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Optimization of Seawater Reverse Osmosis Desalination Networks with Permeate Split Design Considering Boron Removal Yawei Du,*,† Yan Liu,† Shaofeng Zhang,† and Yingjun Xu‡ †

Engineering Research Center of Seawater Utilization Technology of Ministry of Education, School of Marine Science and Engineering, Hebei University of Technology, Tianjin300130, PR China ‡ State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing100875, PR China S Supporting Information *

ABSTRACT: Increasingly strict constraints on the boron concentration for safe drinking and irrigation water present a tremendous challenge for the design of seawater reverse osmosis (RO) desalination systems. This work presents an optimization study of a seawater reverse osmosis RO network with permeate split (PS) design under boron concentration restrictions. Front part permeates with better quality and higher flux are sent directly to the product, and back part permeates are reprocessed in pass 2 with high pH value. The irreversible thermodynamic model is employed to describe the membrane transport behavior of boron. Constraints for the system flow and operation conditions are added to guarantee safe operating of the RO system. Both single-product and two-product RO systems are optimized for different types of feed seawater. Results show that the PS design is mainly dominated by the boron constraints, while the system recovery is mainly controlled by the feed salt concentration. Due to the upper bound of pH for pass 2, PS design could be introduced for pass 2 to improve the boron rejection. For a two-product output system, the permeates from both RO pass 1 and pass 2 could be split and sent to different products. In general, PS design could offer lower water cost, lower energy consumption, and smaller system size compared with normal design. Not only the operation conditions but also the flow structure of the RO system should be adjusted according to both membrane fouling and degradation with time.

1. INTRODUCTION There has been an increasing demand for potable water due to the population boom of our plant. Seawater desalination technologies are the main alternatives to overcome the shortage of drinking water. Reverse osmosis (RO) is one of the most widely used technologies in seawater desalination applications. Nevertheless, there are still a lot of challenges in the design of RO desalination systems, due to the increasing strict constraints of the boron concentration for safe drinking and irrigation.1 The typical boron concentration in a seawater environment is about 4−6 mg/L.2 Although a small amount of boron is necessary for human health and growth of some plants, excessive boron is toxic for both humans and plants.3 On one hand, the World Health Organization (WHO) recommended a maximum guideline of 2.4 mg/L for boron in drinking water.4 Some countries still suggest a strict value of boron in potable water; for instance, the maximum boron concentration recommended by the European Union is 1.0 mg/L. Many RO seawater desalination plants also set very low boron targets, both Ashkelon and Palmahim in Israel deliver high-quality permeate product with boron concentration less than 0.4 mg/L.3 On the other hand, many agricultural crops are unable to withstand excess boron concentration in irrigation water. For example, the boron tolerance is only 0.5 mg/L for blackberry and lemon.5 For Middle East and North Africa areas, where a lot of irrigation water is provided by RO desalination plants, the © XXXX American Chemical Society

boron concentration in permeate should be low enough for the growth of such crops in spite of the drinking water standards.5,6 As one of the mainstream seawater desalination technologies, the effect of boron removal for the RO process is receiving more and more attention. The pH value of natural seawater is 7.9−8.2, at pH below the pKa of boron (the pKa is approximate 8.60 at salinity of 40 kg/m3), the boron has no charge (neutral) and mainly is in the form of boric acid, while, at pH above the pKa, it is in the ionic form (borate ion). Ions in water are hydrated and thus are larger than boric acid, which is not hydrated. Neutrally charged species with molecular weight smaller than about 150 g/mol are poorly rejected by RO membranes. Increasing the pH of seawater can increase the rejection boron for a RO membrane. As a result, at normal operation conditions, a single-pass RO system could not meet the guidelines of drinking and irrigation water for boron. Two-pass and cascade designs with pH value adjustment are usually introduced to improve the boron rejection. Recently, acidification/decarbonation of the feed seawater followed by highpH single RO pass is proposed, which could reduce the energy Received: June 8, 2016 Revised: October 13, 2016 Accepted: November 2, 2016

A

DOI: 10.1021/acs.iecr.6b02225 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

This study presents the RO network optimization with the permeate split (PS) design approach under boron limitations, which is on the basis of our previous work.31 The model provided here is different from those of Saif et al.19,29 and Du et al.31 in terms of the RO membrane transport model and the RO pressure vessel representation. A set of algebraic and differential equations is introduced to describe the membrane transport phenomena inside the pressure vessel. The transport behaviors of boron are expressed by an irreversible thermodynamic model, which is validated from lab-scale experiments.2,13,30 Different from the solution diffusion model, the boron−water coupling effect is described through a reflection coefficient. The pressure vessel model with PS design is on the basis of the concept proposed by Bray32 and Rybar et al.33 As show in Figure 1, a pressure vessel usually contains several

consumption without changing the currently installed infrastructure.7,8 Today, more and more RO desalination plants apply the spiral-wound module (SWM) type membranes. The RO process with a SWM is composed of pressure vessel (PV) arrays, each of them including several membrane modules connected in sequence. The design of a RO plant needs to make choices over a lot of selections that depend on both continuous variables (such as operation pressure and flow rate) and discontinuous variables (existence of RO stages/passes, pumps, etc.).9 Meanwhile, many parameters would have great effects on boron rejection, such as pH value, pressure, and temperature.10−14 Network optimization is required to help the engineer designing the RO system under boron restrictions in order to pursue lower fresh water cost. Many works based on superstructure optimization approaches were made for the design of reverse osmosis networks (RONs).15−22 El-Halwagi15 first proposed a state space based RON optimization approach. Heuristic algorithms and global optimization methods were also developed to pursue a more reasonable process flow structure.16,17 Other efforts focused on the RO system optimization with different feed concentrations and product specifications, membrane fouling, and dynamic operational optimization with time-dependent parameters.20−22 Several mathematical models describing the transport phenomena of boron in RO processes were based on either a phenomenological or a mechanistic model, such as a solution diffusion model and an irreversible thermodynamic model.2,11−14,23 Recently, a more accurate mathematical model was proposed. Both the convective transport model and weak acids’ transport coupled with chemical equilibrium model could help us to understand the transport mechanism of boric acid and borate ions in the RO process.24,25 With the development of the boron transport model during the RO process, researchers focused on the design and optimization of a RO system under boron restrictions.26−30 Park et al.26 developed a stochastic optimization framework to evaluate the investment and operation costs for the RO plants, which could reflect the effects of uncertain future electricity and finance costs on the energy consuming RO process. Boron restriction for the RO permeates was introduced in the optimized problems, but the pH effect on the boron removal was not included, which was an effective method to improve the boron rejection. A network optimization approach was recently employed for designing the RO system considering boron removal.27,28 However, linear or nonlinear fittings of the boron rejection with pH were employed in the optimization models, which could not exactly reflect the boron transport across the membrane along the pressure vessels, due to the inherent nonlinear behaviors of the RO process (such as concentration polarization, variation of operation conditions, etc.). Saif and Almansoori29 developed an optimization model for a RON with a permeate splitting design under boron limitations; the solution diffusion model was introduced to model the salt and boron transport phenomena along the pressure vessel. Progressive water cost savings were made by their model.29 However, there were still some drawbacks. For one thing, the design scheme is difficult to utilize in the present RO plants due to the change of the structure of the pressure vessel; for another, the range of the recovery rate for the optimized RO systems under boron restrictions is only 17%−30%, which still has a lot of room for improvement.

Figure 1. Schematic of PS design with adjustable permeate split ratio. (Reproduced with permission from ref 31. Copyright 2015 Elsevier Science.)

membrane modules, the front part of the RO membranes always produces higher permeate flux with lower salinity than membranes at the back part of the PV; thus, the high-quality permeates could send directly to the product. Flow control valves are installed on one or both sides of the permeate pipelines; thus, the split ratio between the front and back permeates can be adjusted in accordance with actual operation conditions. The schematic the PS design is presented in ref 31. The flow direction of subelement permeate in the pressure vessel is modeled through binary variables. A RO superstructure with multiple-product output is proposed, and system flow constraints are added for the safe operation of the optimized RO systems. Different types of feed seawater and different boron concentration restrictions are investigated, and both the effects of temperature and membrane degradation with year are discussed. Sensitivity analysis is utilized to investigate the influences of several parameters on the system performance.

2. PROCESS MODELING 2.1. pH Effect on the Boron Removal. Boron in seawater is mainly in the form of boric acid ([B(OH)3]). As a Lewis acid, the dissociation of boric acid is carried out: B(OH)3 + 2H 2O ↔ B(OH)4 − + H3O+ ,

pK a ∼ 9.23

At relatively low concentrations (≤216 mg/L as boron), the formation of polynuclear ions or ringed structures is not taken into consideration.6 Thus, under the normal SWRO plant operation conditions, the total boron concentration CTB is the sum of the boric acid concentration and the borate ion ([B(OH)4]−) concentration. The distribution of boric acid is a function of the first acid dissociation constant pKa and the seawater pH value. For both the concentrated and diluted seawaters, pKa could be measured in a wide range of temperatures and salinities;8 the molar percent of borate ion in solution at different salt concentrations as a function of pH was shown in ref 24. B


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Industrial & Engineering Chemistry Research Table 1. RO Membrane Transport Model for a Pressure Vessel equations

Jw, l = (A ref (1 − FFd)Nmlp

meaning

⎡e⎛ 1 ⎞⎤ 1 ⎟⎥ exp⎢ ⎜ − ⎣ R ⎝ 298.15 273.15 + T ⎠⎦

(Pl − σ(πch,mw, l − πch,p, l))

Js , l = Bref (1 + Bin)Nmlp (Cch,mw, l − Cch,p, l) −5

σ = 0.997 − (4.98 × 10 )T

local water transport through subelement l in a PV

(1) local salt transport through subelement l in a PV

(2)

reflection coefficient for salt2

(3)

BTB, l = α0, lB boric,ref e(0.067(T − T0)) + α1, lB borate,ref e(0.049(T − T0)) σTB, l = α0, lσboric + α1, lσborate

(5)

boron reflection coefficient

2291.90 pK a, l = + 0.01756(273.15 + T ) − 3.3850 − 0.32051 273.15 + T ⎛ Cch,mw, l ⎞1/3 ⎜ ⎟ ⎝ 1.80655 ⎠

α0, l = α1, l10

Vw, l =

pKa, l − pH

overall boron permeability constant13

(4)

first acid dissociation constant of boric acid25

(6) fraction of boric acid

(7)

Jw, l + Js, l

Cch,p, l =

C TB,ch,b, l C TB,ch,p, l

ρp

permeate velocity

(8)

Js, l Vw, l

local salt concentration of the permeate

(9)

= 1 + ((σTB, l(1 − exp(− Vw, l(1 − σTB, l)/(BTB, l (1 + BTB,in )Nmlp )))) /((1‐σTB, l) exp(Vw, l /Kl)))

Cch,mw, l − Cch,p, l Cch,b, l − Cch,p, l

⎛ Vw, l ⎞ = exp⎜ ⎟ ⎝ Kl ⎠

Kl = 0.068Rel 0.875Scl 0.25 C TB,ch,mw, l − C TB,ch,p, l C TB,ch,b, l − C TB,ch,p, l

Kl = 0.97K TB, l Pl + 1 = Pl +

Ds de

(10) concentration polarization

(11)

mass transfer coefficient34

(12)

⎛ Vw, l ⎞ ⎟⎟ = exp⎜⎜ ⎝ K TB, l ⎠

concentration polarization for boron

(13)

boron mass transfer coefficient11

(14)

ρ V2 ρ V 2⎞ Δz ⎛ ⎜− λl b l − λl + 1 b l + 1 ⎟ 2 ⎝ de 2 de 2 ⎠

λl = Kλ6.23Rel−0.3

local boron concentration of the permeate12

feed side pressure drop

(15)

friction factor34

(16)

Symbols: Cmw, salt concentration at membrane surface [kg/m3]; π, local osmotic pressures [MPa]; Jw, local volumetric permeate flux [kg/m2·s]; Js, local gravimetric flux of solute [kg/m2·s]; Vw, velocity of permeate [m/s]; ρp, permeate density [kg/m3]; K, local mass transfer coefficient [m/s]; de, equivalent diameter of feed channel [m]; Sl, membrane area of subelement l for a pressure vessel [m2], (Sl = Sm·nm/L), where Sm is the active area of membrane module [m2], nm is the number of modules inside the pressure vessel, L is the number of mesh points; Re, Reynolds number (Re = ρVde/μ), where μ is dynamic viscosity [Pa·s]; Sc, Schmidt number (Sc = μ/ρDs), where Ds is the solute diffusivity [m2/s]; Q, flow rate [m3/h]; V, feed superficial velocity [m/s], (V = Q/(3600Sfcsεsp); Sfcs, feed channel cross-section open area [m2]; εsp, spacer void fraction; Qp,n, total flow rate of permeate [m3/h]; Cp,n, average permeate concentration [kg/m3]; R, universal gas constant; e, membrane activation energy, (25,000 J/mol when T ≤ 25 °C and at 22,000 J/mol when T > 25 °C); FFd, annual decrease in permeate flux; Bin, annual increase in salt permeability; BTB,in, increase in boron permeability per year; T0, reference temperature, T0 = 25 °C; Nmlp, design period; σ, reflection coefficient; α0, α1, fraction coefficients of B(OH)3 and B(OH)4−, respectively. α0 = {H+}/({H+} + K′TB) = [B(OH)3]/([B(OH)3] + [B(OH)4−]); α1 = K′TB/({H+} + K′TB) = [B(OH)4−]/ ([B(OH)3] + [B(OH)4−]) = 1 − α0; pKa = −log(K′TB) = [B(OH)4−]{H+}/[B(OH)3]; pKa, first dissociation constant of boric acid; Δz, integration step [m]; l, index number along z-axis; Yl, binary variable describing the subelement flow direction. (subscript: ch, feed or permeate channel in membrane module; b, brine side; f, feed side; p, permeate side; mw, membrane wall; TB, total boron; lc, front part low-concentration permeate; hc, high-concentration back part permeate). a

modules (nm) and the module length (Lm). The finite difference method was adopted in this study. The pressure vessel is subdivided into 30 subelements. Mesh points along the horizontal axis are denoted as l. Table 2 provides the model equations for material balances and PS design in a PV. For the PV with PS design (Figure 1), permeates are gathered from both sides of the PV (eq 20−28). The front part permeates with relatively low salt and boron

2.2. Spiral-Wound Module Model. As shown in Table 1, the transport phenomena of water and solute (including salt and boron) through RO membranes are modeled using a mathematical model proposed by Mane et al.,2 Geraldes et al.,34 Avlonitis et al.,35 and Du et al.31,36,37 The schematic of a flat feed channel with dimensions h (feed channel thickness) × LPV (pressure vessel length) × W (width of membrane leaf) is illustrated in Figure 2. LPV is the product of the number of C


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Figure 2. Schematic of the rectangular SWM feed channel model.34

concentration could be sent directly to the product, while back permeates with high concentration are reprocessed in the same or the next RO pass. At the end of the process, the permeates from each pass could be mixed to meet the required quality of final product. The boundary conditions are given by

Figure 3. Superstructure of the RO network with PS design.

V = Vin , C = C in , C TB = C TB,in P = Pin when z = 0

devices, and a distribution box (DB). Two RO stages/passes with two product outputs are considered here. The RON contains four sets of streams nodes: pressurization stages Nps, RO stages NRO, a pressure exchanger (PX) Npx, and the product flow Np. The junction of Nps + 1 indicates the brine streams leaving the network. Each stream among the Nps nodes is connected to a pump. The streams pressurized by a highpressure pump (HPP) or not are connected to corresponding RO stages. The RO stages contain several parallel pressure vessels operating under the same conditions. Each stream of the network (the brine and permeate streams leaving all RO stages) may be linked to all the (Nps + NRO + Npx + Np + 1) nodes. Note that the turbine in Figure 3 is only used for the comparison of different energy recovery choices with the alternative models, which is not utilized in other cases. Some unreasonable connections among the process units could be removed from the network. The description of the RON reduction could be found in our previous work.31

(29)

The osmotic pressure π, dynamic viscosity μ, and salt diffusion coefficient Ds along the pressure vessel are calculated by the following nonlinear fittings:12,18,34 π = 4.54047(103C /Msρ)0.987

(30)

μ = (1.4757 × 10−3 + 2.4817 × 10−6C + 9.3287 × 10−9C 2) exp( −0.02008T )

(31)

Ds = 6.725 × 10−6 exp(0.1546 × 10−3C − 2513 /(T + 273.15))

(32)

where Ms is the solute molecular weight. 2.3. RO Network Model. As shown in Figure 3, the proposed reverse osmosis superstructure with PS design is composed of RO stages/passes, pumps, energy recovery

Table 2. Material Balances and Permeate Split Design for a Pressure Vessel equations

Q ch,b, l + 1 = Q ch,b, l − 3600Vw, lSl

meaning flow rate at subelement l + 1

(17)

Q ch,b, l + 1Cch,b, l + 1 − Q ch,b, lCch,b, l = − 3600Vw , lSlCch,p, l

(18)

Q ch,b, l + 1C TB,ch,b, l + 1 − Q ch,b, lC TB,ch,b, l = − 3600Vw , lSlC TB,ch,p, l

Q p,n,lc =

∑ (3600Vw,lSlYl ) l

Q p,n,hc =

total quantity of front low-concentration permeates for a PV with PS

∑ (3600Vw,lSlCch,p,lYl ) l

∑ (3600Vw,lSlCTB,ch,p,lYl )

∑ (3600Vw,lSlCch,p,l(1 − Yl )) l

Q p,n,hcC TB,p,n,hc =

total quantity of higher concentration back permeates for a PV with PS salt concentration of front permeates for a PV with PS

(22)

l

Q p,n,hcCp,n,hc =

boron concentration at subelement l + 1

(21)

l

Q p,n,lcC TB,p,n,lc =

(19)

(20)

∑ (3600Vw,lSl(1 − Yl ))

Q p,n,lcCp,n,lc =

salt concentration at subelement l + 1

salt concentration of back permeates for a PV with PS

(24)

∑ (3600Vw,lSlCTB,ch,p,l(1 − Yl )) l

Q f,n = Q b,n + Q p,n,lc + Q p,n,hc

boron concentration of front permeates for a PV with PS

(23)

boron concentration of back permeates for a PV with PS

(25)

(26)

Q f,nCf,n = Q b,nC b,n + Q p,n,lcCp,n,lc + Q p,n,hcCp,n,hc

total material balance for a PV with PS

(27)

Q f,nC TB,f,n = Q b,nC TB,b,n + Q p,n,lcC TB,p,n,lc + Q p,n,hcC TB,p,n,hc

total mass balance for a PV with PS

(28)

total boron balance for a PV with PS D


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concentration restrictions of the final product, the boron concentration of the RO permeate may not reach the requirement of the product. Thus, the high-quality front permeate of RO pass 2 can be collected as the final product, and the back permeate of RO pass 2 is allowed to be sent back to the same pass for reprocessing. Because of low boron rejection of the RO pass 1 (low pH value of feed stream), the permeate of RO pass 2 is not permitted to be sent back to the feed stream. For the two-product output system, the front and back permeates with different salt and boron concentrations could be collected as different final products. Therefore, the PS design could be introduced for both RO pass 1 and pass 2. As shown in Figure 3, it seems that the pressure energy from the high-pressure brine stream produced by RO pass 2 can also be recovered by a PX or turbine. On one hand, RO pass 1 and 2 operate under different feed pressures. The brine streams from the RO passes should not be mixed directly, according to eq 40. Another PX unit could not be introduced (Due to the relatively low brine pressure and flow rate of the brine stream produced by RO pass 2, the high-pressure stream leaving the PX cannot easily match the feed seawater stream entering the HPP); on another hand, due to low-energy recovery rate and the increase of capital cost, the turbine is only used for the comparison with the alternative models. In order to avoid mixing the highpressure brine produced by RO pass 2 and the feed seawater with different pressure, a throttling value is followed by the high-pressure brine streams produced by RO passes (except for pass 1) being connected to the feed stream, in order to reduce brine pressure to normal pressure. Several streams are gathered to a mixer to obtain a single stream. On contrast, a single stream is divided into several outing streams in the splitter. Each stream can be described by flow rate Q, salinity C, boron concentration CTB, and pressure P. Within the DB, each MIN inlet stream (Q in, Cin, CTB,in, Pin) can be divided into MOUT outgoing streams (Q out, Cout, CTB,out, Pout) after possible isobaric mixing. Auxiliary streams (Q in,out, Cin,out, CTBin,out, Pin,out) are employed to describe the splitters. The DB can be described by the following equations:

Figure 4. Description of RO superstructure reduction (a, possible connections for a two stage/pass RO superstructure; the dashed lines with × denote the eliminated connections; b, reduced superstructure).

The possible connections for a two-stage/pass RON and the reduced superstructure are shown in Figure 4. Concentrated brine recycling to the same or preceding RO stage/pass was removed, since this connection would refer to mixing a high-concentration stream with a lower concentration feed stream into a RO unit. Such connections result in RO units having to treat feed streams with higher concentration, which would in turn require higher energy consumption and membrane area. RO pass 2 usually produces brine streams with smaller flow rate (high average permeate flow rate and low brine flow rate allowed, so that RO pass 2 could operate at higher product water recovery rate) and lower operating pressure (due to its low inlet salt concentration) than RO pass 1. Due to the pressure difference of RO pass 2 and stage 2, the reject stream of pass 2 cannot be directly linked to stage 2, and the reject stream of stage 2 can also not be connected to pass 2. Only brine streams produced by a RO pass are allowed to be sent back to the feed seawater stream, since mixing a RO unit feed stream with lower concentration streams would help reduce the concentration of the feed into the RO units. The front part permeate of the pressure vessel with lower salinity and boron concentration (from both RO pass 1 and pass 2) is allowed to send directly to the product. The back permeate of RO pass 1 is allowed to send to the next RO pass for reprocessing, or send directly to the final product. Permeate recycle back to RO stage 2 is not permitted due to the pressure difference. Permeate recycle back to the same RO units for RO pass 1 is not allowed. These connections are thermodynamically unfavorable, since the separation process achieved would be reversed. But the situation is different for the permeate recycle for RO pass 2. Due to the upper bound of the pH value, for high boron concentration of feed seawater and low boron

MOUT

∑

Q in =

Q in,out

(33)

out = 1

C in,out = C in ,

out = 1, ..., MOUT

C TB,in,out = C TB,in, Pin,out = Pin ,

out = 1, ..., MOUT

out = 1, ..., MOUT

(34) (35) (36)

MIN

Q out =

∑ Q in,out

(37)

in = 1 MIN

Q outCout =

∑ Q in,outCin

(38)

in = 1 MIN

Q outC TB,out =

∑ Q in,outCTB,in

(39)

in = 1

0 = (Pin − Pout)Q in,out ,

in = 1, ..., MIN

(40)

Equations 33−36 denote the splitters for each inlet stream. Equations 37−39 denote the mixers for the outlet streams. The constraint eq 40 for isobaric mixing is ignored for the E


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Industrial & Engineering Chemistry Research Table 3. Material Balances for HPP and PX equations

Q ps,1 = Q hpp + Q pxlin

meaning

(41)

splitter for HPP and PX

Q ps,1Cps,1 = Q hppC hpp + Q pxlinCpxlin

(42)

Q ps,1C TB,ps,1 = Q hppC TB,hpp + Q pxlinC TB,pxlin

Q RO,1 = Q hpp + Q pxhout

salt balance for splitter

(43)

(44)

mixer for HPP and PX

Q RO,1C RO,1 = Q hppC hpp + Q pxhoutCpxhout

(45)

Q RO,1C TB,RO,1 = Q hppC TB,hpp + Q pxhoutC TB,pxhout

Q pxhout = Q pxlin

(47)

Q pxhin = Q pxlout

(48)

boron balance for splitter

Lpx Q pxhin /100 = Q pxhin − Q pxhout

salt balance for mixer

(46)

boron balance for mixer

lubrication of PX

(49)

Lpx [%] = 0.3924 + 0.01238Ppxhin (For ERI PX‐220)

Cpxhout = Mix(Cpxhin − Cpxlin) + Cpxlin

lubrication fitting

(50)

volumetric mixing for salt

(51)

C TB,pxhout = Mix(C TB,pxhin − C TB,pxlin) + C TB,pxlin

volumetric mixing for boron

(52)

2

OF [%] = 100(Q pxhin − Q pxhout)/Q pxhin ( −10% ≤ OF ≤ 15%) CpxloutQ pxlout = Q pxlinCpxlin + Q pxhinCpxhin − Q pxhoutCpxhout

(55)

RO permeate streams from each stage/pass linking to the product flow, and for depressurized high-pressure brine streams produced by RO passes (except for pass 1) being connected to the feed stream (Nps,1 node), since the product flow, the feed stream, and the outlet of the depressurized high-pressure brine streams produced by RO passes are normal pressure. The material balances for the high-pressure pump (HPP) and the PX are described in Table 3. As mentioned above, only one PX unit is introduced in the superstructure, which would provide optimal solutions without proper energy integration in the network. Lubrication Lpx for the PX can be assumed to be linearly correlated with Ppxhin.38 Volumetric mixing Mix (the proportion of the concentrate volume that transfers into the seawater to the flow rate of feed seawater) can be estimated by nonlinear correlation with overflush OF.39 The outgoing streams of the ith pressurization stages are connected to the jth RO stages; the following equations are obtained:

CRO , j = Cps , i C TB, RO , j = C TB, ps , i

PRO , j = P′ps , i

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

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

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

k=1

(56)

boron balance of PX

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

k = 1, 2, ..., K t

(62)

Kt

∑ yj ,k

j = 1, 2, ..., NRO

≤1

k=1

(63)

Yl − Yl + 1 ≥ 0

(64)

where Xk denotes the membrane properties (pure water permeability coefficient A, salt permeability coefficient B, boron permeability coefficient BTB, boron reflection coefficient σTB, active membrane area S, price for the kth type of membrane module Ck, and thickness of the feed channel spacer hk). The binary variable yj,k denotes the kth type of membrane module utilized in the jth RO stage. Equation 62 is introduced to restrict the maximum allowed operation pressure Pk,max for the kth type of RO membrane module. U is an arbitrary large enough number. Kt is the set of RO membrane types. Equation 63 is employed to ensure the search procedure to select only one type of membrane module in the PV in each RO stage/ pass. Logic constraint eq 64 is employed to ensure that each subelement of the front and back permeate in the PV for the PS design has the same flow direction. The overall material balances for the RON and a set of product quantity and quality constraints concerning the minimum desirable product flow rate, as well as the maximum allowable product concentration are presented as follows:

(57) (58) (59) (60)

Np

Q f = Qb +

∑ Q rp (65)

p=1

Np

Kt

∑ yj ,k Xk

salt balance of PX

Pj − Pk ,max ≤ U (1 − yj , k )

where Pps,i ′ is the outlet pressure of the ith pressurization stage. Each pressure vessel in the RO system usually contains two to eight RO membrane modules connected in sequence. The optimal selection of the SWM element types employed in each PV can be expressed by Xj =

overflush of PX

(54)

C BT,pxloutQ pxlout = Q pxlinC BT,pxlin + Q pxhinC BT,pxhin − Q pxhoutC BT,pxhout

Q RO , j = Q ps , i

fitting of volumetric mixing

(53)

Mix = 6.0057 − 0.3559OF + 0.0084OF (For ERI PX‐220)

j = 1, 2, ..., NRO

Q f Cf = Q bC b + (61)

∑ Q rpCrp p=1

F

(66) DOI: 10.1021/acs.iecr.6b02225 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research Np b Q f C TB = Q bC TB +

Note that eqs 78 and 80 are used only to calculate the minimum number of binary variables needed, which are not used as constraints of the optimization model. In order to prevent numerical infeasibilities if a RO pass is in-existence, slack variables sv and svb are included in the model, which are minimized within the objective function with small weight factors. 2.5. Constraints for System Flow and Operation Constraints. A RO membrane system should be designed under a frame of recommended guidelines, in order to make sure that the RO plant could be operated in a safe state. Membrane manufacturers usually provide system design guidance based on many years of operation experiences. Based on the design guideline provided by TORAY,41 sea well per-treatment is assumed in the current work, and the following constraints are applied in the model: the maximum average permeate flux is set to 20 L/(m2·h) (LMH) for RO pass 1, and 40 LMH for RO pass 2. The maximum pressure drop of the PV is set to 0.35 MPa for both pass 1 and pass 2. The maximum permeate flux in the first membrane module in PV is set to 35 LMH for pass 1, and 48 LMH for pass 2. The minimum brine flow rate in the PV is set to 3.6 m3/h for pass 1, and 2.4 m3/h for pass 2. The maximum concentration polarization factor (CPF, the ratio between salinity at the membrane surface Cch,mw,l and bulk concentration Cch,b,l) in the PV is set to 1.2 for pass 1 and 1.4 for pass 2. The maximum brine concentration is set to 90 kg/m3 according to refs 34 and 36. Note the constraints should be adjusted according to the local context. A RO pass is needed for relatively strict product quality constraints36 (In this work, the maximum allowable product salt concentration is 0.20 kg/m3 for the single-product output system, while for the two-product output system, the maximum allowable product salt concentrations are 0.050 and 0.30 kg/m3, respectively). Although the pH of RO pass 1 could be elevated to enhance the boron rejection,7 an additional strong acid and base for the feed pH adjustment and degasification stage would increase both the capital and operation costs; thus, only the pH of RO pass 2 is allowed to be elevated in this work. DOW suggests the pH range of 2−11 for continuous operation of FilmTec RO membranes.42 Therefore, the upper bound of the pH is set to 11 for RO pass 2. The RO stage/pass 1 is operated at seawater normal pH (7.4 in this work) to prevent salt precipitation and scale formation for the RO membrane.2,27,29

p ∑ Q rpCTB, r

(67)

p=1 NRO

Qb =

∑ Q b, N

ps + 1, j

+ Q pxlout (68)

j=1

QbC b =

NRO

∑ Q b,N

C b, Nps + 1, j + Q pxloutCpxlout

ps + 1, j

(69)

j=1

b QbCTB =

NRO

∑ Q b,N

C TB,b, Nps + 1, j + Q pxloutC TB,pxlout

ps + 1, j

j=1

(70)

Q rp =

NRO

∑ Q p,r ,j (71)

j=1

Q rpCrp =

NRO

∑ Q p,r ,jCp,r ,j (72)

j=1

p Q rpC TB, r =

NRO

∑ Q p,r ,jCTB,p,r ,j (73)

j=1

Q rp ≥ Q rp,min

(74)

Crp ≤ Crp,max

(75)

p p C TB, r ≤ C TB, r ,max

(76)

where Q , C , and are the flow rate, salt concentration, and boron concentration of the brine leaving the RON, respectively. Q pr , Cpr , and CpTB,r are the flow rate, salt concentration, and boron concentration of the product water, respectively. Q b,ps+1,j, Cb,ps+1,j, and CTB,b,ps+1,j are the brine flow rate, salt concentration, and boron concentration of the jth RO stage leaving the RON, respectively. The subscripts min and max refer to the minimum and maximum allowable values, respectively. Q p,r,j and Cp,r,j denote the permeate flow rate and concentration of the jth RO stage being connected to the rth product water, respectively. 2.4. Discrete Variable Constraints. The numbers for the RO element nm,j and pressure vessels npv,j should be integers. In this paper, these integer variables are modeled by a set of binary variables:40 b

CbTB

b

nm, j = nmlo +

Nb

∑

2km − 1Zj ,km

(77)

km = 1

⎧ log(n up − n lo) ⎫ m m ⎬ Nb = 1 + int⎨ log(2) ⎭ ⎩ lo n pv, j = n pv +

⎪

⎪

⎪

⎪

Nn

∑

3. SOLUTION STRATEGY The optimization problem can be formulated as mixed integer nonlinear programming (MINLP), and the objective function Total Annualized Cost (TAC) is to minimize the sum of the operation cost, OC, and the capital cost, CC, by subjecting to the constraints mentioned above. TAC = TCC/crf + AOC +

j

(78)

2kpv − 1Zj ,kpv + svj − svbj

kpv = 1 up lo ⎫ ⎧ ⎪ log(n pv − n pv ) ⎪ ⎬ Nn = 1 + int⎨ ⎪ ⎪ log(2) ⎩ ⎭

∑ (svj + svbj)

crf = (79)

upc = (80) G

(Ir + 1)nLT − 1 Ir(Ir + 1)nLT TCC/crf + AOC Q p·24·365

(81)

(82)

(83) DOI: 10.1021/acs.iecr.6b02225 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research EW =

PSWIPQ f 3.6ηSWIPηmoter +

sec =

+

PhppQ hpp 3.6ηhppηmoter

(Phpp − Ppxhout)Q pxhout 3.6ηbpηmoter

(84)

EW Qp

(85)

CCSWIP = 996(Q f 24)0.8

(86)

CC hpp = 52(ΔPhppQ hpp)

(87)

CC bp = 52(ΔPbpQ pxhin)

(88)

CCpx = 3134.7Q pxhin 0.58

(89)

NRO

CCm =

the sum of the annual labor cost OClabor, the annual maintenance cost OCmaint, the annual chemical cost OCch, the annual insurance cost OCinsrce, and the costs of caustic and acid OCreag.26,27,31The cost OCreag of increasing the pH of RO pass 2 by caustic soda and also the acid cost used to neutralize the RO pass 2 discharge as a function of pH is adopted from Chillon Arias et al.,44 and 1.28 is the exchange rate from Euro to U.S. Dollar. According to ref 43, the capital costs for the intake pump and pretreatment are a function of feed flow rate, the capital costs for a pump are a function of flow rate and pressure difference, and the operation cost for a pump is a function of flow rate, pressure difference, pump efficiency, motor efficiency, electricity price, and plant load factor. The capital costs for PX are a function of high-pressure flow rate into the PX, which is provided by ref 20. The operation cost for PX is neglected according to ref 20. The PX efficiency is given by eq 101. It is worth noting that the cost functions mentioned above should be updated according to the local context for commercial RO desalination plants. The RON includes several redundant units. The existence or nonexistence of a process unit can be confirmed indirectly by the flow rate or the pressure of the RO stage/pass. A large number of process units are set as starting points. Once a MINLP problem is solved, the obtained optimum variables (such as the number of PVs installed in each RO stage/pass) are set either to zero or to a value that indicates the existence or nonexistence of the corresponding RO stage/pass. Thus, unnecessary components are eliminated from the optimum system. The DICOPT solver44 in the General Algebraic Modeling System (GAMS) is applied to solve the mathematical programming problems. The problems are calculated on a Laptop PC with an Intel Core2 Duo T5550 and 2 GB RAM. The DICOPT solver is improved to handle integer variables appearing nonlinearly in the model.45 The current model has 86 binary variables and 2812 continuous variables. The default stopping strategy (stopping when the generated nonlinear programming problem becomes worse) for the DICOPT is used, and the other parameters are all set to the default values. Several starting points are performed, but the global solution could not be guaranteed, due to the nonconvex functions in the model. In general, it takes several minutes of CPU time to finish the calculation, and the best local solution is presented for each case study.

NRO

∑ Ck ,jnm,jnpv,j+ ∑ Cpvnpv,j j=1

(90)

j=1

TCC = 1.411(CCSWIP + CC hpp + CCpx + CC bp + CCm) (91)

OCm = 0.2Cm

(92)

OCe = Ce fc · 24· 365·Ew

(93)

OCinsrce = 0.005TCC

(94)

OC labor = Q p· 24· 365·fc ·0.01

(95)

OCch = Q f · 24· 365·fc ·0.0225

(96)

OCmaint = Q p· 24· 365·fc ·0.01

(97)

OCreag = 24· 365Q RO,2 fc exp( −16.726 + 0.91357pH + 0.06847pH2) ·1.28/100

(98)

OCO&M = OCinsrce + OC labor + OCch + OCmaint + OCreag

(99)

AOC = OCm + OCe + OCO&M

(100)

ηpx =

PpxhoutQ pxhout + PpxloutQ pxlout PpxhinQ pxhin + PpxlinQ pxlin

4. CASE STUDY The proposed optimization framework is adopted to obtain the optimum flow process configurations and operating conditions for a two stage/pass RO system. SW30XLE-400i and BW30440i (Named as SW and BW, respectively) of FilmTec RO membrane modules from DOW are included in the case studies. The properties and price of the elements are shown in Table 4. The model parameters are shown in Table 5. The integration step for the finite difference method is set to Δz = 1/30 of the LPV. Optimal RO configurations for three types of feed seawater are investigated, which are typical seawater (35 kg/m3 of salinity, and 0.005 kg/m3 of boron), Arabian Gulf seawater (50 kg/m3 of seawater salinity, and 0.007 kg/m3 of boron), and Eastern Mediterranean seawater (38 kg/m3 of seawater salinity, and 0.013 kg/m3 of boron).27,28 Several boron constraints (0.001 kg/m3, 0.0005 kg/m3, 0.0003 kg/m3) are chosen for

× 100% (101)

Equation 81 refers to the TAC with an assumed interest rate (Ir) of 8% and an RO plant lifetime (nLT) of 25 years. Equation 83 gives the unit product cost in $/m3. The energy consumption of pumps and the specific energy consumption of the RO system are given by eqs 84 and 85. The cost functions from refs 20 and 43 are utilized to calculate the CC, which is the sum of the seawater intake and pretreatment (SWIP), the high-pressure pumps, the booster pumps, and the PX. Equation 91 refers to the total capital cost (TCC) with a practical investment factor of 1.411, which reflects the site development costs and indirect costs connected with the capital cost.43 The OC is the sum of the membrane replacement cost OCm, the energy cost OCe, and the annual operating and maintenance cost OCO&M. Equations 92−99 calculate the OCO&M, which is H


Article


and demonstrates that staged RO operations are more energy efficient than single-stage RO. The model provided in the current work can be extended to multistage, multipass, or closecircuit systems under boron restrictions to achieve high energy efficiency. 4.1. Single-Product System Design. 4.1.1. Effect of Product Boron Concentration. For different maximum product boron concentrations varying from 0.0003 to 0.001 kg/m3, the optimization of the superstructure is calculated for three types of feed seawater mentioned above. The feed temperature is 20 °C, the production capacity is 120 m3/h, and the maximum allowable product salt concentration is 0.20 kg/m3. The optimal results for typical seawater are listed in Table 6. The optimal results for Arabian Gulf seawater and Eastern Mediterranean are listed in the Supporting Information. It can be seen from Table 6 (the entire set of optimization results is fully described in the Supporting Information) that for a feed of typical seawater, a two-pass RO process with permeate reprocessed and brine stream recycled is favored for both the normal and PS design. For the normal design (Figure 5a) with maximum boron concentration of 0.001 kg/m3, feed seawater with 254.1 m3/h flow rate is pressurized in the RO pass 1 with 28 parallel RO pressure vessels. The permeate from the RO pass 1 is split into two streams: one stream with 89.5 m3/h is extracted to the RO pass 2 with eight parallel pressure vessels. The salinity and boron concentration of the permeate are about 0.451 kg/m3 and 0.00176 kg/m3, respectively. Another stream is bypassed to the final product. The pH of RO pass 2 is elevated to 10.20 in order to increase the boron rejection. The salinity and boron concentration of RO pass 2 permeate are 0.00791 kg/m3 and 0.00042 kg/m3, respectively. The brine of the RO pass 2 is sent back to the feed side to decrease the system inlet concentration due to its relatively low salt concentration. Both the RO pass 1 back permeate and RO pass 2 permeate are mixed to meet the product quality requirement. For the PS design (Figure 5b), feed seawater with 234.1 m3/h flow rate is pressurized in the RO pass 1 with 25 parallel RO pressure vessels. The main difference of the flow structure for the PS design is that the front permeate of the PV from the RO pass 1 (with 0.277 kg/m3 of salt and 0.00132 kg/m3 of boron, respectively) is extracted directly to the product. The back permeate stream from the RO pass 1 with 57.1 m3/h flow rate is further refined in the RO pass 2, which has five parallel RO pressure vessels. The feed pH for RO pass 2 is adjusted to 10.46. The permeate salinity and boron concentration for RO pass 2 are about 0.0151 kg/m3 and 0.00040 kg/m3, respectively. The final product is the mixtures of the front part permeate of RO pass 1 and the permeate of RO pass 2. The optimized RO system with PS design could operate at slightly higher recovery rate, and the number of membrane modules in RO pass 2 could be decreased. Generally speaking, there are about 0.67−6.82% unit product cost and 3.28−7.61% energy consumption savings compared with the normal design, but the energy consumption of the Eastern Mediterranean has little increase. For the feed of Arabian Gulf seawater, the optimized system flow structures are similar to the RO system with typical seawater. Due to the higher salt and boron concentrations, both the unit product cost and specific energy consumption are higher than the RO system with typical seawater, and the RO system should be operated at lower level system recovery rate. PS design is not favored for the boron concentration requirement of 0.0003 kg/m3.

Table 4. Transport Characteristics and Module Geometry of the FilmTec Spiral-Wound RO Membrane Modulesa Membrane module type membrane active area [m2] element length [m] element diameter [m] effect length of the element [m] feed channel cross-section open area, Sfcs [m2] feed space height, h [mil]b spacer void fraction, εsp feed channel equivalent diameter, de [m] range of feed flow rate [m3/h] maximum operating pressure [Mpa] range of continuous operating pH pure water permeability coefficient, Aref [kg/m2·s·Pa] salt permeability coefficient, Bref [m/s] B(OH)3 permeability coefficient, Bboric,ref [m/s] B(OH)4− permeability coefficient, Bborate,ref [m/s] B(OH)3 reflection coefficient, σboric [m/s] B(OH)4− reflection coefficient, σborate [m/s] estimated membrane module price [$]

SW30XLE-400i

BW30-440i

37.2 1.016 0.201 0.88 0.0150

40.9 1.016 0.201 0.88 0.0165

28 0.9 8.126 × 10−4 0.8−16 8.3 2−11 3.5 × 10−9

28 0.9 8.126 × 10−4 0.8−17 4.1 2−11 1.128 × 10−8

3.2 × 10−8 1.667 × 10−6

4.421 × 10−8 7.813 × 10−6

9.803 × 10−8

9.387 × 10−8

0.962 0.991

0.843 1.00

1200

900

a

Reproduced with permission from ref 31, Copyright 2015 Elsevier Science, and ref 46, Copyright 2012 Elsevier Science. b1 mil = 0.0254 mm.

Table 5. Parameters for the RO Model average mass density of brine, ρ [kg/m3] universal gases constant, R [J/(mol·K)] solute molecular weight, Ms SWIP outlet pressure, Pswip [MPa] intake/high pressure/booster pump efficiency, ηswip/ηhpp/ηbp PX efficiency, ηpx electric motor efficiency, ηmotor RO plant load factor, fc electricity cost, Ce [$/(kWh)−1] assumed PV price [$] friction factor correction parameter, Kλ interest rate, Ir RO plant service time, nLT [year]

102020 8.3149 58.59 0.536 75% 95% 98% 0.9 0.0820 100020 2.436 8% 25

different freshwater applications (drinking water for different countries, or irrigation water for different types of crops). The general specifications for all case studies are as follows: • assumed annual decrease in pure water permeability FFd: 7% for pass 1 and 2% for pass 2. • assumed annual increase in solute passage (for salt and boron) Bin and BTB,in: 10% for pass 1 and 5% for pass 2. • design average lifetime of RO membrane module: 5 year. • design period Nmlp: 3 years. The RO system with permeate split is named as PS design, if all the variables Yl are zero; thus, the flow rate of the front part of permeates in the PV is fixed to zero, which is called normal design. Only two-stage/pass networks are applied in the case studies, which may not be energy efficient. More stages/passes are not included in the current work. Reference 47 provides an insightful discussion of the staged reverse osmosis operation, I


Article


Table 6. Optimization Results for RO System with Feed of Typical Seawater under Different Boron Concentration Restraints feed conc [kg/m3]

35

feed boron conc [kg/m3]

0.005

feed temp [°C]

20

max. boron conc [kg/m3] process layout feed flow rate [m3/h] system recovery [%] membr type in pass 1 membr type in pass 2 feed pH (pass 1) feed pH (pass 2) No. of modules per PV in pass 1 No. of modules per PV in pass 2 No. of PV in pass 1 No. of PV in pass 2 pressure in pass 1 [MPa] pressure in pass 2 [MPa] sec [kWh/m3] upc [$/m3]

0.001 normal Figure 5a 254.1 47.2 SW BW 7.4 10.20 28 8 7 8 6.79 1.10 3.68 0.660

0.0005 PS Figure 5b 234.1 51.3 SW BW 7.40 10.46 25 5 8 8 6.89 1.24 3.40 0.615

normal Figure 5a 245.3 48.9 SW BW 7.40 10.52 28 13 8 8 6.71 1.04 3.96 0.719

0.0003 PS Figure 5b 241.9 49.6 SW BW 7.40 10.61 27 10 8 8 6.77 1.15 3.83 0.694

normal Figure 5c 250.6 47.9 SW BW 7.40 10.54 31 15 8 8 6.46 1.04 3.97 0.743

PS Figure 5b 247.3 48.5 SW BW 7.40 10.65 29 13 8 8 6.63 1.11 4.01 0.738

Figure 5. Optimized RO systems for single-product output.

the same pass, and only the front permeate of RO pass 2 is sent to the product (Figure 5f). Compared with the optimized results mentioned above, with the decrease in the maximum boron concentration requirement, the front part permeate from RO pass 1 decreases gradually, which implies that the PS design (split ratio between the front and back permeates in the pressure vessel) is mainly controlled by the boron constraints. The system recovery order for the three types of seawater is typical seawater (47.2%− 48.9% for normal design, and 48.5%−51.3% for PS design),

For the feed of Eastern Mediterranean, the permeate split of RO pass 1 is only employed for the boron concentration requirement of 0.001 kg/m3. When the boron concentration requirement is 0.0005 kg/m3, the products are collected from both sides of the pressure vessel from pass 2 (Figure 5e). Although there is little increase in fresh water cost (the TAC for PS design is $824903, while it is $824718 for normal design (Figure 5d), the energy consumption could save about 1.15%. When the boron concentration requirement is 0.0003 kg/m3, the back permeate of RO pass 2 is allowed to be reprocessed in J


Article


Figure 6. Comparison of variation of some variables along the pressure vessel for the RO system with PS and normal designs (the feed is typical seawater, the temperature is 20 °C, and the maximum permeate boron concentration is 0.0005 kg/m3).

Eastern Mediterranean (43.9%−47.1% for normal design, and 46.4%−47.6% for PS design), and Arabian Gulf (41.5%−42.7%

for normal design, and 43.2%−44.3% for PS design), which is in accordance with the order of feed salt concentration. K


Article


be operated at safe state. Figure 6e and Figure 6f show that both the dissociation constant pKa of boric acid and the fraction of boric acid decrease along the PV. The boron permeate flow rate in the pressure vessel is influenced by the changes of the boron permeability constant, the boron concentration gradient across the membrane, and the boron reflection coefficient. Both the boron permeability constant and the reflection coefficient are a function of the distribution of boric acid and borate ions on the membrane surface, which are indirectly related to the salt concentration on the membrane surface (the first acid dissociation constant of boric acid is influenced by salt concentration). The increase in salt concentration along the pressure vessel (due to the RO membrane rejection) enhances the dissociation reaction of the boric acid (shown in eq 6) and creates the decrease in boric acid fraction on the membrane surface. Hence, both the boron first acid dissociation and the permeability constant of boron decrease along the pressure vessel, while the boron reflection coefficient increases along the pressure vessel (shown in Figure 6g and Figure 6h). Because the pH value of RO pass 1 is 7.40, the fraction of boric acid is larger than 90%, and it easily passes through the membrane. While for RO pass 2, due to the pH being higher than 10.50 for both the PS and normal design, boron is mainly in the form of borate ions. As a result, the boron permeability constant of RO pass 1 is much higher than that of pass 1, and, thus the boron rejection of RO pass 2 has greatly improved. As shown in Figure 6i, the front part of PVs in RO pass 1 provide better permeate quality (low salt and boron concentration) and higher flow rate than those at the back part of the PV. The front permeates are then sent directly to the product, while back permeates are treated by RO pass 2 with higher operating pressure than those in the normal design. Therefore, the operating conditions (feed flow rate, salt and boron concentration, pressure, etc.) along the PV in RO pass 2 for the PS design are very different from the normal design. Figure 7 shows the unit product cost breakdown and energy consumption with different types of feed seawater and different maximum permeate boron concentrations. The first two sets of data compare the PS and the normal designs. Since the front

Figure 7. Cost breakdown and energy consumption for the RO system with different types of feed seawater and different maximum permeate boron concentrations.

Thus, the system recovery is mainly controlled by the feed salt concentration. Figure 6 shows the longitudinal variations of some variables along the PV, in order to give more insight into the differences between the PS and normal designs. The feed is typical seawater, and the maximum boron concentration for the product is 0.0005 kg/m3. From Figure 6a and Figure 6b, both the RO pass 1 and pass 2 are operated at higher pressure for PS design. From Figure 6c, the salt concentrations on the membrane surface are larger than the bulk salt concentrations due to the concentration polarization. On one hand, the water driving force across the membrane increases. On the other hand, sparingly soluble salts (such as CaSO4, CaCO3, etc.) may accumulate on the membrane surface beyond their limitation of solubility; as a result, the scaling risk increases. In this work, the concentration polarization factor is restricted in the model. In addition, other operation conditions and continuous operating pH value are also included, so the optimized RO system could Table 7. Optimized Operation Conditions in Different Years feed/max. boron conc. [kg/m3]

35/0.0005

feed temp [°C]

20 a

operating year

0

process layout feed flow rate [m3/h] system recovery [%] membr type in pass 1 membr type in pass 2 feed pH (pass 1) feed pH (pass 2) No. of modules per PV in pass 1a No. of modules per PV in pass 2a No. of PV in pass 1 No. of PV in pass 2 pressure in pass 1 [MPa] pressure in pass 2 [MPa] sec [kWh/m3] upc [$/m3]

Figure 5b 263.1 45.6 SW BW 7.40 10.50 30 9 8 8 5.97 1.07 3.39 0.666

a

a

a

1

2

3

0b

1b

2b

3b

Figure 5b 255.4 47.0 SW BW 7.4 10.62 29 9 8 8 6.20 1.10 3.50 0.673

Figure 5b 249.0 48.2 SW BW 7.40 10.50 28 10 8 8 6.48 1.11 3.69 0.684

Figure 5b 241.9 49.6 SW BW 7.40 10.61 27 10 8 8 6.77 1.15 3.83 0.694

Figure 5b 273.1 43.9 SW BW 7.40 10.68 29 8 7 8 6.15 1.05 3.43 0.665

Figure 5b 267.9 44.8 SW BW 7.40 10.63 29 9 7 8 6.33 1.04 3.56 0.675

Figure 5b 261.9 45.8 SW BW 7.40 10.52 28 10 7 8 6.63 1.04 3.75 0.687

Figure 5b 256.0 46.9 SW BW 7.40 10.70 28 10 7 8 6.83 1.08 3.83 0.699

The number of modules per PV in each pass is fixed to the optimal solutions with the design period of 3 years. bThe number of modules per PV in each pass is fixed to the optimal solutions with the design period of 0 year.

a

L


Article

Industrial & Engineering Chemistry Research Table 8. Optimization Results for RO Systems under Different Feed Temperatures feed conc [kg/m3]

35

max. boron conc [kg/m3]

0.0005

max. product conc [kg/m3]

0.05

feed temp [°C]

15

20

25

30

35

process layout feed flow rate [m3/h] system recovery [%] membr type in pass 1 membr. type in pass 2 pass 1 pH pass 2 pH No. of modules per PV in pass 1 No. of modules per PV in pass 2 No. of PV in pass 1 No. of PV in pass 2 pressure in pass 1 [MPa] pressure in pass 2 [MPa] sec [kWh/m3] upc [$/m3]

Figure 5b 267.8 44.8 SW BW 7.40 10.69 32 10 8 8 6.56 1.16 3.83 0.729

Figure 5b 241.9 49.6 SW BW 7.40 10.61 27 10 8 8 6.77 1.15 3.83 0.694

Figure 5b 241.2 49.8 SW BW 7.40 10.62 30 10 7 8 6.42 1.16 3.62 0.676

Figure 5b 258.3 46.5 SW BW 7.40 10.75 35 11 6 8 5.94 1.01 3.43 0.684

Figure 5c 280.9 42.7 SW BW 7.40 10.79 43 13 5 7 5.48 0.89 3.30 0.699

product cost and the energy consumption are proportional to the feed salinity, while the costs of caustic and acid are proportional to the feed boron concentration. 4.1.2. Optimization of Annual Operating Conditions. Because membrane fouling has a significant impact on the design of the RO process, and on RO membrane degradation with time, the operating conditions of the RO plant should be adjusted accordingly. However, many previous works on the optimal design of the RO system did not take into account the effects of membrane fouling and degradation, such as refs 19, 20, and 29. The annual operating conditions are optimized for the feed of typical seawater and Eastern Mediterranean. The feed temperature is 20 °C. The number of membrane modules employed in the PVs for each pass is fixed to the optimum solution with the design period of 3 years (The parameter Nmlp is set to 3), which is inconvenient to be changed during the working period. In order to compare the difference and how it affects the system design, the optimization design results are also provided with the design period of 0 year (The parameter Nmlp is set to 0, which represents no fouling and degradation for RO membrane). As shown in Table 7 (The entire set of optimization results is fully described in the Supporting Information), since the deterioration of the membrane occurs within a year, the system operating pressure should be increased with time due to a decrease in the pure water permeability. The system recovery and the number of PVs should be adjusted gradually in order to decrease the TAC. With a decrease in membrane boron rejection, the front permeate from RO pass 1 sent to the product should be decreased with time. As a result, both the unit product cost and energy consumption increase gradually. Compared with the optimization design results with the design period of 3 years, the key difference is the number of pressure vessels in RO pass 1 for the design period of 0 year. Due to eight pressure vessels employed in pass 1 for the design period of 3 years, the RO system could be operated at higher recovery rate; thus, both the unit product cost and energy consumption could be saved. 4.1.3. Effect of Feed Seawater Temperature. Since the feed seawater temperature is an important parameter of the design and operation of the RO process, the influence of feed seawater

Table 9. Relative Marginal Values for the TAC (∂(TAC)/∂p)/(p/(TAC)) Typical seawater Ce Cf A1 CTB T pH1 Bboric,1 Qf A2 pH2 P1 Bboric,2 B1 Bborate,2 P2 B2 Bborate,1 a

0.3973 0.2959 −0.1430 0.1387 −0.1265 −0.1066 0.1049 0.0883 −0.0753 −0.0685 −0.0428 0.0331 −0.0274 0.0095 0.0024 −0.0007 0.0004

Arabian Gulf Ce Cf T Qf pH2 CTB pH1 A2 A1 Bboric,1 B1 P2 Bboric,2 Bborate,2 P1 Bborate,1 B2

0.4056 0.2813 −0.1624 0.1321 0.1214 0.0997 −0.0932 −0.0873 −0.0829 0.0732 −0.0591 0.0359 0.0304 0.0118 0.0082 0.0004 −0.0003

Eastern Mediterranean pH2 Qf Ce T P1 Cf A2 A1 P2 B1 CTB pH1 Bboric,1 Bboric,2 Bborate,2 B2 Bborate,1

0.7757 0.4602 0.3968 −0.2286 0.2137 0.2011 −0.0795 −0.0597 0.0377 −0.0320 0.0302 −0.0244 0.0213 0.0185 0.0067 −0.0011 0.0001

Subscript: 1 and 2 denote RO pass 1 and pass 2, respectively.

part permeate of the PV from the RO pass 1 is sent directly to the product, the size of RO pass 2 is decreased; thus, the annualized investment cost, power cost, membrane renewal cost, and cost of caustic and acid for the system with PS design are all decreased, and the energy consumption is saved. The second, third, and forth groups of data compare different maximum boron concentration restrictions with PS design. The results show that both the unit product cost and energy consumption are proportional to the maximum boron concentration restriction. With the increase in the maximum boron concentration restriction, more and more RO pass 1 back permeates are sent to RO pass 2 for further refinement (increased from 57.1 m3/h to 145.1 m3/h, Table S3 in Supporting Information), and the share of the costs of caustic and acid in the unit product cost is increased from 1.24% to 4.10%. The last three groups of data compare different types of feed seawater with PS design, and we can see that under the same maximum boron concentration restrictions, both the unit M


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Industrial & Engineering Chemistry Research Table 10. Optimized Results for Two-Product Output System feed seawater

typical seawater

Arabian Gulf

feed temp [°C] flow rate of 1st product [m3/h]

120

max. conc of 1st product [kg/m3]

0.30

max. boron conc of 1st product [kg/m3]

0.001

flow rate of 2nd product [m3/h]

80

max. conc of 2nd product [kg/m3]

0.050

max. boron conc of 2nd product [kg/m3] process layout feed flow rate [m3/h] overall system recovery [%] membr type in pass 1 membr type in pass 2 pass 1 pH pass 2 pH No. of modules per PV in pass 1 No. of modules per PV in pass 2 No. of PV in pass 1 No. of PV in pass 2 pressure in pass 1 [MPa] pressure in pass 2 [MPa] Ew [kw] TAC [$]

Eastern Mediterranean

20

0.0003 normal Figure 8a 405.0 49.4 SW BW 7.4 10.50 46 18 8 8 6.71 1.07 760.6 1186781

PS Figure 8b 397.3 50.3 SW BW 7.4 10.62 44 13 8 8 6.78 1.14 715.1 1122375

normal Figure 8c 463.7 43.1 SW BW 7.4 10.68 54 19 8 8 7.82 1.19 909.9 1395626

PS Figure 8d 456.1 43.9 SW BW 7.4 10.65 52 15 8 8 7.91 1.31 881.8 1338352

normal Figure 8c 451.7 44.3 SW BW 7.4 11.0 51 21 7 8 6.97 1.17 873.5 1409890

PS Figure 8e 424.7 47.1 SW BW 7.4 10.71 50 20 8 8 6.84 1.21 837.0 1311945

indicates that boron rejection decreases as the feed temperature increases. When the feed temperature is up to 35 °C, PS design is not favored (Figure 5a). 4.1.4. Sensitivity Analysis. The sensitivity analysis method computes the gradients of the objective function (Total Annualized Cost), in order to estimate the influences of the infinitesimal variation parameter (p) on the performance of the RO plant. The sign of the relative marginal values (RMVs) indicates the direction of the change of the objective function. The positive sign of RMVs implies that the objective function increases its value when the relevant parameters are increased, and vice versa. The descriptions of sensitivity analysis are presented in our previous work.36 Three types of feed seawater are all investigated here, the feed temperature is 20 °C, and the maximum salt and boron concentration are 0.5 kg/m3 and 0.0005 kg/m3, respectively. Table 9 shows the RMVs of (∂(TAC)/∂p)(p/TAC) for the TAC of the RO system (PS design is utilized for the RO system with typical seawater and Arabian Gulf, and normal design is utilized for the system with Eastern Mediterranean), which were arranged in terms of their absolute values. As Table 9 shows, since the RO system is an energyconsuming process, electricity cost Ce has a great influence on the system. The feed salt concentration also has a significant effect on the TAC for three types of feed seawater, which needs to be considered due to seasonal rainfalls. The pH of RO pass 1 has an important effect on typical seawater, while for Arabian Gulf with higher boron concentration, the RO system is more sensitive for the pH of RO pass 2. Due to the highest boron concentration of the Eastern Mediterranean, the pH of RO pass 2 should be controlled carefully, which is highly sensitive to the TAC. The feed temperature is another important factor effect on the TAC for the system. 4.2. Two-Product Output System Design. In this case study, the RO project has one feed source and two product outputs.

temperature on the system performance is studied (ranging from 15 to 35 °C). The production capacity is 120 m3/h, and the maximum allowable product salt concentration is 0.20 kg/m3. The optimal configurations and operation conditions are displayed in Table 8. Note, the results listed here are used for the design of RO systems with different feed temperatures; thus, the number of modules in each PV in the optimal results is not fixed. Feed temperature is influencing both the seawater physical properties and the membrane permeability. With the feed temperature increases, the membrane water permeability increases, while water viscosity decreases; as a result, water could pass easily through the membrane. As shown in Table 8 (The entire set of optimization results is fully described in the Supporting Information), increasing the feed temperature would lead to a decrease in operation pressure in RO pass 1; thus, the specific energy consumption decreases. The unit product cost decreases first as the feed temperature increases; when the feed temperature is beyond 25 °C, the unit product cost increases again. On the country, the variation of system recovery has a reverse rule compared with the unit product cost. When the feed temperature is 25 °C, the optimized RO system could achieve the lowest unit product and the highest recovery. Note that feed temperature also has an important influence on the boron rejection. Both the boron permeability coefficient (function of temperature) and boron mass transfer coefficient (function of salt mass transfer coefficient, which increases with the increasing temperature) increase with an increase in temperature. An increase in boron mass transfer coefficient would improve the boron rejection due to a decrease in concentration polarization. An increase in feed temperature would also lead to a decrease in pKa for boric acid (eq 6); thus, the percent of the high rejection borate ions increases. As a result, there is a tradeoff among the above parameters.3,13 A decrease in flow rate for the front permeate in RO pass 1 sent to the final product N


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Figure 8. Optimized RO systems for two-product output.

the membrane conditions, the annual operating conditions are optimized for Arabian Gulf with feed temperature of 20 °C. Both the design periods of 0 and 3 years are provided for comparison. As shown in Table 11, due to the membrane fouling and deterioration, both the flow structure and operating conditions (pressure, number of pressure vessels, system recovery, pH, etc.) should be adjusted with year in order to decrease the fresh water cost. For the design period of 3 years, eight membrane modules are employed for both pass 1 and pass 2. The RO system could be operated at slightly higher recovery rate. PS design is also introduced for the second and third operating years (named double-pass PS design). The loose first product is the mixture of both the front part of pass 1 and the back part of pass 2. The strict second product should be controlled carefully during the operating year (Figure 8f, Figure 8g, Figure 8h, and Figure 8d). For the design period of 0 year, seven membrane modules are employed for pass 1. Both the TAC and energy consumption are increased due to the lower recovery rate. But the operation of the system is more simple than that of the system with design period of 3 years. Since PS design is only employed for RO pass1, the system could be operated at similar flow structure during the operating year (Figure 8i, Figure 8j, and Figure 8b); while for the design period of 3 years, the flow structure should be switched from single-pass PS to double-pass

Three types of feed seawater are investigated, and the feed temperature is 20 °C. The maximum allowed salt and boron concentrations, as well as the product capacity for each product are listed in Table 10. As shown in Table 10, the optimized RO systems with normal design are similar for three types of feed seawater. Both the first and second product are mixtures of the permeates of RO pass 1 and pass 2 for typical seawater (Figure 8a). For Arabian Gulf and Eastern Mediterranean, only the permeates of RO pass 2 are allowed to be sent to the strict second product (Figure 8c). For PS design, the optimized flow structures of RO systems are dependent on the types of feed seawater. For typical seawater, the first product is a mixture of the front and back part permeates of RO pass 1, as well as the permeate of pass 2. Part of the permeate of pass 2 is sent to the second product (Figure 8b). For Arabian Gulf, PS designs are utilized for both the two RO passes. The boron concentrations of the front and back part of RO pass 2 are 0.00019 kg/m3 and 0.00049 kg/m3, respectively. Thus, the permeates from RO pass 2 are split and sent to different products (Figure 8d). For Eastern Mediterranean, only the front part of RO pass 2 is sent to the second product (Figure 8e). In general, PS design could provide lower unit product cost and energy consumption, as well as higher system recovery rate. Because both of the two products are mixtures of several permeate flows, which would be influenced by the change of O


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Industrial & Engineering Chemistry Research Table 11. Optimized Operation Conditions in Different Years for Two-Product Output System Feed seawater

Arabian Gulf

feed temp [°C]

20

flow rate of 1st product [m3/h]

120

max. conc of 1st product [kg/m3]

0.30 3

max. boron conc of 1st product [kg/m ]

0.001

flow rate of 2nd product [m3/h]

80

max. conc of 2nd product [kg/m3]

0.050

max. boron conc of 2nd product [kg/m3]

0.0003 a

process layout feed flow rate [m3/h] system recovery [%] membr type in pass 1 membr type in pass 2 pass 1 pH pass 2 pH No. of modules per PV in pass 1 No. of modules per PV in pass 2 No. of PV in pass 1 No. of PV in pass 2 pressure in pass 1 [MPa] pressure in pass 2 [MPa] Ew [kw] TAC [$]

0 Figure 8f 497.0 40.2 SW BW 7.4 10.59 57 13 8 8 7.20 1.24 807.7 1304495

a

1 Figure 8g 481.9 41.5 SW BW 7.4 10.68 55 13 8 8 7.43 1.29 828.4 1313806

a

2 Figure 8h 470.5 42.5 SW BW 7.4 10.53 54 15 8 8 7.64 1.27 858.7 1325660

a

3 Figure 8d 456.1 43.9 SW BW 7.4 10.65 52 15 8 8 7.91 1.31 881.8 1338352

0b Figure 8i 515.9 38.8 SW BW 7.4 10.56 56 13 7 8 7.34 1.16 822.4 1298515

1b Figure 8j 502.4 39.8 SW BW 7.4 10.68 55 13 7 8 7.53 1.21 840.6 1311799

2b Figure 8b 491.4 40.7 SW BW 7.4 10.62 54 14 7 8 7.76 1.25 873.3 1330053

3b Figure 8j 477.2 41.9 SW BW 7.4 10.71 52 15 7 8 8.04 1.22 894.2 1343792

The number of modules per PV in each pass is fixed to the optimal solutions with the design period of 3 years. bThe number of modules per PV in each pass is fixed to the optimal solutions with the design period of 0 year.

a

(1.2 × 10−8 m/s), but higher boric acid and borate ions permeability (3.43 × 10−6 m/s and 2.02 × 10−7 m/s) than SW30−400i). When the maximum boron concentration is 0.0003 kg/m3, PS design is selected for RO pass 2, and the pH of pass 2 should be kept at the upper bound in order to guarantee the boron rejection. There are two drawbacks of the RO system proposed by Saif and Almansoori;29 for one thing, RO pass 2 is operated at high pressure, and the water driving force is more than 7.0 MPa; thus, the permeate flow rate for the membrane from pass 2 may be much higher than its limits,41 which may be harmful for the membrane. For another, the low pH value of pass 2 would lead to lower boron rejection (Higher molar fraction of boric acid at lower pH condition, which has high boron permeability); as shown in Figure 6j, boron concentration is increased along the pressure vessel, less membrane elements could be employed in the pressure vessel, and the RO system could only be operated at low recovery rates (due to less membrane area).21

PS design. So there is a trade-off between lower cost and easy operation. 4.3. Comparison of the Present Model with Alternative Models. It is interesting to compare the present model with other alternative models. In this section, the proposed model was compared with the work from Sassi and Mujtaba,27 and Saif and Almansoori.29 As shown in Table 12, compared with the results from Sassi and Mujtaba,27 the PS design with turbine could provide lower unit product cost; if a PX device is used, the fresh water cost could be further decreased. We can see that both the RO stage and pass proposed by Sassi and Mujtaba27 are operated at high pressure (the upper bound conditions of the RO membrane); thus, the energy consumption is much higher than the proposed model. Compared with a turbine, a high-efficiency energy recovery device (such as PX) is recommended. As shown in Table 13, when the maximum boron concentration is 0.001 kg/m3, due to high feed seawater boron concentration and low boron rejection (compared to the membrane properties with SW30-400i), PS design is not favored (Figure 5b). If BW30-440i is selected, the RO system could be operated at higher recovery rate with lower fresh water cost. Indeed, in the above case studies, a brackish RO membrane is suitable for pass 2 because of its high water permeability. When SW30-400i is introduced in RO pass 1 (Figure 5b), due to higher water permeability and salt rejection, although the RO system could be operated at a higher recovery rate, the unit product cost is higher than that of the system with the RO membrane provided by Saif and Almansoori.29 Thus, the membrane with higher water permeability and salt rejection is more suitable for pass 1 RO, rather than higher boron rejection (The RO membrane provided by Saif and Almansoori29 has better water permeability (4.47 × 10−9 kg/m2·s·Pa) and higher salt rejection

5. CONCLUSIONS An optimization model of an RO network with a PS design under boron concentration restrictions is presented. In order to take advantage of lower salt and boron concentrations and higher flux for the permeate at the front part of the pressure vessel, permeates are collected from both sides of the PV. An irreversible thermodynamic model is employed to describe the membrane transport behavior of boron. Constraints for the system flow and operation conditions are added to ensure the safe operation of RO systems. First, different types of feed seawater and different boron constraints are investigated for single-product systems. Compared with the optimized results, the main task for RO pass 1 is desalting, and the pH of RO pass 2 is evaluated to P


Article


improve the boron rejection. The PS design is mainly controlled by the maximum boron concentration constraints, while the system recovery is mainly dominated by the feed salt concentration. Due to the upper bound of pH for pass 2, PS design could be introduced for pass 2 to improve the boron rejection. Under the same maximum boron concentration limitations, the unit product cost and energy consumption are both proportional to the feed salt concentration, while the costs of caustic and acid are proportional to the feed boron concentration. Longitudinal variations of variables along the PV are investigated to give more insight into the differences between PS and normal designs. The feed seawater temperature has an important effect on the system design. The RO system is more suitable for operation at 25 °C due to the lowest water cost, the highest system recovery, and the relative low-energy consumption. Sensitivity analysis is performed to evaluate the relative importance of process parameters. The rank of importance of parameters is different due to the differences in salt and boron concentrations for three types of feed seawater. The design and operation for the RO system should take account of local context. Second, two-product output system design is studied; both the permeates from RO pass 1 and pass 2 could be split and sent to different products. Finally, the present model is compared with other alternative models; the membrane type, the energy recovery, and the pH of pass 2 have great influences on the RO system with boron removal. In general, PS design could offer lower fresh water cost, lower energy consumption, and smaller RO system size compared with the normal design. Membrane fouling and degradation with time should be taken into consideration; thus, the RO system should cover all the pipe connections during the design period, and both the flow structure and operation conditions should be optimized and adjusted accordingly.

Table 12. Comparison of the Present Model with Those of Sassi and Mujtabaa feed conc [kg/m3]

35


0.005

feed temp [°C]

20

total water demand [m3/h]

80

max. boron conc [kg/m3]

0.0005 Sassi and Mujtaba27

process layout feed flow rate [m3/h] system recovery [%] membr type in pass 1

BW30-440i 7.40 10.46 20

Present model with PXb Figure 5c 197.9 40.4 SW30XLE400i BW-440i 7.40 10.64 22

6

6

5

5 5 3 8.30 4.10 0.814

8

6

8 5.86 1.07 0.634

8 6.02 1.13 0.557

165 48.5 SW30XLE400 BW30-400

membr type in pass 2 feed pH (pass 1) feed pH (pass 2) No. of modules per PV in stage 1 No. of modules per PV in stage 2 No. of modules per PV in pass 1 No. of PV in stage 1 No. of PV in stage 2 No. of PV in pass 1 pressure in stage 1 [MPa] pressure in pass 1 [MPa] upc [$/m3]

8.82 11

Present model with turbineb Figure 5g 173.9 46.0 SW30XLE-400i

6

a

Reproduced with permission from ref 27. Copyright 2013 Elsevier Science. bThe economic model provided by Sassi and Mujtaba27 is utilized here. Turbine is utilized in Sassi and Mujtaba’s model;27 thus, the PS design with turbine is also calculated. The process layouts obtained by alternative model are not provided here.

Table 13. Comparison of the Present Model with Those of Saif and Almansooria feed conc [kg/m3]

40


0.013

feed temp [°C]

25 3

max. boron conc [kg/m ]

0.001 Saif and Almansoori

process layout feed flow rate [kg/s] system recovery [%] membr type in pass 1 membr type in pass 2 feed pH (pass 1) feed pH (pass 2) No. of modules per PV in pass 1 No. of modules per PV in pass 2 No. of PV in pass 1 No. of PV in pass 2 pressure in pass 1 [MPa] pressure in pass 2 [MPa] upc [$/m3]

101.9 29.4 SWc SWc 7.20 8.80 26 9 4 3 7.8 7.67 891818

Present modelb Figure 5d 91.3 32.9 SWc SWc 7.20 10.82 59 20 8 8 4.84 1.35 818587f

0.0003 Present modelb Figure 5d 80.7 37.2 SWc BWe 7.20 10.64 35 11 7 8 5.56 0.98 640956f

Present modelb Figure 5b 69.3 43.3 SWd BWe 7.20 10.63 29 9 7 8 6.22 1.06 659169f

Saif and Almansoori 174.5 17.2 SWc SWc 7.20 9.40 44 13 2 3 8.0 8.0 1477738

Present modelb Figure 5f 84.3 35.6 SWc BWe 7.20 11.00 36 17 8 8 5.40 0.96 789713f

a

Reproduced with permission from ref 29. Copyright 2015 Elsevier Science. bThe economic model in the current work is utilized. cRO membrane from Saif and Almansoori.29 Because some properties (such as feed channel cross-section open area, spacer void fraction, etc.) are not provided, these parameters are set the same as SW30-400i. Solution diffusion model is utilized because the reflection coefficients are also not available. dSW30400i is used in pass 2 for comparison. eBW30-440i is used in pass 2 for comparison. fBecause the economic model of the proposed mode is different from Saif and Almansoori,29 thus the unit product cost could not be compared; only the differences between the flow structure and operation conditions are discussed. Q


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Js = gravimetric solute flux pass through membrane [kg/m2·s] Jw = volumetric water flux pass through membrane [kg/m2·s] K = mass transfer coefficient [m/s] Kλ = friction factor correction parameter l = mesh point along the z-axis direction on the PV L = number of discretization mesh points Lpv = total pressure vessel length [m] Lm = membrane module length [m] Mix = PX volumetric mixing Nb = minimum number of binary variables required for integer conversion Nn = minimum number of binary variables required for integer conversion nLT = RO plant service time [year] nm = number of membrane modules in series in each PV npv,j = number of pressure vessels utilized in the jth RO stage Nmlp = design period [year] OCbp = energy cost for the booster pump [$] OCSWIP = energy cost for the intake pump and pretreatment [$] OChpp = energy cost for the high-pressure pump [$] OCs = cost for spares [$] OCch = cost for chemical treatment [$] OCO&M = operation and maintenance costs [$] OCreag = annual costs of caustic and acid [$] OF = overflush of PX pKa = first acid dissociation constant of boric acid P = operating pressure [MPa] Q = flow rate [m3/h] Re = Reynold’s number sec = specific energy consumption [kWh/m3] Sc = Schmidt number Sm = membrane module active area [m2] sv = slack variable to ensure mathematically feasible if RO stage is nonexisting svb = slack variable to ensure mathematically feasible if RO stage is nonexisting T = temperature [°C] T0 = reference temperature [°C] TAC = total annualized cost [$] TCC = total capital cost [$] TCF = temperature correction factor upc = unit product cost [$/m3] V = feed superficial velocity [m/s] Vw = permeate velocity [m/s] W = membrane leaf width [m] yj,k = binary variable denoting the membrane module type Yl = binary variable denoting the subelement permeate flow direction Zj,km = binary variable used to express discrete number of membrane modules Zj,kpv = binary variable used to express discrete number of PVs z = longitudinal direction in spiral-wound module [m]

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b02225. Optimization results for RO system with feed of Arabian Gulf under different boron concentration restraints; optimization results for RO system with feed of Eastern Mediterranean under different boron concentration restraints; and entire set of design and optimization results obtained by the proposed model (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 022 60202743. Fax: +86 022 60204274. E-mail address: [email protected] (Y.-W. Du). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially support by the National Natural Science Foundation of China (No. 21606067), the Hebei Province Natural Science Foundation for Youths of China (B2014202082), the Hebei Province Higher Learning Institution Science Research Foundation for Youth Top-notch Talents of China (BJ2016016), and the National Key Research and Development Project of China (2016YFB0600504).

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NOMENCLATURE Aref = water permeability coefficient at T0 = 25 °C without fouling [kg/m2·s·Pa] Bref = salt permeability coefficient at T0 = 25 °C without fouling [m/s] Bboric,ref = B(OH)3 permeability coefficient at T0 = 25 °C without fouling [m/s] Bborate,ref = B(OH)4− permeability coefficient at T0 = 25 °C without fouling [m/s] Bin = salt passage increase per year [%] BBT,in = boron passage increase per year [%] C = salt concentration [kg/m3] CCbp = booster pumps capital cost [$] CCequip = plant equipment cost [$] CChp = high-pressure pumps capital cost [$] CCm = total membrane module cost [$] CCpx = pressure exchangers capital cost [$] CCSWIP = seawater intake and pretreatment capital cost [$] Ce = electricity cost [$/(kWh)] Ck = membrane element price [$] Cmw = solute concentration at the membrane surface [kg/m3] CPF = concentration polarization factor Cpv = pressure vessel price [$] crf = capital recovery factor DCC = direct capital cost [$] de = equivalent diameter of feed channel [m] Ds = salt diffusion coefficient [m2/s] Ew = RO system energy consumption [kW] fc = load factor of the RO plant FF = membrane fouling factor h = height of feed channel [m] ICC = indirect capital cost [$] Ir = interest rate

Greek Symbols

α0 = fraction coefficients of B(OH)3 α1 = fraction coefficients of B(OH)4− η = efficiency of a pump or a PX λ = friction factor μ = seawater dynamic viscosity [kg/(m·s)] π = osmotic pressure [MPa] ρ = mass density [kg/m3] σ = reflection coefficient

R


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Industrial & Engineering Chemistry Research Subscripts

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b,j = jth RO stage brine stream bp = booster pump ch = feed channel in the membrane module f = feed seawater hpp = high-pressure pump L = number of mesh points lc = front low-salinity permeate in PV hc = higher salinity back permeate in PV in = intake seawater k = kth element type motor = electric motor p = permeate p,j = jth RO stage permeate stream ps,i = ith pressurization stage PX = pressure exchanger pxhin = high-pressure stream to the PX pxlin = low-pressure stream to the PX Pxhout = high-pressure stream leaving the PX pxlout = low-pressure stream leaving the PX r = rth product water ref = reference RO,j = jth RO stage TB = total boron

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