Systems Engineering in Osmotic Membrane Processes

Transcription

1 Systems Engineering in Osmotic Membrane Processes Mingheng Li, Professor Department of Chemical and Materials Engineering California State Polytechnic University, Pomona Tel: (909)

2 Outline I. Introduction/Background II. Optimization of SEC in SWRO III. Comparison between SWRO and BWRO IV. Hydrodynamics and Concentration Polarization V. Power Generation by Pressure Retarded Osmosis VI. An Industrial Case Study

3 Section I Introduction/Background

4 Industrial Water Desalination Pretreatment RO Purification Post Treatment Chemical addition Cartridge filter RO membrane to remove dissolved solids CO 2 removal, ph adjustment Disinfection Distribution RO is the most versatile industrial technology to produce drinking water, consuming approximately 0.5 kwh/m 3 and 3.5 kwh/m 3 energy.

5 Reverse Osmosis: How it Works Controlled variables: permeate rate water recovery courtesy of M. Busch and J. Johnson, Dow Chemical Manipulated variables: pump speed retentate valve opening ratio

6 Sustainability Issues in RO Water recovery can never be close to 100% because of skyrocketing energy consumption required to drive the pump. In inland areas, any unrecovered water, or brine, is considered as an industrial waste. The brine disposal cost of brackish water RO is approximately $900/mega gallon. A higher recovery would require a higher energy consumption and/or capital investment in membrane elements.

7 Section II Optimization of SEC in Seawater RO (SWRO) Li, M. Minimization of Energy in Reverse Osmosis Water Desalination Using Constrained Nonlinear Optimization, Industrial & Engineering Chemistry Research, 49, , Li, M. Reducing Specific Energy Consumption in Reverse Osmosis (RO) Water Desalination: An Analysis from First Principles, Desalination, 276, , Li, M. Energy Consumption in Spiral-Wound Seawater Reverse Osmosis at the Thermodynamic Limit, Industrial & Engineering Chemistry Research, 53, , 2014.

8 Seawater RO Characteristic Equation Assumptions: Negligible pressure drop Negligible concentration polarization Negligible permeate osmotic pressure Negligible salt across membrane dddd = dddd LL pp (ΔPP Δππ = dddd LL pp (ΔPP QQ ff ΔP transmembrane hydraulic membrane Δπ transmembrane osmotic pressure Δπ 0 transmembrane osmotic pressure at entrance L p hydraulic permeability Q retentate flow rate Q f feed flow rate Q p permeate flow rate A membrane area QQ ΔΔππ 0 QQ pp ΔΔΔΔ + ΔΔππ 0QQ ff (ΔΔΔΔ) 2 ln 1 ΔΔππ 0 ΔΔΔΔ 1 QQ pp ΔΔππ 0 QQ ff ΔΔΔΔ = AALL pp

9 Dimensionless Form Coupled relationship among membrane properties, operating parameter and process performance γγ = αα YY + αα ln αα = ΔΔππ 0 ΔΔΔΔ: dimensionless pressure YY = QQ pp QQ ff : recovery 1 αα 1 YY αα ββ = αα 1 + αα YY ln 1 αα 1 YY αα α= π 0 / P Y=Q p /Q f γ=al p π 0 /Q f 3 ββ = γγ = AALL pp ΔΔππ 0 AALL pp ΔΔππ 0 QQ pp : membrane capacity production ratio QQ ff : membrane capacity intake ratio

10 Energy Consumption in RO Specific Energy Consumption SSSSSS = QQ ff ΔΔΔΔ ηη pppppppp QQ pp = 1 ηη pppppppp ΔΔππ 0 αααα Normalized Specific Energy Consumption NNSSSSSS = SSSSSS ΔΔππ 0 = 1 1 ηη pppppppp αααα Pump efficiency is usually assumed to be constant for simplified analysis

11 Constrained Optimization Model Contour of NSEC ignoring pump efficiency Optimization of NSEC min NNNNNNNN mm = αα,zz 1 αααα ss. tt. YY = (1 αα)(1 ee zz ) γγ = αα(yy + αααα) The constrained nonlinear optimization may be solved by various computational tools, e.g., Excel, Matlab (fmincon), Lingo and GAMS etc.

12 Optimization Results NSEC gradually reduces as γ increases. The lowest NSEC occurs at the thermodynamic limit where driving force is zero. For single-stage without ERD, as γ, the minimum of NSEC is 4 and the corresponding recovery is 50%.

13 Trade-off between Capital Investment and Energy Consumption min αα,zz JJ = ii 1 αααα + jjββ ss. tt. YY = (1 αα)(1 ee zz ) γγ = αα(yy + αααα) ββ = γγ/yy

14 Effect of Staged Operation and ERD Retentate from a RO stage is pressurized by a booster pump and sent as feed to the next stage. An energy recovery device (ERD) is used to recover the hydraulic energy of the high pressure brine reject, thus reducing feed pump power consumption.

15 Optimization Model SSSSCC mm min = αα jj,yy jj ΔΔππ 0 ss. tt. 0 = γγ jj αα jj YY jj + αα jj ln NN 1 YY jj jj=1 + 1 ηη eeeeee(1 YY NN ) αα jj αα NN αα NN 1 NN jj=1 ( 1 YY jj ) 0 = γγ tttttttttt γγ αα jj 1 YY jj αα jj (jj = 1,..., NN) NN 1 jj=2 jj 1 γγ jj ( 1 YY kk ) 2 kk=1 0 = γγ jj γγ jj+1 (1 YY jj ) 2 (jj = 1,..., NN 1) 0 αα jj (jj = 1,..., NN) 0 1 αα jj (jj = 1,..., NN) 0 αα jj+1 αα jj /(1 YY jj )(jj = 1,..., NN 1) 0 1 ( 1 YY jj ) YY mmmmmm NN jj=1

16 Optimization Results without ERD

17 Optimization Results with ERD (η ERD = 90%)

18 Optimization Results with ERD (η ERD = 90%, Y min = 80%)

19 Observations of Optimization Results A larger γγ allows SWRO to be operated closer to the thermodynamic limit, thus reducing NSEC. However, The NSEC flattens out when γγ becomes sufficiently large. Using more stages not only reduces NSEC, but also improves overall recovery. The NSEC flattens out when the number of stages increases. ERD can significantly reduce NSEC, theoretically to 1, while the corresponding recovery approaches 0. It is possible to obtain an NSEC below 3 while maintaining 80% recovery using all three strategies (e.g., 3-stage, ERD with an efficiency of 90% and a γγ tttttttttt of 2).

20 NSEC of RO at Thermodynamic Limit NSEC for multi-stage RO with booster pumps and ERD: NNNNNNNN = NN 1 YY jj jj=1 + 1 ηη eeeeee (1 YY NN ) αα jj αα NN αα NN 1 NN jj=1 1 YY jj At thermodynamic limit, αα jj + YY jj = 1 Optimal solution: NNNNNNNN = NN 1 jj=1 NN + (1 ηη αα eeeeee ) jj 1 NN jj=1 αα jj αα 1 = αα 2 =... = αα NN = (1 YY oo ) 1/NN NNNNNNNN = NN 1 YY 1 NN oo 1 + (1 ηη eeeeee YY oo

21 Theoretical Value of NSEC at Thermodynamic Limit For single- or multi-stage spiral wound RO, the reduction in NSEC due to an ERD at the thermodynamic limit is ηη eeeeee /YY oo. Without ERD, the minimum of NSEC with infinite stages and inter-stage booster pumps is Infinite number of RO stages with booster pumps and a 100% ERD is equivalent to an ideal theoretically reversible RO process, or NNNNNNNN = ln 1 YY oo Multi-stage design works better at high recoveries. ERD works better at low recoveries. Brine recirculation would not reduce NSEC. YY oo

22 Section III Differences and Similarities between SWRO and BWRO Li, M. A Unified Model-Based Analysis and Optimization of Specific Energy Consumption in BWRO and SWRO, Industrial & Engineering Chemistry Research, 52, , 2013.

23 Difference in Seawater and Groundwater RO Process model accounting for pressure drop in feed channel dddd(xx) dddd = AA LL pp ΔPP QQ 0 QQ Δππ 0 dd(δδδδ(xx)) dddd = kk QQ 2 QQ(xx) = QQ = 0 ΔPP(xx) = ΔPP = 0 dddd(xx) dddd = κκκκqq 2 (xx) dddd(xx) = γγ pp(xx) dddd αα 1 qq(xx) pp(xx) = = 0 qq(xx) = = 0 αα = Δππ 0 /ΔPP 0, γγ = AALL pp Δππ 0 /QQ 0, κκ = kkqq 0 2 /Δππ 0, qq = QQ/QQ 0, pp = ΔPP/ΔPP 0 κκ = kkqq 0 2 /Δππ 0 = 2ff(LL pppp /DD HH )ρρ(qq 0 /AA cc ) 2 /Δππ 0

24 Plant Design Parameters Correlation of γγ and κκ based on literature data from various plants Two important parameters show the difference between SWRO and BWRO: γγ = AALL pp Δππ 0 /QQ 0 κκ = kkqq 0 2 /Δππ 0 Δππ 0 = 390 psi for seawater RO and psi for brackish water RO. Current BWRO plants are not built to have a large γγ. Effect of retentate pressure drop may not be ignored in BWRO because of a large κκ.

25 Optimization Model Left: Single- or multi-stage without booster pump Right: Two-stage (2:1 layout) with booster pump min αα 1 JJ = 1 αα 1 (PP bbbb PP pp ) ΔΔ ππ 0 ηη pppppppp 1 NN ii=1 qq ii (ii ss. tt. ddpp ii (xx) dddd = κκ ii αα ii qq 2 ii (xx), ii = 1,2,..., NN ddqq ii (xx) pp ii (xx) = γγ dddd ii 1 αα ii qq ii (xx), ii = 1,2,..., NN pp ii (xx) = = ii 1, ii = 1,2,..., NN qq ii (xx) = = ii 1, ii = 1,2,..., NN min JJ = αα 1,αα 2 1 αα αα 2 pp 1 (1)qq 1 (1) 1 qq 1 (1)qq 2 (2) ss. tt. ddpp ii (xx) dddd = κκ ii αα ii qq 2 ii (xx), ii = 1,2 ddqq ii (xx) pp ii (xx) = γγ dddd ii 1 αα ii qq ii (xx), ii = 1,2 pp ii (xx) = = ii 1, ii = 1,2 qq ii (xx) = = ii 1, ii = 1,2 γγ 1 = 2 3)γγ tttttttttt γγ 2 = γγ 1 2 qq 2 1 (1) κκ 2 = 4κκ 1 qq 3 1 (1) αα 2 αα 1 pp 1 (1 ) qq 1 (1) αα ii 0, ii = 1,2 αα ii 1, ii = 1,2

26 Optimization of Single-Stage RO γγ κκ αα NNNNNNNN YY pp(0)/αα-1/qq(0) pp(1)/αα-1/qq(1) BWRO SWRO Pressure drop effect may be ignored in SWRO but not in BWRO. The optimal recovery for BWRO is much higher mainly because of a smaller γγ. Operation near thermodynamic limit is only valid for SWRO but not for BWRO.

27 Effect of RO Stage Configuration a) One stage b) Two stage without booster pump c) Two stage with booster pump d) One stage with brine recirculation

28 Optimization Results for Two Cases κκ = 1 (based on the first-stage in a two-stage RO) κκ = 0.1 (based on the first-stage in a two-stage RO)

29 Observations of Optimization Results For BWRO, single-stage is better than two-stage in terms of NSEC (However, industrial design employs two-stage to achieve a more uniform flow). Using booster pump does not improve NSEC under optimal conditions because of a very small γγ. For SWRO, two-stage with booster pump could be better than one-stage in terms of NSEC if γγ is sufficiently large. Using booster pump does improve NSEC under optimal conditions. Brine recirculation does not improve NSEC in BWRO due to increase in feed salinity and retentate pressure drop.

30 Section IV Hydrodynamics and Concentration Polarization in Industrial RO Feed Channel Li, M.; Bui, T.; Chao, S. Three-Dimensional CFD Analysis of Hydrodynamics and Concentration Polarization in an Industrial RO Feed Channel, Desalination, 397, , 2016.

31 Concentration Polarization JJ ww cc + DD = JJ ww cc pp cc = cc = δδ DD cc = cc = 0 Concentration Polarization Modulus: ΔΔππ eeeeee cc ww cc pp JJ ww = exp ΔΔΔΔ cc rr cc pp DD/δδ DD Mass transfer boundary layer in narrow flat channel: δδ DD = 1.475xx HH 2/3 1/3 2DD 2xx uu mmmmmm HH It is discussed extensively in literature that concentration polarization has a strong adverse effect on water flux. However, we argue that its effect may not be so significant in commercial RO under realistic industrial operating conditions.

32 Commercial RO Feed Channel with Spacer Filaments Spiral wound RO feed spacer Geometry construction using COMSOL courtesy of M. Busch and J. Johnson, Dow Chemical

33 Comparison of Hydrodynamics between Flat and Spacer-Filled Channels

34 Comparison of Salt Concentration and Water Flux between Flat and Spacer-Filled Channels

35 Comparison of Mass Transfer between Flat and Spacer-Filled Channels

36 Observations of the Effect of Feed Spacer Filaments The pressure drop v.s. average longitudinal velocity can be approximated by ΔPP cc uu 1.67 and the trend matches an empirical correlation previously derived from plant data. Substantial wall-parallel velocity near the membrane surface is observed, which helps suppress boundary layer development. Rolling cells are formed in the center of the feed channel, which promote transverse mixing. Different from concentration polarization phenomenon in flat, narrow channels, concentrated islands are isolated in regions near spacer filaments where flow is relatively stagnant. The local mass transfer coefficient kk mm oscillates. longitudinally but the cell-average kk mm appears fairly constant in cells adjacent to each other. It is shown that kk mm uu 0.40 under plant operating conditions. Concentration polarization is not very significant in modeling industrial BRWO.

37 Section V Power Generation from Seawater or SWRO Brine by Pressure Retarded Osmosis Li, M. Analysis and Optimization of Pressure Retarded Osmosis for Power Generation, AIChE Journal, 61, , 2015.

38 Pressure Retarded Osmosis PRO may be used to generate power from seawater or brine from SWRO. There are discussions in literature about integration of PRO with RO to reduce the energy consumption of RO. Flux: JJ ww = LL pp (Δππ ΔPP) is usually assumed to be constant in literature, which may not be true. Power Density: PPPP = LL pp (Δππ ΔPP)ΔPP Maximum occurs at ΔPP oooooo = Δππ/2 based on literature.

39 Basic Definitions in PRO Specific Energy Production (SEP) SSSSSS= QQ 0 (qq dd 1)ΔPP/QQ 0 = (qq dd 1)ΔPP qq dd : dilution ratio at the end of the membrane ΔPP: applied pressure Normalized SEP or Osmotic to Hydraulic Efficiency NNNNNNNN = SSSSSS/ππ 0 DD = (QQ 0 SSSSSS)/(QQ 0 ππ 0 DD ) = ηη OOOOO Power Density (PD)

40 Characteristic Equation without Concentration Polarization Local water flux (assuming ππ FF = ππ FF 0 ): dddd = LL DD dddd pp Δππ ΔPP = LL pp (ππ QQ 0 0 ππ QQ 0 FF ΔPP) Dimensionless form: dddd dddd = γγ 1 qq θθ θθ = (ΔPP + ππ FF 0 )/ππ DD 0, qq = QQ/QQ 0, and γγ = AALL pp ππ DD 0 /QQ 0 Solution: γγ = 1 θθ 1 qq dd + 1 θθ ln 1 θθ 1 qq dd θθ q d : dilution ratio at the end of the membrane

41 Optimization of NSEP Observations from profiles of qq dd and NSEP qq dd increases as ΔPP reduces and/or γγ increases. At a fixed γγ, there is an optimal ΔPP corresponding the maximum NSEP. Optimization of NSEP: max αα,zz = (qq dd 1) 1 αα rr ss. tt. qq dd = αα (αα 1)ee zz γγ = αα(1 qq dd + αααα) 1 αα 0 1 qq dd 0

42 Optimization Results Observations: The optimal ΔPP shifts away from Δππ 0 /2 as γγ = AALL pp ππ 0 DD /QQ 0 increases. An increase in rr (rr = ππ 0 FF /ππ 0 DD ) significantly reduces qq dd and NSEP. When rr = 0 (or fresh water is used as feed solution), the largest NSEP occurs at forward osmosis conditions, i.e., ΔPP oooooo = 0.

43 Optimal Driving Force in PRO Similarities between RO and PRO A larger γγ allows the PRO to be operated closer to its thermodynamic limit, thus improving SEP. A larger γγ allows the RO to be operated closer to its thermodynamic limit, thus improving SEC.

44 Optimization of PRO Accounting for Concentration Polarization AA max ΔΔΔΔ JJww 0 dddd ΔΔΔΔ AA dddd dddd = JJ ww JJ ww = LL pp ππ DD bb exp ( JJ 1 ππ bb FF DD ww ππ eeeeee ( JJ wwkk) eeeeee ( JJ ww ) kkmm ) bb kk mm 1 + BB ΔPP [eeeeee ( JJ JJ ww KK) 1] ww JJ ww is in an implicit form.

45 Short-Cut Optimization Method If JJ ww /kk mm << 1 and JJ ww KK << 1, JJ ww may be approximated by JJ ww LL pp (σσδππ ΔPP), where σσ = 1/(1 + BBBB) and LL pp = LL pp /(1 + LL pp Δππππ/kk mm ). The characteristic equation becomes γγ = 1 (1 qq θθ dd) + σσ θθ AALL pp QQ 0 /ππ DD 0. ln σσ θθ σσ qq dd θθ, where γγ = Optimization model: max αα,zz NN SSSSSS = (qq dd 1) 1 αα rr ss. tt. qq dd = αααα (αααα 1)ee zz γγ = αα(1 qq dd + αααααα) 1 σσ αα 0 1 qq dd 0 Note: It is found that this method provides very accurate solution to ΔPP oooooo. However, flux profile, NSEP and PD are better calculated using the original concentration polarization model and the derived ΔPP oooooo.

46 Optimization Results Parameters are taken from literature (Achilli, JMS, 2009) Comparison between short-cut and rigorous optimization methods (values obtained using the short-cut optimization method, if different from the rigorous method, are presented in parenthesis): Parameters kk mm KK BB LL pp Δππ 0 Value m/s s/m m/s m/s/kpa 2763, 4882 kpa ΔΔππ 00 = 2763 kpa ΔPP, kpa JJ ww, μμm/s PD, W/m 2 γγ qq dd ηη OOOOO, % Δππ = Δππ (1316) 2.16 (2.18) QQ 0 /AA = 8μμm/s 1300 (1295) 1.78 (1.79) QQ 0 /AA = 4μμm/s 1260 (1259) 1.56 (1.56) QQ 0 /AA = 2μμm/s 1190 (1186) 1.28 (1.28) QQ 0 /AA = 1μμm/s 1070 (1067) 1.00 (1.01) ΔΔππ 00 = 2763 kpa ΔPP, kpa JJ ww, μμm/s PD, W/m 2 γγ qq dd ηη OOOOO, % Δππ = Δππ (2325) 3.38 (3.47) QQ 0 /AA = 8μμm/s 2260 (2244) 2.64 (2.66) QQ 0 /AA = 4μμm/s 2140 (2133) 2.24 (2.25) QQ 0 /AA = 2μμm/s 1950 (1943) 1.79 (1.80) QQ 0 /AA = 1μμm/s 1680 (1685) 1.38 (1.38)

47 Power Density and Flux Profile Six cases: Black: Δππ = Δππ 0 no CP. Red: Δππ = Δππ 0 with CP. Magenta: QQ 0 /AA = m/s. Yellow: QQ 0 /AA = m/s. Blue: QQ 0 /AA = m/s. Green: QQ 0 /AA = m/s.

48 Conclusions from PRO Optimization Short-cut optimization yields essentially the same solution as the rigorous solution. Moreover, it provides parameters to explain the effect of ICP, ECP and dilution in DS. Shift of optimal ΔPP from Δππ 0 /2: Dilution effect (i.e. γγ is not zero). Internal concentration polarization (i.e., σσ < 1). Nonlinearities and conflicting power density and efficiency in process scale-up Realistically, up to 25% of the osmotic energy in SWRO brine may be recovered if similar membranes are invested in PRO (i.e., the capital investment in RO elements will be doubled).

49 Section VI An Industrial Case Study Li, M.; Noh, B. Validation of Model-Based Optimization of Brackish Water Reverse Osmosis (BWRO) Plant Operation, Desalination, 304, 20-24, Li, M. Optimization of Multitrain Brackish Water Reverse Osmosis (BWRO) Desalination, Industrial & Engineering Chemistry Research, 51, , Li, M. Optimal Plant Operation of Brackish Water Reverse Osmosis (BWRO) Desalination, Desalination, 293, 61-68, 2012.

50 Chino I Desalter Draws raw water from 15 groundwater wells Processes 14 MGD of drinking water 1.7 megawatt (0.5 megawatt is for RO) Serves the Chino basin and neighboring areas Wells 1-4 Wells 5-15 VOC RO 2 MGD 7 MGD Final Blended Product 14 MGD Product Quality Requirement TDS: 350 mg/l Nitrate: 25 mg/l Ion Exchange 5 MGD

51 Desalination RO Unit Consists of 4 process trains, each equipped with: a dedicated membrane feed pump with VFD 9 stage vertical turbine pump with 300 hp motor, 1450 gpm, 625 ft TDH at 1785 rpm

52 RO Stage Configuration and Layout Two-stage pressure vessel array (28+14)x7 = 294 RO elements No inter-stage booster pump

53 Typical Brackish Feedwater Analysis Parameter Value Calcium (Ca), mg/l 174 Magnesium (Mg), mg/l 40 Sodium (Na), mg/l 48 Potassium (K), mg/l 3 Carbonate (as CO 3 ), mg/l 0 Bicarbonate (as HCO 3 ), mg/l 490 Sulfate (SO 4 ), mg/l 55 Chloride (Cl), mg/l 102 Nitrate (as NO 3 ), mg/l 170 Silica (as SiO 2 ), mg/l 37 Barium (Ba), mg/l 0.20 Fluoride (F), mg/l 0.20 Strontium (Sr), mg/l 1.3 Total Dissolved Solids (TDS), mg/l 924 ph, units 6.5 Temperature, degrees C 20

54 RO Process Model dq( x) = A L dx Q f π = π 0 Q d( P( x)) = k Q x = 0, Q( x) = x = 0, P( x) = p ( P π ) f P 2 o + P pump P p k pressure drop factor ΔP pressure difference across the membrane P o feed pressure prior to pump ΔP pump pressure increase across pump P p permeate pressure Q retentate flow rate Q f feed flow rate Δπ o osmotic pressure change across the membrane entrance

55 Plant Production Data Train 1 Parameter Value Number of pressure vessels per train 42 Number of 1st stage pressure vessels 28 Number of 2nd stage pressure vessels 14 Number of membrane elements per vessel 7 Area per element, ft Feed pressure, PP 0, psi 40.6 Feed osmotic pressure, Δππ 0, psi 9 Feed flow, QQ ff, gpm 1,525 Permeate pressure, PP pp, psi 16.4 Permeate flow, QQ pp, gpm 1,234 Recovery, YY, % 80.9 Retentate pressure drop in 1st stage, ΔPP rr1, psi 24.9 Retentate pressure drop in 2nd stage, ΔPP rr2, psi 18.2 Pump head, HH, ft 360

56 Parameter Identification from Plant Operation Data k = psi/gpm 2 (in the first stage) L p = 0.11 gfd/psi

57 Optimization Model min QQ ff ΔΔPP pppppppp QQ ff,yy QQ pp ΔΔππ 0 ηη pppppppp ss. tt. ηη pppppppp = ηη pppppppp (QQ ff, HH dddd(xx) dddd = AA LL pp ΔPP QQ ff QQ Δππ 0 dd(δδδδ(xx)) dddd = kk QQ 2 QQ(xx ) = QQ = 0 PP(xx ) = ΔPP 0 + ΔPP pppppppp PP = 0 ΔPP pppppppp = HH QQ pp = QQ ff QQ(2 YY = QQ pp QQ ff YY YY mmmmmm YY YY mmmmmm gg pppppppp (QQ ff, HH 0

58 RO Plant Trial Methodology Data was taken from Train 1 over 4 days Permeate flow rate kept constant at 1235 GPM Recovery rate was varied from 78 to 95% and the resulting field data were recorded for analysis

59 Retentate Valve Pump Speed Position (92% of 1785 rpm) Pump Output RO Input Retentate Flowrate Permeate Flowrate Quality of Permeate Quality of Feedwater

60 Plant Validation of Model

61 Improved Model Incorporating CFD Results dddd dddd = JJ ww AA = 0, QQ = QQ 0 dd(δδδδ) dddd = kk 2 QQ = 0, ΔPP = ΔPP 0 JJ ww = LL pp[δpp Δππ exp JJ ww ( kk 3 QQ 0.40 ) Δππ = QQ 0 Δ ππ 0 QQ

62 Optimization of Multi-train RO A desalination plant may have multiple RO trains with RO elements of different service times. Older membranes tend to have lower L p. By optimally allocating permeate production rates among all trains based on L p, the SEC of the whole plant may be reduced.

63 Economic Considerations for Sustainable Production Model predicts optimum recovery point Power saving ($40 K/year) Reduction in brine volume (>50%) which leads to less disposal cost ($ 360 K/year) Faster membrane fouling not quantified ($ negative) Requires comprehensive optimization study prior to implementation Precipitation in Brine Line after 13 Years of Service

64 Related Publications Li, M.; Bui, T.; Chao, S. Three-Dimensional CFD Analysis of Hydrodynamics and Concentration Polarization in an Industrial RO Feed Channel, Desalination, 397, , Li, M. Analysis and Optimization of Pressure Retarded Osmosis for Power Generation, AIChE Journal, 61, , Li, M. Energy Consumption in Spiral-Wound Seawater Reverse Osmosis at the Thermodynamic Limit, Industrial & Engineering Chemistry Research, 53, , Li, M. A Unified Model-Based Analysis and Optimization of Specific Energy Consumption in BWRO and SWRO, Industrial & Engineering Chemistry Research, 52, , Li, M.; Noh, B. Validation of Model-Based Optimization of Brackish Water Reverse Osmosis (BWRO) Plant Operation, Desalination, 304, 20-24, Li, M. Optimization of Multitrain Brackish Water Reverse Osmosis (BWRO) Desalination, Industrial & Engineering Chemistry Research, 51, , Li, M. Optimal Plant Operation of Brackish Water Reverse Osmosis (BWRO) Desalination, Desalination, 293, 61-68, Li, M. Reducing Specific Energy Consumption in Reverse Osmosis (RO) Water Desalination: An Analysis from First Principles, Desalination, 276, , Li, M. Minimization of Energy in Reverse Osmosis Water Desalination Using Constrained Nonlinear Optimization, Industrial & Engineering Chemistry Research, 49, , 2010.

65 Acknowledgements Students: Sophia Bui, Steven Chao, and Brian Noh. Inland Empire Utility Agency: Moustafa Aly Petroleum Research Fund