Synthesis of reverse osmosis desalination network under boron specifications

Desalination 371 (2015) 26–36

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Synthesis of reverse osmosis desalination network under boron specifications Y. Saif ⁎, A. Almansoori Department of Chemical Engineering, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates

H I G H L I G H T S • • • •

Reverse osmosis desalination network design is considered under boron specifications. Superstructure optimization is proposed as an approach for the design problem. Several mitigation options are considered for optimal boron separation. The results show lower treatment cost with the proposed model.

a r t i c l e

i n f o

Article history: Received 30 March 2015 Received in revised form 5 May 2015 Accepted 9 May 2015 Available online xxxx Keywords: Boron Seawater desalination Reverse osmosis network Mixed integer nonlinear programming

a b s t r a c t Recent regulations regarding water quality motivated research in reverse osmosis (RO) technology for water desalination especially under boron restrictions. Boron control in the permeate products by reverse osmosis technology comprises several mitigation options which impose capital and operation costs. In our study, we investigate the design of RO system under the design concept of split partial second pass reverse osmosis (SPSPRO) in order to allow extraction of permeate streams along the RO pressure vessels. The design approach is based on superstructure optimization which allows the identification of optimal process layout and optimal operation conditions of the process units. pH adjustment of the network streams is also included in the model to control boron species distribution during the separation process. A mixed integer nonlinear program (MINLP) model is subsequently formulated based on the superstructure representation. The mathematical programming formulation is demonstrated on a case study to show the application of the mathematical programming model. The results show lower treatment cost through the proposed mathematical programming model. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Seawater is an abundant source of water for countries which have severe shortage of water supply. Desalination technologies are widespread internationally to reduce several contaminants in seawater up to the acceptable demand constraints. For the past decades, reverse osmosis (RO) has positioned itself as a proven technology in desalination applications. However, there are many difficulties in seawater desalination raised in recent years due to the increasing strict product quality such as boron concentration in drinking and agricultural water [1]. Boron exists in typical seawater at an average value of 5 mg/L. This is an essential element for plant growth if boron concentration is below 1 mg/L especially in agricultural industry [2]. However, destructive impact of boron on the yield of crops has been observed at high boron concentration. Possible toxicological effects of boron on human health have not yet been proven. With the view of these matters, the ⁎ Corresponding author. E-mail address: [email protected] (Y. Saif).

http://dx.doi.org/10.1016/j.desal.2015.05.012 0011-9164/© 2015 Elsevier B.V. All rights reserved.

World Health Organization (WHO) has set a maximum recommended boron concentration of 2.4 mg/L in drinking water product. On industrial scale, there have been many suggestions to control boron concentration in the permeate product. These efforts focus primarily on careful control of the pH values for the streams inside the treatment plants. In general, a single RO pass does not provide an adequate separation of boron in the final permeate product. Multiple passes of RO system were suggested for boron control with inter-stage pH control such as Ashkelon RO plant. This plant delivers high quality permeate product with total dissolved solid (TDS) and boron concentration less than 25 mg/L and 0.4 mg/L, respectively [3–6]. The RO operation conditions and selection evidently provide significant separation performance besides pH control. An RO pressure vessel is a continuous separation operation of seawater stream through several spiral wound elements which are connected in series. The variation of the reject stream properties deteriorates the separation driving force along the RO pressure vessel length. Extraction of permeate streams from the front RO elements allows a designer to achieve high quality permeate properties. In general, high pressure and low temperature

Y. Saif, A. Almansoori / Desalination 371 (2015) 26–36

operational values give enhanced boron rejection in the final permeate products. Besides, high RO reject superficial velocity offers better boron rejection as a result of reduced concentration polarization effects. All these previously mentioned variables require simultaneous optimization in order to achieve lower desalination cost under boron limitations [7–9]. RO network optimization was modeled through the state space representation [10]. This representation gives rich design alternatives of the RO passes and the auxiliary process equipment (e.g., high pressure pumps and energy recovery units) to treat wastewater and seawater streams. An MINLP model was constructed based on the proposed representation, and its solution provides optimal arrangement and operation of RO passes and auxiliary equipment. Later, further improvement of the RO superstructure representation was proposed with heuristic and global search algorithms to seek the network global solution [11–13]. Brackish and seawater treatment by double RO passes was also studied to analyze the RO element geometry effects on the final RO network and the treatment cost [14]. Seawater has a different TDS concentration which is a location dependent property. Different countries may impose different requirements on the permeate product quality. Any RO network design is therefore affected by water demand quality. Sensitivity analysis of different seawater streams and permeate product quality were studied in order to analyze the RO network final layout [15,16]. The study assumed a superstructure which is composed of RO passes, high pressure pumps, and energy recovery units. In general, strict product quality requires several RO passes with permeate processing. The previous RO design studies discuss the RO network problem for the production of a single permeate product with single TDS contaminant. The production of multi-grade permeates from a single RO pressure vessel has been proposed recently as a new RO design concept [17]. This design concept, known as split partial second pass reverse osmosis (SPSPRO), exploits the stream properties inside the pressure vessel and allows extraction of high quality permeate streams. These streams are either directed to the final product permeates or other RO passes. In general, lower treatment cost can be achieved if one adopts the SPSPRO design approach. The abovementioned RO network optimization studies consider only TDS as the sole contaminant. Superstructure optimization was recently proposed for designing the RO system under boron constraints [18,19]. The proposed MINLP models were applied for case studies to analyze the RO system under different operation conditions. There were several assumptions of linear behavior of the reject stream properties along the RO pressure vessels. However, these assumptions do not properly reflect the RO operation due to the inherent nonlinear RO models (e.g., concentration polarization and solution–diffusion models). This study presents the RO network optimization based on the SPSPRO design approach under boron limitations which is based on our previous design model [17]. This model is different than other published models [18,19] in terms of the superstructure representation and the RO pressure vessel modeling equations. A mixed integer nonlinear programming formulation is presented in order to model the RO network under boron and TDS constraints. The proposed model takes into account optimal selection of RO passes, number of RO membrane elements in every RO pass and RO optimal operation conditions, and the number of auxiliary equipments. In addition, the model considers critical issues of boron control options in the final permeate products. These influencing factors such as extraction of high quality permeates from the RO pressure vessels, the hydrodynamics inside the RO pressure vessel, and pH adjustment of the process streams are the main options to mitigate boron concentration in the final permeate streams. In the following section, we discuss several factors which affect boron separation, and possible combination of several mitigation options in the RO design problem. The RO superstructure representation will be analyzed in Section 3 and followed by the MINLP model development in Section 4. A case study for the RO network design under boron constraints will be given in Section 5, and finally the conclusions from this research study will be summarized in Section 6.

27

2. Boron mitigation options 2.1. pH effects There are several factors affecting boron permeation into the permeate product. The most profound factor affecting boron rejection is the water pH since it has a strong influence on the boron distribution species (e.g., boric acid, borate ions) [5–9,20,21]. Normally, boron goes through several dissociation reactions and the one which has the highest importance during the RO operation is given below [4–6]. The total boron concentration is the summation of the boric acid concentration and borate ion concentration. The distribution of boric acid is a function of the first acid dissociation constant and the seawater pH value [22]. H3 BO3 ↔ Hþ þ H2 BO− 3 At low pH values, boric acid exists with a large proportion compared with borate ions. Normally, seawater RO membrane shows poor rejection of boric acid. The dissociated form is fully hydrated which gives a larger radius of the molecule and provides an enhancement of the negatively charged ion rejection by the RO membrane. Accordingly, higher rejection of borate ions is attained through exclusion and repulsion effects by the negatively charged RO membrane [4]. Fig. 1 shows the distribution of boron species as a function of pH values [4,6]. There are several suggestions of pH control through chemical injection (acid or base) prior to RO passes in order to minimize boron concentration in the final water products. In general, the first RO pass should operate at seawater normal pH to eliminate salt precipitation and scale formation on the membrane surface [6–9]. This fouling issue at high pH operation forces a designer to find optimal pH operating conditions in order to avoid scaling and to mitigate boron species in the final water products. In this study, we only allow base injection (e.g., caustic soda) to increase the pH value for the second RO pass. 2.2. RO module design and operation The spiral wound RO element configuration is an attractive option for desalination applications due to their ease of operation, compact density and fouling control on a commercial scale. The RO pressure vessel includes several number of RO elements which are connected in series. In general, the front RO elements in every RO pressure vessel produce high permeate product with low TDS and boron concentration compared with the last elements [7]. The SPSPRO design approach exploits the RO operation and the reject and permeate properties in order to extract high quality permeate streams along the RO pressure vessel length. This design approach seeks permeate properties which either satisfy the final permeate products or process these streams in another RO pass to reach the final permeate products.

Fig. 1. Boron species distribution against water solution pH.

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Increasing the number of elements in the RO pressure vessel increases the permeate recovery, however, TDS and boron consequently increase in the permeate products. It follows that a designer seeks optimal process operation for the RO pressure vessel, optimal number of RO elements in every pressure vessel, and optimal extraction points of high quality permeate streams. These design issues are not obvious if one considers multi-passes of RO process units. Superstructure optimization provides tools to find answers for the previously mentioned issues as will be explained in the following sections. There are other important factors affecting boron rejection during the RO operation [7]. The applied hydraulic pressure, temperature, membrane aging, and reject superficial velocity have relatively less effects on boron rejection as compared with the other factors (e.g., pH, permeate splitting). The applied hydraulic pressure increases the rejection of boron because the membrane becomes denser and less permeable. The increase of RO operating temperature has a negative impact on the boron rejection due to the increase of the permeability coefficients. Desalination time deteriorates the membrane functions and thereby increases the permeability coefficients. Concentration polarization effects are reduced with increasing the brine superficial velocity, and thus enhance the membrane rejection. In our study, we assume isothermal operation under the seawater temperature. Besides, membrane aging is neglected by assuming regular membrane cleaning and replacement practices in order to restore the RO membrane functions. Other factors will be simultaneously optimized in this research study to find an optimal RO layout under TDS and boron limitations. The following section explains the construction of the RO treatment network under the SPSPRO design approach. 3. Reverse osmosis superstructure The RO superstructure represents a large number of process layouts to give a designer an assortment of alternatives for simultaneous evaluation. Within these alternatives, an optimal solution exists which transforms the network feed stream properties through the process equipment in order to achieve the final permeate product properties. In this study, we give compact representation for the process units in every RO pass. In general, every RO pass has sets of mixer and splitter nodes. The mixer nodes are the points for mixing streams from different RO passes in order to provide the RO feed streams, whereas the splitter nodes split the RO pass product streams to other RO passes and to the final product mixer nodes. Fig. 2 depicts an RO pass with its auxiliary equipment that supplements the RO pass operation tasks. Every RO pass may have high pressure pump (HPP), booster pump (BP), pressure exchanger (PE), chemical injection unit (CIU), and parallel RO pressure vessels. The first mixer (MIX1) represents a feed stream which will be processed

through the RO pass. This stream is a result of mixing different streams coming from other RO passes and the network feed stream. Mixing streams will alter the properties of the mixer product stream (e.g., flowrate and chemical composition). A chemical injection unit may be needed after the mixer node to alter the pH value for the RO pass feed stream. In order to raise the RO feed pressure, the RO feed stream can be directed to a high pressure pump. Also, this stream can be split partially to the pressure exchanger unit, and followed by a booster pump to match the high pressure pump exit stream. Another mixer (MIX2) receives a high pressure stream which is a feed stream to the pressure exchanger unit. This node serves the purpose of extracting kinetic energy in the pressure exchanger unit from other RO passes. The splitter nodes act as other venues of interactions between different RO passes. The RO permeate splitter nodes (SP1–SPn) provide locations for the permeate product extraction. After the splitter nodes, permeate streams with different qualities can be directed to the final product permeate streams and other RO passes. The splitter SPn + 1 is the RO brine splitter coming out of the RO pass. This node acts as a source of interaction with other RO passes, other pressure exchangers, and the final reject streams going out of the network. The last splitter SPn + 2 represents a location for the water stream coming out of the pressure exchanger unit which flows out of the network. It should be noted that the energy recovered in the pressure exchanger may not match the high pressure pump exit stream conditions. In this case a booster pump is needed to raise the pressure to the high pressure pump exit stream conditions. The superstructure of the SPSPRO network can be assembled through the given input information of seawater TDS and boron concentrations, set of RO passes, and the final permeate product demand constraints. Any RO pass is composed of parallel RO pressure vessels which are composed of several numbers of RO elements. Any RO feed stream is split equally over all the RO pressure vessels in the RO pass. Besides, high pressure pump, booster pump, and pressure exchanger units supplement the RO pass operation requirements as explained in Fig. 2. The SPSPRO superstructure representation is depicted by Fig. 3. It shows the stream distribution for the SPSPRO network for two RO passes. It is worth pointing out that the representation can be assembled for any number of RO passes following the same concept of Fig. 3. The inlet feed seawater stream is distributed over the RO passes (RO) in the distribution box (DB). These stream assignments link the inlet seawater feed to the mixer nodes for every RO pass. The exit streams from every RO pass (i.e., streams from the splitter SP1 to SPn + 2) enter the DB as feed streams to the RO passes and the final reject and permeate streams. This representation gives rich stream assignments between the inlet seawater feed stream, RO passes, and the final reject and permeate streams. Within this network, a designer looks for an optimal SPSPRO layout to treat the feed seawater stream

Fig. 2. Splitter and mixer node representation for an RO pass with auxiliary equipment.

Y. Saif, A. Almansoori / Desalination 371 (2015) 26–36

29

Fig. 3. SPSPRO superstructure representation.

in order to reach the final permeate product constraints. The following section gives the mathematical programming formulation for the SPSPRO network model taking into consideration the TDS and boron constraints in the treatment network. 4. Reverse osmosis network model 4.1. Transport model The reverse osmosis element has a set of governing equations describing the transport of water mass flowrate (FWat Elem,RO) and salt mass flowrate (FSalt Elem,RO) across the membrane. These equations follow the solution diffusion model. It assumes negligible effects of the channel curvature since the feed channel thickness is much lower than the RO element radius. Furthermore, the permeate channel pressure drop is not significant. The concentration polarization is modeled by the film theory. The water mass flowrate and the salt transfer across the membrane are described by the following equations.


RE J;in FWat Elem;RO ¼ SAElem;RO WaElem;RO PElem;RO −ΔPElem;RO
 RE J PERM −PPERM ∀Elem; RO Elem;RO − πElem;RO −πElem;RO


 salt; R‐Wall P‐Wall −xsalt; FSalt Elem;RO ¼ SAElem;RO TDSPElem;RO xElem;RO Elem;RO

∀Elem; RO ð2Þ

∀Elem; RO

salt;R‐Wall

kElem;RO

Elem;RO
 Vsalt k salt;R‐avg salt;P‐Wall Elem;RO ¼ Xsalt;P‐Wall þ X −X e Elem;RO Elem;RO Elem;RO

salt

0:33 kElem;RO ¼ 0:04Re0:75 Elem;RO ScElem;RO

VElem;RO ¼

DSalt Elem;RO d

Salt BT FWat Elem;RO þ FElem;RO þ FElem;RO

SAElem;RO ρPERM Elem;RO

∀Elem; RO ð4Þ

∀Elem; RO

∀Elem; RO

ð5Þ

ð6Þ

ð1Þ

SAElem,RO is the effective membrane surface area for every RO element. WaElem,RO, and TDSPElem,RO represent the water and salt permePERM ability coefficients, respectively. PREJ,in Elem,RO, ΔPElem,RO, and PElem,RO are the inlet reject pressure, pressure drop, and permeate pressure in the RO element, respectively. The osmotic pressure in the reject and permeate PERM salt, R ‐ Wall P ‐ Wall and xsalt, sides is given by πREJ Elem,RO, and πElem,RO, where xElem,RO Elem,RO are the salt concentration at the reject and permeate membrane wall, respectively. Boron permeates through the membrane wall and the following equation describes the total boron flowrate (FBT Elem,RO).
 BT; R‐Wall BT; P‐Wall BT FBT Elem;RO ¼ SAElem;RO BTPElem;RO xElem;RO −xElem;RO

where BTPBT Elem,RO is the total boron permeability coefficient. In addition, R ‐ Wall P ‐ Wall and xBT, give total boron concentration on the memxBT, Elem,RO Elem,RO brane wall for the reject and the permeate sides, respectively. The concentration polarization modeling provides the concentration of TDS at the reject side membrane wall as given by Eq. (4). The mass transfer (ksalt Elem,RO) and permeate velocity (VElem,RO) are given by Eqs. (5)–(6), respectively. These equations assume a fully developed concentration polarization layer on the RO membrane surface.

ð3Þ

‐ avg is the average TDS concentration at the reject side. xsalt,R Elem,RO ReElem,RO, ScElem,RO, DSalt Elem,RO, and d are Reynold's, Schmidt, salt diffusivity, and feed space thickness, respectively. The RO rejection action on the membrane wall creates TDS concentration higher than the bulk TDS concentration. Therefore, one should account for the boron first ‐ Wall ) at the reject membrane wall prevaildissociation constant (pKaRElem,RO ing conditions as given by Eq. (7) [8,9]. Consequently, the total boron ‐ Wall concentration (xBT,R Elem,RO ) and its constituents are estimated by Eq. (8).

pKaR‐Wall Elem;RO ¼


1=3 2291:9 R‐Wall þ 0:01756 T−3:385−2:631 xsalt; Elem;RO T

ð7Þ

∀Elem; RO ¼ xBA;R‐Wall Elem;RO


1 þ 10

BT;R‐Wall xElem;RO

pHR‐avg −pKaR‐Wall Elem;RO Elem;RO



∀Elem; RO

ð8Þ

The total boron concentration at the reject membrane wall is estimated by Eq. (9) in order to account for the concentration polarization

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effects. Eq. (10) gives the mass transfer coefficient for boron (kBT Elem,RO) as a function of the TDS mass transfer coefficient [5,23]. Elem;RO
 VBT k BT; R‐avg BT;R‐Wall BT;P‐Wall BT;P‐Wall xElem;RO ¼ xElem;RO þ xElem;RO −xElem;RO e Elem;RO

BT

salt

kElem;RO ¼ 1:03kElem;RO

∀Elem; RO

∀Elem; RO

ð9Þ ð10Þ

The total boron permeability coefficient (BTPBT Elem,RO) is estimated at the RO membrane wall as a function of boric acid (BAPBA Elem,RO) and borate ion (BIPBI Elem,RO) permeability coefficients as given by Eq. (11) [8,9,20,21]. BA BI BA BI BTPBT Elem;RO ¼ αElem;RO BAPElem;RO þ αElem;RO BIPElem;RO

∀Elem; RO

ð11Þ

BI αBA Elem,RO, and αElem,RO represent the mass fractions of boric acid and borate ions at the membrane wall for every RO element. The reject flow exhibits pressure drop (ΔPREJ Elem,RO) for every RO element as given by Eq. (12).

J ¼ ΔPRE Elem;RO

9:2  10−13 Q Elem;RO LElem;RO μ Elem;RO

! ∀Elem; RO

3

Wd

ð12Þ

QElem,RO, LElem,RO, μElem,RO, and W are the average volumetric flowrate at the reject side, length of membrane element, reject viscosity, and membrane element width, respectively. Other important transport properties are listed in Appendix A. 4.2. RO pass constraints The overall mass change on the reject side is equivalent to the permeate mass change for every RO element as given by Eq. (13). The TDS and total boron balance (e.g., TDS and boron are represented by set c) on the reject and permeate sides can be calculated by Eqs. (14) and (15).

The overall RO pass flowrate (FRO in) is linked to the pressure vessel equations by the total number of pressure vessels (NPVRO) existing in that pass, Eq. (20). RE J;in Fin RO ¼ FElem¼1;RO NPVRO

∀RO

Similarly, the total permeate withdraw stream (FElem,RO WITHD ‐ Total) from every RO element and the total reject side stream (FRO REJ) in every pass can be linked to the total number of RO pressure vessels. The existence of any RO element is related to a binary variable (yElem, RO) to indicate if there is transport of mass (e.g., water, boron, and salt) across the membrane as described by Eq. (21). Salt BT UP FWat Elem;RO þ FElem;RO þ FElem;RO ≤ FElem;RO yElem; RO

¼

FPERM;out –FPERM;in Elem;RO Elem;RO

∀Elem; RO

ð13Þ

∀Elem; RO

ð21Þ

The RO stage existence is a relation between the first element binary variable in the RO pass with the RO pass inlet flow, Eq. (22). RE J;UP;in UP Fin RO ≤ FElem¼1;RO NPVRO yElem; RO

∀RO

ð22Þ

In addition, the existence of the auxiliary equipments (e.g., HPP, BP, and PE are represented by the set Aux) is a relation between the pressure difference across the unit operation and its binary variable as given by the following equation. in UP Pout Aux −PAux ≤ P yAux

∀Aux

ð23Þ

A chemical injection unit may follow a mixer node to change the solution pH to a target suitable for the second RO stage. The CIU balance equation for the base injection is given by the following equation to determine the pH level prior to the second RO stage. Similar equation can be formulated if one has interest to reduce the pH of a stream through acid injection unit. CIU;in 10− ð14− pH FRO

CIU;in

Þ þ Fbase 10−pOHbase RO

¼ FCIU;out 10− ð14− pH RO

CIU;out

J;in J;out −FRE FRE Elem;RO Elem;RO

ð20Þ

Þ

ð24Þ

∀RO

4.3. DB constraints J;in FRE Elem;in;RO

J;in J;out RE J;out xRE −FRE x c;Elem;RO Elem;RO c;Elem;RO

¼ Fc;Elem;Ro

∀c; Elem; RO

ð14Þ

xPERM;in þ Fc;Elem;RO ¼ FPERM;out xPERM;out FPERM;in Elem;RO c;Elem;RO Elem;RO c;Elem;RO

∀c; Elem; RO

ð15Þ

The reject stream flows from one element to the next one which requires balance equations for the flow, pressure, TDS and boron concentrations, Eqs. (16)–(18). J;in J;out ¼ FRE FRE Elemþ1;RO Elem;RO

∀Elem; RO

ð16Þ

J;in J;out ¼ PRE PRE Elemþ1;RO Elem;RO

∀Elem; RO

ð17Þ

In the DB, there are many mixer and splitter nodes to allow interactions between different stream states in the network. The mixer node requires total flow and component balances as given by Eqs. (25)–(26). FMIX ¼

XSPT

FMIX xc;MIX ¼

FSPT

XSPT

¼

J;out xRE c;Elem;RO

∀c; Elem; RO

∀Elem; RO

∀c; MIX

ð26Þ

XSPT

FSPT 10−pHSPT

∀MIX

ð27Þ

ð18Þ

On the permeate side, withdraw streams exist between any adjacent elements which require total flow balance as given by Eq. (19). The withdrawal stream and the incoming stream to the next element keep the same boron and TDS concentrations, and pressure values from the previous element. ¼ FPERM;in þ FWITHD FPERM;out Elem;RO Elem;RO Elemþ1;RO

FSPT xc;SPT

ð25Þ

In addition to the previous equations, the corresponding pH level for the mixer exit stream can be related to the input streams flowing through the mixer node as given by the following equation. FMIX 10−pHMIX ¼

J;in xRE c;Elemþ1;RO

∀MIX

ð19Þ

A restriction of mixing the input streams flowing through a mixer node is imposed on only streams with equivalent pressure values as given by the following set of equations. FSPT ≤ FUP yMIX;SPT

∀MIX; SPT

ð28Þ

  PMIX −PSPT ≤ PUP 1−yMIX;SPT ∀MIX; SPT

ð29Þ

  ∀MIX; SPT PMIX −PSPT ≥ PLO 1−yMIX;SPT

ð30Þ

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yMIX,SPT is a binary variable to choose input streams through a mixer node with pressure values matching the mixer output stream pressure condition. The set of Eqs. (28)–(30) forces the input streams to diminish if there is no pressure matches with the mixer exit stream pressure. A splitter node has an opposite action compared with the mixer node where a single feed stream is split into several streams with the same properties as given by Eq. (31). FSPT ¼

XMIX

FMIX

∀SPT

ð31Þ

There are demand constraints for the final permeate product streams on the flowrate (FPERMEATE), and the component concentrations as given by the following equations. FPERMEATE ≥ FLO PERMEATE xc;PERMEATE ≤xUP c

∀PERMEATE

∀c; PERMEATE

ð32Þ ð33Þ

4.4. Cost model The objective function in this study is developed to minimize the total annual cost (TAC) for the treatment of seawater stream subject to the abovementioned constraints. The total capital cost (TCC) is composed of pressure vessels and membrane costs, seawater intake pump and feed pretreatment, high pressure and booster pumps, and the pressure exchanger units as given by Eqs. (34)–(39), with a practical investment factor (PIF) reflecting the indirect capital cost as a percentage of total capital cost. CCPV ¼

XMemb XElem XRO þ

XRO

CMemb yMemb;Elem;RO NPVRO

CPV NPVRO

ð34Þ

CCSWIP ¼ CSWIP ð FSWIP Þn1

ð35Þ

CCHPP ¼ CHPP ð FHPP ΔPHPP Þ

ð36Þ

CCBP ¼ CBP ð FBP ΔPBP Þ

ð37Þ




CCPE ¼ CPE FHI PE

n2

ð38Þ

TCC ¼ PIFðCCPV þ CCSWIP þ CCHPP þ CCBP þ CCPE Þ

ð39Þ

The annual operating cost (AOC) has electricity operational cost for the RO pressure vessel, seawater intake pump, high pressure pump, and pressure exchanger units, Eqs. (40)–(43). Other operational costs include insurance, labor, chemical usage for pretreatment, caustic soda consumption, and maintenance for the RO plant, Eqs. (44)–(48). The estimated TAC is given by Eq. (50) assuming an annual interest rate of 5% and plant lifetime set at 25 years. OCPV ¼ OPV CCPV OCSWIP ¼ OSWIP

OCHPP ¼ OHPP

OCPE ¼ OPE

ð40Þ

FSWIP ηSWIP ηMOTOR

FHPP ΔPHPP ηHPP ηMOTOR

FPEHI ΔPPEHI ηPE ηMOTOR

OCLABOR ¼ OLABOR

XPERM

FPERM

OCCHEMICAL ¼ OCHEMICAL FSWIP

ð46Þ

OCbase ¼ Obase Fbase

ð47Þ

OCMAINT ¼ OMAINT

XFPERM

ð48Þ

FFPERM

AOC ¼ OCPV þ OCSWIP þ OCHPP þ OCPE þ OCINSURANCE þ OCLABOR þ OCCHEMICAL þ OCbase þ OCMAINT

ð49Þ

TAC ¼ AF TCC þ AOC

ð50Þ

The mathematical programming model (MINLP) defined by the set of constraints and the objective function TAC has several local optima due to the presence of nonconvex functions. In this study, we applied SBB solver in GAMS to solve the case study [24]. The model equations are represented by 2350 equations, 1595 continuous variables, and 130 discrete variables. The case study will be solved from different random starting points, however, the global solution is not guaranteed. There are many local optimal solutions for the case study and the best local optimal solution is reported. The following section will cover a case study which shows the application of the mathematical programming model. 5. Case study This section covers the desalination case study under boron constraints for Eastern Mediterranean seawater stream. Eastern Mediterranean seawater normally contains high TDS and boron concentrations (e.g., 40,000 ppm of TDS concentration and 13 ppm boron concentration) [19,25]. Although boron concentration of 2.4 ppm in the final permeate product was recommended by the WHO, strict boron concentration demand may be lower than the recommended value as the case of Ashkelon RO desalination plant (e.g., less than 0.4 ppm). Therefore, we solve the proposed model under various constraints of boron concentration for the final permeate product (e.g., 1 ppm, 0.8 ppm, 0.5 ppm, 0.3 ppm) in order to analyze the RO layouts. In addition, the permeate product flowrate and TDS concentration are kept constant for the permeate product (e.g., 30 kg/s permeate flowrate, 500 ppm TDS concentration). Furthermore, we compare the results of the optimization model under two conditions. The first condition allows permeate splitting along the RO pressure vessels and is named PS condition. The second condition excludes permeate splitting streams along the RO pressure vessels and is called PNS condition. Table 1 shows the properties and cost of the RO membrane. In addition, Table 2 provides other parameters (e.g., cost and operation parameters) for the mathematical programming model. The first scenario under consideration represents the final permeate constraints of 30 kg/s flowrate, 500 ppm of TDS concentration, and 1 ppm of boron concentration under both PS and PNS conditions. Fig. 4 depicts the RO optimal process layout for these conditions. The treatment cost for the PS condition is around $891,818 per year, whereas the treatment cost for the PNS condition is around $911,413 per year. Thus, 2.2% treatment cost saving can be achieved by allowing extraction

ð41Þ Table 1 RO membrane properties.

ð42Þ

ð43Þ

OCINSURANCE ¼ OINSURANCE TCC

31

ð44Þ ð45Þ

Active area (m2) Length of the element (m) Feed space (m) Feed flowrate range (kg/s) Max. operating pressure (MPa) Water permeability (kg/m2 s MPa) TDS permeability (kg/m2 s) Boric acid permeability (kg/m2 s) Boron ion permeability (kg/m2 s) Membrane element cost ($)

35.3 0.88 8.126 × 10−4 4.5–0.22 8.3 4.47 × 10−3 1.2 × 10−4 3.43 × 10−3 2.02 × 10−4 1000

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Table 2 Parameters and cost coefficients for the model. Feed water temperature (°C) Diffusion coefficient (m2/s) High pressure pump efficiency n1 n2 Practical investment factor Annualized factor AF (1/year) Pressure exchanger efficiency Electric motor efficiency The cost of electricity ($ (kWh)−1) Pressure vessel cost ($) Seawater intake pump cost (CSWIP), $(kg/s)−0.8 HPP capital cost (CHPP), $(kg/s MPa)−1 BP capital cost (CBP), $(kg/s MPa)−1 PE capital cost (CPE), $(kg/s)−0.58 Operating cost for pressure vessel (OPV), (yr)−1 Seawater intake pump operating cost (OSWIP), $(kg/s yr)−1 HPP operation cost (OHPP), $(kg/s MPa yr)−1 PE operation cost (OPE), $(kg/s MPa yr)−1 Insurance operation cost (OINSURANCE), (yr)−1 Labor operation cost (OLABOR), $(kg/s yr)−1 Chemical pretreatment operation cost (OCHEMICAL), $(kg/s yr)−1 Maintenance operation cost (OMAINT), $(kg/s yr)−1 Caustic soda cost ($/kg)

25 1.493 × 10−9 75% 0.8 0.58 1.114 0.08 90% 98% 0.08 1000 3.53 × 104 187 187 6590 0.2 315 8174 9082 0.063 283.8 638.6 283.8 0.42

of permeate streams along the RO pressure vessels. This is relatively small cost saving, however, higher treatment cost saving is observed under strict boron concentration in the final permeate product which will be explained later in the text.

For the PS condition (Fig. 4a), seawater stream with 101.9 kg/s flowrate is pressurized in the first RO pass which has 26 parallel RO pressure vessels to produce two permeate products from the third and fourth RO elements. The first extracted permeate stream flowrate is around 9 kg/s, with 330 ppm and 3.3 ppm concentrations of TDS and boron, respectively. In addition, the second extracted permeate stream flowrate is around 30.3 kg/s, with 391 ppm and 3.7 ppm concentrations of TDS and boron, respectively. These two extracted permeate streams are mixed and forwarded to the second RO pass for further processing. The second RO pass has 9 RO pressure vessels which process the RO pass feed stream after pressurization and pH adjustment (e.g., feed pH for the second RO pass is around 8.8). In the second RO pass, we observe two extracted permeate streams (e.g., from the first and third RO elements) which supply the final permeate product demand. The permeate stream from the first RO element supplies partially the final permeate product demand. This permeate stream has 8 kg/s flowrate, and with 2 ppm and 0.48 ppm concentrations of TDS and boron, respectively. In addition, the third element delivers an extracted permeate stream with 22 kg/s flowrate, and with 6 ppm and 1.19 ppm concentrations of TDS and boron, respectively. These extracted permeate streams from the RO network satisfy the final permeate product with 30 kg/s flowrate and with 5 ppm and 1 ppm concentrations of TDS and boron, respectively. Finally, the reject streams from the first and second RO passes are depressurized in the pressure exchanger unit and directed to the final reject node. For the PNS condition (Fig. 4b), seawater stream with 105.2 kg/s flowrate is processed in the first RO pass with 31 parallel RO pressure vessels. The permeate stream flowrate from the first RO pass is around 38.5 kg/s, and with 1133 ppm and 5.3 ppm concentrations of TDS and boron, respectively. The permeate stream from the first RO pass is

(a)

(b) Fig. 4. Optimal process layouts under 1 ppm boron concentration specification in the permeate product (a) with permeate split and (b) without permeate split.

Fig. 5. Water transport driving force across the membrane under 1 ppm boron concentration specification in the permeate product for (a) first RO pass and (b) second RO pass.

Y. Saif, A. Almansoori / Desalination 371 (2015) 26–36

further refined in the second RO pass which has 9 parallel RO pressure vessels. In addition, the feed stream to the second RO pass is pressurized, and the feed pH is adjusted (i.e., the feed pH for the second RO stage is around 9.2). This process layout satisfies the final permeate product demand from the permeate stream which is produced from the second RO pass (e.g., 30 kg/s flowrate, and with 15 ppm and 1 ppm concentrations of TDS and boron, respectively). It is worth pointing out that the cost difference between the RO layouts in Fig. 4 is mainly attributed to the arrangement of RO passes, the stream assignments, and the operation conditions. In both conditions, the boron concentration constraint for the final permeate product is a binding constraint in the optimal solution, whereas the TDS concentration constraint is a nonbinding one. This implies that the RO network design is more controlled by the boron constraints compared with the TDS constraints. The operation of the RO elements in every RO pass under PS and PNS conditions provides more understanding of the optimal solutions. Fig. 5 shows the water driving force along the RO pressure vessels for the first and second RO passes under the PS and PNS conditions. This driving force is generated as a result of the hydraulic pressure and the osmotic pressure differences between the reject and permeate sides. The figure shows that the water driving force under the PS condition is higher than the PNS condition for both RO passes. In addition, this separation driving force deteriorates as a result of the hydraulic pressure reduction and an increase of the osmotic pressure along the RO pressure vessels. The TDS flux from the reject to the permeate sides is controlled by the TDS separation driving force. This driving force is generated due to the presence of concentration gradient across the RO membrane wall. Fig. 6 depicts the TDS driving force for both RO passes under the PS and PNS conditions. For the first RO pass, one can observe that the TDS driving force under the PS condition is higher than the other condition. This situation is expected due to the consequence of high water

(a)

(b) Fig. 6. TDS transport driving force across the membrane under 1 ppm boron concentration specification in the permeate product for (a) the first RO pass and (b) the second RO pass.

33

recovery under the PS condition compared with the other condition (Fig. 5a). For the second RO pass, the TDS separation driving force under the PS condition is lower than the other condition. This situation occurs mainly for two major operation factors. First, the water recovery under the PS condition is relatively higher than the PNS condition. Second, the feed stream to the second RO pass under the PS condition has better quality (e.g., feed TDS concentration is 377 ppm) compared with the other condition (e.g., feed TDS concentration is 1133 ppm). In general, the SPSPRO design approach provides better quality for the product permeate in the final permeate stream (e.g., 5 ppm TDS concentration under the PS condition, 15 ppm TDS concentration under the PNS condition). Boron flux from the reject to the permeate sides is affected by the changes of boron permeability coefficient and boron concentration gradient across the membrane along the RO pressure vessels. The boron permeability coefficient is a function of the distribution of boric acid and borate ions at the membrane wall. In addition, this distribution is indirectly related to the TDS concentration at the membrane wall (e.g., Eq. (7)). Thus, high TDS concentration and high pH values enhance the dissociation reaction of the boric acid, and create high fraction of borate ions at the reject membrane wall. In general, TDS concentration increases along the RO pressure vessels due to the RO membrane rejection. In addition, the reject pH value increases along the RO pressure vessels. Therefore, it is expected to see a decreasing trend of the boron permeability coefficient along the RO pressure vessels. However, these changes of boron permeability coefficients are not significant (e.g., see Supplementary data). It can be concluded from these results that boron flux is more influenced by the boron concentration gradient across the membrane wall under the given scenario. The boron driving force distribution has a different trend in comparison with the TDS driving force as given by Fig. 7. This figure shows a

(a)

(b) Fig. 7. Boron transport driving force across the membrane under 1 ppm concentration specification in the permeate product for (a) the first RO pass and (b) the second RO pass.

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semi-concave shape for the results trend in the first RO pass (Fig. 7a), and an increasing trend in the second RO pass (Fig. 7b). For the first RO pass, the boron transport force under the PS condition is higher than the other condition for the same reason as explained before in Fig. 5a (e.g., high water recovery under the PS condition compared with the other condition). The semi-concave shape results from the variation of the boron species distribution around the RO membrane (e.g., changes of pKa and pH values along the RO pressure vessels). In general, there is a continuous boron rejection by the RO membrane along the RO pressure vessels. At the front RO elements, the rejection of boron species at the membrane wall increases steadily with association of boric acid dissociation toward borate ions. This shift of boron species distribution from the front to the end of the RO modules generates higher proportion of borate ions at the end of the pressure vessels compared with the front RO elements. Thus, a reduction of boron driving force is observed at the end of the pressure vessels. In the second RO pass, the RO feed properties (e.g., TDS and boron concentrations) and the pH values are significantly different than the first RO pass under the PS and PNS conditions. In general, the shift of boric acid toward borate ions is not significant as observed for the first RO stage, and an increasing trend of boron transport force is observed as shown by Fig. 7b. Another important operation feature of the design under the PS and PNS conditions is the permeate quality on the permeate side. The permeate quality reflects the overall effects of water, TDS, and boron transport forces presented previously in Figs. 5–7. Fig. 8 shows that the TDS concentration profile on the permeate side under the PS condition has better TDS quality compared with the PNS condition. Although the TDS transport force is high under the PS condition (Fig. 6a), the TDS concentration is low on the permeate side under the same condition

(a)

(b) Fig. 8. Permeate TDS concentration profiles along the RO pressure vessels under 1 ppm boron concentration specification in the permeate product for (a) the first RO pass and (b) the second RO pass.

compared with the PNS condition. This trend appears as a result of high water transport force under the PS condition (Fig. 5a) which dilutes the permeate product in the first RO pass. In the second RO pass, the TDS concentration quality on the permeate side under the PS condition is lower than the other condition (Fig. 8b). This trend generally appears as a result of high water and low TDS transport forces as explained before in Figs. 5b and 6b, respectively. Fig. 9a shows the boron concentration profile in the permeate side under the PS and PNS conditions for the first RO pass. In general, the PS condition gives better boron concentration quality compared with the permeate PNS condition for the same reasons explained before for the TDS concentration profile (Fig. 8a). In the second RO pass (Fig. 9b), the boron concentration quality on the permeate side has a different trend. One can see that the boron concentration under the PS condition is lower than the other condition for the first RO element. This element represents an extraction location for the delivery of high quality permeate stream to the final permeate product (Fig. 4a). In general, the permeate quality for the second and third RO elements under the PNS condition is higher than the other condition. In fact, the last RO element under the PS condition has permeate quality (e.g., 1.2 ppm of boron concentration) which is higher than the final permeate product specification. In addition, this last RO element represents an extraction point for the delivery of a permeate stream to the final permeate product (Fig. 4a). However, mixing the permeate streams from the first and third RO elements provides permeate quality which satisfies exactly the final permeate product demand. These operation conditions show that the SPSPRO design approach has more operation flexibility in order to meet the final permeate product specifications compared with the PNS condition. This operation flexibility stems from allowing the extraction of permeate streams along the RO pressure vessels, and

(a)

(b) Fig. 9. Permeate boron concentration profiles along the RO pressure vessels under 1 ppm boron concentration specification in the permeate product for (a) the first RO pass and (b) the second RO pass.

Y. Saif, A. Almansoori / Desalination 371 (2015) 26–36 Table 3 Summary of the optimal solutions for the case study under 1 ppm boron concentration specification.

Seawater intake, kg/s Feed pH First pass Second pass Feed flowrate, kg/s First pass Second pass Feed pressure, MPa First pass Second pass Feed concentration, ppm First pass (TDS, boron) Second pass (TDS, boron) RO pressure vessel number First pass Second pass Caustic soda consumption, kg/s Specific energy consumption, kWh/m3 TAC, $/year

With permeate splitting

Without permeate splitting

101.9

105.2

7.2 8.8

7.2 9.2

101.9 39.4

105.2 38.5

7.8 7.67

6.4 6.3

40,000, 13 377, 3.6

40,000, 13 1133, 5.3

26 9 0.005 2.9 891,818

31 9 0.011 2.4 911,413

mixing these permeate streams in the RO network in order to reach the final permeate product constraints. Table 3 gives a summary for the design and operation variables presented in Fig. 4. It is also interesting to examine the RO process layouts under different boron concentrations in the final permeate product demand. The RO process layouts and the optimal solution summaries for the boron concentrations of 0.8 ppm, 0.5 ppm, and 0.3 ppm in the final permeate products are given in the Supplementary data. In general, the results show gradual cost saving of 6.3% under the PS condition compared with the PNS condition for the scenario of 0.8 ppm boron concentration in the final permeate product. Further cost saving of 8.9% and 12% under the PS condition compared with the PNS condition is achieved for the scenarios of 0.5 ppm and 0.3 ppm boron concentration in the final permeate product, respectively. It is clear from the given results in this case study that one can gain economic and operation advantages under the PS condition compared with the PNS condition through the SPSPRO design approach.

6. Conclusions The optimization of RO network design problem is presented for seawater desalination applications under boron specifications through the SPSPRO design approach. This given design approach adopts superstructure optimization to provide rich process layouts for the extraction of high quality permeate streams along the RO pressure vessels. The superstructure representation shows RO stages and auxiliary equipment which are linked through stream assignments within the RO network. These stream assignments map seawater feed stream properties to the final permeate product properties through the input and output streams of the process units. A mixed integer nonlinear programming model was formulated based on the proposed superstructure. Binary variables allow the selection of RO membrane elements and passes, and stream assignments in the network. A detailed model is presented to describe the transport of TDS and boron through the RO spiral wound elements which are connected in series in every RO pressure vessel. The objective function was to minimize the annual treatment cost of seawater stream subject to the design and technical constraints. The usefulness of the design approach was verified on a case study which represents the desalination of Mediterranean seawater. In general, the results show progressively cost saving under the PS condition when the boron concentration values for the water permeate product are limited to strict values.

Abbreviations AOC BP DB HPP MINLP PE PIF PS PNS RO SPSPRO TAC TCC TDS WHO

annual operation cost booster pump distribution box high pressure pump mixed integer nonlinear program pressure exchanger practical investment factor permeate splitting permeate non-splitting reverse osmosis split partial second pass reverse osmosis total annual cost total capital cost total dissolved solids World Health Organization

Symbols Sets Aux set of auxiliary equipment BP booster pumps c chemical component set Elem elements in RO stage HPP high pressure pumps MIX mixer nodes in the RO network PE pressure exchanger units PERMEATE final permeate product RO RO stages in the treatment network SPT splitter nodes in the RO network Variables pKa π ΔP AOC BTP CC k OC pH Q Sc TAC TCC ρ F NPV P Re V x y α μ

first acid dissociation constant osmotic pressure, MPa pressure drop, MPa annual operational cost, $/year boron permeability coefficient, kg/m2 s capital cost, $ mass transfer coefficient, m/s operational cost, $/year solution pH for reject or permeate streams volumetric flowrate, m3/s Schmidt number total annual cost, $/year total capital cost, $ density, kg/m3 flowrate, kg/s number of RO pressure vessels pressure, MPa Reynold's number permeate velocity, m/s concentration of TDS or boron, kg/kg binary variable fraction of boric acid or borate ions viscosity, kg/m s

Parameters exponent for seawater intake pump n1 exponent for pressure exchanger n2 AF annual factor BAP boric acid permeability coefficient, kg/m2 s BIP borate ions permeability coefficient, kg/m2 s C capital cost coefficient D diffusivity, m2/s d feed space thickness, m

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L O PIF SA T TDSP Wa W η

References

RO element length, m operational cost coefficient practical investment factor surface area of RO module, m2 temperature, K total dissolved solid permeability coefficient, kg/m2 s water permeability coefficient, kg/m2 MPa s width of RO membrane sheet, m efficiency

Superscript BA boric acid base designate property for base chemical injection point BI borate ions BT total boron CIU chemical injection unit prior to RO stage in inlet condition out outlet condition P-avg averaged value for a property on the permeate side PERM designates a property on the permeate side of RO element P-Wall designates a property at the permeate membrane wall R-avg designates an averaged value on the reject side REJ designates a property on the reject side of RO element R-Wall designates a property at the reject membrane wall Salt designates TDS property Wat designates a property of water WITHD a property for permeate withdraw stream Appendix A Seawater properties [17] Osmotic pressure π ¼ 70xsalt þ 0:1716

ðA:1Þ

Density ρ ¼ 700xSalt þ 998

ðA:2Þ

Viscosity μ ¼ 2  10−3 xSalt þ 0:0009

ðA:3Þ

Reject and permeate pH correlations [19] J;out J;in pHRE ¼ pHRE þ 0:014 Elem;RO Elem;RO

∀Elem; RO

ðA:4Þ

J;in ¼ pHRE −0:08 pHPERM;Wall Elem;RO Elem;RO

∀Elem; RO

ðA:5Þ

Appendix B. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.desal.2015.05.012.

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