Optimization of Multitrain Brackish Water Reverse Osmosis ...

Optimization of Multitrain Brackish Water Reverse Osmosis(BWRO) DesalinationMingheng Li*,†

†Department of Chemical and Materials Engineering, California State Polytechnic University, Pomona, California 91768,United States

ABSTRACT: This work focuses on optimal operation of brackish water reverse osmosis (BWRO) plants employingmultitrains which have different service times and membrane permeability parameters. A nonlinear optimization problem,based on a previously developed comprehensive RO model that accounts for characteristic curves of booster pumps drivingthe RO trains and pressure drop along each RO train, is formulated and solved to minimize the overall specific energyconsumption (SEC) while maintaining the same overall water production. A 16−17% reduction in SEC is possible byoptimizing production allocations among all trains as well as operating conditions within the normal pump operating rangein each train. It is shown that optimizing each train individually (without optimizing production allocations) could yield ahigher SEC.

1. INTRODUCTIONReverse osmosis (RO) membrane separation is a provendesalination technology to make clean and drinking water.Energy consumption is considered to be a very important issuein RO desalination.1,2 To reduce specific energy consumption(SEC), or energy cost per unit volume of permeate flow,research efforts have been made including development of highpermeability membranes,3,4 utilization of energy recoverydevices,4,5 and alternative energy sources to subsidize electricityconsumption,6 as well as first-principles based analysis andoptimization of RO configurations and operating conditions.7,8

It is reported that implementation of energy-efficient ideas isable to make the RO desalination technology more competitivewith alternatives.9,10

In the area of model-based approach, it has been shownthat operating RO near the thermodynamic limit (where theapplied pressure is slightly above the concentrate osmoticpressure) significantly reduces the SEC.11,12 Recent researchhas been focused on a formal mathematical framework toprovide a clear evaluation of production cost by studying theeffect of RO configuration, applied pressure, water recovery,pump efficiency, membrane cost, ERD, stream mixing, andbrine disposal cost.3,13−16 Using model-based control, a re-duction of SEC in an pilot-scale RO experimental system hasbeen demonstrated.17,18

It is acknowledged that energy consumption of boosterpumps to drive the RO membrane elements accounts for amajor portion of the total cost of water desalination.19−21 In aseries of previous papers,22−24 the author provided acomprehensive analysis of NSEC (SEC normalized by thefeed osmotic pressure) of the pump in RO desalination.A dimensionless characteristic equation, based on the assumptionof negligible pressure drop along the RO train, was derived toreveal the coupled relationship between RO configuration, feedconditions, membrane performance, and operating condi-tions.22 The equation involves an important dimensionless

parameter γ = ALpΔπ0/Qf (where A is the membrane area, Lp isthe hydraulic permeability, Δπ0 is the feed osmotic pressure,and Qf is the feed rate) that describes the dimensionlessmembrane capacity. γ determines the best achievable NSEC.Under optimized conditions, the higher the γ, the lower theNSEC. When γ is sufficiently large, the RO is operated near thethermodynamic limit, and the optimal NSEC approaches itsglobal minimum (e.g., 4 for single stage RO without ERD). Inorder to achieve the optimal NSEC, the applied pressure shouldbe determined based on the value of γ, and charts areavailable.22 The theoretical analysis also shows thatincreasing number of stages with interstage pumps mayalso improve NSEC to a limited extent. However, it isdesirable for a high water recovery.23 Employing an ERD cansignificantly reduce NSEC, while the optimal conditiontends to have a low water recovery if no constraint isapplied.22,23 It is therefore recommended to combine allthese methods (a sufficiently large γ, multistage with inter-stage pumps, and an ERD) to reduce NSEC and to maintaina high recovery at the same time. For example, an NSECaround 2.5−2.8 with an 80% water recovery may be possibleusing 3−5 RO stages operated at a γtotal about 3−5 (or Qf =0.2−0.3 AtotalLpΔπ0, where Atotal is the total membrane areain all stages) assuming a 90% ERD efficiency.23 This is lowerthan the theoretical minimum of a single-stage RO withoutERD. The optimization framework also provides analyticalsolutions to RO desalination with/without minimum re-covery constraints at the theoretical thermodynamic limit,where γ approaches infinity.23 The author’s most recentwork focuses on operation of a single BWRO train where thepump, train configurations, and membrane elements are

Received: November 30, 2011Revised: January 24, 2012Accepted: February 8, 2012Published: February 8, 2012

Article

pubs.acs.org/IECR

© 2012 American Chemical Society 3732 dx.doi.org/10.1021/ie202796u | Ind. Eng. Chem. Res. 2012, 51, 3732−3739

pubs.acs.org/IECR

fixed.24 The model-based optimization explicitly accounts forthe effects of pressure drop along the RO train and pumpcharacteristic curves, thus improving the accuracy ofprevious works.22,23 It is shown that the NSEC can bereduced by shifting the operation point on the pumpcharacteristic map while maintaining the same permeateproduction rate.24

As a continuation of the above efforts, this work focuses onoptimal operation of BWRO plants employing multitrains,which has not been addressed previously.24 A modern RO planttypically utilizes several trains which could have different servicetimes and different permeability parameters. Therefore, alloca-tion of production rates among all trains may also have an effecton NSEC.

Figure 1. Schematic of an industrial multitrain RO water desalination process.

Figure 2. Array of pressure vessels in an industrial two-stage RO water desalination train without interstage pump.

Industrial & Engineering Chemistry Research Article

dx.doi.org/10.1021/ie202796u | Ind. Eng. Chem. Res. 2012, 51, 3732−37393733

2. PROBLEM FORMULATION OF MULTITRAIN ROOPTIMIZATION

In this section, the optimization methodology of multitrain ROdesalination will be illustrated using an industrial desalinationplant in Chino, California. This facility has four RO trains withan overall production about 7 mega gallon per day (MGD), asshown in Figure 1. Each RO train has two stages with nointerstage pump. Please note that this is different from brinestaged operation with additional pumps.13 A dedicated boosterpump equipped with a variable frequency drive (VFD) is usedto provide adequate feed pressure in an energy-efficientmanner. A control valve is installed in each concentrate line.The permeate flow and water recovery are controlled bymanipulating pump speed and concentrate valve position usinga RO programmable logic controller (PLC). Each RO trainconsists of pressure vessels in a two-stage array (see Figure 2).The first stage has 28 pressure vessels operated in parallel. Thenumber of pressure vessels in the second stage is only a half ofthe one in the first stage because of a significantly smallervolumetric flow rate. Each pressure vessel contains 7 ROelements in series. The concentrate streams from the first stagepressure vessels are combined and fed to the second stagepressure vessels. The plant is operated at a recovery around80% in order to meet the minimum production and themaximum brine discharge requirements.In the author’s previous work,24 a comprehensive model was

developed to explicitly account for the effects of pressure dropalong each RO train as well as pump characteristic curves.Specifically, the RO model mathematical model has thefollowing form24

− = · · Δ − Δπ

− Δ =− ·

= =

Δ = + Δ − =

⎛⎝⎜⎜

⎞⎠⎟⎟dQ x

dxA L P

Q

Q

d P xdx

k Q

Q x Q x

P x P P P x

( )

( ( ))

( ) @ 0

( ) @ 0

pf

f

pump p

0

2

0 (1)

where Q is the retentate flow rate, and ΔP is the pressuredifference across the membrane. −dQ is the flow rate of wateracross the membrane of area dA (dA = A · dx, where A is thetotal area of all RO elements in each stage and x isdimensionless number with 0−1 and 1−2 representing thefirst and second stage, respectively). Lp is the membranehydraulic permeability. Δπ0 is the osmotic pressure differenceat the entrance of the membrane channel. Qf is the feed flowrate. P0 is the feed pressure before the pump. ΔPpump is thepressure increase across the pump. k is a coefficient describingthe pressure drop along the pressure vessel in the retentatestream. It is important to note that the flow area is reduced by ahalf in the second stage; therefore k is four times of the one inthe first stage. The model is based on the assumptions ofnegligible pressure drop and osmotic pressure in the permeateflow.24

In a previous work, the mathematical model wasimplemented in a computational framework to optimize operat-ing conditions in a single train.23 Based on this model, the

optimization problem of multitrain RO operation accountingfor pump efficiency is formulated as follows

∑

η=

∑ Δ

Δπ

η =η =

=− · · Δ − Δπ =

Δ=− · =

= = =

Δ = +Δ − = =

Δ = · =

= − =

= =

= =

≤ =

≥ =

≤ =

⎛⎝⎜⎜

⎞⎠⎟⎟

NSECQ P

Q

s t

Q H i N

dQ x

dxA L P

Q

Qi N

d P xdx

k Q i N

Q x Q x i N

P x P P P x i N

P H i N

Q Q Q i N

Q Q i N

YQ

Qi N

Y Y i N

Y Y i N

g Q H i N

min( / )

. .

( , ), 1, ...,

( ), 1, ...,

( ( )), 1, ...,

( ) @ 0, 1, ...,

( ) @ 0, 1, ...,

0.4327 , 1, ...,

(2), 1, ...,

, 1, ...,

, 1, ...,

, 1, ...,

, 1, ...,

( , ) 0, 1, ...,

H Q

i f pump pump

p

pump pump f i train

ip i

f

itrain

ii i train

i f train

i pump p train

pump i train

p f i train

ip p train

ip

ftrain

i max train

i min train

pump f i train

, 0

0

2

0

i fi

i i i

total

i i

ii

i

i i i

i

i i

i total

i

i

i

(2)

where Ntrain is the number of RO trains. H is the pump head infeet. ΔPpump is the pressure increase across the pump.ηpump(Qf,H) is the efficiency based on the pump characteristicmap. Y is the water recovery, and Ymax and Ymin are its upperand lower limits. Qp is the permeate flow rate at the exit of theRO train. The inequity constraint gpump(Qf,H) ≤ 0 is toguarantee that each RO train is operated within the normalrange of the booster pump. ΔPpump = 0.4327 · H is theconversion of pump head (ft) to pressure increase (psi) forwater.

3. RESULTS AND DISCUSSION3.1. Model Validation Using Plant Data. The operation

data from all trains with different service times (A, B, C, and D)are shown in Table 1). The parameters k and Lp in themathematical model described in eq 1 are shown in Table 2.These values are determined using nonlinear regression to bestfit the plant data. A similar approach was employed in theauthor’s previous works.24,25 Using these parameters, theprofiles of pressure differences across the membrane (systempressure and osmotic pressure) and flows (permeate andretentate) along the RO train are solved and shown in Figure 3.The measured values of feed and brine flows and the pressuredifferences across the membrane at the exit of the first and thesecond stages are marked with circles for a comparison. A nearlyperfect match between all measurement points is obtained. Itis clearly seen a strong correlation between the permeabilityparameter and the membrane service time, i.e., the longer theservice time, the smaller the membrane permeability Lp. It is also



noticed that three trains (A, B, D) have almost the same param-eter k. However, train C corresponding to the longest servicetime has a larger k than the rest, impling possible scaling andfouling.3.2. Effect of Permeate Allocation on Optimal NSEC.

The optimization of multitrain RO operation is solved using theparameters determined from the current operating conditions(referred to as case i). The objective is to reduce the NSECwhile maintaining the same overall permeate production(i.e., 4,778 gpm). The optimization was done using a nonlinearconstrained multivariable optimization package (fmincon) inMatlab. It is not a global optimization solver; however, differentinitial guesses were used to check the final solutions and

consistency was found. The solving time is only several secondsusing a 2.67 GHz laptop.Two optimization strategies are studied for a comparison. In

one optimal case (case ii), eq 2 is solved where not only theoperating conditions in each RO train but also the allocation ofproduction rates among all trains are optimized. In the otheroptimal case (case iii), each RO train is optimized individually,i.e., only the operating conditions are optimized, however, thepermeate rate of each train is maintained at current productionlevel.24 Unless mentioned specifically, Ymax = 100% and Ymin =50% are used for all studies in this work. The operating con-ditions of these two optimized cases are shown in Table 3, andthe profiles of flow rates and pressure differences across themembrane are plotted in Figure 4. As compared to the currentoperating conditions, both optimized cases suggest higherrecoveries in each train to reduce NSEC. To achieve these, allRO trains are operated at smaller feed rates and more closedvalve openings in the concentrate lines,24 which helps to main-tain a high pressure at the outlet of the second stage and allowsthe pumps to run in slower speeds. A comparison betweencases i and iii also shows a very consistent trend to reduceNSEC at a fixed permeate flow in each train, i.e., a lower feed,a higher pump head, a lower pump speed, and a higherrecovery.It is shown that the reduction of NSEC is about 16−17% in

both optimized cases. Accounting for permeate allocation in theoptimization increases the production in train A (associatedwith the most permeable membranes) and decreases the pro-duction in train C (associated with the least permeablemembranes). Even though the NSEC of train A alone is higher,those of other trains are lower. As a result, the overall NSEC isreduced. From a viewpoint of mathematics, fixing permeateproduction in each train adds constraints to the optimizationproblem; therefore, the objective function is higher than the onein case ii where the constraints are removed.

3.3. Effect of Recovery on Optimal NSEC. From Table 3it is known that the best operating conditions have a water re-covery around 93−94% in all trains. In this subsection, severaladditional optimization studies are done by including an additionalequality constraint of recovery in each case (Y = 80%, 82%, ...,96% in each train). These steady-state optimization studies aimto provide trajectories for incremental reduction in NSEC inplant operation. The results are shown in Figure 5. Except for

Table 1. RO Train Configuration and Operation Data

parameter train A train B train C train D

number of pressure vessels per train 42 42 42 42number of first stage pressure vessels 28 28 28 28number of second stage pressurevessels

14 14 14 14

number of membrane elements pervessel

7 7 7 7

area per element, ft2 400 400 400 400rough service time, days 500 1,000 1,700 1,300feed flow, Qf, gpm 1,525 1,524 1,404 1,506feed pressure before pump, P0, psi 40.6 40.6 40.6 40.6pressure after pump, psi 196.5 247.9 283.8 263.2pump head, H, ft 360 479 562 514feed osmotic pressure, Δπ0, psi 9 9 9 9permeate pressure, Pp, psi 16.4 16.7 16.3 16.8retentate pressure drop in first stage,ΔPr1, psi

24.9 25.3 28.6 25.8

retentate pressure drop in secondstage, ΔPr2, psi

18.2 20.6 17.1 19.3

permeate flow, Qp, gpm 1,234 1,234 1,131 1,179recovery, Y, % 80.9 81.0 80.6 78.3

Table 2. Parameters Used in the Mathematical Model

parameter train A train B train C train D

k in first stage,psi/gpm2

2.1 × 10−5 2.2 × 10−5 2.6 × 10−5 2.1 × 10−5

Lp, gfd/psi 1.1 × 10−1 8.1 × 10−2 6.2 × 10−2 7.0 × 10−2

Figure 3. Simulated profiles of (a) flow rates and (b) pressure differences across the membrane along all RO trains with different service times. Plantdata are marked with circles.



train A at recoveries between 80 and 83%, all RO trains followvery similar trends in pump speed, feed flow, pump head,permeate flow, and NSEC. Based on the graphical results,it can be concluded that increasing the recovery (up to93−94%) can gradually reduce NSEC. However, a furtherincrease in recovery would lead to an increase in theNSEC, primarily because the pump head starts to take off. Itis also noticed that the optimal allocation of permeate rates

among all trains is very consistent when the recovery isbetween 84 and 96%.The optimized results are also plotted in the pump charac-

teristic maps, as shown in Figure 6. The current operatingconditions are marked by circles, and the optimal operatingconditions are marked by diamonds (with optimal allocation ofpermeate productions) and stars (with fixed allocation ofpermeate productions). The operating conditions corresponding

Table 3. Comparison between Current and Optimized Operating Conditions

case train n Qf H ηpump Y Qp NSEC

i A 1,513 1,525 360 0.754 0.809 1,234 28.4B 1,639 1,524 479 0.798 0.810 1,234 35.6C 1,684 1,404 562 0.816 0.806 1,131 41.1D 1,672 1,506 514 0.804 0.783 1,179 39.3overall 4,778 36.0

ii A 1,507 1,418 400 0.795 0.934 1,326 25.9B 1,557 1,302 479 0.815 0.935 1,218 30.2C 1,587 1,150 544 0.811 0.941 1,082 34.2D 1,568 1,230 509 0.819 0.937 1,152 31.9overall 4,778 30.3

iii A 1,434 1,334 367 0.798 0.925 1,234 23.9B 1,571 1,314 487 0.815 0.939 1,234 30.6C 1,628 1,204 567 0.814 0.939 1,131 35.7D 1,590 1,256 522 0.819 0.939 1,179 32.7overall 4,778 30.6

Figure 4. Simulated profiles of (a,c) flow rates and (b,d) pressure differences across the membrane along all RO trains (a,b) with and (c,d) withoutoptimal allocation of production rates.



to recoveries from 80 to 96% are also plotted in order to showthe optimization trajectory. It is clear that all the results are wellwithin the normal range of the pump. The curve in Figure 6(a)explains why the feed and permeate rates of train A follow adifferent trend from the rest when the recovery is between 80 and83% (Figure 5(b) and (e)). In this range, the optimal flow rate andpump head lie on the boundary of the recommended operating

range. If a different pump with a wider operating range is selected,the feed rates in train A could be larger to reduce NSEC.Figure 7 provides a relationship between membrane property

and permeate allocation as well as the effect of permeateallocation on overall NSEC of all trains. For a wide range ofwater recoveries, allocating more productions to RO trains withmore permeable membranes would reduce the overall NSEC.

Figure 5. Relationship of (a) pump speed, (b) feed flow, (c) pump head, (d) pump efficiency, (e) permeate flow, and (f) NSEC and specified waterrecovery.



It is worth noting that the current plant does realize this fact,even though it is not done in a systematic way.

4. CONCLUSIONS

A 16−17% reduction in NSEC in a multitrain RO desalinationprocess might be possible by optimizing operating conditionswithin the normal operating range of each pump and pro-duction rates allocated among all RO trains. It is shown thatRO trains with longer service times (or smaller permeabilityparaments) should produce less water in order to reduce theoverall NSEC. For each train studied in this work, the optimalwater recovery is around 93%-94%.

■ AUTHOR INFORMATION

Corresponding Author*Phone: +1-909-869-3668. Fax: +1-909-869-6920. E-mail:[email protected].

NotesThe author declares no competing financial interest.

■ ACKNOWLEDGMENTS

The author would like to thank Brian Noh and Moustafa Alyfrom Inland Empire Utility Agency for plant tours, operationdata, and fruitful discussions.

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Figure 6. Trajectories of feed flow and pump head on the pump characteristic map (recovery varies from 80% to 96%).

Figure 7. Effect of permeate allocation on overall NSEC.



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Optimization of Multitrain Brackish Water Reverse Osmosis ...

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