Synthesis of integrated membrane desalination and salt production networks

Desalination 400 (2016) 25–37

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Desalination journal homepage: www.elsevier.com/locate/desal

Synthesis of integrated membrane desalination and salt production networks Varun M. Chauhan, Sabla Y. Alnouri, Patrick Linke ⁎, Ahmed Abdel-Wahab Department of Chemical Engineering, Texas A&M University at Qatar, P.O. Box 23874, Education City, Doha, Qatar

H I G H L I G H T S • • • •

First systematic conceptual design approach for integrated desalination and salt production processes Superstructure representation captures large numbers of design alternatives. Structural optimization yields low cost design options. Results highlight the benefits of integrated designs towards lower water production costs.

a r t i c l e

i n f o

Article history: Received 19 June 2016 Received in revised form 8 September 2016 Accepted 8 September 2016 Available online xxxx

a b s t r a c t The development of desalination processes that are coupled with simultaneous salt production opportunities are increasingly receiving attention by the scientific community. This work is the first to propose a superstructurebased optimization approach that enables a systematic identification of high performance designs for such systems. The approach considers hybrid seawater reverse osmosis (SWRO) and nanofiltration (NF) membrane desalination together with salt production processes (SPPs). The proposed mathematical formulation has been developed based on a membrane superstructure, which mainly consists of SWRO, NF, and SPP as its primary synthesis units. The various connectivity options between synthesis units has also been explored in this work. For instance, SWRO and NF membranes follow slightly different connectivity patterns due to NF membrane's lower rejections for monovalent ions. The objective function identifies the minimum cost network embedded in the superstructure. The proposed method is illustrated with an example involving SWRO and NF membrane units as well as two different SPP options. The example highlights potential savings in water production cost as a consequence of salt value extraction. It further illustrates the benefits of integrated design of membrane desalination systems coupled with salt production processes over sequential designs of desalination processes followed by end-of-pipe salt production. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Membrane-based desalination processes using seawater reverse osmosis (SWRO) technology have become the most widely applied. Many alternatives exist for SWRO membrane unit configurations or networks which need to be explored in design. Over the past decades, a number of superstructure optimization methods have been proposed to support the systematic identification of optimal SWRO membrane networks. A superstructure representation consists of all possible connections between SWRO units, from which the best performing design is extracted subject to process constraints [1]. Since the pioneering work by El-Halwagi [2], many refined approaches have been proposed to ⁎ Corresponding author. E-mail address: [email protected] (P. Linke).

http://dx.doi.org/10.1016/j.desal.2016.09.010 0011-9164/© 2016 Elsevier B.V. All rights reserved.

synthesize membrane desalination networks [1,3–6]. These approaches have long modelled seawater as a two component mixture of water and salt (TDS). Recent work has overcome this major limitation and considered water quality in detail by accounting for major ions present in seawater [7], which was then followed by additional efforts that enable the selection of different RO membrane types [8]. Besides the constant drive to reduce cost of desalinated water, an emerging concern with seawater desalination is the potentially negative impact on the marine environment from brine discharges [9]. Several brine treatment processes such as technologies with improved water recovery and technologies for the production of mineral salts from brines have been proposed to achieve reductions in brine discharge [10]. Salts that could be produced from brines can have considerable value. An initial analysis that considers the major ions contained in seawater has shown that the theoretical value of salts that could be

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produced per m3 of seawater can amount to about 20 times the cost of one cubic meter of desalinated water (see Supplementary information). The technologies that have been considered for the production of different salts from desalination brines include crystallization or softening using chemicals such as lime and soda ash [10,11]. The performance of a salt production process depends on feed composition. While significant emphasis has been placed on researching salt production processes and designing desalination plants, the integration of the two processing tasks has received comparatively little attention. Unlike in the case of SWRO desalination processes, there exists no superstructure-based optimal design approach for such systems. Conventionally, salt production processes are placed downstream, yielding a process configuration consisting of a desalination plant with end-of pipe treatment to produce salts [12]. In contrast, the salt production processes may be more tightly integrated with the SWRO membrane network design to enable the routing of intermediate water quality streams to the salt production processes, which may enable better extraction of value. This work is a first attempt to the development of a superstructure representation for integrated membrane desalination and salt production systems. The work also addresses a current gap in membrane desalination networks synthesis by enabling the optimization of hybrid superstructures containing both SWRO and nanofiltration (NF) membrane units. While SWRO membranes have very high rejections for all ions, NF membranes offer higher rejections for bivalent ions over monovalent ions. The inclusion of NF modules provides additional control over the concentration of the different ions in intermediate streams that may be routed to salt production processing steps. The objective of this work is to develop a superstructure based optimization approach for hybrid SWRO-NF membrane and SPP systems. The following section presents the proposed superstructure approach in detail, followed by an illustrative case study. 2. Synthesis units and superstructure The proposed approach is based on superstructure networks that embed the possible combinations of membranes and salt production processes as a basis for optimization. It builds upon earlier work on SWRO membrane network synthesis [1,7]. The superstructures are constructed from basic building blocks termed ‘synthesis units’ as described below. 2.1. SWRO and NF synthesis units The work adopts the SWRO synthesis unit from Alnouri and Linke [7]. A SWRO unit receives a pressurized feed stream from a mixer and produces two product streams, a lean (permeate stream) and a concentrate stream. Each product stream is associated with a splitter. A SWRO synthesis unit contains SWRO elements and is modelled based on data available from commercial membrane element simulators [13]. Hence, the performance of commercially available membranes may be captured while enabling design optimization [7]. The NF synthesis unit is structured and modelled following the SWRO synthesis unit. The difference between the two units is the membrane performance in terms of flux and ion rejection. Both NF and SWRO synthesis units with feed mixers and product stream splitters are shown in Fig. 1. 2.2. Salt production process (SPP) synthesis unit A salt production process receives a saline feed stream and converts it into salt, in addition to 3 different forms of water streams: (1) purified water, (2) brine reject, and (3) water losses. Additionally, desired salt streams may involve heat, power and salt inputs, e.g. for softening. The SPP unit is conceptually represented using a single-input multiple-output model as shown in Fig. 1. In this work, we consider that one SPP unit produces only one salt. Future work may consider processes that co-produce multiple salts.

2.3. Superstructure connectivity A superstructure includes all possible connections amongst the synthesis units present in the superstructure. In this work, we follow the work by Alnouri and Linke [1] and construct a ‘lean’ superstructure, so as to allow the elimination of underperforming connectivity options beforehand. The lean SWRO-NF-SPP superstructure connectivity has been carried out as follows: - Feed connectivity: seawater feed connects to all SWRO and NF synthesis units, as well as the network product water mixer (as a bypass stream). Seawater feed is not allowed into the network brine mixer product, to prevent any unused pretreated feed from being discarded. - SWRO permeate connectivity: a permeate stream leaving a SWRO synthesis unit may be connected based on the same criteria provided by Alnouri and Linke [7]. However, this type of stream is not allowed into an SPP synthesis unit, due to the low concentration of ions. - SWRO brine connectivity: a concentrate stream leaving a SWRO synthesis unit may be connected to all other SWRO units in the network, to the network brine mixer, and to all SPP units. High salinity RO brine is not connected to the same RO membrane feed and the product water mixer to avoid increasing the concentration of the low salinity feed and product water respectively. - NF permeate connectivity: a permeate stream leaving an NF synthesis unit is connected to all SWRO, NF and SPP synthesis units, the product water mixer and the network brine mixer. Since the overall salt rejection of NF membranes is not as high as RO membranes [14], NF permeate streams of higher salt concentrations than product water quality that are not required for further desalination or salt extraction, can be sent to the network brine mixer. As in the case of SWRO, NF permeate streams are not connected to the feed mixer of same NF unit. - NF brine connectivity: a concentrate stream leaving an NF synthesis unit is connected to all SWRO, NF and SPP synthesis units, and the network brine mixer. NF brine streams are also not connected to the feed mixer of same NF unit, due to the same reasoning that was provided for SWRO unit connectivity. - SPP connectivity: the composition of outlet streams from SPPs depends on the specific performance of the specific SPP. In the general case, all outlet streams from an SPP synthesis unit are connected to all other SPP units, SWRO and NF units, the product water mixer and the network brine mixer.

An example of a superstructure consisting of four membranes, two SWRO, two NF and two SPP synthesis units is illustrated in Fig. 2. 3. Optimization model The mathematical formulation of the problem described above is based on the following sets: I {i = 1,2, …, Ni| I is a set of ionic species in a water stream} J {j = 1,2, …, Nm| J is a set of membrane units in the superstructure} S {s = 1,2, …, Ns| S is a set of SPPs in the superstructure} KS {k = 1,2, …, Nk| K is a set of salts fed to SPP ‘s’} The superstructure contains synthesis unit building blocks as described above. Splitters and mixers are used to connect the streams between these three units. Splitters divide and distribute streams to different destinations while mixers receive and mix streams from different splitters to produce one exit stream [1]. Splitters are associated with the seawater feed, every membrane and SPP outlet stream. Mixers are associated with the feed streams of every membrane, SPP, and network outlet streams (such as product water, network brine and lost water). The lost water outlet mixer receives streams of evaporated water from

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27

Fig. 1. The three synthesis units of the superstructure: RO NF membranes and SPP.

any SPP. The following sections describe the problem formulation in terms of the objective function used, as well as the mathematical models behind the three building blocks in the network.

minimize the total annualized cost (TAC) of the network, and is given by Eq. (1) below: TAC ¼ TCISPP þ TCI Membrane þ TOC SPP þ TOC Membrane

ð1Þ

3.1. Objective function The optimization determines the minimum cost network design (including membrane units and SPPs) for a given feed water and product water quality, while accounting for any added product revenue obtained from produced salt. Hence, the objective function aims to

where TOC is the the total annual operating cost and TCI is the total annualized capital investment. Indices ‘SPP’ and ‘Membrane’ refer to salt production and the membrane network respectively. The determination of the capital and operating costs of the membrane network and SPPs is case-study specific and can be determined as a function of the

Fig. 2. Superstructure consisting of 2 RO, 2 NF membranes and 2 SPPs.

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Table 1 Membrane unit and connection type selection equations. NF RO NF ∈ [0, 1] yRO j + yj = 1 ∀ j ∈ J , yj , yj FEED−RO PRO−RO yRO ¼ y ¼ y ¼ yPRO−NF ¼ yPRO−PROD ¼ yBRO−RO j j j; j0 j; j0 j; j0 j; j0

Selection of membrane type Selection of RO membrane connections

(21) (22)

¼ yBRO−NF ¼ yBRO−BRINE ¼ yBRO−S ¼ yPNF−RO ¼ yPRO−RO j; j0 j; j0 j; j0 j0 ; j j0 ; j ¼ yBNF−RO ¼ yBRO−RO ¼ yS−RO s; j j0 ; j j0 ; j

0

∀ j; j ∈ J; j≠j0 ; s∈S

FEED−NF ¼ yPNF−RO ¼ yPNF−NF ¼ yPNF−PROD ¼ yBNF−RO yNF j ¼ yj j; j0 j; j0 j; j0 j; j0

Selection of NF membrane connections

(23)

¼ yBNF−NF ¼ yBNF−BRINE ¼ yBNF−S ¼ yPNF−NF ¼ yPRO−NF j; j0 j; j0 j; j0 j0 ; j j0 ; j ¼ yBNF−NF ¼ yBRO−NF ¼ yS−NF ¼ yPNF−S s; j j;s j0 ; j j0 ; j

system variables that apply to that process. The case study section provides detailed cost functions that were utilized in this work. The total annual operating cost of the SPP includes revenues from salt sales and may result in negative costs (profit). The total water production of the network is a constraint, so that total annualized cost is directly related to specific cost of water. SWRO and NF units have one input and two output streams. FjF −RO is RO P − RO . Fj the flowrate of the inlet stream of ionic concentrations XFj ,− i and FjB−RO are the permeate and brine flowrates of ionic concentrations and XB−RO respectively as shown in Fig. 1. Similarly, the NF input XP−RO j ,i j ,i . FjP−NF and FjB− stream has a flow FjF−NF, and ionic concentrations XF−NF j,i NF , are the NF permeate and brine flowrates of ionic concentrations XP− j, i NF and XBj , −NF respectively as shown in Fig. 1. The flow and component i balances around a SWRO unit ‘j’ are given by F F−RO ¼ F P−RO þ F B−RO j j j

∀j∈J

F F−RO X F−RO ¼ F B−RO X B−RO þ F P−RO X P−RO j j;i j j;i j j;i

ð2Þ ∀j∈J; i∈I

ð3Þ

The flow and component balances around an NF unit ‘j’ are given by F F−NF j

¼

F P−NF j

X F−NF F F−NF j j;i

¼

þ

F B−NF j

∀j∈J

F B−NF X B−NF j j;i

þ

F P−NF X P−NF j j;i

ð4Þ ∀j∈J; i∈I

ð5Þ

The permeate flows of SWRO unit ‘j’ and NF unit ‘j’ are calculated as F−RO F P−RO ¼ RERO j j Fj

∀j∈ J

ð6Þ

F−NF ¼ RENF F P−NF j j Fj

∀j∈J

ð7Þ

NF where RERO j and REj are the recoveries. The permeate compositions are calculated as


 ¼ X i;F−RO 1−γ RO X P−RO i; j i; j j

∀j∈J; i∈I

ð8Þ


 X P−NF ¼ X i;F−NF 1−γ NF i; j i; j j

∀j∈J; i∈I

ð9Þ

0

∀ j; j ∈ J; j≠j0 ; s∈S

NF where γRO i , j and γi , j are the ionic rejections of the membrane in SWRO unit ‘j’ and the NF unit ‘j’ respectively. The recovery and ionic rejections for SWRO and NF membranes can be determined from correlations that are a function of the temperature, pressure or other operating conditions as discussed in [18,19].

3.2. Salt production process A SPP has a single input stream with multiple outlet streams: brine, pure water or evaporated lost water. The input stream has flow FFs − S S and ionic concentrations XFi ,− s . The outlet brine, recovered water and , FS−Re and FS−Lo and ionic concenlost water streams have flows FS−Br s s s S −Br S−Re S−Lo trations Xi ,s , Xi,s and Xi,s respectively. The salt addition and production rates are represented as GKs,k and GN s as shown in Fig. 1. The SPP model determines the flow and composition of all the outlet streams and the amount of salt produced. The water feed to the SPP unit distributes amongst the unit outlet streams as follows: F S−Br ¼ F sF−S βS−Br s s

∀s∈S

ð10Þ

¼ F sF−S βS−Re F S−Re s s

∀s∈S

ð11Þ

¼ F sF−S βS−Lo F S−Lo s s

∀s∈S

ð12Þ

where β represents the fraction of the feed flow that exits the SPP in outlet streams and sums to unity over all three exit streams of an SPP. The ion balance of an SPP involves the ionic inlet flow (ASi , s) from the feed stream and any added salt to the SPP:

Nk

F−S ASi;s ¼ F sF−S X i;s þ k¼1

X

GKs;k δKi;s;k

∀s∈S; i∈I

ð13Þ

where δKi,s,k represents the weight fraction of the ion i in the salt k being added. δKi,s,k is assigned value of 0 for ions that are not part of the added salts. An ion i can leave an SPP unit dissolved in the water exit streams and as solids in the form of produced salts. Parameter δN i , s represents the weight fraction of ion i in the salt being produced in SPP unit s. δN i,s is assigned value of zero for all ions i that do not form part of the

Table 2 Splitter split fraction balances. Splitter

Equation

Feed splitter

Nm Nm FEED−RO FEED−RO FEED−NF FEED−NF FEED−PROD yj þ j¼1 ∑ f j yj þf ¼ 1 ∀ j∈ J j¼1 ∑f j Nm Nm PRO−RO PRO−RO PRO−NF PRO−NF PRO−PROD PRO−PROD y j; j0 þ j0 ¼1 ∑f j; j0 y j; j0 þfj yj j0 ¼1 ∑f j; j0 Nm Nm PNF−RO PNF−RO PNF−NF P−NFNF þj0 ¼1 ∑f j; j0 y j; j0 þ j0 ¼1 ∑f j; j0 y j; j0 0 Ns PNF−PROD PNF−PROD PNF−BRINE PNF−BRINE PNF−S PNF−S þf j yj þfj yj þ s¼1 ∑ f j;s yj ¼ 1 ∀ j; j ∈ J; j≠j0 ; s∈S Nm Nm BRO−RO BRO−RO BRO−NF BRO−NF BRO−BRINE BRO−BRINE y j; j0 þ j0 ¼1 ∑ f j; j0 y j; j0 þfj yj j0 ¼1 ∑f j; j0 Ns Nm Nm BRO−S BRO−S BNF−RO BNF−RO BNF−NF BNF−NF þs¼1 ∑f j;s yj þ j0 ¼1 ∑ f j; j0 y j; j0 þ j0 ¼1 ∑ f j; j0 y j; j0 0 ðBNF−BRINEÞ ðBNF−BRINEÞ ðBNF−SÞ ðBNF−SÞ þf j yj þ f ð j;sÞ yj ¼ 1 ∀ j; j ∈ J; j≠j0 ; s∈S Nm Nm Ns S−RO S−RO S−NF S−S BRINE ys; j þ j¼1 ∑ f s; j yS−NF þ s0 ¼1 ∑ f s;s0 yS−S ¼ 1 ∀ j∈ J; s∈S; s≠s0 j¼1; ∑f s; j s;s0 þ f s s; j

Permeate splitter

Brine splitter

SPP brine splitter

(24) (25)

(26)

(27)

V.M. Chauhan et al. / Desalination 400 (2016) 25–37

29

Table 3 Mixer flow and component balances. Mixer

Equation

RO feed

Nm FEED−RO FEED−RO PRO−RO PRO−RO yj þ j0 ¼1 ∑ F P−RO f j0 ; j y j0 ; j j0 Nm Nm P−NF PNF−RO PNF−RO BRO BRO−RO BRO−RO 0 0 0 0 þj0 ¼1 ∑F j f j ;j y j0 ; j þ j0 ¼1 ∑F j ; j f j ; j y j0 ; j 0 Nm Ns BNF−RO BNF−RO S−RO þj0 ¼1 ∑F B−NF f j0 ; j y j0 ; j þ s¼1 ∑F S−Br f s; j ys;S−RO ∀ j; j ∈ J; j≠j0 ; s∈S s j0 j Nm FEED−RO FEED−RO PRO−RO PRO−RO X i;F−RO ¼ F FEED X FEED fj yj þ j0 ¼1 ∑F P−RO X P−RO f j0 ; j y j0 ; j F F−RO j j i j0 i; j0 Nm Nm P−NF PNF−RO PNF−RO B−RO B−RO BRO−RO BRO−RO 0 0 0 0 0 0 þj0 ¼1 ∑F P−NF X f y þ ∑F X f y 0 0 0 j ¼1 j ;j j ;j j i; j j i; j j ;j j ;j 0 Nm Ns BNF−RO BNF−RO S−RO þj0 ¼1 ∑F B−NF X B−NF f j0 ; j y j0 ; j þ s¼1 ∑F S−Br X S−Br f s; j yS−RO ∀ j; j ∈ J; j≠j0 ; s∈S; i∈I s i;s j0 i; j0 s; j Nm F−NF FEED FEED−NF FEED−NF P−RO PRO−NF PRO−NF ¼F fj yj þ j0 ¼1 ∑F j0 f j0 ; j y j0 ; j Fj Nm Nm PNF−NF PNF−NF BRO−NF BRO−NF þj0 ¼1 ∑F P−NF f j0 ; j y j0 ; j þ j0 ¼1 ∑ F B−RO f j0 ; j y j0 ; j j0 j0 0 Nm Ns BNF−NF BNF−NF S−NF þj0 ¼1 ∑F B−NF f j0 ; j y j0 ; j þ s¼1 ∑ F S−Br f s; j yS−NF ∀ j; j ∈ J; j≠ j0 ; s∈S s j0 s; j

(28)

F jF−RO ¼ F FEED f j

NF feed

(29)

(30)

FEED−NF FEED−NF yj Nm PRO−NF PRO−NF PNF−NF PNF−NF y j0 ; j þ j0 ¼1 ∑F P−NF X P−NF f j0 ; j y j0 ; j j0 i; j0 Nm Nm B−RO B−RO BRO−NF BRO−NF B−NF B−NF BNF−NF BNF−NF þj0 ¼1 ∑F j0 X i; j0 f j0 ; j y j0 ; j þ j0 ¼1 ∑F j0 X i; j0 f j0 ; j y j0 ; j 0 Ns S−NF þs¼1 ∑F S−Br X S−Br f s; j yS−NF ∀ j; j ∈J; j≠j0 ; s∈S; i∈I s i;s s; j Nm FEED−PROD PRO−PROD P−RO PRO−PROD F PROD ¼ F FEED f þ j¼1 ∑ f j Fj yj Nm Ns P−NF PNF−PROD PNF−PROD S−PROD S−Re þj¼1 ∑f j Fj yj þ s¼1 ∑f s Fs j∈ J; s∈S Nm PRO−PROD P−RO P−RO PRO−PROD FEED FEED FEED−PROD ¼ F X f þ ∑f F X i; j y j F PROD X PROD i i j j¼1 j Nm Ns P−NF PNF−PROD PNF−PROD PNF−PROD S−PROD S−Re S−Re þj¼1 ∑f j Fj X i; j yj þ s¼1 ∑f s Fs X i;s ∀ j∈ J; s∈S; i∈I Nm Nm BRO−BRINE B−RO BRO−BRINE BNF−BRINE B−NF BNF−BRINE F BRINE ¼ j¼1 ∑f j Fj yj þ j¼1 ∑ f j Fj yj Nm Ns PNF−BRINE P−NF PNF−BRINE S−BRINE S−Br þj¼1 ∑f j Fj yj þ s¼1 ∑f s Fs ∀ j∈ J; s∈S Nm BRO−BRINE B−RO B−RO BRO−BRINE BRINE BRINE Xi ¼ j¼1 ∑f j Fj X i; j y j F Nm Nm BNF−BRINE B−NF B−NF BNF−BRINE PNF−BRINE P−NF P−NF PNF−BRINE þj¼1 ∑f j Fj X i; j y j þ j¼1 ∑f j Fj X i; j y j Ns S−BRINE S−Br S−Br þs¼1 ∑f s Fs X i;s ∀ j∈ J; s∈S; i∈I Nm Nm BRO−S B−RO BRO−S PNF−S P−NF PNF−S Fj y j;s þ j¼1 ∑ f j;s Fj y j;s F sF−S ¼ j¼1 ∑f j;s 0 Nm Ns BNF−S B−NF BNF−S S−S þj¼1 ∑f j;s Fj y j;s þ s¼1 ∑ f s;s0 F S−Br ∀ j∈ J; s; s ∈S; s≠s0 s Nm Nm BRO−S B−RO B−RO BRO−S PNF−S P−NF P−NF PNF−S F−S ¼ j¼1 ∑f j;s Fj X i; j y j;s þ j¼1 ∑ f j;s Fj X i; j y j;s F sF−S X i;s 0 Nm Ns BNF−S B−NF B−NF BNF−S S−S S−Br þj¼1 ∑f j;s Fj X i; j y j;s þ s0 ¼1 ∑ f s;s0 F S−Br X ∀i∈I; j∈ J; s; s ∈S; s≠s0 s i;s Ns LOST S−Lo ¼ s¼1 ∑F s s∈S F Ns F LOST X LOST ¼ s¼1 ∑F sS−Lo X S−Lo ∀s∈S; i∈I s

(31)

F F−NF X i;F−NF ¼ F FEED X FEED fj j j i Nm

þj0 ¼1 ∑F P−RO X P−RO f j0 ; j j0 i; j0

Product water

Final brine

SPP feed

Lost water

produced salts m, i.e. those ions leave dissolved in the water exit streams and the ion balance becomes: S−Re S−Re S−Lo −FsS−Re Xi;s −FsS−Lo Xi;s ¼0 ASi;s −FsS−Br Xi;s

(33)

(34)

(35)

(36)

(37)

(38) (39)

its solubility limits the maximum amount of salt that can be produced, according to.

∀s∈S; i∈I : δNi;s ¼ 0 ð14Þ

(32)

GNs

  0; min ! Bi;s ≤0   Bi;s ¼ > min N ; min Bi;s N0 : δi;s 8 > <

∀s∈S; i∈I : δNi;s N0

For those ions i that form part of the produced salt, the ion balance becomes:

where

S−Lo S−Br ASi;s −GNs δNi;s −F S−Re X S−Re −F S−Lo X i;s −F S−Br X i;s ¼0 s i;s s s

X S−Br; − F S−Re X S−Re −F S−Lo X S−Lo Bi;s ¼ ASi;s −F S−Br s s i;s s i;s i;s

∀s∈S; i∈I : δNi;s N0

ð16Þ

∀s∈S; i∈I

ð17Þ

ð15Þ and the brine stream to leave the SPP unit is assumed to be saturated: The amount of salt produced in SPP unit s is determined based in the limiting ion, which is present in the least amount in the SPP relative to

¼ SSs MW i X S−Br; i;s

∀s∈S; i∈I

ð18Þ

MWi refers to the ionic molecular weight and SSs is the solubility limit for salt in SPP unit s. Any negative value for Bi,s indicates insufficient ions for salt production.

Table 4 Case study seawater compositions.

3.3. Superstructure network

Formulation notation

Ion

Concentration (mg/L)

1 2 3 4 5 6 7 8 Total dissolved solids (TDS)

Ca Na Cl Mg K SO4 HCO3 CO3

400 10,556 18,980 1262 380 2649 140 0 34,367

Each membrane unit placed into the network can either be a RO membrane or a NF membrane. Binary variables (y) are used in the formulation to select each membrane type. Each membrane unit j is NF assigned two binary variables (yRO j and yj ). Eq. (21) in Table 1 ensures that either RO or NF is assigned as the membrane type for membrane j. Each stream in the superstructure that is connected to a membrane unit has a binary (y) associated with it. Once the membrane unit type binaand yNF ries (yRO j j ) have been selected, Eqs. (22) and (23) in Table 1

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V.M. Chauhan et al. / Desalination 400 (2016) 25–37

1.2

1 K

Rejection

0.8

Na Mg

0.6

Ca 0.4

HCO3 Cl

0.2

SO4

0 0

5

10

15

20

25

30

35

40

Feed TDS (g/L) Fig. 3. Change in ionic rejections with feed concentration for NF270 using ROSA.

ensure that the connection binaries for that membrane type have the same membrane unit type binary value. In addition to the synthesis unit models there are balance equations for the superstructure network. These are formulated using a similar approach from previous work on SWRO superstructure formulation that performs mass balances around every splitter and mixer present in the superstructure [7]. The superstructure has four types of splitters for seawater feed, membrane permeate, membrane brine and SPP outlet streams. Constraints for the splitters are shown by Eqs. (24)–(27) in Table 2 and ensure that stream split fractions f sum up to unity. The superstructure consists of five types of mixing nodes for membrane synthesis unit feed, network brine, product water, lost water and SPP synthesis unit feed. The membrane feed mixer can be for either a RO or a NF membrane depending on the membrane type. Flow and component balances around each mixer are given by Eqs. (28)–(39) in Table 3. Eq. (19) determines the TDS concentration of the seawater feed stream by summing up the component concentrations in the stream. Similarly, the TDS concentration of all the streams in the superstructure is determined by using a similar equation where the component concentrations are added to determine the TDS of the stream. Nc

∀i∈I X FEED ¼ i¼1 ∑X FEED i

ð19Þ

In the membrane network, constraints on the concentration and flow of the product water stream, feed pressure of the membranes and the number of modules in each membrane unit are enforced. In the SPP formulation, technology specific constraints can be enforced. The equations that determine the initial and final pressures of all the streams and the work associated with pumps and energy recovery devices (ERD) were obtained from Alnouri and Linke [7] and are presented in the Supplementary information. The superstructure optimization model minimizes the total cost of the desalination system subject to system constraints, consisting mostly of mass balances around the synthesis units, splitters and mixers. This model has been adopted from previous work by Alnouri and Linke on Table 5 Linear fit equations for ionic rejections as a function of feed concentration. Ion

Notation

Ca Na Cl Mg K SO4 HCO3

γNF 1 ,j γNF 2 ,j γNF 3 ,j γNF 4 ,j γNF 5 ,j γNF 6 ,j γNF 7 ,j

−0.0084 XF−NF + 0.989 j −0.0098 XF−NF + 0.7303 j −0.0102 XF−NF + 0.7641 j F−NF −0.0076 Xj + 0.9913 F−NF −0.0105 Xj + 0.7781 F−NF −0.0004 Xj + 0.9938 −0.0073 XF−NF + 0.8801 j

SWRO desalination network synthesis [1,7,8], and was extended in this work by accounting for salt production opportunities. The overall formulation mentioned in this section is a Mixed Integer Non Linear Program (MINLP), which aims to minimize Eq. (1), subject to the constraints given by Eqs. (21)–(39). The continuous variables of the formulation include the seawater feed flow, stream split fractions and membrane recoveries. The non-continuous variables are the membrane type binaries. Further variables can be assigned within the SPP model formulation. 4. Case study The proposed approach has been illustrated using a case study that aims to explore the design of a desalination plant with a specified production capacity of 100,000 m3/day. Due to membrane cleaning constraints [15], ten parallel desalination trains have been utilized. The superstructure consisted of three membrane units and two SPPs. The composition of the typical seawater feed used in the case study is given in Table 4 [7]. All additional details for membrane and SPP modelling that pertain to this case study have been described in the following sections. 4.1. SWRO membrane modelling The modelling and costing of RO membranes has been adopted from the work of Alnouri and Linke [7]. This case study utilizes Dow's FilmTec SW30 membrane. Eqs. (43)–(48) in Table A-6 have been adopted from previous work to model RO membrane performance [7] and are provided in the Supplementary information. 4.2. NF membrane performance modelling This case study considers Dow's FilmTec NF270, due to its higher rejections of divalent ions compared to monovalent ions [16]. This more selective separation performance of NF membranes could aid in the channeling of selective ions to certain SPPs in the superstructure. Unlike RO membrane rejections, NF rejections vary considerably with feed pressure, temperature, concentration and membrane recovery [17]. A constant high feed pressure of 30 bar was selected since at higher pressures, higher rejections for divalent ions are obtained, guaranteeing the separation of divalent ions from the feed stream [17]. Since ionic rejections for NF membranes are constant for low and intermediate recovery values [18,19], a maximum recovery constraint of 65% was employed for the NF modelling. Furthermore, a constant temperature of 25 °C was assumed during membrane operation. Thus, an NF membrane model function of only the total feed concentration was developed. This model was developed using Dow's ROSA design software [13].

V.M. Chauhan et al. / Desalination 400 (2016) 25–37

31

Table 6 Equations used to determine number of modules in NF270 membrane. Total number of NF membrane modules (per system stage/pass)

NMNF j ¼

4.3. SPP 1 – CaCO3 production The purpose of SPP-1 is to produce calcite (CaCO3) through soda ash (Na2CO3) softening. The softening is assumed to take place in a solids contact clarifier [20]. The removal of calcium ions through Na2CO3 softening of desalination brines has been suggested in literature [21–23]. A simplified representation of SPP-1 is shown in Fig. 4. The soda ash softening reaction is [23]. Ca2þ þ Na2 CO3 →CaCO3ðsÞ þ 2Naþ Using the above equation, a stoichiometric production of CaCO3 was assumed. Since the SPP-1 brine outlet can be sent to the membrane network which operates at a constant pH of 8.1, the effect of the softening process on the pH change of the outlet stream had to be investigated. To do this, the pH effect of the softening on the most monovalent ion rich stream and the most divalent ion rich stream that can be sent to the SPP was determined. The most monovalent ion rich stream from the membrane network is the permeate stream from a NF membrane which treats the permeate stream from another NF membrane. Similarly, the most divalent ion rich stream is the brine stream from a NF membrane which treats the brine stream from another NF membrane. Only two NF membranes are considered for the derivation of these ‘double NF permeate’ and ‘double NF brine’ streams since three NF membranes in a three membrane unit superstructure cannot achieve high product water purity limits. The concentrations of these two ‘extreme case’ streams were calculated by using the ionic concentrations relative to the chloride concentration and assuming minimum NF rejections, a maximum water recovery within the unit, and a maximum total concentration of 98.2 g/L. The reasoning behind these assumptions is presented in the supplementary information. The relative and final concentrations of the ‘double NF permeate’ and ‘double NF brine’ streams are shown in Table 7. The PHREEQC chemical reactions equilibrium software has been used to simulate the softening reactions for the two streams utilizing the high salinity Pitzer model [24]. The final pH for the double-NF brine and double-NF permeate streams were 8.31 and 8.56 respectively. The PHREEQC results showed that 100% pure calcite can be expected with a b0.5 increase in pH for both the streams. Since the membrane

298:6

(40)

∀ j∈ J ∀j∈J

(41)

network was assumed to function at a constant pH of 8.1, HCl was modelled to be added to the precipitator effluent to reduce the pH to 8.1. Using PHREEQC, this HCl addition was determined to be minimal and a conservative estimate of 0.01 mol/L of HCl addition was used. Furthermore, high conversions of soda ash were noticed. For SPP-1, Eqs. (10)–(18) are included with the input data given in Table 8. 4.4. SPP 2 - NaCl production The purpose of this SPP is to produce sodium chloride (NaCl) in two steps. Initially, a solar evaporation pond evaporates water until salt saturation, i.e. just before precipitation would occur. The pond is modelled to operate on a continuous basis. Then, processing continues in a vapor recompression evaporative crystallizer. In the crystallizer, the feed is evaporated to produce salt and concentrated exit brine. The evaporated water is condensed in the heat exchanger of the crystallizer and sent to the product water mixer due to its high purity. Such a configuration to treat desalination brines has been commonly used in zero liquid discharge (ZLD) schemes [12] [25] where a Multiple-effect Distillation (MED) process is used to evaporate the water before sending it to the crystallizer. In this work, a solar pond is used to avoid the high costs of MED operation. Such use of solar ponds to concentrate brine before salt removal has been proposed in several publications [26] [22] [27]. A conceptual SPP-2 flow scheme is shown in Fig. 5. Since an evaporation pond has been used to enable the removal of water up until the onset of precipitation for commonly occurring salts in seawater brine - mainly NaCl and CaCO3, the necessary solubility parameters have been obtained using the ‘double NF permeate’ and ‘double NF brine’ streams. The obtained CaCO3 and NaCl The most monovalent ionities at precipitation onset for the Double NF-Brine stream were 9.77 10−4 mol/L and 4.79 mol/L respectively. For the double NF-Permeate streams, these values were 1.30 10− 3 mol/L and 5.63 mol/L respectively. Low solubility of salts leads to their earlier precipitation in the pond and hence larger evaporation in the crystallizer. Since the operating and capital costs of the crystallizer are larger than those of the pond, low salt solubility increases the overall costs of the salt production process. Therefore, the minimum values of 9.77 10−4 and 4.79 mol/L were chosen as conservative assumptions for CaCO3 and NaCl solubilities respectively. Similarly, PHREEQC was again used to obtain the change in NaCl solubility with the fraction of the feed water removed (1 − βS2− Br) for the ‘double NF permeate’ and ‘double NF brine’ streams. The simulation results are shown in the Supplementary information. A high NaCl solubility means that less NaCl precipitates in the crystallizer, thus decreasing the efficiency of the SPP. Hence the higher solubility curve was chosen as a conservative Table 7 Relative and final concentrations of model double-permeate and double-brine streams. Relative concentrations

Ca Mg Na K SO4 HCO3 Cl Fig. 4. SPP-1 flow diagram.

NF j

F P PfNF j = Ls(ΔPm − (πj − πj ))

NF membrane permeate flux

Using the ionic relative concentrations of typical seawater, compositions of feed streams with TDS ranging from 1000 to 40,000 mg/L were modelled and used to develop the NF270 model. Fig. 3 presents the change in ionic rejections with feed concentration obtained from ROSA. Linear regression fits were performed for all the ions and the resulting fit equations which are used in the model are shown in Table 5. Furthermore, it was assumed that the NF permeate and brine streams have approximately the same pH as the membrane feed [16]. Table 6 presents the NF membrane model equations that determine the permeate flux and number of NF membrane modules.

F jF−NF 3:6 Pf

Final concentrations

Typical seawater

Double NF-brine

Double NF-permeate

Double NF-brine

Double NF-permeate

0.0211 0.0665 0.5562 0.0200 0.1396 0.0074 1

0.0366 0.1219 0.5384 0.0204 0.4107 0.0116 1

0.0069 0.0182 0.5805 0.0195 0.0002 0.0032 1 Total

1681.81 5594.52 24,716.07 935.94 18,853.57 531.06 45,907.03 98,220.00

414.68 1099.31 35,012.81 1178.00 11.35 193.93 60,309.92 98,220.00

32

V.M. Chauhan et al. / Desalination 400 (2016) 25–37 Table 8 Input model parameters for SPP-1.

Table 9 Input model parameters for SPP-2.

Sets

Value

Sets

Value

S K Parameters SS1 GK1 ,1 GK1 ,2 δKi,1, 1 δKi,1, 2 δN i,1 βS−Br 1 S−Re β1 βS−Lo 1

1 2

S K Parameters SS2 δN i,2 XSi,2−Re S −Lo Xi,2 β2S−Br βS−Re 2 βS−Lo 2

2 0

0.3 GN 1 1.06 0.001 FF1−S 36450 [0, 0.434, 0, 0, 0, 0, 0, 0.566] [0, 0, 0.972, 0, 0, 0, 0, 0] [0.4, 0, 0, 0, 0, 0, 0, 0.6] 1 0 0

assumption. Further information regarding solubility predictions for SPP-2 has been provided in the Supplementary information. The precipitation onset solubility of CaCO3 (SCaCO3′) and of NaCl (SNaCl′) were used to determine the fraction of the feed flow that is evaporated in the pond (βS2−Lo) through the following expression.

βS−Lo 2

! F−S0 F−S0 X 1;2 X 2;2 0; min 1− b0 ; 1− SCaCO30 SNaCl0 ! ¼ 0 0! 0 F−S F−S F−S F−S0 > X 1;2 X 2;2 X 1;2 X 2;2 > > > ; min 1− ≥0 ; 1− ; 1− : min 1− SCaCO30 SNaCl0 SCaCO30 SNaCl0 8 > > > > <

ð20Þ X F−S0

X F−S0

CaCO3

NaCl

In the above equation, 1− S 1;2 0 and 1− S 2;2 0 represent the fraction of feed that needs to be evaporated before CaCO3 and NaCl precipitation take place respectively. Since the pond evaporation is stopped before the precipitation of any salt, the minimum of the two fractions is selected. According to the above equation, if the solution is supersaturated beX F−S0

X F−S0

CaCO3

NaCl

fore entering the SPP, the value minð1− S 1;2 0 ; 1− S 2;2 0 Þ will be negative and hence no evaporation occurs in the pond and the stream is sent directly to the crystallizer. The total fraction of water that is removed as lost and recovered water in the SPP (1− βS2−Br) is assigned as a variable which is solved for by the solver. For SPP-2, Eqs. (10)–(18) are solved using the input set values and parameters shown in Table 9. The capital cost of SPP-1 is the cost of the solid contact clarifier. The operating costs for SPP-1 are the cost of purchasing soda ash and selling the produced calcite. The capital cost of SPP-2 is the sum of the land cost of the evaporation pond and capital cost of the crystallizer. The operating costs for SPP-1 are the electrical cost of the crystallizer and selling the produced NaCl. In literature, the costs associated with solid-liquid separation and salt drying in cost analysis for such salt production systems are not accounted for [12,21,26]. Thus, for this case study it was assumed that these processes do not significantly affect the overall cost of the SPP. A Lang factor of 5 is used to determine the total capital investment for the equipment used [28]. The fixed operating cost of maintenance and operation is assumed to be 20% of the operating cost of the crystallizer [28]. The cost equations for SPP-1 and SPP-2 are shown in Table 10. The numbers in brackets in Table 10 represent

(−21.3115 (1 − βS−Br )2 + 24.7568 (1 − βS2−Br) − 1.909)1000 2 [0, 0.393, 0.607, 0, 0, 0, 0, 0] [0, 7.87, 12.13, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0] Variable 1 −βS−Br − βS2−Lo 2 Eq. (22)

conversion in units. The values of the cost parameters (α) are given in Table 11. Table A-8 outlines the values for all case study parameters, and is presented in the Supplementary information. 4.5. Implementation and cases studied The cost of the membrane network was determined using the equations developed by Alnouri and Linke [7] and they are presented in the Supplementary information. The three membrane module superstructure with the two SPPs is shown in Fig. 6. The case study formulation was implemented on a MS Excel 2013 interface with solver What'sBest! 9.0 by LINDO systems and run on a laptop with an Intel Core i7-4500U processor with 1.80 GHz, 8 GB RAM and 64-bit operating system. The case study is solved to determine three cases for comparison: • Case 1: The design of a desalination system without salt production to yield a reference cost of desalinated water ($/m3). This is achieved by optimizing a membrane network of three membrane units considering SWRO and NF membranes in each unit. • Case 2: The design of a sequential base case design with downstream salt production to yield a reference water price with a discount from salt monetization. This is achieved by processing the brine from the optimal Case 1 desalination design downstream in the available SPPs. • Case 3: The integrated design of desalination system with salt production to yield the minimum possible water price after salt monetization. This is achieved by optimizing the full superstructure consisting of three membrane units and both SPPs.

4.6. Case 1 results The optimal design of the no salt production base case consists of two membrane units, one SWRO and one NF (Fig. 7). The entire feed is sent to the SWRO unit, from which the brine is sent to the network brine mixer. A major fraction of the SWRO permeate is sent to the product water mixer. A portion of the SWRO permeate is sent for further desalination to the NF membrane. The permeate from the NF membrane is sent to the product water mixer and the NF brine is recycled to the SWRO unit. Table 13 presents a cost breakdown in terms of capital and operating costs. The water production cost of the optimal design is 0.58 $/m3 of desalinated water.

Fig. 5. SPP-2 flow diagram.

V.M. Chauhan et al. / Desalination 400 (2016) 25–37

33

Table 10 Cost equations for salt production processes. CCSPP−1 = αcr FF1−S (86.4) OCNa2CO3 = GM 1 ,1(0.031536) αNa2CO3 OCHCl = GM 1 ,2(0.031536) αHCl OCCaCO3 = −GN 1 ,1(0.031536) αCaCO3 OCSPP−1 = OCNa2CO3 + OCCaCO3 + OCHCl

Capital cost of clarifier in SPP-1 Cost of soda ash Cost of HCl Revenue from calcite sale Total operating costs for SPP-1 Capital cost of evaporation pond

αp F 2F−S dp ð3600Þ α er (3.6) CCcrys = αC FF−S 2 OCcrys = αk αo FF2−S(1 − dp)(31536) N OCNaCl = −G2 ,1(0.031536) αNaCl

CC pond ¼

Capital cost of crystallizer Operating cost of crystallizer Revenue from NaCl sale Total operating costs for SPP-2 Total capital investment for salt production

OCSPP−2 = OCcrys + OCNaCl ðCC

þCC

Þ5þCC

pond TCI SPP ¼ crys SPP−1 L TOCSPP = OCSPP−2 + OCSPP−1 + 0.2 OCcrys

Total operating cost for salt production

4.7. Case 2 results Next, the SWRO-NF base case design shown in Fig. 7 was optimized considering end of pipe (EOP) salt production, i.e. SPPs downstream on the brine from the membrane network. The design exhibits a reduced water cost of 0.47 $/m3, i.e. a 19% saving over Case 1 (desalination without salt production). The cost breakdown in terms of capital and operating costs for this optimized case is outlined in Table 14. The percent differences between the total cost of the EOP treatment and the cost from the superstructure optimization are also provided in Table 14.

4.8. Case 3 results The optimization of the superstructure of three membrane units and both SPPs yields the hybrid membrane and salt production network shown in Fig. 8. The design employs two SWRO membranes and one NF membrane. The feed is sent to an NF unit. The resulting NF permeate, which is rich in Na and Cl, is then sent to an SWRO unit. The permeate from this SWRO unit is sent to the product water mixer, while the brine is sent to SPP-1. Thus, this SWRO membrane unit concentrates the monovalent rich NF permeate stream. The divalent rich NF brine stream is sent to another SWRO membrane unit, the permeate of which enters the product water mixer while the retentate (brine) is divided into two fractions. A small fraction is recycled back to the NF unit while the other major fraction is sent to the network brine mixer. The calcium deficient outlet stream from SPP-1 is sent to the feed mixer of SPP-2. Thus, SPP-1 and SPP-2 operate in series. Since evaporation of water costs less in the solar pond than in the crystallizer, SPP-1 reduces the calcium concentration of the feed into SPP-2 and increases the fraction of the water that can be evaporated in the evaporation pond. The outlet streams from SPP-2 are sent to their respective mixers. The compositions of a few key streams in the optimal design are provided in Table 12. The cost breakdown for the optimal hybrid design is provided in Table 13. The water production cost is 0.45 $/m3 of desalinated water. The water cost is reduced by 22% compared to Case 1 and approximately

Table 11 Case study cost parameters. Cost parameter

Value

Source

αcr αCaCO3 αNa2CO3 αer αp αC αk αo αNaCl αHCl

36 $/m3/day feed 62 $/ton 331 $/ton 417 g/m2 h 50 $/m2 33,000 $/m3/h feed 0.05 $/kwh 0.339 kwh/m3 feed 65 $/ton 85 $/ton

[21] [31] [32] [33] [34] [35] [7] [12] [36] [37]

(42) (43) (44) (45) (46) (47) (48) (49) (50) (51) (52) (53)

5% compared to Case 2. The improved performance of the integrated design (Case 3) over the sequential design (Case 2) primarily stems from a decline in the total salt production cost due to better quality streams being channeled to the SPPs in the integrated design as compared to the EOP design. The results illustrate that an integrated approach to design that simultaneously considers membrane desalination and salt production yields designs with enhanced performance.

4.9. Adjusted NF models In the above case study, the NF270 membrane rejections for the different ions were obtained from ROSA, which have been reported to be inaccurate at high concentrations and pressures in recent research contributions [29]. Therefore, we have assessed the implications of experimentally observed rejections on the case study. Ionic rejection data for NF270 at 30 bar for a seawater feed stream (~29 g/L feed) was obtained [16] and compared with the rejection values from ROSA at the same conditions of feed pressure, concentration and rejection. Fig. 9 shows that rejections predicted by ROSA for monovalent ions are higher compared to experimentally observed rejections reported in the literature. On the other hand, rejections obtained from ROSA for divalent ions are lower than those reported in the literature. To estimate the effect of experimentally observed NF rejections on the type of cost optimal network designs obtained, rejection trends were modelled based on literature data for NF270 [30] and used to resolve Cases 2 and 3. Details regarding the NF modelling are given in the Supplementary information. The adjusted NF modelling has a minimal effect on the design and economics of Case 2, the water production cost of which remains at $0.47/m3 of desalinated water. The optimal integrated design for Case 3 is shown in Fig. 10. Table 15 presents the compositions of key streams in the optimal design. A comparison of the stream data from Table 12 with those from Table 15 shows that using more accurate NF models led to a reduction in the calcium concentration in the feed stream to SPP-1, which reduced softening costs. Furthermore, an increase in the concentrations of sodium and chloride into SPP-1 was also obtained. This increased the efficiency of SPP-2 since the major product of this SPP is NaCl. These economic improvements are observed from the total annualized costs, and the cost breakdown, reported in Table 16. The production cost decreased from 0.45 $/m3 to 0.39 $/m3, as compared to the results obtained with rejections from ROSA earlier, i.e. water cost is reduced by 33% compared to Case 1 (desalination only) and by 17% compared to Case 2 (desalination with EOP salt production). In other words, the results developed considering experimentally observed NF270 rejections result in significant underperformance of the conventional, sequential design (Case 2) compared to the integrated design (Case 3) that can be systematically identified using the novel superstructure optimization approach proposed in this work. Table 16 compares the new optimized costs for Case 3 with those for Case 2 (EOP salt production).

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V.M. Chauhan et al. / Desalination 400 (2016) 25–37

Fig. 6. Case study superstructure.

5. Concluding remarks The salts that can be produced from desalination brines represent significant value compared to the cost of desalinated water. The development of efficient integrated designs that coproduce desalinated water and salts requires the coordinated exploitation of interactions between desalination and salt production processing steps. This work is the first effort to introduce a systematic, superstructure based approach that can screen through vast numbers of combinations of membrane desalination units (SWRO and NF) and salt production processes (SPPs). The approach makes use of a representation of three types of synthesis units (SWRO, NF and SPP) that are systematically interconnected in superstructure networks. The superstructure network synthesis problem is developed into an MINLP optimization formulation that can systematically identify low cost designs. The proposed methodology has been demonstrated in a case study. A superstructure of three membrane-units and two common salt production processes (CaCO3 and NaCl) has been optimized. Salt monetization in the integrated design has resulted in significant reductions of water production costs of up to 33% when compared to the base case of desalination without salt production. The integrated designs identified by the approach consistently outperform sequential designs with end-of-pipe salt production, which highlights the need to simultaneously consider desalination and salt production in design.

The paper has detailed the superstructure optimization based conceptual design approach and illustrated its use on the basis of a case study developed from data and information available in the open literature. In process design, especially of novel processes and configurations as is the case in integrated desalination and salt production systems, experimental validation of process performance is essential. We foresee a coordinated use of the proposed conceptual design approach and experimental campaigns to achieve validated, high-performance designs. A significant benefit of the proposed approach is that design alternatives can be quickly explored and assessed in relation to times involved in experimental design validation studies and that sensitivities of design performance with respect to model parameters established. This allows coordination and focus of experimental validation efforts in terms of operating conditions of each processing step to be validated as well as identification of those parameters that govern overall design performance on which experimental validation should focus to quickly reduce uncertainties with targeted efforts. There are many other directions for future work in this emerging research area of integrated desalination with salt value extraction. This includes the development of models for alternative salt production processes, in particular for the various other salts that are of higher value than the two salts CaCO3 and NaCl considered in the case study. Furthermore, more accurate NF rejection models are required given their significant economic design impacts. Future experimental work

Fig. 7. Optimized design of base case for typical seawater.

V.M. Chauhan et al. / Desalination 400 (2016) 25–37

35

Fig. 8. Optimized design with salt production for typical seawater.

should aim at higher accuracy rejection data for NF membranes that more accurately predict membrane performance at high pressures and high feed concentrations. Nomenclature f split fraction at a splitter node F mass flow rate of stream (kg/s) X TDS in a stream (mg/L) y binary variable used to decide the existence of a membrane type P pressure (bar) PI initial pressure of a connection (bar) PF final pressure of a connection (bar) H hydraulic head of a connection γ rejection of ions by membrane NM number of module RE membrane recovery L plant lifetime (years) TAC total annualized costs TCI total capital investment DCC direct capital c SC soft costs CC capital costs TOC total operating costs VOC variable operating costs FOC fixed operating costs OC operating and maintenance costs

PWPumps power required for all the pumps in the membrane network (kW) PWERDs power made by all the ERDs in the membrane network (kW) T temperature (°C) NS number of skids A ionic feed flow into a SPP (mg/s) β fraction of SPP feed that is distributed to SPP outlet streams δ ionic mass fraction in salt being added or produced salt addition rate (mg/s) GKs,k salt production rate (mg/s) GN s fraction of SPP-2 feed that is converted to lost and recovered dt water fraction of SPP-2 feed that is lost as evaporated water dp SPP-2 feed concentration of calcium (mol/L) XF−S′ 1,2 SPP-2 feed concentration of sodium (mol/L) XF−S′ 2,2 precipitation onset solubility of CaCO3 (mol/L) SCaCO3′ precipitation onset solubility of NaCl (mol/L) SNaCl′ NF membrane permeate flux (m/s) PfjNF solution permeability (m/s·bar) Ls applied pressure difference in membrane ΔPm osmotic pressure of feed πFj osmotic pressure of permeate πPj ΔP pressure drop in membrane maximum RO membrane feed pressure PF−RO,MAX j maximum NF membrane feed pressure PF−NF,MAX j XPROD,MAX maximum TDS of product water maximum ionic concentration of product water XPROD,MAX i

Table 12 Summary of key stream compositions in optimized design. Typical seawater Ions

K Na Mg Ca CO3 HCO3 SO4 Cl TDS

SPP-1 feed SPP-2 feed Network (mg/L) (mg/L) permeate (mg/L)

Post treatment permeate (mg/L)

Brine (mg/L)

1090.33 31,424.74 1812.82 635.02 0.00 262.87 288.65 54,945.65 90,460.10

6.50 137.38 10.00 30.00 57.82 2.53 7.70 248.06 500.00

1610.47 33,938.78 5403.56 1330.65 0.00 593.46 11,344.31 63,191.54 117,412.77

1090.33 32,141.22 1812.82 12.00 0.00 262.87 288.65 54,981.12 90,553.55

6.50 137.38 4.00 1.28 0.00 2.53 7.70 248.06 407.45

Table 13 Cost breakdown of base case and optimized designs along with product water discount due to optimization approach. Typical seawater

Membranes Total cost ($/m3) Desal operating ($/m3) Desal capital ($/m3) SPP operating ($/m3) SPP capital ($/m3) Salt revenue ($/m3)

Only desalination

Desalination with SPP

RO-NF 0.58 0.45 0.12 – – –

RO-RO-NF 0.45 0.51 0.12 0.14 0.24 0.56

% water discount 21.98

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V.M. Chauhan et al. / Desalination 400 (2016) 25–37

Table 14 Cost breakdown and comparison between typical brine treatment and hybrid membrane optimization approaches. Typical seawater

Table 16 Cost breakdown and comparison between typical brine treatment and hybrid membrane optimization approach using approximate NF model from literature. Typical seawater

Membranes Total cost ($/m3) Desal operating ($/m3) Desal capital ($/m3) SPP operating ($/m3) SPP capital ($/m3) Salt revenue ($/m3)

EOP salt production

Optimized salt production

RO-NF 0.47 0.43 0.12 0.15 0.25 0.48

RO-RO-NF 0.45 0.51 0.12 0.14 0.24 0.56

% difference

4.56 −17.02 −4.99 4.55 4.55 17.26

NM RO−MAX maximum number of modules in RO membrane unit j minimum number of modules in RO membrane unit NM RO−MIN j maximum number of modules in NF membrane unit NM NF−MAX j minimum number of modules in NF membrane unit NM NF−MIN j AðπÞ j RO membrane permeability temperature correction factor in RO membrane for memTCFj brane permeability fouling factor for RO membrane FFj average pressure drop for RO membrane ΔPfc,j C log mean concentrate side to feed concentration ratio in RO ðCfcf Þ j membrane FEED-RO superscript denoting the feed splitter to RO feed connection FEED-NF superscript denoting the feed splitter to NF feed connection FEED-PROD superscript denoting the feed splitter to NF feed connection PRO-RO superscript denoting the RO permeate to RO feed connection PRO-NF superscript denoting the RO permeate to NF feed connection PRO-PROD superscript denoting the RO permeate to product water connection BRO-RO superscript denoting the RO brine to RO feed connection BRO-NF superscript denoting the RO brine to NF feed connection BRO-BRINE superscript denoting the RO brine to network brine connection BRO-S superscript denoting the RO brine to SPP feed connection PNF-PROD superscript denoting the NF permeate to product water connection PNF-RO superscript denoting the NF permeate to RO feed connection PNF-NF superscript denoting the NF permeate to NF feed connection PNF-S superscript denoting the NF permeate to SPP feed connection BNF-RO superscript denoting the NF brine to RO feed connection BNF-NF superscript denoting the NF brine to NF feed connection BNF-BRINE superscript denoting the NF brine to network brine connection BNF-S superscript denoting the NF brine to SPP feed connection S-RO superscript denoting the SPP brine to RO feed connection

Membranes Total cost ($/m3) Desal operating ($/m3) Desal capital ($/m3) SPP operating ($/m3) SPP capital ($/m3) Salt revenue ($/m3)

S-NF S-PROD S-BRINE S-LOST S-S F-RO P-RO B-RO F-NF P-NF B-NF F-S S-Br S-Lo S-Re PROD FEED j j,j’ j,s s s,j s,s' i k

EOP salt production

Optimized salt production

RO-NF 0.47 0.43 0.12 0.15 0.25 0.48

RO-RO-NF 0.39 0.48 0.12 0.15 0.26 0.62

% difference

16.08 −12.03 −5.52 −1.85 −1.85 29.56

superscript denoting the SPP brine to NF feed connection superscript denoting the SPP recovered water to product water connection superscript denoting the SPP brine to network brine connection superscript denoting the SPP lost water to network lost water connection superscript denoting the SPP brine to SPP feed connection superscript denoting the RO feed stream superscript denoting the RO permeate stream superscript denoting the RO brine stream superscript denoting the NF feed stream superscript denoting the NF permeate stream superscript denoting the NF brine stream superscript denoting the SPP feed stream superscript denoting the SPP brine stream superscript denoting the SPP lost water stream superscript denoting the SPP recovered water stream superscript denoting the network brine stream superscript denoting the network feed stream subscript denoting membrane unit ‘j’ subscript denoting connection from membrane unit j to ‘j’ subscript denoting connection from membrane unit j to SPP ‘s’ subscript denoting SPP ‘s’ subscript denoting connection from SPP ‘s’ to membrane unit ‘j’ subscript denoting connection from SPP ‘s’ to another SPP ‘s’ subscript denoting ion ‘i’ subscript denoting added salt ‘k’

Acknowledgments This publication was made possible by NPRP grants no. NPRP 41191-2-468 and 7-724-2-269 from the Qatar National Research Fund 1

Table 15 Summary of key stream compositions in optimized design using approximate NF model from literature.

0.9 0.8

Ions

K Na Mg Ca CO3 HCO3 SO4 Cl TDS

SPP-1 feed SPP-2 feed Network (mg/L) (mg/L) permeate (mg/L)

Post treatment permeate (mg/L)

1064.91 29,688.50 752.88 238.54 0.00 432.39 1580.33 58,966.49 92,724.04

6.60 135.36 10.00 30.00 60.77 2.84 6.30 248.13 500.00

1064.91 29,949.03 752.88 12.00 0.00 432.39 1580.33 59,001.95 92,758.03

6.60 135.36 3.00 0.95 0.00 2.84 6.30 248.13 403.18

Brine (mg/L) 1698.13 35,435.68 5702.69 1650.06 0.00 625.00 11,970.23 66,520.05 123,601.86

Rejections

0.7 Typical seawater

0.6 0.5

Literature

0.4

ROSA

0.3 0.2 0.1 0 HCO3

Cl

K

Na

Mg

Ca

SO4

Ion Fig. 9. Comparison of rejection values from ROSA and literature.

V.M. Chauhan et al. / Desalination 400 (2016) 25–37

37

Fig. 10. Optimized design with salt production for typical seawater using approximate NF model from literature.

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