Optimum design of reverse osmosis system under different feed concentration and product specification

Journal of Membrane Science 287 (2007) 219–229

Optimum design of reverse osmosis system under different feed concentration and product specification Yan-Yue Lu a, Yang-Dong Hu a,∗, Xiu-Ling Zhang b, Lian-Ying Wu a, Qing-Zhi Liu a a

Key Laboratory of Marine Chemistry Theory and Technology, Ministry of Education, College of Chemistry and Chemical Engineering, Ocean University of China, Qingdao 266003, China b Department of Chemistry, Dezhou University, Dezhou 253011 , China

Received 7 July 2006; received in revised form 16 October 2006; accepted 20 October 2006 Available Available online 25 October 2006

Abstract

The design of various multistage RO systems under different feed concentration and product specification is presented in this work. An optimization method using the process synthesis approach to design an RO system has been developed. First, a simplified superstructure that contains all the feasible design in present desalination process has been presented. It offers extensive flexibility towards optimizing various types of RO system system and thus may be used for the selection selection of the optimal structural structural and operating operating schemes. schemes. A pressure pressure vessel vessel model model that takes into account the pressure drop and concentration changes in the membrane channel has also been given to simulate multi-element performance in the pressure vessel. Then the cost equation relating the capital and operating cost to the design variables, as well as the structural variables of the designed system have been introduced in the objective function. Finally the optimum design problem can be formulated as a mixed-integer nonlinear programming (MINLP) problem, which minimizes the total annualized cost. The solution to the problem includes optimal arrangement of the RO modules, pumps, energy recovery recovery devices, the optimal operating conditions, and the optimal selection of types and number of membrane elements. The effectiveness of this design methodology has been demonstrated by solving several seawater desalination cases. Some of the trends of the optimum RO system design have been presented. © 2006 Elsevier B.V. All rights reserved. Keywords: Reverse osmosis; Seawater desalination; Optimum design; Structure; Module model

1. Introductio Introduction n

Desali Desalinat nation ion of sea and bracki brackish sh water waterss is the main main source source for supply supplyingfreshwate ingfreshwaterr in theregionssuff theregionssufferi ering ng from from thescarcityof thescarcityof natural fresh water supplies. Reverse osmosis (RO) is the major technologies for large-size plants for desalinating water. Since 1960s, due to the development of new RO modules and membranes, RO has become an attractive process for both seawater and brackish water desalination [1–5] [1–5].. The rapid growth of RO process is because it is able to produce duce fres fresh h wate waterr with with lowe lowerr cost cost [3] [3].. The other other attrac attracti tive ve featur featuree of RO proc proces esss is that that the the plan plantt desi design gn and and oper operat atio ion n is simp simpli lici city ty and modularity. Membrane plants are often more compact, can be scaled up easily and installed more quickly than thermal separations plants. Also, it makes the maintenance of RO systems

∗

Corresponding author. Tel.: +86 53266781875. E-mail address: [email protected] (Y.-D. Hu).

0376-7388/$ 0376-7388/$ – see front matter © 2006 Elsevier B.V. B.V. All rights reserved. doi:10.1016/j.memsci.2006.10.037 doi:10.1016/j.memsci.2006.10.037

easier [6,7] [6,7].. Anothe Anotherr advant advantageof ageof theRO proces processs is that that it is able able to meet varying varying feed water water concentra concentration tion and varying varying production production water quantity and quality requirement through change system construction and operation condition. RO membrane manufacturers turers have have deve develop loped ed vario various us membra membrane ne types types to precis precisely ely meet meet the varying need of a wide range of industrial, municipal, commercial and drinking water application, such as high flux, high rejection rejection membranesand membranesand fouling fouling resistant resistant membranes membranes,, low prespressure, high rejection membrane etc. [8,9,30] [8,9,30].. All this advantages have made the design of RO process more flexible. Consid Considera erable ble effort effortss for the resear research ch of the optimu optimum m RO syssystem design have been made [6,10–13] [6,10–13].. Based on the state-space approach, El-Halwagi [14] develope developed d a structural structural represenrepresentation tation of RO networ networks. ks. The RO netwo networks rks were were descri described bed using using four boxes: boxes: a pressuriza pressurization/d tion/depres epressuriz surization ation streamstreamdistribut distribution ion box, a pressuriza pressurization/ tion/depre depressur ssurizati ization on matching matching box, a reversereverse-osmos osmosis is stream-dis stream-distrib tribution ution box, a reverse reverse-osmosis matching box. The function of the distribution boxes was to represent all possible combinations of stream splitting,

220

Y.-Y. Lu et al. / Journal of Membrane Science 287 (2007) 219–229

mixing, mixing, bypass bypass and recycle. recycle. The matching boxes locate all possible stream assignments to units. With this formulation, all possible structure arrangements could be represented. The mathematical model was formulated as a mixed integer nonlinear programming (MINLP). In the further work, Zhu and El-Halwagi [15] used El-Halwagi’s representation and included a factor for flux decline over time. Voros and Maroulis [16,17] simplified the El-Halwagi’s representation by reducing the distribution tribution boxes boxes to junctions. junctions. Consequently Consequently,, the model model was formulated as a nonlinear programming (NLP) by using a variable split ratio. They have considered the effect of various feed conditions and product requirements. Maskan and Wiley [18] used a directed graph and connectivity matrix to represent the RO networks superstructure. In the mathematical model of the superstructure, a variable reduction technique is performed to accelerate the computational process. Nemeth [19] studied the behavior of the ultra-low pressure RO membranes in the fullscale system system and presented presented recommenda recommendations tions to improve improve system system design. Van der Meer [20,21] [20,21],, and Wessels and Van der Meer [22] have developed a simplified mathematical model to optimize mize the perfor performan mance ce of NF and RO membra membrane ne filtrat filtration ion plants plants.. The study showed that the productivity of nanofiltration plants can be significantly improved by installing a reduced number of membrane elements serially in pressure vessels (PV) and changing system configuration. See et al. [23] used a systematic method to calculate the optimal cleaning schedule for a given RO network. Malek and Hawlader [24] provided the realistic economic model that relates the various operational and capital cost elements to the design variable values. Most of previous studies presented the general representation of RO networks, which contains all the possible designs that are to be considered as candidates for the optimal solution. Following their research efforts, this study presented a simplified superstructure representation that contains all the feasible design design in presen presentt desali desalinat nation ion proces process. s. The model model of supers superstru truccture ture could could be easier easier solved solved with with less less calcul calculati ation on time. time. A pressu pressure re vessel model has also been given. The model could be used for the optimum selection of types and number of membrane element, according to its performance characteristics, the prices, and the design requirements of a specific desalination application.Thereforethe optimal optimal design design of ROsystemswas formulated formulated as a mixed integer nonlinear programming problem (MINLP). The objective is to determine the optimal system structure and operating conditions for a given feed water concentration and water production requirement. The solution to the problem also includ includes es the most most approp appropria riatel tely y choice choice of the types types of membra membrane ne elements in each stages and the optimal number of membrane elements in each PV. 2. RO unit model model

and optimization, it is necessary to adopt the appropriate modeling equations equations that can satisfact satisfactorily orily predict the membrane performance with reasonable computational complexity. Therefore the solution diffusion model is the one most commonly used in RO system design. The model is mainly based on two parameters: the water permeability, A, and the solute transport parameter, B. The values for these two parameters are usually specified by membrane manufactures. According to the model, the pure water flux, J w (kg/m2 s), and the salt flux, J s (kg/m2 s), are given as follows: J w = A



P f f − P p −

P f f

2



− (πw − πp )



6 × 10

J s = B(Cw − Cp ) π=

0.2641C(T + 273)

V w = Cp =

1.0 × 106 − C J w + J s

V w

× 1000

(3)

(5)

where Pf , Pp (MPa) denote the feed pressure and the permeate pressure, respectively. respectively. Pf is the the pres pressu sure re drop drop in the the memb membra rane ne channel. Π w (MPa) is the osmotic pressure of the brine at the membrane wall concentration C w (ppm), and Π p and C p are correspond corresponding ing variable variabless for the permeate. permeate. ρp denotes denotes the density density of the permeate. V w (m/s) is the permeate velocity. 2.2. The model model for RO module module

In the practical RO process, a PV with up to eight membrane elements that are connected in series consists of a RO module. The concentrate of the first element becomes the feed to the second, and so on. The product tubes of all elements are coupled and connected to the module permeate port [20–22] [20–22].. For every application a suitable hydraulic design can be made (2–8 serial elements), based on the actual situation. Maskan and Wiley [18] developed a model of the tubular membrane elements. Al-Bastaki and Abbas [25,26] have given the models of the spiral-wound and hollow-fiber membrane elements, which took into account the pressure drop and concentration changes in the membrane channel. The PV performance can be approximately mately simpli simplified fied to the perform performanc ancee of the membra membrane ne elemen elements ts connected in series. Therefore, base on the models mentioned above, we have presented a pressure vessel model with spiralwound membrane element. The model could be used for the optimal selection of the types and numbers of membrane element. The equations of the model are shown as follow. Fig. 1

2.1. The mass transfer transfer model of RO RO membrane

There There arenumer are numerous ous membrane membraneperfor performanc mancee models models that have have been introduced [7,25,26] [7,25,26].. They are derived from different theories and all of them can be simplified to the solution diffusion model, as shown in Eqs. (1) and (2). (2). For the RO system design

(2)

(4)

ρp J s

(1)

Fig. 1. Schematic diagram of a RO RO unit.


221

indicates the schematic representation of a RO unit and the variable: Cw = Cp +



Cf + Cb

2

− Cp



eV w /K

(6)

K (m/s) is the mass transfer coefficient, which can be calculated

from empirical relations such as K = 0.04 Re0.75 Sc0.33 Re =

Ds d

Vρd

(7) (8)

μ

where Re and Sc are the Reynold’s and the Schmidt numbers and Ds is the solute diffusivity. d is the feed spacer thickness, ρ the feed side solution density and μ is the water viscosity. V denotes the flow velocity that was calculated using the averaged value valuess of the inlet inlet and outlet outlet flow flow rates rates in the membra membrane ne channe channel. l. For For a spiral spiral-wo -wound und membra membrane ne module module,, each each of the permea permeate te and feed side flows can be considered as a flow between two parallel plates with a length L, a width W and a spacing d . hence the pressure drop on the feed side can be calculated as follows: P f f =



0.0033QLpv μ Wd 3



(9)

Lpv = mLm

(10)

P f f ≤ 0.35

(11)

where Q (m3 /h) is the flow rate that was calculated using the averaged values of the inlet and outlet flow rates in the membrane channel. Lpv and Lm denote the length of the PV and the length length of a membrane membrane element, element, respecti respectively vely.. The m is thenumber thenumber of the membrane elements in each PV. It determines the optimum selection of number of membrane element. The maximum allowable pressure pressure drop of the pressure vessel is 0.35 MPa. The technical constraint is usually specified by membrane manufacturers. For the spiral-wound membrane element, the membrane width (W ), ), can be calculated by the membrane area (S m ) and the number of leaves ( N l ): S m = WLm N l

(12)

The total permeate flow rate of the nth pressure vessel, Qp,n the total brine flow rate and concentration, Qb,n (m3 /h) and C b, (ppm), can be calcul calculate ated d from from the mass mass and salt salt balanc balancee b,n (ppm), equations: (m3 /h),

Qp,n = 3600V w S m m

(13)

Qf ,n ,n = Qb,n + Qp,n

(14)

Qf ,n ,n Cf ,n ,n = Qb,n Cb,n + Qp,n Cp,n .

(15)

3. RO network network representation representation 3.1. Problem description

For a give given n specifi specificat cation ion of feed feed water water,, the design design object objectiv ivee is to identi identify fy the most most cost cost effec effecti tive ve RO networ network k configu configurat ration ion,, the

Fig. 2. The process flow diagram of typical RO system.

operating conditions, and the optimal arrangement of the membrane elements. Several RO system configurations commonly used in seawater and brackish desalination applications have been investigated (shown as Fig. 2). 2). In the single stage RO system with pressure exchanger (PX) type energy recovery device, the main high pressure pump is sized to approximately equal the RO permeate flow, not the full system feed flow. Therefore, the PX significantly reduces the capital and operating cost. The multiple PX-arrays are similar to membranes arrays providing the operator with beneficial redundancy [27–29] [27–29].. El-Halwagi [14,15] and Voros and Maroulis [16,17] have used the state space approach to develop the structural representation of RO network. Here we adopt and properly simplify the approach according to the practical RO process. Compared to the previous representation the characteristic differences in this paper are: 1. It was assumed that the RO RO network has only one input. The fresh-feed supply to stage 1. 2. The distri distribu butio tion n boxes boxes were were reduce reduced d to juncti junctions ons.. The stream stream mixed at the pressurization stages and split at the RO stages. 3. The stream split ratio and isobaric-mi isobaric-mixing xing constraints constraints were used used in the model model of supers superstru tructu cture. re. These These constr constrain aints ts simply simply the mathematical description of stream mixing and splitting. 4. The struct structura urall repres represent entati ation on has includ included ed the pressu pressure re exchanger (PX) type energy recovery device. As shown in Fig. 3, 3, a RO network consists of N ps ps pressurization stages and N RO RO reverse osmosis stages. The number of stream stream junctions junctions employed employed is N ps 2,where 2 indi indica cate ted d the the brin brinee ps + 2,where and product streams leaving the network. Each stream node among the N ps ps nodes represents a stream connected to a pump. The streams pressurized by high pressure (HP) pump or not are connected to a corresponding RO stages. The RO stages consist of multiple parallel reverse osmosis pressure vessels operating at the same conditions. Each stream of the network (the brine and permeate streams leaving all reverse osmosis stages) may be linked to all the N ps nodes. ps + 2 nodes.

222


Qps,i Cps,i =

N RO RO

N RO RO





Qb,j xb,i,j Cb,j +

j =1

Qp,j xp,i,j Cp,j ,

j =1

i = 2, 3, . . . , Nps

(22)

N ps ps +2

xb,px,j +



xb,i,j = 1,

j = 1, 2, . . . , NRO

(23)

i=1

N ps ps +2



xp,i,j = 1,

j = 1, 2, . . . , NRO

(24)

i=1

where Qps,1 , C ps,1 ps,1 denote the flow rate and concentration of the first pressurization stage, Qf , C f f denote the feed flow rate and feed concentration of the RO network, Qps,i , C ps, ps,i denote the flow rate and concentration of the ith pressurization stage, respectively. Qb, j j , C b, b, j j denote the brine flow rate and concentration of the jth RO stage, Qp, j j , C p, p, j j denote the permeate flow rate and concentration of the jth RO stage, respectively. x b, p,i, j j b,i, j j , x p, indicate the stream split ratios of the brine and the permeate, respectively. The values determine the flow rates of brine and permeate leaving the jth RO stage and being linked to the ith pressurization stage. Pf , Pps,1 are the feed pressure of the RO network and the inlet pressure of the first pressurization stage, respectively. Qpx , C px px is the flow rate and concentration of high pressure brine entering pressure exchanger, exchanger, respectiv r espectively ely.. Followin Following g are the stream-mixi stream-mixing ng constraint constraints. s. Whenever Whenever mixing occurs, it is necessary that only streams with equal pressure can be mixed together:

Fig. 3. representation of the RO network via the superstructure.

3.2. Mathematical formulation

The complete mathematical model that describes the superstructure is presented as follow by means of the appropriate relationships between the variables (mass balance equations, technical and operational constraints): Qps,1 = Qf +

N RO RO

N RO RO





Qb,j xb,1,j +

j =1

Qps,1 Cps,1 = Qf Cf +

(16)

j =1

N RO RO

N RO RO





Qb,j xb,1,j Cb,j +

Qp,j xp,1,j Cp,j

j =1

(17)

j = 1, 2, . . . , NRO

(P ps ps,i − P p,j )Qp,j xp,i,j = 0,

(18)

N RO RO

Qpx =



(19)

Qb,j xb,px,j

j =1

N RO RO

Qpx Cpx =



Qb,j xb,px,j Cb,j

(20)

j =1

Qps,i =

N RO RO

N RO RO





Qb,j xb,i,j +

j =1

QP,j xp,i,j ,

(25) i = 1, 2, 3, . . . , Nps ,

i = 2, 3, . . . , Nps

j =1

(21)

(26)

where Pps,i denotes the inlet pressure of the ith pressurization stage. Pb, j j , Pp, j j denote the brine and permeate pressure of the jth RO stage, respectively. The streams leaving the ith pressurization stages are correspondingly connected to the jth RO stages. Therefore the following equation can be obtained: QRO,j = Qps,i ,

P ps ps,1 = P f f

i = 1, 2, 3, . . . , Nps ,

j = 1, 2, . . . NRO

Qp,j xp,1,j

j =1

(P ps ps,i − P b,j )Qb,j xb,i,j = 0,

j = i, j = 1, 2, 3, . . . , NRO

(27)

CRO,j = Cps,i ,

j = i, j = 1, 2, 3, . . . , NRO

(28)

 P RO RO,j = P ps,i ,

j = i, j = 1, 2, 3, . . . , NRO

(29)

where QRO, j j , C RO, RO, j j , PRO, j j denote the feed flow rate, concentration, and operation pressure of the jth RO stage, respectively.  P ps ,i is the outlet pressure of the ith pressurization stage. The mathematical models that predict the performance of each RO stage have been presented in detail in the previous section. These model equations relate the flow rate and concentration of the brine and permeate leaving an RO stage to the flow rate, concentration, and pressure of the stream entering the stage. The arrays of pressure vessels (PV) with 2–8-membrane elem elemen ents ts per per PV cons consis istt of a RO stag stage. e. In this this pape paperr, the the opti optima mall

223


PV structure has been researched. Four different types of spiral wound FilmTec reverse reverse osmosis membrane elements have been considere considered. d. According According to its performanc performancee characteri characteristics stics and the design requirements of a specific desalination application, the optimum selection of types and numbers of the membrane element employed in each PV can be determined by the following equations: 4

Aj =



Zj,kAk ,

j = 1, 2, 3, . . . , NRO

(30)

Zj,kBk ,

j = 1, 2, 3, . . . , NRO

(31)

k=1

4

Bj =

 k=1

4. Solution Solution methodolog methodology y

The optimization design problem is formulated as a mixedinteger nonlinear programming (MINLP) for minimizing the total annualized cost subject to thermodynamic, technical, and flexibility constraints. The total annualized cost (TAC) of the system consists of two terms: annual operating cost (OC) and annual annualize ized d capita capitall cost cost (CC). (CC). The annual annual operat operating ing cost cost includ includes es the energy cost ( E ) necessary for pumps, the cost of membrane module maintenance (OCm ). The annualized capital cost is for the initial membrane module, pumps and pressure exchanger. The objective function is presented as follows: TAC = (CCin + CChpp + CCpx + CCbp + CCm )1.411 × 0.08 + OCin + OChpp + OCbp + OCm

4



Zj,k ≤ 1,

j = 1, 2, 3, . . . , NRO

(32)

k =1

In the present work, it was assumed that the membrane element ment empl employ oyed ed in the the PV in the the same same RO stag stagee are are the the same same.. The The membrane membrane intrinsic intrinsic properties properties ( A, B) are are assu assume med d to be cons consta tant nt.. th Z j,k is the binary variable. It takes the value of 1 when the k th elem elemen entt type type is util utiliz ized ed in the the PV in the the jth RO stage. stage. Otherw Otherwise ise,, it takes the value of 0. The overall material balances for the RO network and a set of product quantity and quality constraints concerning the minimum desirable product flow rate, and the maximum allowable product concentration are presented as follows: Qf = Qb + Qp

(33)

Qf Cf = Qb Cb + Qp Cp

(34)

N RO RO

Qb =



Qb,j xb,j + Qpx

(35)

j =1

N RO RO

Qb Cb =



Qb,j xb,j Cb,j + Qpx Cpx

(36)

j =1

N RO RO

Qp =



Qp,j xp,j

(37)

j =1

N RO RO



(38)

Qp ≥ Qpmin

(39)

Cp ≤ Cpmax

(40)

Qp Cp =

Qp,j xp,j Cp,j

j =1

where Qb , C b are the flow rate and concentration of the brine leaving the RO network, respectively. Qp , C p are the flow rate and concentra concentration tion of the product product water, water, respecti respectively vely.. x b, b, j j , x p, p, j j are the outlet outlet stream stream split split ratios ratios.. Qp min refers refers to the minimu minimum m desir desir-able product flow rate, C p max refers to the maximum allowable product concentration.

CChpp

=

52(PQhpp )0.96

(41) (42)

0.58 3134.7Qpx

(43)

Qps,1 = Qhpp + Qpx

(44)

CCpx

=

Cm =

N RO RO 4

N RO RO





Zj,kCk mj,knj +

j =1 k=1

OChpp ηPX =

=

3.6ηhpp ηmotor (PQ)out (PQ)in

(45)

j =1

PQCe f c

 

Cpv nj

× 100%

(46) (47)

where CC in px is the capital cost of the seawain , CC hpp hpp , CC bp bp , CC px ter intake pump, the high pressure pump, the booster pump, and the pressure exchanger (PX), respectively. OCin , OChpp , OCbp is the energy cost necessary for these pumps. Their functions refer to the papers [2,6,15,24] [2,6,15,24].. The main high pressure pump capacity equals the full feed flow of the RO system minus the brine flow entering the PX. The required capacity of the PX and the booster pump should equal the brine flow entering the PX. C m denotes the total membrane module cost. C k k is the price of the k th th membrane element and C pv pv is the price of the pressure vessel. The n j is the number of pressure vessel employed in the jth RO stage. 1.411 is the coefficient that used to calculate the practical investment. 0.08 is the capital charge rate. C e is the cost of electricity and f c is the load factor. ηhpp , ηmotor , ηpx are the efficiency of the HP pump, the electric motor, and the PX. The terms of capital cost items take into account the number and type of RO modules utilized for each RO stage, and the number and capacity of each pump and PX. The existence of the specific device may be determined indirectly by operational variables, such as the input flow rate to the unit, the pressure of the pressu pressuriz rizati ation on stage stage or RO stage. stage. The struct structura urall optimi optimizat zation ion may take place in terms of eliminating all unnecessary pressurization stages or RO stages. This procedure is carried out by introducing an excessive number of units as an initial guess, while at the optimum certain design variables, such as stream split ratios, are either set to zero or to a value that indicate the absence or presence of the specific stage.

224


The MINLP can be solved using the software GAMS. It solves the problem by decomposing it into a series of nonlinear (NLP) sub-problems and mixed integer (MIP) master problems. Seve Several ral starti starting ng points points are used used to obtain obtain the best best possib possible le solution. 5. Case study

The proposed proposed methodolog methodology y for RO system optimizatio optimization n design has been applied to the investigation of the operational and structural characteristics of multi-stage RO system. Four different types of FilmTec reverse osmosis membrane elements from DOW have been included in the design studies of the current work. They are the low energy, high productivity element SW30XLE-400, the high rejection, high productivity element SW30HR-380 SW30HR-380,, the high rejection, rejection, fouling fouling resistant resistant element element SW30HR-320, and the high productivity, high rejection brackish water RO element BW30-400. The product specifications and the membrane transport properties (membrane pure water permeability, solute transport parameter) of these elements are given in Table 1 [30] [30].. The parameters for calculation, which are given based on Refs. [6,15,24] [6,15,24],, are listed in Table 2. 2. In general, solving the mathematic programming problem take between 0.27 and 0.84 CPU time (s), 134 and 856 iterations to finish. 5.1. The study of varying feed composition composition

Several cases were solved, in which the feed water concentration vary while the product demand and quality constraints mainta maintain in at same same level levels. s. The total total produc productio tion n requir required ed is 3 120m /h, and the maximum allowed salt concentration is 500 ppm. For the relatively higher feed concentrations concentrations varying from 38,000 to 48,000 ppm, the results of the RO system optimization design were presented in Table 3. 3. As indicated in the table, the simple one stage structure is favored (shown as Fig. 4) 4) in the range of concentration. The number of elements in each PV is a contin continuou uouss varia variable ble in the presen presentt work. work. With increa increasin sing g feed concentration the values increase lightly. Therefore, they are all take the value of 5 after rounding. In stage 1, the number of PV is 40 after rounding. The selected type of membrane element is the SW30XLE-400 that offers very high productivity and rejection, enabling the lowest total cost of water for sea-

Table 2 The parameters for calculation Feed water temperature, T (◦ C) Average brine density, ρ (kg/m3 ) The brine viscosity, viscosity, μ (kg/m s) Diffusion coefficient, Ds (m2 /s) High pressure pump efficiency, efficiency, ηhpp Pressure exchanger efficiency, efficiency, ηpx Electric motor efficiency, ηmotor The cost of electricity, C e ($ (kWh) (kWh)−1 ) The pressure vessel cost (estimation) ($)

25 1020 1.09 × 10−3 1.35 × 10−9 75% 90% 98% 0.08 1000

Fig. 4. The optimum RO system for feed concentration varying varying from 38,000 to 48,000 ppm.

water desalination. In this range of concentration, increasing the operating pressure is the main method to meet the product constraints. For the medium feed concentrations varying from 20,000 to 35,000 ppm, the design results results were presented presented in Table 4. 4. The two-stage structure in which the brine coming from stage 1 enter fully to stage 2 ( x b,1,2 been identified identified in this b,1,2 = 1) have been range of concentration (shown as Fig. 5). 5). Because the feed con-

Fig. 5. The optimum RO system for feed concentration varying varying from 20,000 to 35,000 ppm.

Table 1 Characteristics of FilmTec spiral wound reverse osmosis membrane elements Element type

SW30XLE-400

SW30HR-380

SW30HR-320

BW30-400

Active area (ft2 ) (m 2 ) Length of the element (in.) (mm) Diameter of the element (in.) (mm) Feed space (mil)a Feed flow rate range (m 3 /h) Permeate flow (gpd) (m 3 /d) Stabilized salt rejection (%) Maximum operating pressure (psig) (MPa) Pure water permeability constant, A (kg/m2 s Pa) Salt permeability constant, B (kg/m2 s) Membrane element cost ($) (estimation)

400 (37.2) 40 (1016) 7.9 (201) 28 0.8–16 9000 (34.1) 99.70 1,200 (8.3) 3.5 × 10−9 3.2 × 10−5 1200

380 (35.3) 40 (1016) 7.9 (201) 28 0.8–16 6000 (22.7) 99.70 1,200 (8.3) 2.7 × 10−9 2.3 × 10−5 1000

320 (29.7) 40 (1016) 7.9 (201) 34 0.8–14 6000 (22.7) 99.75 1,200 (8.3) 3.1 × 10−9 2.2 × 10−5 1400

400 (37) 40 (1016) 7.9 (201) 34 0.8–19 10,500 (40) 99.5 600 (4.5) 7.5 × 10−9 6.2 × 10−5 900

a

1 mil= 0.0254mm. 0.0254mm.

225


Table 3 Design and optimization results for the feed concentrations varying varying from 38,000 to 48,000 ppm Feed concentration, C f f (ppm)

Process flow System feed flow, Qf (m3 /h) System overall recovery Product concentration, C p (ppm) Membrane type in stage 1 Number of elements per PV in stage 1 Number of PV in stage 1 Operating pressure in stage 1, P1 (MPa) Unit product cost ($/m 3 )

48,000

45,000

42,000

38,000

One stage system, Fig. 4 264 45% 380 SW30XLE-400 5 40 8.1 0.58




Table 4 Design and optimization results for the feed concentrations varying varying from 20,000 to 35,000 ppm Feed concentration, C f f (ppm)

Process flow System feed flow, Qf (m3 /h) System overall recovery Product concentration, C p (ppm) Membrane type in stage 1 Membrane type in stage 2 Number of elements per PV in stage 1 Number of elements per PV in stage 2 Number of PV in stage 1 Number of PV in stage 2 Operating pressure in stage 1, P1 (MPa) Operating pressure in stage 2, P2 (MPa) Unit product cost ($/m 3 )

35,000

30,000

25,000

20,000

Two stage system, Fig. 5 191 63% 300 SW30XLE-400 SW30XLE-400 2 5 29 20 7.3 8.3 0.5




centration of stage 2 increases, In order to meet the product quanti quantity ty requir requireme ement, nt, it is necess necessary ary to pressu pressuriz rizee the brine brine comcoming from stage 1 and to increase the number of elements in each PV in stage 2. The selected type of membrane element is the SW30XLE-400 in both stages. For the lower lower feed concentration concentrationss (3000–16,00 (3000–16,000 0 ppm), the design results were presented in Table 5. 5. In the range of concentration, the multi-stage RO systems with brine re-processing are favored and the selected types of membrane element are the BW30-400. With decreasing feed concentration, the structures employed during the design vary from two-stage to three-stage with brine recycle. It leads to the result that the overall recovery ratio increase and the unit product cost decrease. When the concentration centration of feed stream is 12,000 ppm, there is a bypass bypass into the second stage for the brine coming from the first unit of stage 1 (shown as Fig. 6), 6), while the others enter the second unit of

stage 1 straightly ( x b,1,2 0.526). The brine bypass is useful useful to b,1,2 = 0.526). dilute the feed stream of stage 2. As indicated in Figs. 6 and 7, 7, the stage 1 can be made of more unit blocks in series. The feed pumps between units were omitted. Thecostsfor thehigh pressu pressure re pump pump arenot smoothfunct smoothfunction ionss of the flow rate and operating pressure. In the present study, the pump cost is about a given range of flow rate and operating pressure. If a different pump cost model is used, some pumps could be eliminated from the optimal structure. For the feed stream stream of concentrat concentration ion 3000 ppm, the optimal RO struct structure ure has been been shown shown as Fi Fig. g. 8. The The brin brinee leav leavin ing g stag stagee 3 partly partly recycl recyclee ( x b,3,3 0.233) 3),, whil whilee the the othe others rs come come into into the the PX. PX. b,3,3 = 0.23 In this case, there is another solution closing to the optimal one. The calculation results indicated that the structure employed in the suboptimum solution is two-stage arrangement (shown as Fig. 7), 7), its unit product cost is $0.23 and the overall recovery is 83%. The unit cost is a little larger than that of the optimal one,

Fig. 6. The optimum RO RO system for feed concentration 12,000 12,000 ppm.

Fig. 7. The optimum RO RO system for feed concentration 6000 6000 ppm.

226


Table 5 Design and optimization results for the feed concentrations varying varying from 3000 to 16,000 ppm Feed concentration, C f f (ppm)

Process flow System feed flow, Qf (m3 /h) System overall recovery Product concentration, C p (ppm) Membrane type in stage 1 Membrane type in stage 2 Membrane type in stage 3 Number of elements per PV in stage 1 Number of elements per PV in stage 2 Number of elements per PV in stage 3 Number of PV in stage 1 Number of PV in stage 2 Number of PV in stage 3 Operating pressure in stage 1, P1 (MPa) Operating pressure in stage 2, P2 (MPa) Operating pressure in stage 3, P3 (MPa) Unit product cost ($/m 3 )

16,000

12,000

6000

3000

Two stage system, Fig. 5 171 70% 250 BW30-400 BW30-400



3 5

2 6

2 6

26 15

34 12

35 7

3.9 4.5

3.6 4.2

2.7 3.3

0.32

0.29

0.24

Three stage system, Fig. 8 140 86% 60 BW30-400 BW30-400 BW30-400 3 3 5 22 12 8 2.0 2.3 2.4 0.22

but its structure is relatively simple. Therefore, the suboptimum solution may be better for the case from operative point of view. In general, for different feed concentration (varying from 3000 to 48,000 ppm), the design results results (shown as Tables 3–5) 3–5) indica indicate te that that the unit unit produc productt cost cost is propor proportio tional nal to the feed feed conconcentration. With increasing raw feed concentration the overall recovery recovery ratio decrease decrease and the product product water water quality quality deteriorate deteriorate.. For processing higher feed concentration, the high operating pressure is necessary. However, the number of elements and pressure vessels employed in RO system is less than that of lower feed concentration. It indicated that the arrangement and operation of RO system are more flexible when the operating pressure is relatively lower. lower. When the high operating pressure is necessary, the simple one stage structure is more favored. The optimization of RO networks were affected by feed concentration and permeate recovery per module. As shown in the Figs. 4–8, 4–8, the transition from one structure to the other is continuous when the feed concentration changes. With decreasing feed concentration, the structural schemes vary from single to three-stage with brine bypass and recycle. For the feed concentration tration of 12,000 12,000 ppm, there is a brine bypass in the optimum structure (shown as Fig. 6). 6). The feed stream of the stage 2 could be diluted with the brine bypass stream. With decreasing feed concen concentra tratio tion, n, the brine brine bypass bypass ratio ratio decrea decreases ses consta constantl ntly y. In the vicinity of 6000 ppm, the bypass disappeared. The feed concenconcentration of stage 2 still meets the requirement although without

the bypass stream. For lower feed concentration concentration (3000 ppm), a brine brine recycl recyclee around around stage stage 3 that that leads leads to higher higher overa overall ll recov recovery ery appears in the optimum structure (shown as Fig. 8). 8). Although the brine recycle will increase the feed concentration of stage 3, the brine concentration coming from stage 2 is relatively lower, and the third stage can still produce permeate required.

For For differ different ent value valuess of the produc productt qualit quality y constr constrain aints ts varyi varying ng between 300 and 50 ppm, the optimization of the superstructure superstructure has been carried out at a constant raw feed stream of concentration 35,000 35,000 ppm and the product product requirement requirement of 120 m3 /h. The design results are presented in Table 6. 6. The optimal structure employed in the design is strongly dependent on the required product concentration. For the looser permeate concentration requiremen requirementt (300 ppm), two-brine two-brine staging staging configurati configuration on (shown (shown as Fig. 5) 5) is favored that increase the system recovery ratio. For the product quality requirement of concentration concentration 200 ppm, the optimal RO structure changes to the single stage (shown as Fig. 4). 4). For the lower permeate quality requirement of concentration centration 100 ppm, the three-stag three-stagee structure structure with permeate permeate re-processing and brine recycle have been identified (shown as Fig. 9). 9). The permeate leaving stage 1 mostly split into the stage 2 ( x p,1,2 feed p,1,2 = 0.852), the other come to the product output. The feed stream of stage 3 include the full brine coming from stage 2 and

Fig. 8. The optimum RO RO system for feed concentration 3000 3000 ppm.

Fig. Fig. 9. TheoptimumRO TheoptimumRO systemfor systemfor feed feed concen concentra tratio tion n 35,00 35,000 0 ppm, ppm, theproduct theproduct concentration 100 100 ppm.

5.2. The study of varying product product composition

227


Table 6 Design and optimization results for the product concentrations varying from 300 to 50 ppm Feed concentration, C f f (ppm)

Process flow System feed flow, Qf (m3 /h) System overall recovery Product concentration, C p (ppm) Membrane type in stage 1 Membrane type in stage 2 Membrane type in stage 3 Number of elements per PV in stage 1 Number of elements per PV in stage 2 Number of elements per PV in stage 3 Number of PV in stage 1 Number of PV in stage 2 Number of PV in stage 3 Operating pressure in stage 1, P1 (MPa) Operating pressure in stage 2, P2 (MPa) Operating pressure in stage 3, P3 (MPa) Unit product cost ($/m 3 )

35,000

35,000

35,000

35,000

Two stage system, Fig. 5 191 63% 300 SW30XLE-400 SW30XLE-400

One stage system, Fig. 4 264 45% 200 SW30XLE-400

2 5

4

29 20

40

7.3 8.3

7.1

0.5

0.52

Three stage system, Fig. 9 295 41% 100 SW30XLE-400 BW30-400 BW30-400 7 8 7 45 19 29 5.8 0.84 0.84 0.74

Three stage system, Fig. 10 300 40% 50 SW30XLE-400 BW30-400 BW30-400 7 8 7 46 22 34 5.8 0.84 0.84 0. 0.78

the partly recycle brine leaving stage 3 ( x b,3,3 0.867). For the the b,3,3 = 0.867). tighter tighter permeate permeate quality requiremen requirementt of concentrati concentration on 50 ppm, the structure employed in the design is similar to the previous three-stage structure (shown as Fig. 10). 10). The split ratio of permeate entering to the stage 2 ( x p,1,2 p,1,2 ) has increased up to 0.978, and the recycle ratio of brine entering to the stage 3 ( x b,3,3 b,3,3 ) has slightly decreased. With decreasing concentration of the product, the overall system recovery ratio decrease, the unit cost of the product increase, and the feed stream of stage 2 varies from brine to permeate. Therefore the selected types of membrane element also vary from the SW30XLE-400 to BW30-400. Consequently, the required operating pressure has decreased. For the product product requiremen requirementt of concentration concentration 100 ppm, the calculati calculation on results results indicated indicated that the permeate coming from the stage 1 (concentra (concentration tion 400 ppm) is re-process re-processed ed in stage 2 (shown as Fig. 9) 9). The permeate concentration and the brine concentra concentration tion leaving leaving stage 2 are 10 ppm and 670 ppm, respecrespectively tively.. Then, Then, the permeate permeate concentrati concentration on leaving leaving stage 3 increase increase up to 70 ppm because because of a brine re-circulation re-circulation around around stage 3. The product water consist of the permeate coming from each stag stage. e. The The prop propor orti tion on of the the perm permea eate te comi coming ng from from stag stagee 3 is the the larges largest, t, while while that that comingfrom comingfrom stage stage 1 is thesmallest thesmallest.. Theref Therefore ore,, the brine re-circulation around stage 3 is useful in increasing the overall recovery ratio and making the product concentration meet to the requirement.

For the case that the product water water concentration concentration is 50 ppm, there is another solution without recycle closing to the optimal one. The structure is shown as Fig. 11. 11. The calculation results indicated that the unit product cost of the suboptimum solution is $0.86, the overall recovery is 32%. The cost is 10% higher than that of the optimal one. Mathematically, the optimum RO structure is the one shown in Fig. 10, 10, of which the unit product cost is the lowest. However, current RO systems are normally operated at two-stage or three-stage structure without recycle stream because of the operational and engineering limit to the performance of multi-stage system. Therefore, the three-stage (shown as Fig. 11) 11) or even two-stage structure may be better from operative point of view.

For a typical typical seawater seawater desalination desalination process, which has a fixed feed concentrati concentration on (35,000 (35,000 ppm) and product product concentra concentra-tion tion requir requireme ement nt (300 (300 ppm), ppm), the effec effectt of unit unit costs costs on the design design result resultss were were shown shown in Table 7. Three Three types types of membra membrane ne elemen elementt (SW30XLE-400, SW30HR-380, SW30HR-320) were included in the present study, and the unit price of each was assumed to be 1200, 1000, 1400 $, respectively. The table shows that the unit product cost is very sensitive tive to electricit electricity y price. price. When the electricit electricity y price increase increase −1 (0.08–0.12 (0.08–0.12 $ (kWh) ), the unit produc productt cost cost increa increase se 28%. 28%.

Fig. 10. The optimum RO system system for feed concentration 35,000 ppm, the product concentration 50ppm.

Fig. 11. Another solution solution closing closing the optimal optimal one for feed concentratio concentration n 35,000 ppm, the product product concentration 50 ppm.

5.3. The effect effect of unit costs costs

228


Table 7 Sensitivity analysis for electricity, membrane element unit prices Electricity price ($) (kWh)−1 [membrane element price ($)]

Operating pressure in stage 1, P1 (MPa) Operating pressure in stage 2, P2 (MPa) The number and type of membrane employed in stage 1 The number and type of membrane employed in stage 2 Overall recovery Unit product cost ($/m 3 )

0.05 (1200, 1000, 1400)

0.12 (1200, 1000, 1400)

0.08 (1200, 1000, 1400)

0.08 (1600, 1400, 1800)

0.08 (800, 600, 1000)

8.1 9.2 52, SW30XLE

6.8 7.8 98, SW30XLE

7.3 8.3 58, SW30XLE

7.6 8.6 54, SW30XLE

7.0 8.1 68, SW30XLE

82, SW30XLE

92, SW30HR-320

100, SW30XLE

85, SW30XLE

132, SW30HR- 38 380

67% 0.4

59% 0.64

163% 0.5

64% 0.52

62% 0.48

While a 33% increase in membrane price results in only 4% increa increase se in unit unit produc productt cost. cost. When When the electr electrici icity ty price price decrea decrease se (0.08–0.05 (0.08–0.05 $ (kWh)−1 ), or the membrane price decrease (1200, 1000, 1000, 1400–8 1400–800, 00, 600, 600, 1000 1000 $), the lower lower product product cost cost can be achieved by applying high operating pressure or increasing the membrane area. However, the product cost is more sensitive to changes in electricity price (operating cost) than membrane price (capital cost). Increasing operating pressure achieves higher overall recovery and lower unit product cost than than increa increasin sing g membra membrane ne area. area. Thus, Thus, reduct reduction ion in operat operat-ing costs is more important than reduction in capital cost in decreasing product cost. The electricity is the major cost component. It dominates because of the high pressure of the optimal designs. 6. Conclusion Conclusion

The optimum design of RO systems under different feed concentrati concentration on and product product specificati specification on has been studied studied in this this work. work. A simpli simplified fied supers superstru tructu cture re that that contai contains ns all the feasible design in present desalination process has been presented. It offers extensive flexibility towards optimizing various types of RO system and thus may be used for the selection of the optima optimall struct structura urall and operat operating ing scheme schemes. s. A prespressure sure vess vessel el mode modell has has also also been been give given. n. It coul could d be used used for the optimal selection of types and number of membrane elements, elements, according to its performanc performancee characteri characteristics stics,, the prices, and the design requirements of a specific desalination application. The design task has been formulated as an MINLP, which seeks to minimize the total annualized cost of the RO system while considerin considering g the thermodyna thermodynamic, mic, modeling, modeling, economic, economic, and feasibility constraints. The objective is to determine the optimal system structure and operating conditions for a given feed water concentration and water production requirement. The solution to the problem also includes the most appropriately choice of the types of membrane elements in each stages and the optimal number of membrane elements in each PV. The effectiveness of this design methodology has been demonstrated by solving seve several ral seawa seawater ter desali desalinat nation ion cases. cases. The result result indica indicated ted that that it is possib possible le to obtain obtain lower lower produc productt water water cost cost by using using this this method method presented.

Nomenclature A B C C e C k k C m C pv pv C w

CCbp CChpp CCin CCpx d Ds J s J w K Lpv Lm m n j N l

OCin OChpp OCbp P Pf Q Qp,n Re Sc S m T

TAC V w W

water permeability (kg/m2 sPa) solute transport parameter (kg/m2 s) concentration of solute (ppm) electricity cost ($/(kWh)) the price of the k th th membrane element ($) membrane module cost ($) the price of the pressure vessel ($) concentration at the membrane wall (ppm) capital cost of the booster pump ($) capital cost of the high pressure pump ($) capital cost of the seawater intake pump ($) capital cost of the pressure exchanger ($) the feed spacer thickness (m) the solute diffusivity (m2 /s) salt flux (kg/m2 s) water flux (kg/m2 s) the mass transfer coefficient (m/s) length of the pressure vessel (m) the length of a element (m) the number of membrane elements in each PV the number of pressure vessel employed in the jth RO stage the number of leaves in a membrane element energy cost of the intake pump ($) energy cost of the high pressure pump ($) energy cost of the booster pump ($) operating pressure (MPa) the pressure drop in the membrane channel flow rate (m3 /h) the total permeate flow rate of the nth pressure vessel (m3 /h) Reynold’s Reynold’s number Schmidt number the membrane area per element (m2 ) temperature (◦ C) total total annual annualize ized d cost cost ($) the permeate velocity (m/s) membrane width (m)


x b, b,i, j j

x p, p,i, j j

Z

the stream split ratio of the brine leaving the jth RO stage stage andbeing linke linked d to the ith pressuriza pressurization tion stage the stream split ratio of the permeate leaving the jth RO stage and being linked to the ith pressurization stage binary integer

Greek η μ Π Π w ρ

pump efficiency the water viscosity viscosity (kg/m s) osmosis pressure (MPa) osmosis pressure of the brine at the membrane wall (MPa) density (kg/m3 )

Subscripts

b b, j bp f hpp hpp in k

p p, j j ps, i px RO, j

brine stream the brine stream of the jth RO stage booster pump feed stream high high pres pressu sure re pump pump intake seawater the k th th element type permeate stream the permeate stream of the jth RO stage the ith pressurization stage pre pressur ssuree excha change nger the jth RO stage

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Optimum design of reverse osmosis system under different feed concentration and product specification

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