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Journal of Membrane Science 282 (2006) 7–13

Optimum design of reverse osmosis seawater desalination systemconsidering membrane cleaning and replacing

Yan-yue Lu a, Yang-dong Hu a,∗, Dong-mei Xu b, Lian-ying Wu a

a College of Chemistry and Chemical Engineering, Key Laboratory of Marine Chemistry Theory and Technology,Ministry of Education, Ocean University of China, Qingdao 266003, China

b College of Chemistry and Environmental Engineering, Shandong University of Science and Technology, Qingdao 266003, China

Received 18 November 2005; received in revised form 6 April 2006; accepted 17 April 2006Available online 27 April 2006

bstract

The seawater reverse osmosis (RO) desalination is an attractive and viable method for the production of fresh water in many areas. This paperddresses the optimal design of RO desalination system considering membrane cleaning and replacing during the 5-year maintenance period, andnly a single stage configuration with pressure exchanger is analyzed. A mathematical model for the prediction of the performance of RO processs presented in detail. Simultaneously, this paper also addresses the new fouling model and the criterion of cleaning and replacing. Then the relevantconomic models to the RO desalination process are developed, which relate the cost of investment and operation with the design variables, thetructural variable, as well as the binary variable that determine the membrane regeneration. The optimum design problem can be formulated as a

ixed-integer non-linear programming (MINLP) problem, which minimizes the total annualized cost. The mathematical programming problem

s solved with GAMS software. As a result, the optimal operational parameters and the optimal cleaning and replacing scheduling are given.ccording to this model, one example is solved to illustrate the advantage and effectiveness of the suggested method.2006 Published by Elsevier B.V.

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eywords: Reverse osmosis; Seawater desalination; Optimum design; Membra

. Introduction

In the last few years, the seawater reverse osmosis (SWRO)esalination has gained much popularity, which will become themportant method to solve the problem of fresh water lack. Theechnology of RO process has gone through a remarkable trans-ormation. The new high rejection and high flow membranesere permitted operating at high pressures (up to 80–90 bar),

nd thus making conversions to 55–60% economically feasible.higher efficient energy recovery device, pressure exchangers

PX), that in the past was only used in small RO seawater plant,s also slowly gaining acceptance in large desalination plants.ydraulic efficiency of this type of equipment is in the range of

0–94%. All these advances have simplified the RO processingrom a two-stage treatment shift to a single-stage array, and haveesulted in lowering RO system capital and operating costs [1–6].

∗ Corresponding author. Tel.: +86 053282032141.E-mail address: ydhuhd@ouc.edu.cn (Y.-d. Hu).

osmsln(

376-7388/$ – see front matter © 2006 Published by Elsevier B.V.oi:10.1016/j.memsci.2006.04.019

uling; Cleaning and replacing scheduling

esigning a cost effective RO desalination system is still a com-lex work, which relate to many variables, such as feed flow rate,perating pressures, recovery rate, the number of modules, andn the meantime have to identify the RO system configuration. Inddition, fouling and scaling are major factors affecting the ROystem performance. It will lead to rapid increase of operatingressure and decrease of membrane permeability, and the sub-equent need to clean or replace fouled modules, as a result, theperating cost increase sharply. So it is significantly importantrom the operational and design point of view to have a sys-ematic method to calculate the optimal cleaning and replacingchedule for a RO process [7,8].

Considerable efforts for the development of new design meth-ds of industrial plants have been made [9–11]. Based on thetate-space approach, El-Halwagi [12] developed an integratedethod to yield an optimal set of values of all operational and

tructural variables in the RO system design problem. The prob-em may be formulated either as an MINLP (mixed-integeronlinear programming) or, a significantly easier to tackle, NLPnonlinear programming) problem. Voros and Maroulis [13,14]

8 mbrane Science 282 (2006) 7–13

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nd Zhu and El-Halwagi [15] proposed unified methodologiesncorporating sophisticated mathematical programming tech-iques to tackle the RO network synthesis problem. They haveonsidered the effect of various feed conditions and membraneouling respectively. See et al. [16] used a systematic method toalculate the optimal cleaning schedule for a given RO network.alek and Hawlader [17] provided the realistic economic modelhich relates the various operational and capital cost elements

o the design variable values.In the study, following the research efforts mentioned above, a

ew fouling model which can appropriately describe membraneodules performance and the criterion of modules cleaning and

eplacing are given. A systematic scheduling analysis based on aiscrete time interval approach during a long maintenance peri-ds of 5-years has been used to determine the optimal operatingosts. Under specific conditions of temperature, feed solute con-entration, the work has analyzed the optimization design prob-em of a single stage configuration with pressure exchanger typenergy recovery device. The configuration is normally employedn the present RO desalination plant.

. RO unit model

Several researches have been directed towards modeling ROembrane module. A mass transfer solution–diffusion model

as been extensively proposed in many Refs. [12–15]. The models mainly based on two parameters: the water permeability, A,nd the solute transport parameter, B. According to the model,he permeate flow rate, Qp (m3 h−1), and the concentration, Cp

�L L−1), are predicted as follows:

p = 3.6 × 106AS(�P −�Π) (1)

p = B(Co − Cp)

A(�P −�Π)(2)

= 0.2641C × (T ∗ + 273)

1.0 × 106 − C(3)

P f + Pb

P =2

− Pp (4)

o = Cf + Cb

2(5)

tsie

Fig. 2. Schematic diagram

Fig. 1. Schematic diagram of a membrane module.

here S (m2) is the module surface area,�P (MPa) is the differ-nce of trans-membrane pressure, �Π (MPa) is the differencef trans-membrane osmotic pressure, Co and Cp denote feedverage concentration and permeate concentration, respectively.ig. 1 indicates a schematic representation of a membrane unitnd the variables.

The corresponding material balance relationships for mem-rane unit are given by

f = Qb +Qp (6)

fCf = QbCb +QpCp (7)

he average feed flow rate per module (Qf) is limited for avoid-ng concentration polarization and excessive pressure drop. Theressure drop in the flow across each membrane unit is assumedo be constant. All these are usually specified by membrane man-factures.

fmin ≤ Qf ≤ Qfmax (8)

b = P f − δP (9)

. RO module fouling model

It is a common occurrence that membrane performance dete-iorates with operating time. Both membrane permeability andalt rejection may decline at a certain rate. So it is necessaryo determine the optimum maintenance schedule at the designtage, then the RO modules can be cleaning or replacing in timeo satisfy the performance.

The scheduling problem is constructed by partitioning the

otal time horizon, t, into n intervals of equal duration �T. Ashown in Fig. 2, t1, t2, . . ., indicate the first interval or the secondnterval, etc. The ‘operating day’ parameter, T, is analyzed atach subinterval q. q = x or y, where x and y denote the start

of the scheduling.

Y.-y. Lu et al. / Journal of Membrane Science 282 (2006) 7–13 9

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T

T

T

Z

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B

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Fig. 3. Membrane performanc

nd the end of each period, respectively [16]. T1 represents theength of time since the last cleaning action was performed. T2epresents the length of time since the last replacing action waserformed.

Cleaning or replacing is only allowed at the start of eacheriod and is described by decision variables, Z and K, respec-ively. Z takes the value of 0 if no cleaning is required and 1 whenleaning is necessary. In the same way, K takes the value of 1hen replacing is necessary, otherwise, it takes 0. It is assumed

hat no downtime is incurred for membrane regeneration as theime involved (a few hours) is negligible compared to the lengthf each interval. We set the interval as 2 months. The operatingay T can be calculated as follow:

1,n,x = (1 − Zn)T1,n−1,y (10)

1,n,y = T1,n,x +�T (11)

2,n,x = (1 − kn)T2,n−1,y (12)

2,n,y = T2,n,x +�T (13)

n ≥ kn (14)

When the membrane module performance deteriorates withperating time, it can be restored with effective cleaning.owever, after prolonged exposure to fouling conditions,erformance restoration through membrane cleaning is less

han effectively, and the limits of system performance (feedressure and permeate quality) are exceeded. Then, replacingld membranes with new elements is the only means to restoreystem performance.

ss

Fig. 4. The RO proces

riorates with operating time.

Many studies on membrane fouling model have been reported15,16]. See et al. [16] assumed an exponential decay in waterermeability (A) over time. In this study, a more appropriateouling model that consider incomplete cleaning and moduleeplacement are given as follow:

n,q = A0(1 − Ψ1T2,n,q) exp

(−T1,n,q

Γ1

)(15)

n,q = B0(1 + Ψ2T2,n,q) exp

(T1,n,q

Γ2

)(16)

here A0 and B0 denote initial water permeability and soluteransport parameter respectively, which are specified by mem-rane manufactures. ψ1, ψ2 are the constants that denote theembrane degraded extent. Γ 1, Γ 2 are membrane performance

ecay constants. They are determined by experiment. Fig. 3 indi-ates the change of parameters An,q and Bn,q.

The criterion of modules cleaning and replacing are given asollow:

n,q ≥ A0C1 (17)

n,q ≤ B0(1 + C2) (18)

here C1 is water permeability decrease rate, C2 is solute trans-ort parameter increase rate.

. System model

In the current work, a single stage configuration with pres-ure exchanger type energy recovery device was adopted. Fig. 4hows the RO process flow diagram.

s flow diagram.

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0 Y.-y. Lu et al. / Journal of Me

The desalination section can be separated into several inde-endent RO trains with respective high pressure feed pumps andnergy recovery devices. First, an excessive number of trains,, is introduced as an initial guess. Then at the optimum certaininary variables are either set to zero or to one that indicateshe absence or presence of the specific train. Finally, an opti-

al value of trains is given. The corresponding material balanceelationships for RO process are presented as follow:

fn,q =

U∑u=1

Qfu,n,q (19)

pn,q =

U∑u=1

Qpu,n,q (20)

bn,q =

U∑u=1

Qbu,n,q (21)

pn,q =

U∑u=1

Qpu,n,qC

pu,n,q

Qpn,q

(22)

fn,q = Qp

n,q +Qbn,q (23)

fn,qC

fn,q =

U∑u=1

Qbu,n,qC

bu,n,q +

U∑u=1

Qpu,n,qC

pu,n,q (24)

fn,q = Qf,1

n,q +Qf,2n,q (25)

f,2u,n,q = Qb

u,n,q (26)

∗ =U∑u=1

Ru (27)

uQfmin ≤

(Qfu,n,q

Nu

)≤ QfmaxRu (28)

uQomin ≤

(Qbu,n,q

Nu

)≤ QomaxRu (29)

max = max(NuRu|u = 1, 2, . . . , U) (30)

min = min(NuRu|u = 1, 2, . . . , U) (31)

max ≤ 3Nmin (32)

pn,q ≥ Qpmin (33)

pn,q ≤ Cpmax (34)

here U* is the optimal value of trains. Ru is binary variable thatndicates the absence or presence of the specific train. Nu is theumber of modules in the u train. Qomin, Qomax refer to the brineinimum outlet flow rate and the maximum outlet flow rate,

espectively. In order to guarantee much more against excessive

ocal polarization, a minimum brine outlet flow rate should bexed. The module number of train is a variable. In order to avoid

he train sizes differentiate excessively, it is necessary that theodule number of the maximum size train (Nmax) should be less

s(Ss

ne Science 282 (2006) 7–13

han three times the module number of the minimum size trainNmin). Qpmin refers to the minimum desirable product flow rate,pmax refers to the maximum allowable product concentration.

. Solution methodology

The optimization design problem is formulated as a mixed-nteger nonlinear programming (MINLP) model for minimizinghe total annualized cost subject to thermodynamic, technical,ouling, and flexibility constraints. The total annualized costTAC) of the system consists of two terms: annual operatingost (OC) and annualized capital cost (CC). The annual oper-ting cost includes the energy cost (E) necessary for pumps,he cost of membrane module cleaning and replacing (OCc andCr). The annualized capital cost is for the initial membraneodule, pumps and pressure exchanger. The objective function

s presented as follow:

AC =(Cm

U∑u=1

Nu + CCin + CCHpp + CCpx + CCbp

)

× 1.411 × 0.08 + (OCin + OCHpp + OCbp)Co

+ OCcCo + OCrCo (35)

Cpx = 3134.7Q0.58px (36)

CHpp = QPCe

ηHppηmotor(37)

Cc =U∑u=1

n∑n=1

((Zu,n −Ku,n)Nu × 200 + Zu,n × 200) (38)

Cr =U∑u=1

n∑n=1

Ku,nNu × 800 (39)

here Cm denotes the membrane module cost that is specifiedo be $1000 per module, it involves the cost of pressure ves-el. 1.411 is the coefficient that used to calculate the practicalnvestment. 0.08 is the capital charge rate. CCin, CCHpp, CCbp,Cpx is the capital cost of the seawater intake pump, the high-ressure pump, the booster pump and the pressure exchanger,espectively. OCin, OCHpp, OCbp is the energy cost necessary forhese pumps. Their functions refer to the paper [11,15,17]. TheX cost function provide a convenient estimate at various flowates, which obtained by regression of the cost data providedy the Energy Recovery, Inc. [18] The function is given by Eq.32). The cleaning cost, OCc, involves a variable cost of $200er module cleaned, and a fixed cost of $200 for downtime inhich cleaning or replacing occurs. It is specified that the mem-rane replacing cost is $800 per module. Co is the operating costharge rate during the maintenance periods.

The MINLP can be solved using the software GAMS. It

olves the problem by decomposing it into a series of nonlinearNLP) sub-problems and mixed integer (MIP) master problems.everal starting points are used to obtain the best possibleolution.

Y.-y. Lu et al. / Journal of Membrane Science 282 (2006) 7–13 11

Table 1Input data for the design

Feed concentration, �L L−1 34800Feed water temperature, ◦C 25Minimum flowrate per module, m3 h−1 1Maximum flowrate per module, m3 h−1 2Pressure drop per module, MPa 0.2Initial water permeability, kg s−1 N−1 3.0 × 10−10

Initial solute transport parameter, kg s−1 m−2 4.0 × 10−6

MM

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Table 2The parameters for calculation

High pressure pump efficiency, ηHpp 75%Pressure exchanger efficiency, ηpx 90%Electric motor efficiency, ηmotor 98%Coefficients of Eq. (15), ψ1, Γ 1 ψ1 = 1.67 × 10−4, Γ 1 = 328Coefficients of Eq. (16), ψ2, Γ 2 ψ2 = 1.67 × 10−4, Γ 2 = 650Parameter of Eq. (17), C1 40%Parameter of Eq. (18), C2 60%Parameter of Eq. (30), C 20%T

otps

tbdt

sc

odule operating pressure bounds, MPa 5.0–9.2embrane area per module, m2 152

. Case study

This example deals with the desalination of seawater usinguPont B-10 hollow-fiber RO modules, which specified a life-

ime of 5 years. In this case, the minimum acceptable perme-te flow rate is 80 m3 h−1, the maximum allowable permeateoncentration is 500 �L L−1. The properties of the membraneodule and the data of membrane performance deteriorates with

ime are taken from Ref. [15]. Table 1 presents the input dataor the design. The parameters for calculation, which are givenased on Refs. [15,17], are listed in Table 2.

The calculations were conducted for a single stage configura-

ion with pressure exchanger RO system. The maximum numberf trains, U, is set as 3. In order to show the difference clearly, theathematical programming problems of the systems consisting

rer

Fig. 5. Optimal mainte

o

he cost of electricity, Ce, $(kwh)−1 0.08

f one train, two trains and three trains are calculated, respec-ively. The process flow diagram shows in Fig. 4. A maintenanceeriod of 5-years is specified. Table 3 shows the result of the ROystem design.

The optimum maintenance schedule of the RO system duringhe operating period of 5-years is shown in Fig. 5, where thelack thick line denotes that the modules are cleaned and theouble black line denotes that the modules are replaced at thatime.

The resulting design, as shown in Table 3, indicates that theystem consisting of three trains has the lowest total annualizedost among three instances, so the optimal value is 3. But the

esults obtained are very sensitive to the cost and fouling modelsmployed in the simulation. If the fixed cost for each cleaning oreplacing increases, the total annual cost of the system consisting

nance schedule.

12 Y.-y. Lu et al. / Journal of Membra

Table 3The result of the design

Number of RO trains 1 2 3Total number of modules 190 165 165Number of modules in train u1 190 55 38Number of modules in train u2 110 82Number of modules in train u3 45Train u1 feed pressure, MPa 8.1 8.0 6.7Train u2 feed pressure, MPa 7.5 8.1Train u3 feed pressure, MPa 8.0Total power of the HP pump, kW 300 300 300Raw seawater feed flow, m3 h−1 190 165 165Permeate flow, m3 h−1 80 80 80Recovery ratio, % 42 48 48Total annualized cost, $ 409060 385710 381800Specific energy consumption, kwh/m3 4.0 4.0 4.1Product water cost, $/m3 0.66 0.61 0.60

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Acknowledgement

Financial support from the National Natural Science Foun-dation of China (No. 20376078) is gratefully acknowledged.

Nomenclature

A water permeability (kg s−1 N−1)B solute transport parameter (kg s−1 m−2)C concentration of solute (�l L−1)Ce electricity cost ($(kwh)−1)Cm membrane module cost ($)Co the operating cost charge rateC1 water permeability decrease rate

Fig. 6. The profile of operating pressure in train u3,2.

f several trains may be obviously increase because they haveore cleaning times.The train u3,2, which among the system consisting of 3 trains,

ith 82 modules. It has more than the other two. So the modulesf the train u3,2 need not be replaced during the maintenanceeriod, however, this train has the highest frequency of cleaningperation among the three trains. The train u3,3 with 45 moduless replaced at the 1020th day (see Fig. 5). The reason is that thelgorithm may consider that would effectively provide enoughompensation for the difference in fouling among the trains toeeting the product targets.In the system, at least one of the trains should be cleaned at

very period after 180 days. The fluctuation of operating pres-ure of train u3,2 during the first 2 operating years (see Fig. 6)eflects the above phenomena, namely the cleaning actions ofhe other two trains affect the operating pressure of train u3,2.

hether the train u3,2 is cleaned or the other two trains areleaned, the operating pressure of train u3,2 is sharply degres-ive. The permeability variation with operating pressure in the

rain u3,2 shown in Fig. 7. In general, the permeate rate decreaseshen the pressure reduces. At the 240th and the 540th day, theodules of the train u3,2 are cleaned and therefore the perme-

Fig. 7. The profile of permeate rate in train u3,2.

ne Science 282 (2006) 7–13

te rate increases. At the other intervals, the operating pressureust increase to maintain the permeate rate steady because theembrane performance deteriorate with time. So the proposed

esign model, which assumes that the module numbers of trains a variable, provides enough compensation for the differencen fouling among the trains to meeting the product targets. It is

ore flexible and its cost is more effective than the configurationith equal number of modules per train [16].Table 3 also presents that the optimal recovery ratio of the

ystem consisting of 3 trains is 48%, the specific energy con-umption is 4.1 kwh/m3, and the minimum product water costs $0.60/m3. The results indicated that it is possible to obtainower product water cost.

. Conclusion

This work has presented a systematic methodology for theptimal design of RO desalination system which consideringembrane module cleaning and replacing. The design task has

een formulated as an MINLP which minimizes the total annu-lized cost while subject to the thermodynamic, modeling, eco-omic, environmental, and feasibility constraints. The optimumO maintenance schedule is also determined in the design stage.he effectiveness of this design methodology has been demon-trated by solving a case study. This work used just a segmentf system capital and operating cost. It is possible that if all con-ributions to capital and operating cost would be included in the

odel, the result of optimization could be different.

C2 solute transport parameter increase rateCo average concentration on the high-pressure side

(�L L−1)CCbp capital cost of the booster pump ($)CCHpp capital cost of the high-pressure pump ($)CCin capital cost of the seawater intake pump ($)CCpx capital cost of the pressure exchanger ($)Nmax the module number of the maximum size trainNmin the module number of the minimum size trainNu the number of modules in the u trainOCbp energy cost of the booster pump ($)OCc the cost of membrane module cleaning ($)

Y.-y. Lu et al. / Journal of Membrane Science 282 (2006) 7–13 13

OCHpp energy cost of the high-pressure pump ($)OCin energy cost of the intake pump ($)OCr the cost of membrane module replacing ($)P operating pressure (MPa)Q flow rate, (m3 h−1)S module surface area (m2)t1 the first interval�T length of each scheduling interval (d)T* temperature (K)T1 operating day after the last cleaning (d)T2 operating day after the last replacing (d)TAC total annualized cost ($)u membrane trainsU total number of membrane trainsU* the optimal value of trainsZ,K,R binary integer

Greek symbolsΓ 1, Γ 2 membrane performance decay constantsδP trans-membrane pressure drop (MPa)ηHpp high pressure pump efficiencyηmotor electric motor efficiencyηpx pressure exchanger efficiencyΠ osmosis pressure (MPa)ψ1, ψ2 the constant that denote the membrane degraded

extent

Superscriptsb brine streamf feed streamfmax upper bound on feed flow ratefmin lower bound on feed flow rateomax the brine maximum outlet flow rateomin the brine minimum outlet flow ratep permeate stream

Subscriptsbp booster pumpHpp high-pressure pump

in seawater inlet streamn schedule interval

px pressure exchangerq schedule subinterval

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[14] N.G. Voros, Z.B. Maroulis, Short-cut structural design of reverse osmosisdesalination plants, J. Membr. Sci. 127 (1997) 47–68.

[15] M. Zhu, M.M. El-Halwagi, Optimal design and scheduling of flexiblereverse osmosis networks, J. Membr. Sci. 129 (1997) 161–174.

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[18] PX, Energy Recovery, Inc., San Leandro.