3551-3562 Vol.6.
[18] B. Iung, M. Monnin, A. Voisin, P. Cocheteux, and E. Levrat, "Degradation state model-based prognosis forproactively maintaining product performance," CIRP Annals - Manufacturing Technology, vol. 57, pp. 49-52, 2008.
References 141
[19] Z.-J. Zhou, C.-H. Hu, W.-B. Wang, B.-C. Zhang, D.-L. Xu, and J.-F. Zheng, "Condition-based maintenanceof dynamic systems using online failure prognosis and belief rule base," Expert Systems with Applications,vol. 39, pp. 6140-6149, 2012.
[20] WHO/UNICEF, "Progress on Drinking Water and Sanitation: 2012 Update," World Health Organizationand UNICEF, Geneva, Switzerland 2012.
[21] P. Rekacewicz and E. Bournay, "Proportion of population with improved drinking water supply in 2002"Arendal, Norway: UNEP/GRID-Arendal, 2007.
[22] P. Rekacewicz, "Water Scarcity Index," in Vital Water Graphics - An Overview of the State of the World'sFresh and Marine Waters. 2nd Edition. Nairobi, Kenya: UNEP, 2008.
[23] H. Ahlenius, "Natural resource - solar power (potential) " in Environment & Poverty Times No. 5 Arendal,Norway: GRID-Arendal, 2008.
[24] A. M. Bilton, R. Wiesman, A. F. M. Arif, S. M. Zubair, and S. Dubowsky, "On the feasibility ofcommunity-scale photovoltaic-powered reverse osmosis desalination systems for remote locations,"Renewable Energy, vol. 36, pp. 3246-3256, 2011.
[25] A. M. Bilton, L. C. Kelley, and S. Dubowsky, "Photovoltaic reverse osmosis - Feasibility and a pathwayto develop technology," Desalination and Water Treatment, vol. 31, pp. 24-34, 2011.
[26] A. M. Bilton, "A Modular Design Architecture for Application to Community-Scale Photovoltaic-PoweredReverse Osmosis Systems," Ph D Thesis, Cambridge, MA: Massachusetts Institute of Technology, 2013.
[27] A. M. Bilton and S. Dubowsky, "The modular design of photovoltaic reverse osmosis systems: makingtechnology accessible to nonexperts," Desalination and Water Treatment, vol. 51, pp. 702-712, 2012.
[28] J. Kucera, Reverse Osmosis. Salem, MA: Scrivener Publishing, LLC, 2010.[29] "Cleaning Procedures for DOW FILMTEC FT30 Elements." Form No. 609-23010-0211, DOW Chemical
Company, 2011.[30] S. Lu, Y.-C. Tu, and H. Lu, "Predictive condition-based maintenance for continuously deteriorating
systems," Quality and Reliability Engineering International, vol. 23, pp. 71-81, 2007.[31] S. K. Yang, "A condition-based failure-prediction and processing-scheme for preventive maintenance,"
Reliability, IEEE Transactions on, vol. 52, pp. 373-383, 2003.[32] H. Liao and M. Rausch, "Spare part inventory control driven by condition based maintenance," in
Reliability and Maintainability Symposium (RAMS), 2010 Proceedings - Annual, 2010, pp. 1-6.[33] E. Deloux, B. Castanier, and C. Berenguer, "Predictive maintenance policy for a gradually deteriorating
system subject to stress," Reliability Engineering & System Safety, vol. 94, pp. 418-431, 2009.[34] X. Zhao, M. Fouladirad, C. Berenguer, and L. Bordes, "Condition-based inspection/replacement policies
for non-monotone deteriorating systems with environmental covariates," Reliability Engineering & SystemSafety, vol. 95, pp. 921-934, 2010.
[35] E. Becker and P. Poste, "Keeping the blades turning: Condition monitoring of wind turbine gears," Refocus,vol. 7, pp. 26-32, 2006.
[36] W. Wang and M. Carr, "A stochastic filtering based data driven approach for residual life prediction andcondition based maintenance decision making support," in Prognostics and Health ManagementConference, 2010. PHM '10., 2010, pp. 1-10.
[37] Y. Dong, Y. Gu, K. Yang, and J. Zhang, "Applying PCA to establish artificial neural network for conditionprediction on equipment in power plant," in Intelligent Control and Automation, 2004. WCICA 2004. FifthWorld Congress on, 2004, pp. 1715-1719 Vol.2.
[38] Z.-J. Zhou, C.-H. Hu, D.-L. Xu, M.-Y. Chen, and D.-H. Zhou, "A model for real-time failure prognosisbased on hidden Markov model and belief rule base," European Journal of Operational Research, vol. 207,pp. 269-283, 2010.
[39] D. Bansal, D. J. Evans, and B. Jones, "A Real-Time Predictive Maintenance System for Machine Systems -An Alternative to Expensive Motion Sensing Technology," in Sensorsfor Industry Conference, 2005, pp.39-44.
References 142
References 142
[40] P. Sadegh, J. Concha, S. Stricevic, A. Thompson, and P. J. Kootsookos, "A framework for unified design offault detection & isolation and optimal maintenance policies," in American Control Conference, 2006,2006.
[41] K. Bouvard, S. Artus, C. Berenguer, and V. Cocquempot, "Condition-based dynamic maintenanceoperations planning & grouping. Application to commercial heavy vehicles," Reliability Engineering &System Safety, vol. 96, pp. 601-610, 2011.
[42] B. Y. Yu, T. Honda, G. M. Zak, A. Mitsos, J. Lienhard, K. Mistry, S. Zubair, M. H. Sharqawy, M. Antar,and M. C. Yang, "Prognosis of Component Degradation Under Uncertainty: A Method for Early StageDesign of a Complex Engineering System," in ASME 2012 11th Biennial Conference on EngineeringSystems Design and Analysis, 2012, pp. 683-694.
[43] M. Dong, D. He, P. Banerjee, and J. Keller, "Equipment health diagnosis and prognosis using hidden semi-Markov models," The International Journal ofAdvanced Manufacturing Technology, vol. 30, pp. 738-749,2006.
[44] L. Jianhui, M. Namburu, K. Pattipati, Q. Liu, M. Kawamoto, and S. Chigusa, "Model-based prognostictechniques [maintenance applications]," in A UTOTESTCON 2003. IEEE Systems Readiness TechnologyConference. Proceedings, 2003, pp. 330-340.
[45] M. D. Le and C. M. Tan, "Optimal maintenance strategy of deteriorating system under imperfectmaintenance and inspection using mixed inspection scheduling," Reliability Engineering & System Safety,vol. 113, pp. 21-29, 2012.
[46] E. Tzen and R. Morris, "Renewable energy sources for desalination," Solar Energy, vol. 75, pp. 375-379,2003.
[47] C. Fritzmann, J. Lowenberg, T. Wintgens, and T. Melin, "State-of-the-art of reverse osmosis desalination,"Desalination, vol. 216, pp. 1-76, 2007.
[48] "PVInsights: Solar Photovoltaic (Polysilicon wafer cell and panel) Prices and Research Reports,"PVinsights Co. Ltd., 2015.
[49] A. Bermudez-Contreras, M. Thomson, and D. G. Infield, "Renewable energy powered desalination in BajaCalifornia Sur, Mexico," Desalination, vol. 220, pp. 431-440, 2008.
[50] R. Wood, "Sun- and wind-powered solar cube is a self-contained water purification system," Journal of theAmerican Water Works Association, vol. 99, pp. 38-40, 42, 2007.
[51] A. Ghermandi and R. Messalem, "Solar-driven desalination with reverse osmosis: the state of the art,"Desalination and Water Treatment, vol. 7, pp. 285-296, 2009.
[52] D. Herold and A. Neskakis, "A small PV-driven reverse osmosis desalination plant on the island of GranCanaria," Desalination, vol. 137, pp. 285-292, 2001.
[53] M. Papapetrou, C. Epp, and E. Tzen, "Autonomous desalination units based on renewable energy systems-A review of representative installations worldwide," in Solar Desalinationfor the 21st Century: Springer,2007, pp. 343-353.
[54] M. Thomson, "Reverse-Osmosis Desalination of Seawater Powered by Photovoltaics Without Batteries."vol. Thesis Leicestershire, UK: Loughborough University, 2003.
[55] M. B. Baig and A. A. Al Kutbi, "Design features of a 20 migd SWRO desalination plant, Al Jubail, SaudiArabia," Desalination, vol. 118, pp. 5-12, 1998.
[56] A. Antony, J. H. Low, S. Gray, A. E. Childress, P. Le-Clech, and G. Leslie, "Scale formation and control inhigh pressure membrane water treatment systems: A review," Journal of Membrane Science, vol. 383, pp.1-16, 2011.
[57] S. Lee and C. Lee, "Scale formation in NF/RO: mechanism and control," Water Science & Technology, vol.51, pp. 267-275, 2005.
[58] A. Jawor and E. M. V. Hoek, "Effects of feed water temperature on inorganic fouling of brackish water ROmembranes," Desalination, vol. 235, pp. 44-57, 2009.
[59] C. Y. Tang, T. H. Chong, and A. G. Fane, "Colloidal interactions and fouling of NF and RO membranes: Areview," Advances in Colloid and Interface Science, vol. 164, pp. 126-143, 2011.
References 143143References
[60] T. H. Chong, F. S. Wong, and A. G. Fane, "Implications of critical flux and cake enhanced osmoticpressure (CEOP) on colloidal fouling in reverse osmosis: Experimental observations," Journal ofMembrane Science, vol. 314, pp. 101-111, 2008.
[61] L. Song and G. Singh, "Influence of various monovalent cations and calcium ion on the colloidal foulingpotential," Journal of Colloid and Interface Science, vol. 289, pp. 479-487, 2005.
[62] X. Jin, A. Jawor, S. Kim, and E. M. V. Hoek, "Effects of feed water temperature on separation performanceand organic fouling of brackish water RO membranes," Desalination, vol. 239, pp. 346-359, 2009.
[63] A. I. Radu, J. S. Vrouwenvelder, M. C. M. van Loosdrecht, and C. Picioreanu, "Effect of flow velocity,substrate concentration and hydraulic cleaning on biofouling of reverse osmosis feed channels," ChemicalEngineering Journal, vol. 188, pp. 30-39, 2012.
[64] J. S. Vrouwenvelder, C. Picioreanu, J. C. Kruithof, and M. C. M. van Loosdrecht, "Biofouling in spiralwound membrane systems: Three-dimensional CFD model based evaluation of experimental data," Journalof Membrane Science, vol. 346, pp. 71-85, 2010.
[65] J. S. Baker and L. Y. Dudley, "Biofouling in membrane systems: A review," Desalination, vol. 118, pp. 81-89, 1998.
[66] J. S. Vrouwenvelder, C. Hinrichs, W. G. J. Van der Meer, M. C. M. Van Loosdrecht, and J. C. Kruithof,"Pressure drop increase by biofilm accumulation in spiral wound RO and NF membrane systems: role ofsubstrate concentration, flow velocity, substrate load and flow direction," Biofouling, vol. 25, pp. 543-555,2009.
[67] J. Thompson, N. Lin, E. Lyster, R. Arbel, T. Knoell, J. Gilron, and Y. Cohen, "RO membrane mineralscaling in the presence of a biofilm," Journal ofMembrane Science, vol. 415-416, pp. 181-191, 2012.
[68] J. S. Vrouwenvelder, S. A. Manolarakis, H. R. Veenendaal, and D. van der Kooij, "Biofouling potential ofchemicals used for scale control in RO and NF membranes," Desalination, vol. 132, pp. 1-10, 2000.
[69] R. Higgin, K. J. Howe, and T. M. Mayer, "Synergistic behavior between silica and alginate: Novelapproach for removing silica scale from RO membranes," Desalination, vol. 250, pp. 76-81, 2010.
[70] B. A. Qureshi, S. M. Zubair, A. K. Sheikh, A. Bhujle, and S. Dubowsky, "Design and performanceevaluation of reverse osmosis desalination systems: An enphasis on fouling modeling," Applied ThermalEngineering, vol. 60, pp. 208-217, 2013.
[71] A. Abbas and N. Al-Bastaki, "Performance decline in brackish water Film Tec spiral wound ROmembranes," Desalination, vol. 136, pp. 281-286, 2001.
[72] E. M. V. Hoek, J. Allred, T. Knoell, and B.-H. Jeong, "Modeling the effects of fouling on full-scale reverseosmosis processes," Journal of Membrane Science, vol. 314, pp. 33-49, 2008.
[73] Y. G. Lee, Y. S. Lee, D. Y. Kim, M. Park, D. R. Yang, and J. H. Kim, "A fouling model for simulatinglong-term performance of SWRO desalination process," Journal ofMembrane Science, vol. 401, pp. 282-291, 2012.
[74] K. L. Chen, L. Song, S. L. Ong, and W. J. Ng, "The development of membrane fouling in full-scale ROprocesses," Journal ofMembrane Science, vol. 232, pp. 63-72, 2004.
[75] M. Barger and R. P. Carnahan, "Fouling prediction in reverse osmosis processes," Desalination, vol. 83,pp. 3-33, 1991.
[76] A. I. Radu, J. S. Vrouwenvelder, M. C. M. van Loosdrecht, and C. Picioreanu, "Modeling the effect ofbiofilm formation on reverse osmosis performance: Flux, feed channel pressure drop and solute passage,"Journal ofMembrane Science, vol. 365, pp. 1-15, 2010.
[77] C. Picioreanu, J. S. Vrouwenvelder, and M. C. M. van Loosdrecht, "Three-dimensional modeling ofbiofouling and fluid dynamics in feed spacer channels of membrane devices," Journal ofMembraneScience, vol. 345, pp. 340-354, 2009.
[78] L. Kelley, H. Elasaad, and S. Dubowsky, "Autonomous operation and maintenance of small-scale PVROsystems for remote communities," Desalination and Water Treatment, pp. 1-13, 2014.
[,79]l J. Mvi. Arnal, B. Garcia-Fayos, and M. a. Sancho, "Membrane Cleaning," in Expanding Issues inDesalination, R. Y. Ning, Ed. Rijeka, Croatia: InTech, 2011, pp. 63-84.
[80] J. P. Chen, S. L. Kim, and Y. P. Ting, "Optimization of membrane physical and chemical cleaning by astatistically designed approach," Journal ofMembrane Science, vol. 219, pp. 27-45, 2003.
References 144
[81] Hydranautics, "Technical Service Bulletin: Foulants and Cleaning Procedures for composite polyamide ROMembrane Elements (ESPA, ESNA, CPA, LFC, NANO and SWC) ". TSB 107.22, Oceanside, CA: NittoCorporation, 2013.
[82] M. Fazel and S. Chesters, "RO membrane cleaning using microbubbles at 6,800 m3/d wastewater RO plantin UAE," Desalination and Water Treatment, pp. 1-9, 2014.
[83] S. P. Chesters, M. W. Armstrong, and M. Fazel, "Microbubble RO membrane cleaning reduces fouling onWWRO plant," Desalination and Water Treatment, pp. 1-9, 2014.
[84] D. Feng, J. S. J. van Deventer, and C. Aldrich, "Ultrasonic defouling of reverse osmosis membranes used totreat wastewater effluents," Separation and Purification Technology, vol. 50, pp. 318-323, 2006.
[85] W. S. Ang, S. Lee, and M. Elimelech, "Chemical and physical aspects of cleaning of organic-fouled reverseosmosis membranes," Journal ofMembrane Science, vol. 272, pp. 198-210, 2006.
[86] M. Luo and Z. Wang, "Complex fouling and cleaning-in-place of a reverse osmosis desalination system,"Desalination, vol. 141, pp. 15-22, 2001.
[87] S. S. Madaeni, T. Mohamamdi, and M. Kazemi Moghadam, "Chemical cleaning of reverse osmosismembranes," Desalination, vol. 134, pp. 77-82, 2001.
[88] Y.-y. Lu, Y.-d. Hu, D.-m. Xu, and L.-y. Wu, "Optimum design of reverse osmosis seawater desalinationsystem considering membrane cleaning and replacing," Journal ofMembrane Science, vol. 282, pp. 7-13,2006.
[89] S. I. Graham, R. L. Reitz, and C. E. Hickman, "Improving reverse osmosis performance through periodiccleaning," Desalination, vol. 74, pp. 113-124, 1989.
[90] J. C. Schippers and J. Verdouw, "The modified fouling index, a method of determining the foulingcharacteristics of water," Desalination, vol. 32, pp. 137-148, 1980.
[91] E. Brauns, E. Van Hoof, B. Molenberghs, C. Dotremont, W. Doyen, and R. Leysen, "A new method ofmeasuring and presenting the membrane fouling potential," Desalination, vol. 150, pp. 31-43, 2002.
[92] K. G. Tay and L. Song, "A more effective method for fouling characterization in a full-scale reverseosmosis process," Desalination, vol. 177, pp. 95-107, 2005.
[93] S. El-Manharawy and A. Hafez, "Molar ratios as a useful tool for prediction of scaling potential inside ROsystems," Desalination, vol. 136, pp. 243-254, 2001.
[94] S. El-Manharawy and A. Hafez, "A new chemical classification system of natural waters for desalinationand other industrial uses," Desalination, vol. 156, pp. 163-180, 2003.
[95] H. J. See, V. S. Vassiliadis, and D. 1. Wilson, "Optimisation of membrane regeneration scheduling inreverse osmosis networks for seawater desalination," Desalination, vol. 125, pp. 37-54, 1999.
[96] M. Zhu, M. M. El-Halwagi, and M. Al-Ahmad, "Optimal design and scheduling of flexible reverse osmosisnetworks," Journal of Membrane Science, vol. 129, pp. 161-174, 1997.
[97] K. M. Sassi and I. M. Mujtaba, "Optimal design and operation of reverse osmosis desalination process withmembrane fouling," Chemical Engineering Journal, vol. 171, pp. 582-593, 2011.
[98] H. Chen and A. S. Kim, "Prediction of permeate flux decline in crossflow membrane filtration of colloidalsuspension: a radial basis function neural network approach," Desalination, vol. 192, pp. 415-428, 2006.
[99] D. Libotean, J. Giralt, F. Giralt, R. Rallo, T. Wolfe, and Y. Cohen, "Neural network approach for modelingthe performance of reverse osmosis membrane desalting," Journal of Membrane Science, vol. 326, pp. 408-419, 2009.
[100] A. n. Zafra-Cabeza, M. A. Ridao, and E. F. Camacho, "A mixed integer quadratic programmingformulation of risk management for reverse osmosis plants," Desalination, vol. 268, pp. 46-54, 2011.
[101] C. W. McFall, A. Bartman, P. D. Christofides, and Y. Cohen, "Control and Monitoring of a High RecoveryReverse Osmosis Desalination Process," Industrial & Engineering Chemistry Research, vol. 47, pp. 6698-6710, 2008.
[102] A. Gambier, N. Blumlein, and E. Badreddin, "Real-time fault tolerant control of a Reverse Osmosisdesalination plant based on a hybrid system approach," in American Control Conference, 2009. ACC '09.,2009, pp. 1598-1603.
References 145
References 145
[103] "FILMTEC Membranes System Design: System Performance Projection." Form Number 609-02057-604Dow Chemical Corporation. Available http://www.dow.com. Accessed 13 December 2010, 2010.
[104] M. Wilf and K. Klinko, "Performance of commercial seawater membranes," Desalination, vol. 96, pp. 465-478, 1994.
[105] "Technical Manual Excerpt: Filmtec Membranes Addendum: Temperature Correction Factor." FormNumber 609-02129-804. Dow Chemical Corporation. Available http://www.dow.com. Accessed 18December 2014, 2008.
[106] "Membrane Performance Factors: Temperature Correction," Applied Membranes, Inc., 2012. Availablehttp://appliedmembranes.com Accessed 4 February 2015.
[107] "FILMTEC Membranes System Design: Membrane Systen Design Guidelines for Commercial Elements."Form Number 609-02054-0812: Dow Chemical Corporation. Available http://www.dow.com. Accessed 3February 2014, 2010.
[108] L. C. Kelley and S. Dubowsky, "Thermal control to maximize photovoltaic powered reverse osmosisdesalination systems productivity," Desalination, vol. 314, pp. 10-19, 2012.
[109] L. C. Kelley, "The Design and Control of a Thermal Management System for a Photovoltaic ReverseOsmosis System," in Mechanical Engineering. vol. SM Cambridge: Massachusetts Institute of Technology,2011.
[110] E. W. Weisstein, "Delta Function," in Math World - a Wolfram Web Resource: Wolfram Research, Inc.,2014. http://mathworld.wolfram.com/DeltaFunction.html.
[111] "FILMTEC Membranes System Design: Membrane System Design Guidelines for Commercial Elements."Form Number 609-02054-0812: Dow Chemical Corporation., 2010. Available http://www.dow.com.Accessed 3 February 2014.
[112] C. Rigollier, 0. Bauer, and L. Wald, "On the clear sky model of the ESRA -- European Solar RadiationAtlas -- with respect to the heliosat method," Solar Energy, vol. 68, pp. 33-48, 2000.
[114] L. Ljung, System Identification: Theoryfor the User, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, Inc.,1999.
[115] M. Chapman, F. Leitz, and A. Tiffenbach, "Variable Salinity Desalination," Denver, CO: Bureau ofReclamation, United States Department of the Interior, 2013.
[116] C. Gabelich, T. I. Yun, J. F. Green, I. H. Suffet, and W. R. Chen, "Evaluation of Precipitative Fouling forColorado River Water Desalination Using Reverse Osmosis," Denver, CO: Bureau of Reclamation, UnitedStates Department of the Interior, 2002.
[117] C. J. Gabelich, T. I. Yun, B. M. Coffey, and I. H. M. Suffet, "Pilot-scale testing of reverse osmosis usingconventional treatment and microfiltration," Desalination, vol. 154, pp. 207-223, 2003.
[118] NASA, "NASA Surface meteorology and Solar Energy: Global/Regional Data," National Aeronautics andSpace Administration, Atmospheric Science and Data Center. Available http://eosweb.larc.nasa.gov/sseAccessed 18 December 2013, 2013.
[119] "Statistics on Water in Mexico, 2010 Edition," National Water Commission of Mexico, CoyoacAn, D.F.2010.
[120] F. Kasten and G. Czeplak, "Solar and terrestrial radiation dependent on the amount and type of cloud,"Solar Energy, vol. 24, pp. 177-189, 1980.
[121] D. P. Bertsekas and J. N. Tsitsiklis, Introduction to Probability, 2nd ed. Belmont, MA Athena Scientific,2008.
[122] M. M. Zweng, J. R. Reagan, J. I. Antonov, R. A. Locarnini, A. V. Mishonov, T. P. Boyer, H. E. Garcia, 0.K. Baranova, D. R. Johnson, D.Seidov, and M. M. Biddle, "World Ocean Atlas 2013. Volume 2: Salinity,"NOAA Atlas NESDIS 74, 2013. Available: https://www.nodc.noaa.gov/OC5/woal 3/pubwoa 1 3.html.
[123] H. Elasaad, A. Bilton, L. Kelley, 0. Duayhe, and S. Dubowsky, "Field Evaluation of a Community ScaleSolar Powered Water Purification Technology: A Case Study of a Remote Mexican CommunityApplication," Submitted to Desalination, 2015.
References 146
[124] S. L. Zhou, T. A. McMahon, A. Walton, and J. Lewis, "Forecasting operational demand for an urban watersupply zone," Journal of Hydrology, vol. 259, pp. 189-202, 2002.
[125] "Water," in Dietary Reference Intakes for Water, Potassium, Sodium, Chloride, and Sulfate NationalResearch Council. Washington, DC: The National Academies Press, 2005, pp. 73-185. Accessed 14October 2014. Available: http://www.nal.usda.gov/fnic/DRI//DRIWater/73-185.pdf.
[126] "Cleaning Procedures for AM- 11: Thin Film Composite RO Membrane Acid Cleaner," AppliedMembranes, Inc., 2014. Available http://appliedmembranes.com Accessed 25 March 2015.
[127] "Cleaning Procedures for AM-22: Thin Film Composite RO Membrane Alkaline Cleaner," AppliedMembranes, Inc., 2014. Available http://appliedmembranes.com Accessed 25 March 2015.
[128] "Disinfecting Membranes and System with PS-77," Applied Membranes, Inc., 2014. Availablehttp://appliedmembranes.com Accessed 25 March 2015.
[129] "RO Membrane Cleaning & Fouling Chemicals for Scale and Organics Removal for Water Treatment,"WaterAnywhere, 2015. Available http://www.wateranywhere.com Accessed 25 March 2015.
[130] "Neutra Sul Hydrogen Peroxide - 2 - 2.5 Gallon Bottles," US Water Systems, Inc., 2015. Availablewww.uswatersystems.com Accessed 25 March 2015.
[131] D. Verner, Activities, Employment, and Wages in Rural and Semi-Urban Mexico: The World Bank, 2005.
[132] NASA, "NASA Surface meteorology and Solar Energy: Global/Regional Data," National Aeronautics andSpace Administration, Atmospheric Science and Data Center. Available http://eosweb.larc.nasa.gov/sseAccessed 26 March 2015, 2015.
References 147147References
References 148
APPENDIX
ARELATING SOLAR POWER To FEED WATER
PRESSURE
The case studies in Chapters 4 and 6 use an empirically derived equation that relates
electrical power generated by a solar panel to the feed water pressure at the RO pressure vessel
inlet. This equation is based on operating data collected from a small, laboratory-size PVRO
system constructed and operated in the Field and Space Robotics Lab at MIT [25]. This system
is designed to produce 300 liters per day of clean water from seawater, using single-axis sun
tracking and maximum power point tracking. It uses a custom-designed, computer controlled,
variable DC to DC converter to adjust the voltage applied to the motor/pumps based on the
amount of power coming from the solar panel. It also incorporates an energy recovery device,
which is how the PVRO system is able to boost the water pressure to sufficiently high pressure
for seawater desalination. Full details of this system are available [123].
The brackish water system design used in simulations in Chapters 4 and 6 is based on a
fielded PVRO system in La Mancalona, Mexico, with one major difference. The fielded system
in La Mancalona uses batteries for energy storage. The system used for these case studies is
assumed to have a custom-designed, computer controlled, variable DC to DC converter that
facilitates variable operation of the high pressure pump/motor, thus expensive batteries are not
needed.
Appendix A. Relating Solar Power to Feed Water Pressure 149149Appendix A. Relating Solar Power to Feed Water Pressure
In any RO system, high pressure is maintained in the vessel by a pressure regulating
valve following the brine (concentrate) port. In Figure A. 1, this valve is labeled Rb . The other
symbols in the figure are defined:
qf is the feed water flow rate (L/s).
p1 is the feed water pressure at the RO vessel inlet (bar).
p is the average water pressure in the RO vessel on the feed side of the membrane (bar).
qb is the brine (concentrate) flow rate (L/s).
q, is the clean water (permeate) flow rate (L/s).
Patm is atmospheric pressure (bar).
Rm1 is the RO membrane resistance to clean water permeation, defined as:
R = I' K(t),Am (A.1)
In general, this resistance will increase over time as the RO membrane fouls. Since fouling is a
slow process (on the order of weeks to months), the membrane permeability and hence the
membrane resistance can be assumed constant over short periods of time. Equation (A. 1) can be
substituted into Equation (3.1) to yield:
qP =RMn (A.2)
qf qpj R
Rb qP, patm
b I Pat.t
Figure A.1: RO pressure vessel as a fluid resistance network
150Appendix A. Relating Solar Power to Feed Water Pressure
The resistance of the pressure-regulating valve, Rb, will be a function of its setting and
the flow rate of water through it [26]. At a given RO pump operating point, the brine flow is
assumed proportional to the pressure drop across the valve in Figure A.1, and an equivalent
resistance seen by the pump, ReqI can be defined as:
R - R,,Rb _ Rb
eq R, +Rb K(t)A,,Rb +1 (A.3)
The feed water volumetric flow rate q, can be calculated:
q, = PReq (A.4)
The power transferred from the solar panels to the RO fluid can be approximated by:
P1 = qff =P, elp77m ?ec (A.5)
where qp and rq, are the energy conversion efficiencies of the pump and motor, respectively
and Pe,,i is the electrical power from the solar panel, as described in Equation (3.8). Substituting
Equation (A.4) into Equation (A.5) to eliminate qf yields:
2Pf
f Req (A.6)
Both the PVRO system modeled for simulation purposes and the MIT laboratory-sized PVRO
system contain a single RO membrane element housed in a small pressure vessel. For this
reason, the average water pressure p is assumed to be approximately the same as the feed water
pressure p,.
Equation (A.6) is an approximation that is valid at constant operating points for short
periods of time. When operating a PVRO system at variable power levels for long durations of
Appendix A. Relating Solar Power to Feed Water Pressure 151
time, the flow rates and pressure levels will change since both the membrane resistance and the
pressure drop through the brine-side valve are functions of pressure and flow, respectively. With
a physical system and sensors, one can use physics-based modeling techniques to create a high-
fidelity mathematical model describing this behavior. This is impractical without a physical
system, especially when the downstream loading is both complex and unknown. Therefore, in
order to describe the conversion of electrical power to feed water pressure for long-term
simulations under variable power levels, electrical power, water flow and pressure experimental
data from MIT laboratory-sized PVRO system were scaled to electrical power, water flow and
pressure levels for a 1,000 L/day brackish water PVRO system. Since pressure is roughly
proportional to the square-root of the power, the following equation was fit to the scaled data
using the curve fitting tool in Matlab:
p = aP-' +a 2(A.7)
The curve in Equation (A.7) fits the experimental data almost perfectly (coefficient of
determination R2 value of 0.999) when the coefficients al and a2 are 1.298 and -6.182,
respectively. Another empirical relation that fits the data well (R2 value of 0.997) was found
previously, and has also been used in simulations: