Sustainable operation of membrane distillation for hypersaline applications: Roles of brine salinity, membrane permeability and hydrodynamics

Desalination 445 (2018) 123–137

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

Sustainable operation of membrane distillation for hypersaline applications: Roles of brine salinity, membrane permeability and hydrodynamics Guoqiang Guana, Chenglong Yaoa, Shuaitao Lua, Yanbing Jianga, Hui Yub, Xing Yangc,

T

⁎

a

School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou, 510640, PR China School of Chemical Engineering, Sichuan University, Chengdu, 610060, PR China c Institute for Sustainability and Innovation, College of Engineering and Science, Victoria University, Melbourne 14428, Australia b

G R A P H I C A L A B S T R A C T

A R T I C LE I N FO

A B S T R A C T

Keywords: Direct contact membrane distillation Supersaturation Numerical simulation Solute transport at feed side Concentration polarization

This study aims to explore the role of brine salinity in achieving sustainable operation of membrane distillation (MD), particularly in hypersaline applications where highly concentrated or saturated solutions are treated. Given the state-of-the-art MD modeling work mainly focused on the mass and heat transfer phenomena for dilute systems, our simulation work predicts the trends of permeation flux in direct contact MD (DCMD) with elevated feed concentrations up to saturation, by a newly-developed exponential decay function. Also, a semi-empirical equation of the solute transport coefficient Sherwood number (Sh) is derived as Sh = (α1ωF + α2) Reβ Sc0.33, which for the first time incorporates the influence of feed concentration into the concentration polarization calculation in MD. Numerical analysis on the supersaturation ratio, concentration factor and concentration polarization effect showed that low to modest membrane permeability, reasonably high feed temperature and modest hydrodynamics (500 < Re < 2000) may help to prevent supersaturation and potentially reduce membrane scaling in hypersaline applications.

1. Introduction Desalination is regarded as a promising technology to overcome water scarcity, which has threatened the lives of over one-third of the world's population [1,2]. Accompanied by the dramatic increase in freshwater production in the desalination industry, efficient

⁎

management of the concentrated brine to be disposed of is urgently needed due to the increasingly stringent environmental regulations and the demand for sustainable solutions [3]. Alternatively, the waste brine to be disposed of can be treated as a source of raw materials, of which valuable minerals and solutes can be recovered such as sodium [4], magnesium [5] and lithium [6] salts. The conventional methods for

Corresponding author. E-mail address: [email protected] (X. Yang).

https://doi.org/10.1016/j.desal.2018.07.031 Received 17 February 2018; Received in revised form 17 June 2018; Accepted 30 July 2018 0011-9164/ © 2018 Published by Elsevier B.V.

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model the heat and mass transfer in MD and correlate the interfacial and bulk parameters such as temperature and concentration. However, such models have been questioned due to the prevailing assumption that the membranes matrix was considered as solid metal walls [31,32], i.e. an analogy of MD to traditional heat exchanger, which does not involve mass transfer. In recent years, computational fluid dynamics (CFD) simulation has emerged as a promising alternative to investigate the role of hydrodynamics in MD with coupled mass and heat transfer [33]. Both 2- and 3-dimensional CFD simulation were conducted to explore the influence of MD operating parameters on temperature distribution, temperature polarization effect and thermal efficiency [34,35]. On the contrary, the concentration polarization has been rarely incorporated in these models [36]. Only a few CFD studies examined the feed-side concentration distribution and polarization effect in the flow chamber associated with hydrodynamics [37–39]. However, thus far only dilute brine system (e.g. up to 3.5 wt% NaCl solutions) was investigated. Hence, there is a lack of understanding the hypersaline MD systems in terms of the role of solution concentration in affecting the solute transport across the flow chamber and ultimately the permeation flux, which determines the sustainability of the MD operation in challenging saturated conditions. Therefore, this current simulation work aims to explore for the first time the combined effect of solute transport in the feed-side chamber and transmembrane vapour transfer on sustaining the MD performance when approaching saturation state in brine processing. The investigations of various feed concentrations and operating parameters (i.e., influent temperature and velocity) were conducted via CFD simulations, where the effect of solute transport at the feed side on the membrane permeation flux will be quantified with the proposed semiempirical correlation, which can be used to predict both the flux decay and concentration polarization at given feed concentration. Through sensitive analysis, recommendations for achieving sustainable operation of DCMD are provided to prevent or reduce membrane scaling and wetting.

mineral recovery such as evaporation ponds have the drawbacks of low efficiency, reliance on climate conditions, time consuming and large footprint [7]. In recent years, membrane distillation (MD) has received much attention and is emerging as a promising technology towards zero liquid discharge (ZLD) and resource recovery [8]. In MD, with a piece of hydrophobic and microporous membrane as the physical barrier, water vapour and volatiles spontaneously transfer from the feed side (heated brine) to the permeate side (cooled distillate) driven by the vapour pressure difference. Thus, with distillate continuously collected at the permeate side, the feed-side brine is simultaneously concentrated and can potentially reach saturation. In the past two decades, MD research and commercialization efforts were focused mostly on enhancing the production of fresh water [9]. Recently, solute enrichment of the concentrated brine has gained much attention to serve the dual purpose of solute and water recovery. For example, the concentration of thermal sensitive food streams such as juice and nutrients [10,11] and recovery of valuable volatiles such as ammonia [12] and phenol [13] from industrial waste water. In particular, the development of MD crystallization [14,15] and a membrane crystallizer [16,17] has been dedicated to recovering solid products. This will require MD to deal with highly concentrated solutions under near saturation or supersaturation conditions. Since MD is driven by the vapour pressure difference across the membrane, the interfacial temperature and solute concentration are critical parameters to determine the driving force of transmembrane permeation in thermodynamics. Unlike most MD desalination studies, where the brine concentrations were far below saturation and hence the effect of concentration polarization was often ignored, dramatic flux decline (to essentially zero) was observed in treating highly concentrated or saturated solutions due to scaling formation on the membrane surface and subsequent liquid/solid intrusion into the membrane pores, namely pore wetting [18–20]. In extreme cases, negative flux across the membrane (i.e. from permeate to feed) occurred and was reported in the literature [21]. Thus, to achieve the ultimate goal of sustainable MD performance in resource recovery applications, it is essential to understand the fundamental brine chemistry and flux limiting factors in treating hypersaline solutions with MD crystallization or a membrane crystallizer. The prevention of membrane scaling and wetting in high concentration MD can only be possible if it can be predicted. Therefore, it is critical to obtain a comprehensive description of the temperature and concentration fields in the boundary layer and across the bulk solution. These parameters are also important for controlling the crystalline morphology, habits and crystal size distribution in terms of crystal harvesting [22]. However, either the temperature and concentration profiles are not easily acquired. Both invasive [23] and non-invasive techniques have been utilized in measuring the temperature profiles along the MD module, e.g., nuclear magnetic resonance [24] and thermos-chromatics [25]. On the other hand, there is little available in literature on the experimental measurements of concentration distributions in the feed stream. Besides the experimental efforts, theoretical approaches such as mathematical modeling have been developed to predict the coupled heat and mass transfer across the membrane and within the feed/permeate flow channels [26]. Most of the current models are based on the well-known Dusty-Gas model where the combination of three transport mechanisms was considered, i.e. Knudsen diffusion, Poiseuille and molecular flow [27]. The apparent transfer resistance, which is described as the MD coefficient, can be determined based on the dominant transport mechanisms and the measurable membrane structural parameters such as pore size, porosity and tortuosity [28–30]. Meanwhile, the fluid properties and membrane surface temperatures are needed to evaluate the transmembrane heat and mass transfer by using these models to accurately predict the MD performance including permeation flux and thermal efficiency. Due to the temperature and concentration polarization effects currently the empirical expressions of transfer coefficients were commonly used to

2. Flat-sheet DCMD experiments 2.1. Membranes and materials To investigate the DCMD performance at high concentration applications, three types of membranes were used and compared in various simulation scenarios, as listed in Table 1, i.e. the ePTFE provided by the Ningbo Changqi Porous Membrane Technology Co Ltd. (NBCQ, Zhejiang, China), and the PVDF and PTFE membranes from the Singapore Membrane Technology Centre (SMTC, Nanyang Technological University, Singapore) fabricated using an electrospinning technique [40,41]. The ePTFE membrane was selected as the representative of commercial membranes produced in large scale, which has relatively Table 1 Properties of membranes used in DCMD experiments. Manufacture

Thickness Contact angle Thermal conductivity ⁎ Liquid entry pressure Permeation flux ⁎⁎

ePTFE

PVDF

PTFE

NBCQ

SMTC

SMTC

μm Degree W m−1 K−1

180.0 ± 10.6 132.4 ± 2.8 0.04

107.6 ± 1.8 110.7 ± 1.2 0.22

216.8 ± 6.9 125.8 ± 5.2 0.12

Barg

0.71

2.10

3.88

kg m−2 s−1

2.98 × 10−3

1.43 × 10−3

1.17 × 10−3

Notes ⁎ Calculated as the porosity-weighted summation of the polymer and air's thermal conductivity based on method provided in literature [43]. ⁎⁎ Measured at ωF = 0, TF = 320 K, TP = 298 K, vF = 0.01 m/s and vP = 0.01 m/ s. 124

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Fig. 1. Flat-sheet DCMD experimental system and computational domain of co-current membrane module: (a) picture of DCMD experimental system, (b) process flowsheet of DCMD experimental setup, (c) design sketch of DCMD module and geometric size, and (d) simulation coordinates, computational domain and boundary conditions.

current flow pattern is usually preferred due to the low permeation flux and hence slow concentrating rate, which help to produce large-size solid crystals as observed in conventional crystallization processes [22]. The module has two chambers to separate the feed and permeate streams with the membrane, and each chamber is the same size of 150 (L, length) × 12 (H, height) × 20 (W, width) mm as shown in Fig. 1(c) and (d). The feedstock brine with varied NaCl concentrations (up to 22 wt% NaCl) was stored in the reservoir. The concentration was measured by the on-line conductivity meter (SUNTEX EC-4110-RS, Taiwan, China). After heating to the desired temperature (313.2–353.2 K) using a heating mantle with a magnetic stirrer (Dragon MS-H-Pro+, Beijing, China), the brine was recirculated using a peristaltic pump (Cole-Parmer Masterflex L/S, Iowa, US) at a flowrate range of 11–1100 mL/min. Deionized water was recirculated co-currently at the permeate side of the DCMD module by another peristaltic pump (flowrate 11–1100 mL/min) and cooled to the desired temperature (293.1–313.1 K) by a chiller (Cole-Parmer POLYSTAT 12122–58, Iowa, US). The increase in permeate/distillate mass was measured at set time intervals and recorded with an analytical balance (Minqiao FA2004N, Shanghai, China, rated accuracy of 0.1 mg). The permeation flux of the DCMD system can be calculated by dividing the effective membrane area, m2, into the mass rate of distillate, kg/s.

higher membrane permeability and high porosity of 0.93 [42]. While the PVDF and PTFE nanofiber membranes were recently developed through novel methods targeting at high salinity applications due to their much higher liquid entry pressures (LEPs), with respective porosity values of 0.54 and 0.52 [41]. Having strong association with the membrane properties, the permeation fluxes of various membranes at the same operating conditions were used as indicators to show the differences in membrane characteristics. The analytical grade sodium chloride (NaCl) was purchased from Guangzhou Chemical Reagent Factory (Guangdong, China) and used to prepare synthetic NaCl solutions at varying NaCl mass fractions from 0 (pure water) to 0.22. Water used in the experiments was RO deionized water with a conductivity of 5.2 μS.

2.2. MD performance experiments A flat-sheet DCMD system was designed to conduct experiments to correlate the parameters in CFD model and further verify the simulations. The flowsheet of the DCMD system is as shown in Fig. 1 (a) and (b), which was similar to that in our previous work [44] but in this study a flat-sheet module was used with a co-current flow pattern instead. In the recovery of mineral salts through crystallization, co125

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be found in Fig. A1 of the Appendix A.2. Another term to indicate the single pass concentration effect of the feed brine is the concentration factor (CF), defined as:

All instruments were calibrated to ensure high accuracy. The inlet and outlet temperatures of the feed and permeate were recorded through real-time data acquisition (software NI Labview 2017). Each experimental condition was repeated 3 times to ensure reproducibility. The DCMD experimental results were divided into two groups: one for CFD model correlation and the other for the simulation verification. The detailed experimental settings can be found in Table A1 in the Appendix A.1.

CF =

ωmax ωF

(3)

where ω is the mass fraction of NaCl, and the subscript ‘max’ indicates the maximum concentration at the feed-side stream. The probability of salt precipitation occurring on the membrane surface can be predicted by the supersaturation ratio, which can also be expressed via CF (Eq. (3)), as below:

3. Transport phenomena in DCMD module 3.1. Theoretical assumptions

SSmax =

ωmax ω = F CF ωsat ωsat

(4)

In this work 2-dimensional (2-D) simulations have been conducted to only include the mass and heat transfer in the normal (to the membrane) and flow directions, i.e., in both the feed/permeate bulk flows and across the membrane in DCMD. Thus the simulation results will best represent the transfer characteristics of the middle channel of the module. The following assumptions are made for the simulations:

where the subscript ‘sat’ indicates the saturation at the feed temperature. Accompanying the mass transfer as shown in Eq. (1), the heat flux (JH, W m−2) across the membrane is defined as:

1. The membrane module is considered as a steady-state adiabatic unit in thermodynamic equilibrium state during operation. 2. Non-slip boundary conditions [45] are assumed for both walls and membrane-liquid interfaces. 3. Gravitational effects are ignored and no heterogeneous phase existed in the computational domain. 4. The membrane has uniform properties and theoretically 100% rejection to non-volatile components.

where the subscript of H indicates the heat; the Δh is the latent heat (J kg−1), λm is the thermal conductivity of the membrane (W m−1 K−1), δ is the thickness of the membrane (in unit of m), TW,F and TW,P are respectively the interfacial temperature at the feed and permeate sides (in unit of K). The first term on the right side of Eq. (5) is the latent heat due to evaporation, and the second one is the conductive heat through the membrane, which is considered as heat loss that should be minimized. In MD, due to the variation of membrane surface temperature and concentration along the membrane module, the local JM and JH values may vary accordingly and can be correlated by Eqs. (1) and (5). The integral averaged local JM and JH were obtained from the CFD simulations.

JH = ∆hJM +

3.2. Heat and mass transfer within DCMD module The heat and mass transfer in the DCMD module involve three coupled steps including transmembrane, feed- and permeate-side transport [46]. In this work 2-dimensional (2-D) Cartesian co-ordinate system was established based on the DCMD working principles, as shown in Fig. 1 (d). The feed-side stream was simplified as the aqueous sodium chloride solution; while the distillate water was assumed at the permeate side.

(1)

where J indicates the flux, and subscript of M means the mass; p is the vapour pressure (Pa), correlated by the Reynolds fitting polynomial function [46,47], and the subscripts of w, F and P indicate the membrane surface, feed and permeate side, respectively; C is the membrane distillation coefficient (kg m−2 s−1 Pa−1), which was determined by the membrane structure properties and operating temperature [48,49]. Instead of adopting the existing reciprocal relation to correct the coefficient C with the supersaturation ratio (SS) [4], as JM = C(pF − pP) / SS, an exponential decay function of C to elucidate the concentration effect was proposed as follows,

C = C0 ⎡a ⎢ ⎣

SS exp ⎛ ⎞ − c⎤ ⎥ ⎝ b ⎠ ⎦

(5)

3.2.2. Models for feed-side solute transport The deviations of respective temperature and concentration in the bulk solution and at the membrane surface will cause simultaneous heat and mass transfer through the feed side channel. Commonly, the classical transport formula with the heat and flux boundary condition (i.e., Neumann boundary condition) could be used to solve the temperature and concentration distributions in feed side of MD. However, it's incapable of developing the boundaries containing simultaneous heat and mass fluxes with most solvers including FLUENT. Thus, to obtain reliable solutions in this current CFD study, the feed-side fluid was divided into two parts as the bulk flow and interfacial fluids (adjacent to membrane surfaces). The bulk-flow fluid, which locates in the domain of 0 < x < 150 and y > 0 (Fig. 1(d)), can be expressed by the classic transport equations; the interfacial fluid adjacent to the membrane surface (0 < x < 150 and y = 0) is expressed through the transport formula containing internal sink or source terms of heat and mass transfer. Therefore, the overall transport formula at the feed side can be expressed as the steady-state equations of continuity, motion, energy and species conservation in terms of Einstein summation convention [45], as follows:

3.2.1. Coupled heat and mass transfer across membrane matrix The permeation flux (JM, kg m−2 s−1) of the membrane is defined as:

JM = C (pw,F − pw,P )

λm (Tw,F − Tw,p) δ

∂i (ρvi ) = SM ⎧ ⎪ ∂i (ρvi vj ) = −∂j p + μ∂i ∂i vj ⎨ ∂i (ρvi cp T ) = λ ∂i ∂i T + SH ⎪ ⎩ ∂i (ρvi ω) = ρD ∂i ∂i ω + SM

(2)

where C0 indicates the membrane distillation coefficient for MD with pure water as feed and can be determined by the reported model [49]. The fitting parameters a, b and c can be regressed experimentally as shown in the Section 5 “Results and discussion”. It is noted that Eq. (2) incorporates the effects of both membrane properties (in terms of C0) and feed concentration (in the square brackets of Eq. (2)). This proposed correlation is applicable for brine systems with low to extreme concentrations, i.e., saturation. The detailed parameter regression can

(6)

where the operator ∂i means partial differential in space component i, (i.e., ∂/∂i), i and j variants respectively represent the x and y coordinates in Fig. 1 (d). vi and vj are the velocity components in i and j directions (in m/s), cp and λ are the specific heat (J kg−1 K−1) [50] and thermal conductivity (W m−1 K−1) [51] of the concentrate, respectively; μ and D are the dynamic viscosity (in Pa s) and binary diffusivity (m s−1) of the NaCl-H2O system, respectively [52]; and ω is the mass 126

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fraction of NaCl in the brine; SH (in W m−3) and SM (in kg/s m−3) are the source/sink terms of heat and mass transfer, which are respectively given for the computational domain depicted in Fig. 1 (d) with considering the dimensional consistence between the sink/source term and flux as:

presented in the dimensionless form of the Sherwood number, Sh that is defined as avg.k*H/D, where the characteristic length H is the height of feed-side chamber in Fig.1c. Alternatively, the Sh can be expressed in terms of Reynolds number (Re) and Schmidt number (Sc) as [45],

JH / h for 0 < x < 150, y = 0 SH = ⎧ ⎨ ⎩ 0 for 0 < x < 150, y > 0 −JM/ h for 0 < x < 150, y = 0 SM = ⎧ ⎨ 0 for 0 < x < 150, y > 0 ⎩

Sh = αRe β Sc 0.33,

where the parameters of α and β were found to be 0.66 and 0.5 respectively in DCMD seawater desalination [56]. Their values in high concentrations MD will be derived numerically in later sections. With this correlation of Sh, one will conveniently predict the solute transport with the given influent parameters (known Re and Sc).

(7)

where h (in m) is the chosen grid thickness in the y direction [53]; the x and y variants are the dimensions of the membrane module described in Fig. 1. In the bulk flow (0 < x < 150, y > 0), as shown in Eq. (7), the values of source/sink terms (SH and SM) are zero, so Eq. (6) will become the classical conservation equations of continuity, motion, energy and species [45]. To model the heat and mass transfer induced by water permeation through the membrane, the source/sink terms are applied in in solving the governing equations of the fluid adjacent to the membrane surface (0 < x < 150, y = 0), in the forms of heat and mass input/output JH/h and −JM/h through the interfacial cells as expressed in Eq. (7). Due to the boundary layer effect, the solute concentration at the feed-membrane interface differs from that in the bulk feed solution. This phenomenon is known as concentration polarization, which is likely to reduce the separation performance of the membrane and increase the potential for membrane fouling and scaling [54]. The term concentration polarization coefficient (CPC) is used to describe this phenomenon and expressed as [4,55]:

CPC =

ωw J = exp ⎛⎜ M ⎞⎟ ω ρk ⎝ ⎠

(9)

3.2.3. Models for permeate-side transport The permeate-side transport phenomena are similar to the feed side except for the solute transport. The governing equations listed in Eq. (6) are still valid by ignoring the term of species transfer. Hence, the corresponding source/sink terms of energy and continuity conservation are expressed as:

−JH / h for 0 < x < 150, y = 0 SH = ⎧ ⎨ ⎩ 0 for 0 < x < 150, y < 0 JM/ h for 0 < x < 150, y = 0 SM = ⎧ ⎨ 0 for 0 < x < 150, y < 0 ⎩

(10)

4. CFD simulation The simulation platform used in this work is the commercial CFD software ANSYS FLUENT 17.0. The inlet flowrates, temperatures and concentration of simulated cases can be found in the Table A2 of Appendix A.1. Corresponding to the feed- and permeate-side channels, as shown in Fig. 1(d), CFD simulation was developed in two conjugated domains. Each computational domain contains 14,400 quad-shape meshes in total with an optimized mesh size of 0.5 mm, which were built by using the pre-processing software ANSYS ICEM. The boundary conditions for FLUENT simulation, as indicated in Fig. 1(d), are similar to that in previous work [53]. Based on the theories developed in Section 3, Eqs. (1), (5) and (6) have to be solved simultaneously in an iterative fashion to acquire concentration and temperature profiles in the flow channel and across the membrane. Thus, a computational procedure was developed as shown in the flowchart of Fig. 2, in which 3 iteration steps were involved. In Step 1, a user-defined function (UDF) in FLUENT was developed to identify the adjacent meshes to the liquid-membrane boundary layers, and then another UDF was coded and embedded into FLUENT for acquiring the temperature and concentration profiles of identified meshes in each iteration; In Step 2, with the given MD

(8)

where k is the solute transport coefficient of solute diffusing from the bulk solution to the boundary layer. It can be expressed as k = (JM/ρ) ln−1CPC based on Eq. (8). Clearly, k is an important function revealing the influences of concentration polarization and membrane permeability. Eq. (8) also clearly shows that both the CPC and k will vary with the change of solute concentration. The deviation of CPC and k can be expressed with respect to the dimensionless distance x*, which is defined as x* = x/L where x is the distance along the x direction of the module as indicated in Fig. 1d and L is the length of feed-side chamber in DCMD module as shown in Fig. 1c. To conveniently evaluate the solute transport for the given DCMD module at the known influent parameters, the integral averages of CPC and k were used, namely as avg.CPC and avg.k, respectively. Thus, the averaged CPC and k could be obtained according to the local CPC and k, which are derived from the concentration profiles in the MD module. The averaged k is often

Fig. 2. Computational flowchart for DCMD steady-state CFD simulation of DCMD. 127

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coefficient determined by Eq. (2), the flux is calculated based on Eqs. (1) and (5) in each iteration; In Step 3, the UDFs for source/sink terms of heat and mass transfer were respectively developed as shown in Eqs. (7) and (10), and embedded into the FLUENT build-in solver, where the semi-implicit method for pressure linked equations (SIMPLE) algorithm for pressure–velocity coupling and quadratic upstream interpolation for convective kinetics (QUICK) algorithm for discretization of the conservation equations were used, and the default convergent accuracy was chosen as 1 × 10−4 for solving Eq. (6). After the mass, momentum, heat and species conservation equations (Eq. (6)) were iteratively solved in both flow channels, the flow, temperature and concentration fields could be obtained and updated in each iteration step. Above three steps would be performed interactively until the root-mean-square difference between the new interface temperatures and previous outputs was < 5.0 × 10−4, which reflects the accuracy of the coupling solution. In the simulations, the physiochemical properties of the NaCl-H2O binary solution, such as density, activity coefficient, dynamic viscosity, thermal conductivity, specific heat capacity, saturation concentration, latent heat and vapour pressure, were coded in the corresponding UDFs and these codes can be found in the open-source repository of GitHub.

JM,exp [kg m-2 s-1] 0.002

0.004

0.006

0.008

0.010

330

temperature of feed-side effluent temperature of permeate-side effluent permeation flux

325

0.010

320

Tsim [K]

315 0.006

310 305

0.004

JM,sim [kg m-2 s-1]

0.008

300 0.002

295 290 290

295

300

305

310

315

320

325

330

Texp [K] Fig. 3. Verification of CFD model with experimental measurement in this study (hollow markers, where feed concentration was up to 0.22) and literature data [57] (solid markers).

5. Results and discussion

detailed profiles of temperature and concentration across the bulk and membrane, which will be difficult to obtain experimentally. With the ePTFE membrane employed and using the same operating conditions as described in experimental section, i.e., the feed and permeate inlet temperatures of TF = 320.1 K & TP = 293.0 K, feed and permeate influent velocities of vF = 0.0106 m/s & vP = 0.01 m/s at feed initial concentration of ωF = 0.22, the simulation results are illustrated in Fig. 4. According to the top part of in Fig. 4, due to the existence of thermal boundary layers adjacent to both membrane surfaces (feed and permeate), which are defined as the asymptotic solution of flowing and energy equations between the bulk flow and non-slip wall [59], the surface temperature at the feed side is lower than the bulk flow; while the temperature on the permeate side membrane surface is higher than the bulk. The temperature difference between the bulk flow and interface is about 8 K for the case investigated, which is similar to previous data obtained from the hollow fibre DCMD module [53]. Also, the thickness of the thermal boundary layer grows along the flow direction and expands to about one-fifth of the channel width. Detailed studies on temperature field could be found in the literature [26]. The concentration contribution in the MD module, which has rarely been investigated in the MD literature, is also shown in Fig. 4 as the bottom section. It is noted that no concentration distribution was assumed at the permeate side (distillate) based on the theoretical assumption 5 in the Section 3.1 “Theoretical assumptions”. It was observed that a gradual build-up of concentration boundary layer along the flow direction is observed. With a NaCl mass fraction of 0.22 as the inlet feed concentration, the liquid-membrane interfacial concentration quickly rises to 0.2221 immediately after the entry zone (1/10 of the module length); while the bulk concentration is relatively constant.

5.1. DCMD experiments and model verification As described in the Section 2 “flat-sheet DCMD experiments”, three types of membranes were used in the DCMD experiments. The membrane performance was measured in terms of permeation flux under varying operating conditions of feed inlet temperature and flow velocity. When pure water was used as feed i.e. ωF = 0, and operated at TF = 320 K, TP = 298 K, vF = 0.01 m/s and vP = 0.01 m/s, the measured permeation fluxes are listed in Table 1. Apparently, the ePTFE membrane exhibited the highest flux; while the PTFE membrane showed the lowest. To incorporate the impact of feed concentration on the permeation flux, the MD coefficient C was first obtained based on Eq.(2), where the constants a, b and c were found to be 1.164, 0.4575 and −0.1778, respectively. With the corrected C, the CFD model was further verified using both current DCMD experimental results and literature data. The current results were obtained via testing the ePTFE and PTFE membranes up to 22 wt% synthetic NaCl solution; while literature data was based on the DCMD tests on the PTFE membrane with 1 wt% synthetic NaCl solution [57]. As observed from Fig. 3, where the closer the data points to the diagonal line the higher accuracy of simulation results, the averaged relative errors of feed- (hollow downward triangle ), permeate-side temperature (hollow upward triangle ) and the permeation flux (hollow rectangle ) for this work are 0.14%, 0.19% and 3.23% respectively; while the errors produced by the literature data [57] for the same parameters (solid markers) are 0.16% 0.28%, and 5.22%, respectively. This CFD simulation shows a higher accuracy than the previous work by Aspen flowsheet simulation [58], where the derived 1-D transport model with boundary correlation exhibited averaged 10% derivation from the experimental results.

5.2.2. Profile of concentration polarization coefficient (CPC) The inhomogeneous concentration distribution of the feed-side flow (bottom graph of Fig. 4) is commonly known due to the concentration polarization effect, which is very well studied in pressurized membrane processes such as reverse osmosis. However, it was often assumed to be negligible in previous MD studies due to the minor impact on the vapour pressure at increased salt concentration [60]. Nevertheless, in the case of high concentration or near saturation brine, the slight increase in salt concentration adjacent to the membrane surface could lead to saturation or supersaturation, which may significantly influence the membrane performance associated with surface deposition and solid

5.2. Temperature and concentration polarization in high-concentration DCMD 5.2.1. Temperature and concentration distribution profiles The MD operation with high-concentration feed can possibly lead to regional accumulation of salt solutes on the membrane surface, namely concentration polarization (CP), which may cause performance deterioration associated with serious membrane scaling and wetting. To prevent this from happening, a thorough understanding of the concentration and temperature distributions in the flow chamber is essential. Thus, in this study CFD simulation was employed to acquire 128

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Fig. 4. Temperature and concentration profiles along the flat-sheet DCMD module (shown in Fig.1) with ePTFE membrane, simulated with the process parameters (ωF = 0.22, TF = 320.1 K, TP = 293.0 K, vF = 0.0106 m/s, vP = 0.01 m/s).

length, which is consistent with the length of hydrodynamic entry zone of a vessel [61]. This initial rapid growth of CPC can be explained by the strong solute transport within the entry zone due to the large temperature difference across the membrane, as shown in Fig. 5 (a). In the downstream along the module length, the combined effect of diffusion and convection will improve flow mixing and lead to a gradual decrease in CPC. The distribution curves of the membrane flux JM along the module, as shown in Fig. 5(b), confirms the strong transmembrane flux occurring at the entry zone. It was found that JM is the highest at the module inlet and rapidly decreases within the entry zone, which corresponds to the dramatic rise in the interfacial concentration as shown in Fig. 5(a). Due to the combined heat transfer and boundary layer effect, the transmembrane temperature difference reduces (Fig. 4) along the module length and therefore the permeation flux gradually decreases after the entry zone. It can also be observed in Fig. 5(a) that the overall CPC decreases with increasing feed concentration from 0.03 to 0.27. For instance, the maximal CPC is of 1.023 at NaCl mass fraction of 0.03; while it is only 1.017 for ωF = 0.27. This is due to the lower permeation flux at the higher feed concentration as shown in Fig. 5(b).

intrusion to the membrane pores causing a wetting issue. Hence, the quantification of concentration polarization effect in MD is essential for predicting the membrane behaviour. Fig. 5(a) illustrates the concentration polarization coefficient (CPC. Eq. (8)) as a function of dimensionless module length x⁎, as defined in Section 3.2.2. The membrane simulated was the ePTFE membrane. The CPC profiles at various feed concentration are given at inlet temperatures of TF = 353.2 K and TP = 293.2 K. It is observed that all CPC curves exhibit a similar downward U shape, which shows a dramatic increase initially at the module inlet and then a gradual decline until the module exit. The peaks of all CPC curves coincidently occurred at about 1/10 of effective membrane

5.3. Influence of feed concentration on MD dewatering ability 5.3.1. Variation of concentration factor (CF) Aiming to recover the non-volatiles by MD, it is necessary to further increase the feed-side concentration. The high concentration of feed, however, will lead to a deterioration in MD performance due to the undesirable effects of membrane blockage and wetting, especially in the uneven concentration field along the module length as previously discussed in Fig. 5. The concentration factor (CF, Eq. (3)) is used to evaluate the concentrating capability of MD. The CFs of the three types of membranes in DCMD were calculated based on the simulation results at various feed concentrations. The detailed simulation parameters can be found as Scenarios S1, S2 and S3 in Table A2 of Appendix A.1. The results of CF with respect to ωF are shown in Fig. 6(a). As shown in Fig. 6(a), all the curves of CF vs ωF have shown a similar pattern of monotonic decline. For instance, when using the ePTFE membrane, the CF value at ωF of 0.27 (near saturation) is 1.029, which is 98.8% of that at a typical seawater level concentration of 0.03. It indicates that the increase of feed concentration will reduce the dewatering capability in MD. It was also found that the ePTFE membrane had the highest CF curve; while the PTFE membrane had the lowest curve. This result is consistent with the order of membrane flux presented in Table 1, indicating that the greater dewatering (or enrichment) capability can be achieved using more permeable membranes. As anticipated, the CF value obtained from a single-pass operation is rather insignificant. The CF vs ωF relationship derived from Fig. 6(a) is

Fig. 5. Variation of concentration polarization coefficient CPC (a) and permeation flux JM (b) along the dimensionless module length x⁎ at varying feed concentration from 0 to near saturation (ePTFE membrane; vF = vP = 0.006 m/ s; TF = 353.2 K, TP = 293.15 K). 129

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Fig. 6. (a) Influence of feed concentration on the single-pass concentration factor (CF) for the co-current flat-sheet DCMD with different membranes at varying concentrations (ωF = 0.03–0.27) and operated with constant parameters (ePTFE, PVDF and PTFE membranes, vF = vP = 0.006 m/s, TF = 353.2 K, TP = 293.2 K); (b) an example of estimating the effluent concentration in multi-pass MD using e-PTFE membrane.

helpful in determining the potential CF in a multi-pass or multi-step MD system, where the feed-side effluent of the i-th pass is the influent of the next pass. Fig. 6(b) provides an example of this concept using synthetic NaCl solution and the e-PTFE membrane. With an initial mass fraction of 0.07 with a corresponding CF of 1.040, the MD effluent concentration rises to 0.073 (=1.04 × 0.07) at the exit of the 1st-pass and 0.272 (saturation) after the 38th-pass. Thus, the acquisition of a concentration profile in various scenarios can guide the design of the practical MD system for resource recovery. 5.3.2. Depression of permeation flux In MD, the ability to dewater or concentrate (i.e. CF) is a key indicator towards zero liquid discharge or effective recovery of mineral resources from brines. The dewatering capability is determined by the CF and the magnitude of the permeation flux (JM). Therefore, with the pure water flux JM,0 as the benchmark, in this study, the variation of JM at varying feed concentration is evaluated via a dimensionless parameter, namely relative flux JM⁎ (i.e. JM/JM,0 ≤ 1). While the feed concentration is also expressed as a relative concentration (ωF⁎), which is defined as the ratio of inlet concentration of the feed flow to saturation at the same temperature (i.e. ωF/ωsat ≤ 1). With the influent velocity and temperature at both sides of membrane module kept constant, i.e. vF = vP = 0.006 m/s, TF = 353 K, TP = 293 K (detailed parameter settings in Table A2 of Appendix A.1), the effect of ωF⁎ at varying initial feed concentration on JM⁎ is investigated and plotted in Fig. 7. It is shown that the influent concentration has a negative impact on the permeation flux, i.e. the MD dewatering capability. Other than the vapour pressure depression at increased concentration of feed, due to the decrease of water activity, the flux limiting factors could include the incremental resistance of transmembrane mass transport, indicated by the decrease of C based on Eq. (2). The permeation flux is determined by the transmembrane transport mechanisms and process driving force that is influenced by thermodynamics and solute transport. It was observed that the JM⁎ decreases with ωF⁎ for all types of membranes tested. Based on the data regres-

(

∗ = a exp − sion, an exponential-decay expression, JM

ωF∗ b

+c

Fig. 7. Effect of relative feed concentration ωF⁎ on dimensionless permeation flux JM⁎ for the co-current flat-sheet DCMD with using different membranes.

better predicted for a wide range of operating concentrations and membrane types. 5.4. Solute transport correlation at the feed side in MD As MD is considered as a promising technology for mineral recovery and zero liquid discharge [62], ensuring its ability to work under high concentration and even up to saturation level is critical. To further elaborate on its dewatering ability associated with permeation flux, the feed-side solute transport was investigated at various feed concentrations. The most permeable membrane, i.e. the ePTFE membrane, was used in the simulations.

) was de-

rived to correlate the relationship between JM⁎ and ωF⁎, which is similar to that of the vapour pressure (Antoine equation [27]) and MD coefficient C (Eq. (2)). Although the absolute fluxes of various membranes were significantly different (Table 1), the JM⁎ vs. ωF⁎ fitting curve in Fig. 7 seems capable of predicting the membrane performance at any given feed concentration. The simulation results are all located within the 95% confidence zone of the fitting curve. Thus, the derivation of such a correlation has significant implications for the development of high concentration MD processes, where the flux behaviour can be

5.4.1. Effect of concentration on feed-side solute transport In MD the uneven concentration field at the feed side leads to the mass transfer of solutes between the bulk flow and boundary layer adjacent to the membrane surface, which can be quantified through the dimensionless solute transport coefficient Sh (Eq. (9), i.e., dimensionless form of averaged k). Simulations of the Sh were conducted at varying influent concentrations from 0.03 to 0.27 and two feed flow velocities of 0.006 and 0.06 m/s (as listed in as Scenarios S1 and S4 in Table A2 of Appendix A.1). The results are plotted in Fig. 8 in terms of 130

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Fig. 8. Influence of feed concentration (ωF) on Sherwood number (Sh) of feedside flow at two different influent velocities (ePTFE membrane, TF = 353.2 K, TP = 293.15 K).

Fig. 9. Plot of log(Sh/Sc0.33) and log Re (co-current flat-sheet DCMD with ePTFE membrane, TF = 353.2 K, TP = 293.15 K, vF = vP = 0.08–0.8 m/s, ωF = 0.09–0.27).

log Sh as a function of ωF. It was found, in Fig. 8 that the logarithmic Sh (log10Sh) rises linearly with increasing feed concentration ωF from the seawater NaCl mass fraction of 0.03 to near saturation of 0.27. The slope increment of the linear curve of log10Sh vs ωF is very small, indicating insignificant enhancement in solute transport through the feed side flow. As described in the Section 3.2, k is determined by both ln−1CPC and JM based on Eq. (8). When the influent concentration increases from seawater concentration to near saturation, the feed concentration has a negative effect on JM, i.e. about 70% decrease of JM as shown in Fig. 7, while the ln−1CPC exhibited some 1.5 times increase as shown in Fig. S2 in the Appendix A.3. The decrease of JM offsets the increase of ln−1CPC, so the Sh performs a slight increase with increasing feed concentration, as shown in Fig. 8. On the contrary, the Sh increases by 10-fold as the flow velocity vF increases from 0.006 to 0.06 m/s, indicating the significant effect of hydrodynamics on reducing the thickness of boundary layer and hence mitigating concentration polarization. The enhancement on Sh will eventually lead to improved solute transport coefficient k.

Table 2 Semi-empirical correlation of solute transport coefficient for varied influent concentration. Correlation equation

β

Sh = α Re Sc

Fitting parameters

0.33

α β Adjusted R2

Feed mass fraction of NaCl (ωF) 0.03

0.09

0.15

0.21

0.27

2.2199 0.9403 0.9999

2.2345 0.9945 1.0000

2.4077 0.9952 1.0000

2.6291 0.9960 1.0000

2.9083 0.9967 1.0000

Table 3 Improved semi-empirical correlation of solute transport coefficient with correction of influent mass fraction of NaCl.

5.4.2. Correlation of feed-side solute transport coefficient With ePFTE selected as the model membrane, the averaged k values have been calculated via CFD simulations, where the flow hydrodynamics (i.e. influent velocities at both sides) were varied from 0.08 to 0.80 m/s at varying feed concentrations from 0.09 to 0.27. The investigated range of influent velocity is limited to laminar flow as suggested in a previous study [63], considering the energy consumption and further implementation of the concept towards a high GOR system. The detailed simulation cases are listed as Scenario S5 in Table A2 of Appendix A.1. According to Eq. (9), the Sh/Sc0.33 is plotted against the Re in logarithmic scale, as presented in Fig. 9, where both the Sc and Re are calculated based on the influent properties. A linear relationship is observed in Fig. 9 for all feed concentrations with an adjusted coefficient of determination (adjusted R2) close to unity. The intercept and slope of the linear equations derived from the plots are α and β, respectively, based on Eq. (9), which are listed in Table 2. It was found that at various feed concentrations the slope β for all the plots consistently approached one; while the intercept α varies. Thus, the salt concentration is factored into the expression of Sh through a modified relation of Sh = (α1ωF + α2) Reβ Sc0.33. The α1 and α2 of the correlation are listed in Table 3 as 30.66 and 3.648, respectively, where the solute transport coefficient in terms of Sh has been well correlated with the hydrodynamics (i.e. Re) and fluid properties (i.e. Sc and ωF). This newly proposed semi-empirical correlation of Sh provides a convenient means to calculate the solute transport coefficient k and hence predicts the concentration polarization phenomenon

Correlation equation

Fitting parameters

CI LB#

CI UB#

Sh = (α1ωF + α2) Reβ Sc0.33

α1 α2 β Adjusted R2

27.75 3.266 0.9734

33.58 4.030 1.002

30.66 3.648 0.9878 0.9977

#

CI LB and CI UB respectively mean the lower and upper bound of 95% confidence interval.

and flux behaviour in MD. This offers an operational short cut to avoiding the challenges associated with high concentration MD operation, such as mineral scaling on the membrane and control of interfacial crystallization. 5.5. High-concentration brine processing towards sustainable DCMD operation The operation of MD at high salt concentration or near saturation is extremely challenging [64] due to the potential of salt precipitation at the mouth of membrane pores, which will deteriorate the membrane performance through scaling and subsequent wetting. As investigated previously [65], the operating temperatures and hydrodynamics are the most commonly adjusted parameters for achieving sustainable MD operation. The former is related to the thermal energy utilization in MD; while the latter is important in determining the power consumption [66,67]. 5.5.1. Effect of feed temperature To indicate the degree of brine saturation and potential for solid precipitation, the maximal supersaturation (SSmax, Eq. (4)) was used to correlate the CF and ωsat, both of which are temperature dependent 131

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Fig. 10. Influence of feed temperature on maximal supersaturation SSmax and concentration factor CF (co-current flat-sheet DCMD with PTFE, ePTFE and ωF = 0.27, TP = 293.15 K, PVDF membrane, vF = vP = 0.12 m/s, TF = 313.2–353.2 K).

Fig. 11. Influence of feed side Reynolds number on the local and averaged CPCs along dimensionless membrane length x* (ePTFE membrane, vF = vP = 0.00015–1.2 m/s, TF = 353.2 K, and TP = 293.15 K, ωF = 0.27).

factors. With all other parameters kept constant, the effect of feed side temperature was investigated via testing of three types of membranes at a specified salt concentration of 0.27. The detailed simulation settings are given as Scenarios S6, S7 and S8 in Table A2 of Appendix A.1. The simulation results are presented in terms of SSmax and CF, as shown in Fig. 10. The simulation results show that the CF value grows with increasing feed influent temperature. This is due to the increase of membrane permeation flux at elevated temperatures based on the Antoine equation [27]. On the contrary, the SSmax decreases with rising feed temperature. The reason is that the SSmax is proportional to CF and reversely proportional to ωsat, as shown in Eq. (4). Although increasing the feed temperature promotes the increases of both CF and ωsat, the magnitude of delta CF is smaller than that of ωsat leading to a decreased SSmax. It is also observed in Fig. 10 that the membrane permeability has a rather significant influence on both CF and SSmax, i.e. the most permeable membrane ePTFE shows the highest CF and SSmax curves, followed by the PVDF and then the least permeable PTFE membranes (Table 1). Thus, to achieve sustainable DCMD operation, operating parameters should be carefully designed, such as relatively less permeable membranes and high feed temperature may help prevent supersaturation and reduce solid precipitation occurring within membrane module.

length) suppresses the y-direction species diffusion (vertical to module length) leading to the rising avg. CPC values in the low Re range, as indicated in Fig. 11. As the Re increases further (10 < Re < 500), convection becomes the dominant mass transfer mechanism, which is much more effective than molecular diffusion. Hence, the liquid boundary layer of the concentration field becomes thinner and hence a rapid decline of avg. CPC is observed in the moderate Re range in Fig. 11. As Re continues to increase above 500, the convection-enhanced mixing of bulk flow and stagnant boundary layer adjacent to membrane surface will continue to improve the mass and heat transfer. It will, however, plateau at the maximal effect leading to a much slower increase of avg. CPC over Re. Hence, CFD simulation can visualize and help to identify the most suitable hydrodynamic conditions to sustain the operation of high concentration MD. The key message delivered in Fig. 11 is that, for example, poorly selected flow conditions (i.e. Re of 10 in this study) will lead to severe concentration polarization, which results in unfavourably high salt concentrations on the membrane surface that will likely cause salt precipitation and pore wetting issues. On the other hand, high Re (> 2000) may not be necessary as the mitigation of polarization effect is rather limited but the pumping energy consumption could be too high to justify the benefit. Thus, appropriate hydrodynamic conditions (500 < Re < 2000) is preferred to achieve compromised outcomes while sustaining long-term operation.

5.5.2. Effect of flow velocity Apart from the feed temperature, the velocity is another important operating parameter that can be altered to improve the heat and mass transfer in MD. CFD simulations on the effect of feed-side Re at a feed concentration of 0.27 were conducted. The detailed simulation settings are presented as Scenario S9 in Table S2 of Appendix A.1. The results are shown in Fig. 11 as 3-dimensional (3-d) profiles of CPCs in the laminar flow regime (Re = 1–2000). Through obtaining the velocity distribution in the flow chamber, both local CPC along the dimensionless module length x⁎ and the integral average of CPCs at certain Re, namely avg. CPC, are analysed. It was found that the local CPC curves at various Re exhibit the same U-shape pattern as that in Fig. 5. While the avg. CPC curve exhibited an initial increase at the relatively low Re range (1 < Re < 10), and then a rapid decline at a moderate Re range (10 < Re < 500), and finally a slow decrease at relatively high Re range (500 < Re < 2000). This is because in the case of extremely low Re (1 < Re < 10), the molecular diffusion dominates the mass transfer of solutes and creates a relatively homogenous distribution of concentration in the feed flow. As the velocity increases, the dominant x-direction flow (horizontal to module

6. Conclusions This study explores the role of feed concentration in overcoming the challenges associated with interfacial crystallization and membrane wetting to achieve sustainable MD operation. The main conclusions of this work are drawn as follows: 1) The exponential decay function was derived to predict the decline of MD dewatering capacity at high feed concentration. 2) A new semi-empirical correlation of Sh was proposed to provide a convenient means to calculate the solute transport coefficient in the feed channel of the MD module, and hence predict the concentration polarization phenomenon and transmembrane behaviour. 3) It was identified that relatively less permeable membranes and a selective high feed temperature may help prevent supersaturation and reduce solid precipitation occurring within the membrane module. 4) The optimization of flow hydrodynamics showed that a modest velocity range (500 < Re < 2000) should be chosen based on the 132

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China (21676097 and 91434126), Guangdong Natural Science Foundation (2014A030312007 and 2017A030313075) and Science and Technology Planning Project of Guangzhou, China (201707010314) are greatly appreciated. Xing Yang gratefully acknowledges the Australian Research Council Discovery Project (No. DP170102391).

mitigation of concentration polarization coefficient along the membrane module. Acknowledgement Financial supports from the National Natural Science Foundation of Appendix A. Appendix A.1. Parameter settings for experiments and simulations

The detailed settings for experiments and simulations could be found in Table A1 and Table A2, respectively. For each investigated case, a series number is used to identify the specifications for experiment or simulation. For instance, the scenario number of E3–5 indicates the fifth case of scenario E3, where the PVDF membrane was used to process the feed with NaCl mass fraction of 0.220 at the feed-side influent temperature of 320 K and permeate-side one of 293.0 K. The feed- and permeate-side influent velocities were kept constant at 0.0106 and 0.0101 m/s, respectively in the DCMD experiments. Experimental results in Scenario E1 were used to train the model, i.e., regress the parameters in Eq. (2). The rest experimental results (i.e., scenario E2–4) were used to verify the CFD simulations. Table A1 Preset parameters in flat-sheet DCMD experiments. Scenario # Parameters

Variables Case #

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

E1

E2

E3

E4

Membrane

PVDF

ePTFE

ePTFE

PTFE

ωF TF (K) vF (m/s) TP (K) vP (m/s)

varied 320.0 0.0106 293.0 0.0100

0.000 Varied Varied Varied Varied

Varied 320.0 0.0106 293.0 0.0100

Varied 320.0 0.0106 293.0 0.0101

ωF

TF

TP

vF

vP

ωF

ωF

0.000 0.065 0.124 0.174 0.220

306.0 310.7 313.6 320.0 325.4 320.0 319.9 319.9 319.9 319.9 319.9 319.9 320.0 319.9 319.9 320.0 320.0 320.0 319.9 319.9

293.2 293.2 293.2 293.1 293.7 293.1 298.2 303.1 308.1 313.1 293.1 293.1 293.1 293.1 293.2 293.1 293.1 293.1 293.1 293.1

0.0106 0.0106 0.0106 0.0106 0.0106 0.0106 0.0106 0.0106 0.0106 0.0106 0.0053 0.0079 0.0106 0.0132 0.0159 0.0106 0.0106 0.0106 0.0106 0.0106

0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0050 0.0075 0.0100 0.0125 0.0150

0.000 0.065 0.124

0.000 0.065

Table A2

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Parameters setting for sensitivity analysis by CFD simulation. Scenario # Parameters

Membrane ωF TF (K) vF (m/s) TP (K) vP (m/s)

Variables Case #

Amount of cases

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

S1

S2

S3

S4

S5

S6

S7

S8

S9

ePTFE Varied 353.20 0.006 293.15 0.006

PVDF Varied 353.20 0.006 293.15 0.006

PTFE Varied 353.20 0.006 293.15 0.006

ePTFE Varied 353.20 0.06 293.15 0.06

ePTFE Varied 353.20 Varied 293.15 Varied

ePTFE 0.27 Varied 0.12 293.15 0.12

PVDF 0.27 Varied 0.12 293.15 0.12

PTFE 0.27 Varied 0.12 293.15 0.12

ePTFE 0.27 353.20 Varied 293.15 Varied

ωF

ωF

ωF

ωF

vF = vP

ωF

TF

TF

TF

vF = vP

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27

0.08 0.16 0.24 0.32 0.40 0.48 0.56 0.64 0.72 0.80 0.08 0.16 0.24 0.32 0.40 0.48 0.56 0.64 0.72 0.80 0.08 0.16 0.24 0.32 0.40 0.48 0.56 0.64 0.72 0.80 0.08 0.16 0.24 0.32 0.40 0.48 0.56 0.64 0.72 0.80 0.08 0.16 0.24 0.32 0.40 0.48 0.56 0.64 0.72 0.80

353.2 348.2 343.2 338.2 333.2 328.2 323.2 318.2 313.2

353.2 348.2 343.2 338.2 333.2 328.2 323.2 318.2 313.2

353.2 348.2 343.2 338.2 333.2 328.2 323.2 318.2 313.2

0.00015 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.006 0.008 0.01 0.02 0.04 0.08 0.12 0.16 0.2 0.4 0.6 1.2

10

10

10

10

0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 50

9

9

9

21

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A.2. Regression of membrane distillation coefficient To correlate the parameters in Eq. (2), the measured permeation fluxes (JM) for different supersaturation ratios (SS), i.e., SS = ωF / ωsat(TF), are needed. For the given operating conditions as shown in scenario E1 of Table A1 as an example, the corresponding membrane distillation coefficients (C) can be found to produce the minimal derivation of JM between simulation and experiment. The given influent temperature (TF) and feed concentration (ωF) can also deduce the supersaturation ratio. Hence, the varied C can be obtained for various SS as shown in Fig. A1. After substituted the SSs and corresponding Cs into the exponential decay function, the fitting parameters (a, b and c) of Eq. (2) can be regressed with the least square algorithm. For other membrane, similar procedure could be performed.

Fig. A1. Various permeation flux and corresponding membrane distillation coefficient for different feed concentration (ωF = 0–0.22) at the constant operating conditions as scenario E1 in Table A1 in the co-current flat-sheet DCMD with using PVDF membrane.

A.3. Relationship of concentration polarization coefficient and the feed concentration In scenario E1 (as seen in Table A2), the CPC profiles can be obtained for various feed concentrations (ωF) ranged from 0.03 to 0.27. The integral average of CPC (avg.CPC) can be further calculated and the relationship of the averaged CPC and feed concentration are shown in Fig. A2.

Fig. A2. The relationship of concentration polarization coefficient and the feed concentration for the flat-sheet DCMD with ePTFE membrane in scenario S1 (where vF = vP = 0.006 m/s, TF = 353.15 K, TP = 293.15 K, ωF = 0.03–0.27).

Nomenclature c C CF CPC D h i j

specific heat, J kg−1 K−1 membrane distillation coefficient, kg m−2 Pa−1 s−1 concentration factor concentration polarization coefficient diffusivity, m2 s−1 minimal mesh size, m variant of x or y variant of x or y 135

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k p Re Sc Sh SS T v x y

solute transport coefficient, m/s pressure, Pa Reynolds number Schmidt number Sherwood number supersaturation temperature, K velocity, m x-coordinate, m y-coordinate, m

Greek letters α β γ δ Δh ρ λ μ

fitting parameter of Eq. (9) fitting parameter of Eq. (9) activity coefficient membrane thickness, m latent heat, J kg−1 density, kg m−3 thermal conductivity, J m−1 s−1 dynamic viscosity, Pa s

Subscripts 0 F H H2O i j M max NaCl P sat w

Feed as pure water feed-side heat water component of x- or y-coordinate component of x- or y-coordinate mass maximal sodium chloride permeate-side saturation membrane surface

Abbreviations CFD DCMD MD QUICK SIMPLE UDF

computational fluid dynamics direct contact membrane distillation membrane distillation quadratic upstream interpolation for convective kinetics semi-implicit method for pressure linked equations user defined function

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