Aoyi Luo, Noam Lior, Critical Review of Membrane Distillation Performance

Desalination and Water Treatment 57 (2016) 20093–20140 www.deswater.com September

doi: 10.1080/19443994.2016.1152637

Critical review of membrane distillation performance criteria

Aoyi Luo, Noam Lior* Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA, email: [email protected] (A. Luo), Tel. +1 215 898 4803; Fax: +1 215 573 6334; email: [email protected] (N. Lior) Received 23 November 2015; Accepted 21 January 2016

ABSTRACT

The number of published papers about membrane distillation (MD) has been growing exponentially and many evaluation and performance criteria are used to measure it; but, there is no established tradition or evaluation standard for them. This makes the evaluations difﬁcult to compare, or even incomplete. This paper presents therefore a comprehensive critical review and clariﬁcation of the major evaluation criteria for the MD components and systems, aimed to offer some recommendations for their more uniform usage, provide clearer quantitative goals in research and industrial use, and to facilitate more correct and honest representations and comparisons. General description and models of MD are

presented ﬁrst, followed by criteria used to characterize the membranes, and performance criteria to evaluate the distillate production rate, product quality, energy efﬁciency (including conventional energy performance criteria and exergy performance criteria), transport process, and long-time operation. Since exergy analysis of the process is less known, a detailed example is presented.

Keywords: Membrane distillation; Membrane distillation performance criteria; Water desalination performance criteria; Exergy and energy performance; Transport criteria; Non-equilibrium thermodynamics criteria

1. Introduction means, most commonly by condensation of the vapor at lower temperature (thus creating a lower vapor Membrane distillation (MD) is a thermally driven pressure), by ﬂowing (sweeping) gases/vapors, or by membrane separation process which uses transmem- pulling a vacuum, as described in detail in [1–3]. brane vapor pressure difference, generated by trans- There are four basic types of MD membrane mod- membrane temperature difference, as the driving force ules which differ in the way they condense the vapor for the product vapor generation and ﬂow. The sepa- through the membrane as shown in Fig. 1: (a) direct ration membrane is hydrophobic, which thereby pre- contact membrane distillation (DCMD), where the vents the penetration of liquids but allows vapors to cooling solution is in direct contact with the mem- pass through it. In this process, liquid feed to be trea- brane at the permeate side and (b) air gap membrane ted is heated and placed in contact with one side of distillation (AGMD), where an air gap is interposed the membrane directly. The other side of the mem- between the membrane and a condensation surface (to brane is kept at a lower vapor pressure by various reduce the conductive heat transfer loss), and the vapor is condensed on the condensation surface after *Corresponding author.

various and increasing applications, including water desalination, wastewater treatment, and several in biomedical, food, and fermentation industries [4,6–10]. These promising aspects of MD have fostered increasing R&D and publications addressing membrane materials, configurations and fabrication, transport phenomena, analysis and modeling, membrane scaling and fouling, system heat recovery, module and system design, applications, and long-time operation. Many evaluation and performance criteria are necessary for these studies and projects, some based on fundamental aspects of the process and some on specific applications and needs. Since there is no evaluation standard, the authors often used criteria developed independently, which makes it difficult to effectively compare results, or which may be incomplete for the feature of interest, or, in the worst case, may be misleading both for the fundamental aspects and for use in system design, industrial use, and system representation. The deficiencies are especially in exergy analysis and evaluation of long-term operation. This paper thus presents a comprehensive critical review and clarification of the MD component and system major evaluation criteria, aimed to offer some recommendations for their more uniform usage, to provide clearer quantitative goals in research and industrial use, and Fig. 1. Schematics of the four leading MD configurations. to facilitate more correct and honest representation. This review of commonly used criteria in MD is classified according to their evaluation objects and applica- crossing the air gap, (c) sweeping gas membrane dis- tion level, with discussion about their advantages and tillation (SGMD), where a sweeping gas is used to limitations. drive the vapor out of the membrane module and Brief descriptions of the different fundamental and then condensed outside, (d) vacuum membrane applied aspects of MD are provided, to the extent distillation (VMD), where vacuum is applied in the needed for clarifying the performance criteria. permeate side of the membrane module which carries Detailed explanations of the process can be found in the vapor outside of the membrane module and con- the books and reviews including [2,4,5,9,11]. densed outside. As to the format and style of this review, it is MD promises to have many advantages in compar- aimed both to guide those who are learning about the ison with other desalination processes, including (a) a process, and is therefore somewhat didactic, and to high separation factor of non-volatile solute so that it serve as a reference for the practitioner and is thus can produce high purity distillate, about 30-fold formatted to allow examination of individual higher than RO, (b) mostly uses relatively low temper- performance criteria without having to read the entire ature(currently typ. <90˚C) rather than mechanical paper. power that is of high exergy, cost, and environmental emissions, (c) operation at much lower pressure (around atmospheric (0.1 MPa) or below) when com- 2. MD process and systems description pared with reverse osmosis (RO, conducted at about 2.1. Hydrophobicity of the membrane 2.5–8.5 MPa, increasing with feedwater concentration), (d) low driving temperature that allows use of low- Hydrophobicity of the membrane is an indispens- grade waste heat and/or renewable energy sources ably required feature of MD, since the membrane sus- such as solar and geothermal, (e) less sensitivity to tains the liquid/gas interface and prevents liquid from concentration polarization and fouling than other penetrating it. The pressure difference across the membrane separation processes such as RO [1,4,5], membrane must not exceed its mechanical strength, and (f) high compactness and low weight. It has its compaction that would excessively close the pores, A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20095

2 and the liquid entry pressure (LEP) deﬁned as the of the feed stream (W/(m K)), Tf—temperature of the critical transmembrane pressure difference that mem- feed bulk (K), Tf,m—temperature at the membrane brane hydrophobicity could sustain, where a larger feed-side surface (K). pressure difference will result in solution penetrating Then heat is transferred across the membrane by the membrane as illustrated in Fig. 2. LEP for the conduction and latent heat of evaporation: membrane can to ﬁrst approximation be calculated from the Laplace equations: 00 ¼ D þ ¼ qmem J Hfg hm Tf;m Tp;m Hm Tf;m Tp;m (3)

cos 00 2BcL h 2 LEP ¼ DP ¼ (1) where qmem is heat flux across the membrane (W/m ), inter 2 rmax J—mass flux (kg/(m s)), hm—conduction heat transfer 2 Δ coefficient of the membrane (W/(m K)), Hfg— specific enthalpy of vaporization (J/kg), Tf,m—temper- D where LEP is liquid entry pressure (Pa), Pinter— ature at the membrane feed-side surface (K), Tp,m— pressure difference at the liquid/gas interface (Pa), temperature at the membrane permeate-side surface γ B—geometric factor (dimensionless), L—liquid surface (K), Hm—total heat transfer coefficient of the mem- tension (N/m), θ—membrane/liquid contact angle brane (W/(m2 K)). (˚ or rad), rmax—largest pore radius (m). Here, we define the total heat transfer coefficient B is a factor determined by the geometric structure of the membrane (Hm) which combines the heat trans- of the pore, and for a cylindrical pore, the geometric fer of conduction and evaporation as: factor (B) equals to 1 [5]. 00 JDH þ h T ; T ; ¼ qm ¼ fg m f m p m Hm (4) 2.2. Heat transfer Tf;m Tp;m Tf;m Tp;m In MD, the heat transfer across the membrane has two paths, one is the sensible heat conduction through Then heat is transferred across the permeate stream the membrane material and the gas within the mem- boundary layer: brane pores, and the other is the latent heat of evapo- 00 ¼ ration associated with the mass flux. The sensible heat qp hp Tp;m Tp (5) transferred is regarded as an energy loss because it has negligible contribution to the vapor mass flux. 00 where qp is the heat flux across the permeate stream The heat transfer in MD can be split into stages. In 2 boundary layer (W/m ), hp—convective heat transfer DCMD, the heat first is transferred across the feed coefficient of the permeate stream (W/(m2 K)), stream boundary layer: Tp—temperature of the permeate bulk (K). At steady state, and ignoring heat transfer from 00 ¼ qf hf Tf Tf;m (2) the membrane or module periphery:

00 00 ¼ 00 ¼ 00 ¼ 00 where qf is heat flux across the feed stream boundary qt qf qmem qp (6) 2 layer (W/m ), hf—convective heat transfer coefficient 00 2 where qt is total heat flux (W/m ). The temperature profile in DCMD is thus shown in Fig. 3. According to Eqs. (2)–(6), the total heat flux is calculated by:

00 Tf Tp q ¼ (7) t 1 þ 1 þ 1 hf Hm hp

Considering the heat transfer resistances analog in DCMD, the driving force is the temperature difference Fig. 2. Schematic of the DCMD process with a non-wetting (T − T ). The resistances are the heat transfer resis- membrane (on the left) and a membrane having a wetted f p pore (right). tance of the feed stream (1/hf), the membrane (1/Hm), 20096 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

Fig. 5. The temperature proﬁle in AGMD.

Fig. 3. The temperature proﬁle in DCMD.

and the permeate stream (1/hp) in series, as shown in Fig. 4. For AGMD, additional heat transfer resistances caused by the air gap (Rg), the condensate thin ﬁlm (Rf), and the cooling plate (Rc) are present and the method to calculate their values can be found in [8]. The total heat ﬂux can thus be calculated by:

00 Tf Tp q ¼ (8) t 1 þ 1 þ þ þ þ 1 Rg Rf Rc hf Hm hp Fig. 6. The heat transfer resistance analog in AGMD. where Rg is heat transfer resistance of the air gap 2 ((m K)/W), Rf—heat transfer resistance of the conden- Eq. (6) does not hold and must be developed based on 2 sate thin film ((m K)/W), Rc—heat transfer resistance the specific system configuration. of the cooling plate ((m2 K)/W). The temperature profile in AGMD is shown in Fig. 5 and the heat transfer resistance analog in 2.3. Mass transfer AGMD is shown in Fig. 6. The mass flux (J) across the membrane (the term In SGMD and VMD, the vapor is condensed by an mass flux is used here to denote the flux of the distil- external condenser (Fig. 1), so the heat flux balance of late across a membrane) is generally calculated by: ¼ J Cpf;m pp;m (9)

where C is membrane permeability (kg/(m2 s Pa)), pf,m—apor pressure at the membrane feed-side surface (Pa), pp,m—vapor pressure at the membrane permeate- side surface (Pa). The vapor pressure of the solution can be calculated by:

p ¼ p a (10)

where p is vapor pressure of the solution (Pa), p*—vapor pressure of pure solvent (Pa), a—activity of Fig. 4. The heat transfer resistance analog in DCMD. the solvent (dimensionless). A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20097

σ The activity (a) accounts for the deviations from where kB is Boltzman constant (J/K), —collision ideal behavior of chemical substances in a mixture. It diameter of the molecule (m), T—temperature (K), can be calculated by: P—pressure (Pa). For membranes with pores smaller than the vapor a ¼ cx (11) free path (Kn > 1) where molecule-to-wall collisions dominate and the continuum approach does not hold, the dominant mass transport mechanism is the where γ is activity coefficient (dimensionless), x—mole Knudsen mechanism characterized by: fraction (dimensionless). The value of activity coefficient (γ) can be esti- 1 mated from experimental data or models. The data of 2 ¼ 2 re 8M the activity coefficients of various solutions have been J pf;m pp;m (14) 3 sd pRTmem reported in [12]. The models by Pitzer and co-workers [13,14] were recommended in [14] as the most accu- where r is average pore radius (m), ε—membrane rate for predicting the activity coefficients while many porosity (dimensionless), δ—membrane thickness (m), other simpler models are applicable to some specific τ—membrane tortuosity (dimensionless), M—molecu- conditions and are described in [15–17]. lar weight of vapor (kg/mol), R—ideal gas constant To determine the mass flux, the dusty gas model is (J/(mol K)), Tmem—average temperature in the the most general model for flux through porous media membrane (K). [5]. Three mass transport mechanisms are generally For membranes with pores bigger than the vapor considered in MD [5] and the mass transfer resistance free path (Kn < 0.01) where the continuum approach corresponding to these three mechanisms is shown in holds, two mechanisms may dominate. The ordinary Fig. 7. The mass flux can be decomposed into the sum molecular diffusion model represents the diffusion of of the convection flux and the diffusion flux. The con- the vapor flux through stationary air driven by the vection flux is driven by the total pressure gradient concentration gradient across membrane. This where the mass transfer resistance is represented by mechanism dominates when air is presented in the the viscous flow model. The diffusion flux is driven membrane pores and both sides of the membrane are by the concentration gradient (or the partial pressure kept at same total pressure, and the mass flux can be gradient) where the mass transfer resistance is repre- calculated by: sented by the Knudsen model (which represents the mass transfer resistance due to molecule-to-wall collisions) and/or the ordinary molecular diffusion model ¼ e DM Pmem J pf;m pp;m (15) (which represents the mass transfer resistance due to sd RTmem pair inter-molecule collisions). The general mass transfer resistance analog is where D is diffusion coefficient for vapor (m2/s), shown in Fig. 7, but one or more mass transfer resis- Pmem—average total pressure in the membrane (Pa), tances may be negligible for a specific MD process, pair—average partial pressure of the non-condensable and the Knudsen number (Kn) provides a guideline in gas in the membrane (Pa). determining the relative importance of these mecha- The viscous flow model (Poiseuille flow) represents nisms as described further down. The Knudsen num- the convective flux across the membrane, driven by ber is defined as: the total pressure gradient. This mechanism dominates for the case when one side of membrane has lower k pressure than the other side and air is not present Kn ¼ (12) 2r (degassed process). In this case, the flux can be calculated by: where Kn is Knudsen number (dimensionless), λ— mean free path of vapor (m), r—average pore radius 2 1 r e Mpmem (m). J ¼ P ; P ; (16) 8l sd RT f m p m The mean free path of molecule (λ) is the average mem distance traveled by molecules between collisions and μ can be calculated from kinetic theory [5]: where is viscosity of vapor (Pa s), Pmem—average vapor pressure in the membrane (Pa), Pf,m—total pressure at the membrane feed-side surface (Pa), Pp, kBT k ¼ pffiffiffi (13) m—total pressure at the membrane permeate-side P 2pr2 surface (Pa). 20098 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

When 0.01 < Kn < 1 and both sides of the are the temperature and the chemical potential gradi- membrane are kept at the same total pressure, both ents. The entropy generation rate is used to identify the inter-molecular collisions and molecule-to-wall the forces and fluxes, and can be represented by: collisions cannot be neglected. So the mass transfer mechanism is in the transition region between the Knudsen and the ordinary diffusion mechanism, and _ ¼ 00r 1 1r s qt JT l (20) the mass transfer resistances of both the Knudsen T and the ordinary diffusion mechanism must be _ 3 00 included as shown in Fig. 7 and the mass flux is where s is entropy production rate (W/(K m )), qt — 2 calculated by: total heat flux (W/m ), T—temperature (K), J—mass flux (kg/(m2 s)), μ—chemical potential of the solution 8 "# (J/kg). < 1 1 2 ¼ 2 re 8M Thus the fluxes and forces are: J : 3 sd pRTmem ) (17) 00 1 1 J1 qt and J2 J (21) þ e DM Pmem pf;m pp;m sd RT p air 1 X r and X T 1rl (22) 1 T 2

2.4. Non-equilibrium thermodynamics of the transport Substituting these terms into Eq. (18) yields the fol- process lowing expressions for the 2 fluxes: Non-equilibrium thermodynamics has been applied to membrane separation processes [18] and 00 1 q ¼ L r þ L T 1rl ¼L T 2rT þ L T 1rl MD [19,20]. Following this approach, the Onsager phe- t 11 T 12 11 12 nomenological relations between fluxes and forces in (23) their linear form are: 1 1 2 1 X J ¼ L21r þ L22T rl ¼L21T rT þ L22T rl ¼ T Jj LjkXk (18) k (24) where Jj—fluxes, Ljk—kinetic (phenomenological) where L11 is inverse temperature-driven heat flux coefficients, Xk—driving forces. kinetic coefficient ((K W)/m), L12—chemical potential- The kinetic coefficients satisfy the Onsager driven heat flux kinetic coefficient ((K kg)/(m s)), reciprocal relationships: L21—inverse temperature-driven mass flux kinetic coefficient ((K kg)/(m s)), L22—chemical potential-dri- 2 ¼ ven mass flux kinetic coefficient ((K kg )/(m s J)). Ljk Lkj (19) Knowledge of the imposed driving forces and of the kinetic coefficients thus allows calculations of the In MD, the major fluxes are those of heat (here j =1) fluxes and thus solution of the problem. A procedure and of the solvent (j = 2), and the major driving forces to calculate the latter is outlined below. Using Eqs. (3), (6), and (24):

00 ¼ r þ D qt hm T J Hfg ¼ þ D 2 r D r hm HfgL21T T HfgL22 l (25)

where hm is conduction heat transfer coefﬁcient of the 2 Δ membrane (W/(m K)), Hfg—speciﬁc enthalpy of vaporization (J/kg). Using Eqs. (23) and (25) give: Fig. 7. The mass transfer resistance analog across a L ¼h T2 þ DH L (26) membrane. 11 m fg 21 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20099

¼D As the second step, consider the case in which the L12 HfgL22 (27) mass flux is driven only by the chemical potential gradient, holding the temperature to be the To derive the kinetic coefficient expressions, first same at both sides of the membrane, and Eq. (28) consider the case in which the mass flux is driven leads to: only by the temperature gradient, holding the chemical potential to be same at both sides of the p ; p ; l ; l ; @p membrane. ¼ f m p m p m f m ðÞr J Cd Cd @ lme l lf;m lp;m d l T Using: (32) ¼ J Cpf;m pp;m (28) Eqs. (24) and (32) lead to: 2 where C is membrane permeability (kg/(m s Pa)), pf;m pp;m @p L ¼ CdT CdT ðÞl p —vapor pressure at the membrane feed-side 22 @ me (33) f,m lf;m lp;m l T surface (Pa), pp,m—vapor pressure at the membrane permeate-side surface (Pa). μ where me is mean chemical potential of the solution and assuming here for simplicity that: at both sides of the membrane surface (J/kg). Since Tp;m Tf;m lp;m lf;m rT and rl (29) d d @ ¼ ln af;m l ¼ RvT lf;m lp;m RvT RvT @ af;m ap;m δ ap;m a T ame where is membrane thickness (m), Tf,m—temperature (34) at the membrane feed-side surface (K), Tp,m—tempera- μ ture at the membrane permeate-side surface (K), f,m— ¼ chemical potential of the solution at the membrane pf;m pp;m p af;m ap;m (35) μ feed-side surface (J/kg), p,m—chemical potential of the solution at the membrane permeate-side surface According to Eqs. (33)–(35): (J/kg). p a ; ap;m Cdp a Eqs. (10), (28) and (29) lead to: ¼ d f m me L22 C ln ln (36) Rv af;m ap;m Rv ame p ; p ; ¼ f m p m Tp;m Tf;m where af,m is activity at the membrane feed-side sur- J Cd Tf;m Tp;m d face (dimensionless), ap,m—activity at the membrane @p feed-side surface (dimensionless), Rv—gas constant of d ðÞr C ame @ Tme T (30) vapor (J/(kg K)), calculated by: T l

where ame—mean activity of both sides of the mem- R Rv ¼ (37) brane surface (dimensionless), pf;m—vapor pressure of M pure solvent at the membrane feed-side surface (Pa), pp;m—vapor pressure of pure solvent at the membrane where R is ideal gas constant (J/(mol K)), M—molecu- permeate-side surface (Pa), Tme—mean temperature of lar weight of vapor (kg/mol). both sides of the membrane surface (K). Using Eqs. (27) and (36), lead to: Eqs. (24) and (30) lead to: ¼D p af;m ap;m D Cdp ame L12 HfgCd Hfg p ; p ; @ ln ln ¼ 2 f m p m 2 p ðÞ Rg af;m ap;m Rg L21 CdT ame CdT ame @ Tme (31) Tf;m Tp;m T l (38) 20100 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

From the Clausius–Clapeyron equation: represent the relationship between the given driving forces and the resulting fluxes. 2 @ D ¼ RvT p ðÞ Hfg @ Tme (39) 2.5. Energy analysis p T l While heat is consumed in the coupled mass and Using Eqs. (31), (38), and (39), the Onsager reciprocal heat transfer process across the membrane, and is also relationship yields: lost to the environment, typical practical use includes many other auxiliary energy-consuming units which @p consume not only heat but also electrical energy, such L ¼CdT2a ðÞT ¼ L (40) 12 me @T me 21 as those used for pumping, pre- and post-treatment, l disposal of wastes, instrumentation, control, and plant operations such as lighting, HVAC, security, and such. According to Eqs. (26) and (31): As in all desalination processes, integration of heat recovery is critical for the successful commercial use @ ¼ 2 D p ðÞ 2 of MD and must thus be included in the energy analy- L11 hmT HfgCd @ Tme T (41) T l sis. A simple demonstration of this issue is that the heat required for water evaporation is about 2,400 kJ/ The four kinetic coefficients can be simplified to be kg while the minimal energy required for the separa- expressed as: tion of water from 3.5% salinity seawater is only about 3 kJ/kg [21]. Since the produced vapor must be condensed, the heat of condensation accounts for much of 0 @p L ¼L =T2 ¼ h þ DH Cd ðÞT (42) the huge energy demand difference between these val- 11 11 m fg @T me l ues, and is therefore typically used for preheating the feed solution and thus “recovering” some of the @ 0 ¼ = 2 ¼ p ðÞ invested heat and thereby reducing the heat demand. L21 L21 T Cdame Tme (43)

@ T l Current practice in thermal water desalination processes uses performance ratios (PRs) of about 8 to 30, 0 @l @a ¼ = ¼D d i.e. only 1/30–1/8 of the latent heat must be L12 @ L12 T HfgC p @ (44) c T c T expended. Fig. 8 shows a DCMD system with heat recovery. For a system as Fig. 8 shows and neglect the 0 @l @a energy and mass losses to the environment, the energy ¼ = ¼ d L22 @ L22 T C p @ (45) c T c T balance yields: where c is volumetric molar concentration (mol/m3). _ þ _ þ _ þ _ þ _ ¼ _ þ _ Hin;f Hin;p We;f We;p Qin Hout;f Hout;p (48) Substituting Eqs. (42)–(45) into Eqs. (23) and (24), the two fluxes can thus be expressed as: _ _ where Hin;f is enthalpy of the feed inflow (W), Hin;p— 00 ¼ 0 r þ 0 r _ qt L11 T L12 c (46) enthalpy of the permeate inflow (W), We;f —electrical energy consumption of the feed flow pump (W), 0 0 _ J ¼ L rT þ L rc (47) W ; —electrical energy consumption of the permeate 21 22 e p _ _ flow pump (W), Qin—heat input rate (W), Hout;f —en- 0 _ ; where L11 is temperature-driven heat flux kinetic thalpy of the feed outflow (W), Hout p—enthalpy of the 0 coefficient (W/(m K)), L12—concentration-driven heat permeate outflow (W). 2 0 flux kinetic coefficient ((W m )/mol), L21—tempera- and the mass balance yields ture-driven mass flux kinetic coefficient ((kg K)/(m s)), L0 —concentration-driven mass flux kinetic coefficient 22 _ þ _ ¼ _ þ _ ((kg m2)/(mol s)). min;f min;p mout;f mout;p (49) All the kinetic coefficients can be determined from _ experiments or simulations based on the chosen pro- where min;f is mass inflow rate of the feed solution _ cess conditions. (kg/s), min;p—mass inflow rate of the permeate (kg/s), _ It is noteworthy that the kinetic coefficients are mout;f —mass outflow rate of the feed solution (kg/s), _ also a form of process performance criteria, since they mout;p—mass outflow rate of the permeate (kg/s). A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20101

We now describe the energy and mass balance of input energy is used for a power plant, and the lower the membrane module and the heat exchanger (in grade rejected from the power plant is used to operate dashed-line box of Fig. 8), and implement the typical an MSF or MED desalination plant, thus generating neglect of energy and mass losses to the environment, both power and water [22–26]. The rejected heat can and of mass transfer in the heat exchanger. In the similarly be used to operate an MD plant. Compared membrane module, the heat and mass are transferred with single-purpose power plants, dual purpose across the membrane from the feed stream to the per- plants sacrifice some power generation capacity to the meate stream, thus the energy and mass balance of benefit of water production, and dual-purpose plants the membrane module yield: are typically more economical and have somewhat less negative impact on the environment than separate _ m _ m ¼ _ m _ m ¼ 00 power-only and water-only systems [22]. Fig. 9 shows Hin;f Hout;f Hout;p Hin;p qt A (50) a dual-purpose desalination plant where the MD sys- _ m tem shown in Fig. 8 is coupled with a vapor power where H ; is enthalpy of the feed inflow to the in f _ m system. The two systems are coupled by the con- membrane module (W), H ; —enthalpy of the feed out f _ m denser of the vapor power system where the low outflow from the membrane module (W), H ; — out p grade rejected heat is transferred from the power sys- enthalpy of the permeate outflow from the membrane _ m tem to the MD system. Neglecting the plant’s energy module (W), H ; —enthalpy of the permeate inflow to in p loss to the environment, the energy balance of the MD the membrane module (W), q00—total heat flux across t system is the same as shown in Eq. (48) except that membrane (W/m2), A—membrane area (m2). _ the heat input (Q ) in Eq. (48) is now replaced by the in _ heat exchanged in the condenser (Qe). The energy bal- _ m _ m ¼ _ m _ m ¼ min;f mout;f mout;p min;p JA (51) ance of the vapor power system yields:

m where m_ ; is mass inflow rate of the feed solution to _ _ _ _ in f Q þ W ; ¼ Q þ W ; _ m fuel e w e e t (54) the membrane module (kg/s), mout;f —mass outflow rate of the feed solution from the membrane module _ m (kg/s), mout;p—mass outflow rate of the permeate from _ _ m where Qfuel is heat input rate by the fuel (W), the membrane module (kg/s),min;p—mass inflow rate _ W ; —electrical energy consumption of the water of the permeate to the membrane module (kg/s), e w _ 2 pump (W), Q —heat exchange rate in the condenser J—mass flux (kg/(m s)). _ e The energy and mass balance of the heat exchan- (W), We;t—electrical energy output of the vapor power ger yield: system (W).

_ h _ h ¼ _ h _ h ¼ _ Hin;f Hout;f Hout;p Hin;p Qr (52)

_ h where H ; is enthalpy of the feed inflow to the heat in f _ h exchanger (W), H ; —enthalpy of the feed outflow out f _ h from the heat exchanger (W), H ; —enthalpy of the out p _ h permeate outflow from the heat exchanger (W), Hin;p— enthalpy of the permeate inflow to the heat exchanger _ (W), Qr—heat recovery rate (W).

_ h ¼ _ h _ h ¼ _ h min;f mout;f and mout;p min;p (53)

_ h where min;f is mass inflow rate of the feed solution to _ h the heat exchanger (kg/s), mout;f —mass outflow rate of the feed solution from the heat exchanger (kg/s), _ h mout;p—mass outflow rate of the permeate from the _ h heat exchanger (kg/s), min;p—mass inflow rate of the permeate to the heat exchanger (kg/s). Fig. 8. Schematic of a DCMD system with heat recovery Many of the thermal desalination plants are (dashed lines denote the control volume of the membrane designed as dual-purpose ones, where the high grade module and heat exchanger). 20102 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

system undergoes a process between initial and ﬁnal equilibrium states. Generally, the exergy input and output involved in MD process are exergy of thermal and electrical energy and ﬂow exergy. For exergy of thermal and electrical energy, they can be calculated by: _ ¼ _ T Ethermal Q 1 (56) T0

_ ¼ _ Eelectrical We (57) _ where E is rate of the thermal exergy transferred _ thermal (W), Q—rate of the heat transferred (W), T—tempera- _ ture (K), T —dead state temperature (K), E —rate 0 electrical_ of the electrical exergy transferred (W), We—rate of the electrical energy transferred (W). For flow exergy, since MD can treat various solutions such as sea water, brines with high salinity, wastewater and food solution, a general method to calculate the flow exergy is needed (e.g. [15,27]). The flow exergy can be decomposed into physical exergy (thermal, pressure, velocity, and elevation) and chemical exergy:

Fig. 9. Schematic of a dual purpose desalination plant _ ¼ _ P þ _ C Eflow E E (58) (dashed lines denote the MD system and vapor power plant). _ where Eflow is rate of the ﬂow exergy transferred (W), _ P _ C E —rate of the physical exergy transferred (W), E — The energy balance of the dual-purpose desalina- rate of the chemical exergy transferred (W). tion plant according to Eqs. (48) and (54) thus yields: The physical exergy can be calculated by: _ þ _ þ _ þ _ þ _ þ _ Hin;f Hin;p We;f We;p Qfuel We;w ¼ _ þ _ þ _ 2 Hout;f Hout;p We;t (55) _ P v E ¼ mH_ H T ðÞþs s þ gzðÞ z (59) 0 0 0 2 0

2.6. Exergy analysis where m_ is mass flow rate (kg/s), H—specific As stated in the above discussion about energy enthalpy (J/kg), H0—specific enthalpy at dead state analysis in MD, different qualities of energy (thermal, (J/kg), T0—dead state temperature (K), s—specific mechanical, chemical…) are involved in the MD pro- entropy (J/(K kg)), s0—specific entropy at dead state (J/(K kg)), v—velocity (m/s), g—gravitational accelera- cess but energy analysis (that is by definition based on 2 the first law of thermodynamics) does not distinguish tion (m/s ), z—height (m), z0—dead state height (m). between them. Exergy analysis based on the second With the kinetic and potential exergy neglected, law of thermodynamics taking into account the quality the physical exergy of flow for incompressible fluid of energy provides a more appropriate measure of the treated in MD can be calculated by: effectiveness of the energy use and evaluates the irreversibilities in the process. Exergy is defined as the _ P E ¼ mH_ ½ H T ðÞs s maximal theoretical useful work a system can produce 0 0 0 P P T as it comes into equilibrium with its environment, or ¼ mC_ ðÞþT T 0 C T ln (60) v 0 q p 0 the minimal work that needs to be supplied as a T0 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20103

where Cv is specific heat capacity at constant volume Fig. 10 shows a simple DCMD system. The exergy (J/(K kg)), Cp—specific heat capacity at constant pres- input of this DCMD system includes the flow exergy 3 _ sure (J/(K kg)), ρ—density (kg/m ). of the feed inflow (E ; ) and the permeate inflow _ in f Generally, there is no chemical reaction in MD but (E ; ), the exergy of the electrical energy consumption in p _ only the concentration change of the species during of the feed flow pump (W ; ) and the permeate flow _ e f the MD separation process. So the chemical exergy pump (W ; ) and the exergy of the heat consumption e p _ can be calculated by: of the heater (Qin): X _ C ¼ _ T E mi li li;0 (61) _ ¼ _ þ _ þ _ þ _ þ _ in Einput Ein;f Ein;p We;f We;p Qin 1 (66) i T0

_ where mi is mass flow rate of species i (kg/s), μ μ _ i—specific chemical potential of species i (J/kg), i,0— where E ; is flow exergy of the feed inflow (W), _ in f _ specific chemical potential of species i at dead state Ein;p—flow exergy of the permeate inflow (W), We;f — (J/kg). electrical energy consumption of the feed flow pump _ The difference of chemical potential can be (W), W ; —electrical energy consumption of the per- e p _ evaluated by: meate flow pump (W), Qin—heat input rate (W), Tin— temperature of the heat input (K). ðÞ; ; ; ; ¼ ln ai The exergy output of this DCMD system includes li T0 P0 xi li T0 P0 xi;0 RiT0 (62) _ ai;0 the flow exergy of the feed outflow (E ; ) and the per- _ out f meate outflow (Eout;p): where ai is activity of species i (dimensionless), ai,0—activity of species i at dead state (dimensionless), _ ¼ _ þ _ Eoutput Eout;f Eout;p (67) Ri—gas constant of species i (J/(kg K)), calculated by: _ where Eout;f is flow exergy of the feed outflow (W),

R ¼ _ Ri (63) E ; —flow exergy of the permeate outflow (W). Mi out p The exergy input of the AGMD system shown in Fig. 11 includes the flow exergy of the feed inflow where R is ideal gas constant (J/(mol K)), Mi—molecu- _ _ lar weight of species i (kg/mol). (Ein;f ) and the coolant inflow (Ein;c), exergy of the

Thus the chemical exergy can be calculated by: X _ C _ ai E ¼ miRiT0 ln (64) ; i ai 0

The calculation of the activity is discussed in the pre- vious Section 2.3. The value of the exergy depends on the selection of the dead state (ambient conditions). For general water desalination applications, the dead state is usually chosen as T0 = 25˚C, p0 = 101.325 kPa and solutes mass fraction ws,0 = 0.035 kg/kg. These values will be different depending on conditions such as the speciﬁc geographic location and solute composition. Unlike energy, exergy is not conserved but destroyed in any real process, and the exergy balance yields:

_ ¼ _ _ Edes Einput Eoutput (65)

_ _ where E is exergy input rate (W), E —exergy input _ output Fig. 10. Exergy analysis ﬂow diagram of a simple DCMD output rate (W), Edes—exergy destruction rate (W). system. 20104 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

Fig. 11. Exergy analysis ﬂow diagram of a simple AGMD system.

Fig. 12. Exergy analysis flow diagram of a simple SGMD system. electrical energy consumption of the feed flow pump _ _ (We;f ) and the coolant flow pump (We;c) and the _ exergy of the heat consumption of the heater (Qin). _ ¼ _ þ _ þ _ þ _ þ _ Tin Einput Ein;f Ein;g We;f We;b Qin 1 (70) T0 _ ¼ _ þ _ þ _ þ _ þ _ Tin Einput Ein;f Ein;c We;f We;c Qin 1 (68) T0 _ where E ; is flow exergy of the sweeping gas inflow _ in g (W), W ; —electrical energy consumption of the _ e b where Ein;c is flow exergy of the coolant inflow (W), sweeping gas blower (W). _ We;c—electrical energy consumption of the coolant The exergy output of this SGMD system includes _ flow pump (W). the flow exergy of the feed outflow (E ; ), the sweep- _ out_ f The exergy output of this AGMD system includes ing gas outflow (E ; ), the distillate (E ; ), and the _ out g _out d the flow exergy of the feed outflow (Eout;f ), the coolant exergy of heat output of the condenser (Q ). _ _ out outflow (Eout;c), and the distillate (Eout;d). _ ¼ _ þ _ þ _ þ _ Tout _ ¼ _ þ _ þ _ Eoutput Eout;f Eout;g Eout;d Qout 1 (71) Eoutput Eout;f Eout;c Eout;d (69) T0 _ _ where E ; is flow exergy of the coolant outflow (W), where E ; is flow exergy of the sweeping gas out- _ out c out g_ Eout;d—flow exergy of the distillate (W). flow (W), Qout—heat output rate (W), Tout—tempera- The exergy input of the SGMD system shown in ture of the heat output (K). Fig. 12 includes the flow exergy of the feed inflow The exergy input of the VMD system shown in _ _ (E ; ) and the sweeping gas inflow (E ; ), the exergy Fig. 13 includes the flow exergy of the feed inflow in f in g _ of the electrical energy consumption of the feed (E ; ), the exergy of the electrical energy consumption _ in f _ flow pump (W ; ) and the sweeping gas blower of the feed flow pump (W ; ) and the vacuum pump _ e f _ e f (W ; ), and the exergy of the heat consumption of the (W ; ), and the exergy of the heat consumption of the e b _ e v _ heater (Qin). heater (Qin). A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20105

operations, and of regulated environmental impacts of all, where typically the raise of the first results in a drop of the latter three, design is to be based on opti- mization. Reduction of energy consumption is especially important because of its costs and their sharp fluctuations, because of its significant fraction of the environmental impacts, and of depletion of non-renewable energy resources (only a negligible fraction of distillation is currently done using renewable energy). A comprehensive evaluation of MD should therefore include at least the specific distillate production rate as a function of operating time, the energy efficiency, and the distillate quality. Also, the criteria for evaluating the transport process in MD are often useful to understand the transport process and further improvement of the MD. They can be classified into four levels based on the objects they characterize and evaluate:

(1) The membrane level where the criteria are used to characterize the membrane performance independently of the rest of the system/appa- ratus. These criteria are often used in studies focused on the membrane itself, including membrane fabrication and modiﬁcations. Fig. 13. Exergy analysis ﬂow diagram of a simple VMD (2) The MD membrane module level, where the crite-

system. ria are used to evaluate the performance of the entire MD membrane module, used in membrane module analysis, modeling, design, and improvement. The membrane module is the _ ¼ _ þ _ þ _ þ _ Tin Einput Ein;f We;f We;v Q 1 (72) component in which the entire distillation pro- in T 0 cess takes place, which in addition to the membranes also includes the feed and the distillate _ streams, as well as components on the cold where W ; is the electrical energy consumption of the e v side of the membrane that depend on the vacuum pump (W). specific design, such as an air gap, condensate The exergy output of this VMD system includes _ liquid film, cooling plate and coolant stream in the flow exergy of the feed outflow (E ; ), the distil- _ out f AGMD, sweeping gas in SGMD, vacuum sub- late (E ; ) and the exergy of heat output of the con- out_d system in VMD. A qualitative schematic of the denser (Q ). out temperature profile in a DCMD membrane module is shown in Fig. 3 and of the tempera- _ ¼ _ þ _ þ _ Tout ture profiles in an AGMD membrane module Eoutput Eout;f Eout;d Qout 1 (73) T0 is shown in Fig. 5. (3) The MD system level that in addition to the membrane module also includes other devices 3. Performance criteria necessary for the overall distillation system operation, such as pumps, flow pipes, heat 3.1. Introduction exchangers, condenser, pre- and post- treat- As in all separation and concentration processes, ment devices, where the criteria are used to the ultimate goal in MD is to get maximal production evaluate the performance of the entire MD sys- (here of distillate or concentrated feed solution) rate of tem. These criteria are used in the studies and a product of adequate quality at the lowest lifetime evaluations such as design of multi-effect MD cost. Since the cost is based on the sum of that of capi- system, MD system coupled with other separa- tal investment in the distillation, of energy and tion processes, and MD systems driven by 20106 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

different energy supply system. Schematics of Higher porosity provides more area for evapora- simple MD systems are shown in Figs. 10–13 tion, lower vapor flow resistance, and less volume of and a schematic of a DCMD system with heat the membrane material. Also, the membrane solid recovery is shown in Fig. 8. matrix material has higher thermal conductivity than (4) The MD long-time operation level where the cri- the gas in the pores, so higher membrane porosity teria are used to evaluate the performance of results in smaller portion of the membrane solid MD in long-time operation. These criteria are matrix material which reduce the membrane effective often used in researches focused on scaling, thermal conductivity and transmembrane conduction fouling, and membrane effective life. heat loss as shown in Eqs. (3) and (84). At the same time, higher porosity is associated with higher pore The paper first presents the criteria used to charac- radius and reduces the ability of the membrane to pre- terize the membranes, and then the performance vent liquid phase flow through it (Eq. (1)), so an opti- criteria with respect to the production rate, the pro- mal porosity must be selected. duct quality, the energy efficiency (including conventional energy performance criteria and exergy 3.2.1.2. Membrane thickness (δ) (m). A larger thickness performance criteria), the transport process, and long- leads to a smaller mass flux and smaller heat loss by time operation. conduction, since mass transfer and heat conduction resistance increase with the membrane thickness as discussed in Section 2.3 and is shown in Eq. (84). 3.2. Membrane characteristics Membrane distillation uses hydrophobic mem- 3.2.1.3. Membrane tortuosity (τ) (dimensionless). The ratio brane to create the interface for evaporation, and of the average length of pores to the membrane membrane properties obviously affect the process per- thickness. formance. The performance criteria used to characterize the membrane used in MD are discussed in this lp section. s ¼ (76) d

where τ is membrane tortuosity (dimensionless), 3.2.1. Basic membrane properties δ lp—average length of pores (m), —membrane thick- This subsection lists the basic properties of interest ness (m). in MD. Larger membrane tortuosity means that the vapor flow path is longer, which results in higher mass 3.2.1.1. Membrane porosity (ε) (dimensionless). Defined as transfer resistance, so a membrane with larger mem- the volume of the pores divided by the total volume brane tortuosity has a smaller mass flux as discussed of the membrane. in Section 2.3.

3.2.1.4. Membrane pore size (dp) (m). Increasing the pore Vp e ¼ (74) size raises the mass ﬂux, but also increases the possi- V mem bility of membrane wetting, according to the Eq. (1). In fact, the pores in a single membrane have differ- where ε is membrane porosity (dimensionless), ent sizes, characterized by a size distribution. Several V —volume of the pores (m3), V —total volume of p mem technologies have been applied to determine the mean the membrane (m3). pore size and pore size distribution, including ε can also be determined by the Smolder–Franken Scanning Electron Microscopy (SEM), Atomic Force equation [28]: Microscopy (AFM), wet/dry ﬂow method, and gas permeation test [2] While the calculated permeability q e ¼ 1 mem (75) can be different when using the mean pore size qmat instead of using the pore size distribution [29], Martinez et al. [30] found that the values are similar. ρ where mem is density of the membrane(including the It is also noteworthy that the pore sizes change with 3 ρ pores)(kg/m ), mat—density of the membrane solid operation, due to mechanical and chemical effects, matrix material (kg/m3). temperature changes, and fouling. A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20107

3.2.1.5. Membrane material thermal conductivity (ks) 3.2.2. Liquid entry pressure (LEP) (W/(m2·K)). As shown in Eqs. (3) and (84), membrane The LEP is defined as the critical transmembrane material with lower heat conductivity is desirable pressure difference that membrane hydrophobicity because it results in smaller transmembrane conduc- could sustain before a larger pressure difference will tion heat loss. result in membrane wetting. LEP for the membrane can be approximated from the Laplace equation 3.2.1.6. Membrane/liquid contact angle (θ) (˚ or rad). The shown in the Eq. (1): MD process relies on the hydrophobicity of the membrane and the contact angle is a measure of the cos hydrophobicity. Larger contact angles are preferable 2BcL h LEP ¼ DPinter ¼ (77) to ensure the hydrophobicity and prevent feed solu- rmax tion from entering the pores according the Eq. (1). It should be noted that the contact angle depends on the where LEP is liquid entry pressure (Pa). membrane material and on liquid composition (in- The liquid/membrane contact angle depends not cluding even trace amounts of surfactants) and on the only on the membrane material but also on the operat- operating temperature. ing temperature and liquid composition. The temperature and composition also influence the liquid surface 3.2.1.7. Membrane mechanical strength. Generally, MD tension. A correlation of the surface tension of the sea- operates at around atmospheric pressure (0.1 MPa) or water was reported in [34]: below, so the requirement for mechanical strength is not that high when compared with RO, but sufficient c ¼ 77:09 0:1788T þ 0:0221S (78) strength is still needed to prevent membranes from L compacting or cracking. The mechanical strength can be estimated by tensile strength, Young’s module, and where T is temperature (K), S—salinity (‰). burst pressure. More information about measuring the Valid for 273.15 < T < 313.15 K; 10 < S < 35‰. membrane mechanical properties can be found in [31]. It should also be noted that the LEP changes with

operation time. Foulants usually form on the mem- 3.2.1.8. Membrane chemical stability. It is commonly brane and its hydrophobic surface, and the chemical agreed that in MD the membrane only serves as a composition and surface of the membrane are likely to support of the vapor/liquid interface and is not change, all resulting in a lower contact angle and LEP. involved in the mass transport process [4]. It must, Exceeding the LEP causes high concentration feed however, be chemically stable for operation with the solution to pass through the membrane and thus feed solution and foulants at the operating tempera- impair the separation, so high LEP is needed to ensure tures. Chlorine, sulfuric acid, hydrochloric acid, and the product quality. sodium hydroxide solutions are most often used as test solutions to evaluate the chemical stability of the membrane. When the chemical stability is needed for 3.2.3. Membrane permeability (C) a specific application, specific applicable solutions can The membrane permeability is defined as the ratio be used as test solutions. The chemical stability can be of the mass flux to the vapor pressure difference estimated by visual comparison, change of other mem- across the membrane: brane properties such as thickness, porosity, contact angle, and tensile strength, before and after test. More information about measuring the membrane chemical ¼ J C (79) stability can be found in [31]. pf;m pp;m

3.2.1.9. Membrane thermal stability. Membranes used in where C is membrane permeability (kg/(m2 s Pa)), 2 MD should have good thermal stability to ensure J—mass ﬂux (kg/(m s)), pf,m—vapor pressure at the long-time operation at the operating temperature (so membrane feed-side surface (Pa), pp,m—vapor pressure far usually below 100˚C). Thermal stability essays such at the membrane permeate-side surface (Pa). as differential scanning calorimetry (DSC) and thermo- C is used to characterize the membrane’s ability to gravimetric analysis (TGA) can be used to evaluate produce a mass ﬂux for a given vapor pressure differ- the thermal stability of the membrane. Detailed infor- ence. C can be determined from experiments, but mass mation about these technologies can be found in transport models can also be used as discussed in [32,33]. Section 2.3. 20108 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

In DCMD, the vapor pressure at the feed and the For the ordinary molecular diffusion mechanism: permeate side of the membrane surface is usually calculated using the saturated pressure of the membrane ¼ e DM Pmem feed and permeate side surface temperatures. In J pf;m pp;m sd RTmem pair AGMD, SGMD, and VMD, the vapor pressure at the ¼ DM Pmem permeate side of the membrane surface is just the par- PF pf;m pp;m (82) RT pair tial pressure of the vapor while the vapor pressure at the feed side of the membrane surface is calculated For the viscous flow mechanism: using the saturated pressure corresponding to the temperature at the membrane feed side surface. 2 As explained in Section 2.3 about the mass trans- 1 r e Mpmem J ¼ P ; P ; port mechanisms, the permeability depends on the 8l sd RT f m p m mem properties of the membrane and on the operating con- ¼ 1 Mpmem PF Pf;m Pp;m (83) ditions, such as temperature, total pressure, and the 8l RTm partial pressure of the air and non-condensable gas present in the membrane. The air and other non-con- It can be seen that in all these mass transport mecha- densable gases present in the membrane pores create nisms, the mass flux is a function of membrane prop- additional mass transport resistance to the vapor, so erties and operating conditions. PF is the term generally the mass flux decreases as the partial pres- representing the effect of membrane properties. How- sure of the non-condensable gas in the membrane ever, when more than one mechanism plays an impor- pore increases [35,36]. tant role in overall mass flux, this method cannot be applied since the relative importance of each mechanism should be considered. 3.2.4. Mass transport pre-factor (PF)

The “mass transport pre-factor” [37] is used to 3.2.5. Conduction heat transfer coefﬁcient of the

evaluate the membrane’s mass transport ability based membrane (hm) on its major transport-related properties and is defined as: The conduction heat transfer coefficient of the membrane is defined as the ratio of the effective membrane thermal conductivity to the membrane rb e PF ¼ (80) thickness: s d e þð eÞ where β is exponential factor depends on the mass km kg 1 ks hm ¼ ¼ (84) transport mechanism. For the Knudsen diffusion d d mechanism, β = 1; for the viscous flow mechanism, β = 2; for the ordinary molecular diffusion mechanism, where hm is conduction heat transfer coefficient of the − 2 β =0. PF—mass transport pre-factor (m 1) for β =0, membrane (W/(m K)), km—effective membrane ther- δ (dimensionless) for β = 1, (m) for β =2, r—average mal conductivity (W/(m K)), —membrane thickness ε pore radius (m), ε—membrane porosity (dimension- (m), —membrane porosity (dimensionless), kg—ther- less), τ—membrane tortuosity (dimensionless), mal conductivity of the gas present in the pores (W/ δ—membrane thickness (m). (m K)), ks—membrane material thermal conductivity As discussed in Section 2.3, three mass transport (W/(m K)). mechanisms are generally considered in MD. They As discussed in Section 2.2, the transmembrane can be expressed as follows: conduction heat transfer is considered as a heat loss in the MD process and is proportional to hm,sohm influ- For the Knudsen mechanism: ences the energy efficiency of the MD process.

1 2 ¼ 2 re 8M 3.3. Production rate criteria J pf;m pp;m 3 sd pRTmem 1 The performance criteria used to evaluate the 2 ¼ 2 8M PF pf;m pp;m (81) production rate of MD process are discussed in this 3 pRTmem section. The product of the MD process can be the A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20109 distillate and/or the concentrated feed solution, with consumption, electrical energy consumption, and the production rate of these two closely related. Since exergy analysis), product quality, and of course cost of they are the two products of the same process, a unit product. higher production rate of the distillate means a higher concentration rate of the feed solution. 3.3.3. Relative concentration change rate (CR) _ 3.3.1. Product mass flow rate (mpro) The relative concentration change rate is defined as the time rate of change of the ratio of the solutes (or, The product mass flow rate is defined as the mass rarely, solvent) concentration to the initial concentra- production of product per unit time. tion:

dmpro m_ ¼ (85) cðtÞ 1 CF pro dt CR ¼ ¼ (89) cinitial t t _ where m is product mass flow rate (kg/s), m—mass − pro where CR is relative concentration change rate (s 1), c production of the product (kg), t—time period (s). (t)—concentration of the solvent or solute at time t The flow rate of the product is sometimes defined _ (mold/m3), c —concentration of the solutes at ini- volumetrically (not by mass) V : initial pro tial condition (mol/m3), t—time period (s). CR is directly related to the mass flux. For a feed _ dVpro solution that contains non-volatile solutes and with a Vpro ¼ (86) dt pure distillate, mass conservation requires:

_ 3 where Vpro is product volumetric flow rate (m /s), = V —volumetric production of the product (m3). ¼ Nso Vinitial JvAt ¼ Vinitial pro CR = (90) The product mass flow rate directly evaluates the Nso Vinitial Vinitial JvAt production rate of MD process. where Nso is mole number of the solutes (mol), Vini- 3 tial—initial volume of the solution (m ), Jv—average 3.3.2. Mass flux (J) volumetric flux (m/s). The term “mass flux” is used here to denote the flux of the distillate across a membrane, defined as the 3.4. Product quality criteria mass flow rate of the distillate across the membrane per unit membrane area: The performance criteria used to characterize the product quality of MD process are discussed in this section. m_ J ¼ d (87) A 3.4.1. Volumetric molar concentration (c) 2 _ where J is mass flux (kg/(m s)), md—mass flow rate of the distillate (kg/s), A—membrane area (m2). The volumetric molar concentration is defined as The flux is sometimes defined volumetrically (not the number of moles of the species divided by the volume of the solution: by mass) Jv:

_ V N J ¼ d (88) c ¼ (91) v A V _ where Jv is volumetric flux (m/s), Vd—volumetric flow where c is volumetric molar concentration of the spe- 3 rate of the distillate (m3/s). cies(mol/m ), N—mole number of the species (mol), V 3 Mass flux is a widely used performance criterion —volume of the solution (m ). in MD. Practical long-time use of MD requires addi- The mass fraction is also widely used as an tional important performance criteria, led by long-time alternative criterion of molar concentration. The mass operational effects (such as fouling and membrane fraction is defined as the mass of the species divided deterioration) on it, energy consumption (such as heat by the mass of the solution: 20110 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

3.4.4. Separation factor (α) msp w ¼ (92) mt The separation factor is deﬁned as: where w is mass fraction of the species (dimension- xp= 1 xp a ¼ (95) less), msp—mass of the species (kg), mt—mass of the = xf 1 xf solution (kg). The mass fraction is often expressed in % or ppm. where α is separation factor (dimensionless), x —mole Speciﬁcally, for water desalination application, the p fraction of the desired component in the permeate mass fraction of solutes in water is called salinity. stream (dimensionless), x —mole fraction of the The molar concentration or the mass fraction serve f desired component in the feed stream (dimensionless). as a criterion to evaluate the quality of the distillate Though most of the MD applications deal with and concentrated feed solution. Measurement of the non-volatile solutes, some studies use MD to separate concentration requires chemical analysis, so it is in aqueous solution containing volatile organic com- some cases measured much more simply and quickly pounds [38–42]. For these applications, the separation by measuring the solution electrical conductivity and factor provides an evaluation of the concentration dif- using an empirical relation between the solute concen- ference between the feed component of interest and tration and that conductivity, which of course depends the permeate streams, thus evaluating the ability of also on the types of solutes and solution temperature. MD to separate that component.

3.4.2. Rejection factor (R) 3.5. Energy performance criteria The rejection factor is deﬁned as the ratio of the Most of the energy performance criteria evaluate solutes molar concentration difference between the the energy efﬁciency of the MD on the system level, feed solution and the distillate, to the solutes molar which includes not only the membrane module but concentration of the feed solution: also other components needed for the overall opera-

tion of the MD process. For an MD system shown in cf cd R ¼ (93) Fig. 8, the control volume of this system is outlined by c f the dashed line in Fig. 14. where R is rejection factor (dimensionless), cf—solutes molar concentration of the feed solution (mol/m3), 3.5.1. Specific heat consumption (SHC) cd—solutes molar concentration of the distillate (mol/ The specific heat consumption is defined as the 3 m ). amount of heat supplied to produce a unit mass of the It is a criterion used to evaluate the quality of the product. This performance criterion is used to evaluate distillate and it modifies the concentration information the heat utilization performance of the MD on the sys- to a dimensionless ratio. tem level (Fig. 14).

_ 3.4.3. Concentration factor (CF) Q SHC ¼ in (96) m m_ The concentration factor is defined as the ratio of pro the solutes concentration to the initial concentration: where SHC is specific heat consumption per unit m _ c mass of the product (J/kg), Qin—total heat input rate CF ¼ (94) _ (W), mpro—mass flow rate of the product (kg/s). cinitial It can also be expressed as the amount of heat sup- where CF is concentration factor (dimensionless), plied to produce a unit volume of the product. 3 c—molar concentration of the solutes (mol/m ), cini- _ Qin tial—molar concentration of the solutes at initial SHCV ¼ (97) 3 _ condition (mol/m ). Vpro The concentration factor of the feed solution evaluates the extent of the feed solution being concentrated where SHCV is specific heat consumption per unit vol- 3 _ or the volatile solutes being removed from the feed ume of the product (J/m ),Vpro—volumetric flow rate solution. of the product (m3/s). A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20111

Consider now the MD system shown by Fig. 14, _ where the total electrical energy input (We;in) is the sum of electrical energy input of the feed ﬂow pump _ _ (We;f ) and the permeate ﬂow pump (We;p). As discussed in Sections 2.5 and 2.6, though MD is a thermally driven distillation process, electrical energy is still needed to accomplish tasks such as to drive the feed and the distillate streams, to maintain vacuum in VMD, to drive gas stream in SGMD and run auxil- iaries including pre- and post-treatment for the operation of the whole system. Also, since heat and electrical energy have different thermodynamic quality and they generally come from different source, it is necessary to use a criterion to properly evaluate the electrical energy consumption and other criteria that combined thermal and electrical energy consumption in MD processes.

3.5.3. Membrane thermal efficiency (η) Fig. 14. Schematic of the control volume of a MD system. The membrane thermal efficiency is defined as the ratio of the heat flux by distillate evaporation to total heat flux across the membrane. SHC evaluates how well the MD heat input is utilized to produce the desired product on the system 00 00 JDH ¼ qv ¼ qv ¼ fg level. g 00 00 00 (100) þ D þ qt qv qc J Hfg hm Tf;m Tp;m

3.5.2. Specific electrical energy consumption (SEEC) where η is membrane thermal efficiency (dimensionless), q00—heat flux across the membrane by evapora- The specific electrical energy consumption is v tion (W/m2), q00—heat flux across the membrane by defined as the amount of electrical energy supplied to c conduction (W/m2), q00—total heat flux across the produce a unit mass of the product. This performance t membrane (W/m2), ΔH —specific enthalpy of vapor- criterion is used to evaluate the electrical energy per- fg ization (J/kg), hm—conduction heat transfer coefficient formance of the MD on the system level (Fig. 14): 2 of the membrane (W/(m K)), Tf,m—temperature at the membrane feed-side surface (K), T —temperature at _ p,m ¼ We;in the membrane permeate-side surface (K). SEECm _ (98) 00 mpro As discussed in Section 2.2, qv is the heat exclu- sively used for production of the distillate, and the 00 where SEEC is specific electrical energy consumption sensible heat transferred qc is regarded as an energy m _ per unit mass of the product (J/kg), We;in—total elec- loss, so the membrane thermal efficiency evaluates the _ trical energy input rate (W), mpro—mass flow rate of heat utilization efficiency for distillation of the heat the product (kg/s). transport process across membrane (A in Fig. 15). It It can also be expressed as the amount of electrical should be noticed that, as shown in Sections 2.2 and energy supplied to produce a unit volume of the 2.3, the membrane thermal efficiency depends on not product. only the membrane properties, but also the operation conditions and module configurations. Also, if the _ energy losses to the environment are neglected, it can ¼ We;in also be used to evaluate the heat utilization efficiency SEECV _ (99) Vpro of the membrane module (B in Fig. 15), since the heat transfer across the membrane is the only energy inter- where SEECV is specific electrical energy consumption action between the feed and the permeate stream. 3 _ per unit volume of the product (J/m ), Vpro—volumet- An important issue is that some energy perfor- ric flow rate of the product (m3/s). mance criteria like membrane thermal efficiency focus 20112 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

indicates. However, this term is correct only when the heat supplied by externally delivered condensing steam and its condensate, and the vapor ﬂow across the membrane, are all saturated without sensible heat change. A more general deﬁnition of the second term on the right-hand side is given in Eq. (102):

00 _ D q A md Hfg;d GOR ¼ v ¼ (101) _ _ D ; Qin ms Hfg s

where GOR is gain output ratio (dimensionless), 00 qv—heat flux across the membrane by evaporation 2 2 _ (W/m ), A—membrane area (m ), Qin—heat input rate _ _ (W), md—mass flow rate of the distillate (kg/s), ms— Δ mass flow rate of the input steam (kg/s), Hfg,d— specific enthalpy of vaporization for the distillate (J/ Δ kg), Hfg,s—specific enthalpy of vaporization for the steam (J/kg). A fundamental constraint of defining GOR by the second term on the right-hand side of Eq. (101) is that expression of the ratio between the heat quantities _ needed for producing a mass flow rate md of distilled product, and the heat provided by the mass flow rate _ Fig. 15. Schematic of the control volume of the membrane ms of the input steam, must take into account that: (a) (dashed line in A) and the membrane module (dashed line neither the distillation heat demand, nor the steam in B). heat supply are performed exactly at the saturation conditions at practical plant conditions: the produced only on a single system component or aspect, most distillate vapor is typically superheated and is there- notably the membrane transport, but a plant typically fore first cooled to the saturation point before it is con- includes many other auxiliary energy-consuming units densed, consequently demanding this sensible heat of as discussed in Section 2.5. Unless such units have cooling, and the distillate condensate is typically negligible impact on overall plant energy performance, somewhat supercooled, consequently demanding also they must be included in calculating its energy perfor- the sensible heat of subcooling, and these amounts of mance, which also requires the definition of an overall heat should then be added to the latent heat of evapo- energy performance criterion. Also, the overall energy ration of the feed solution. The heat supplied by the consumption depends on the use of the heat recovery steam input similarly has the sensible heat compo- devices which cannot be revealed by this membrane nents of superheat and subcooling, and (b) the feed thermal efficiency. solution enthalpy and latent heats of evaporation and condensation depend on the evaporation temperature and pressure of the feed solution that, in turn, depend 3.5.4. Gain output ratio (GOR) on solution composition and concentrations, and on The gain output ratio (GOR) in MD is usually the plant design. A correct definition is given in defined as the ratio of the transmembrane heat trans- Eq. (102). fer rate by the distillate evaporation for the generation of the distillate, to the heat input rate. This perfor- 00 ¼ qvA mance criterion is used to evaluate the heat utilization GOR _ Q ÂÃ performance of the MD on the system level (Fig. 14). in m_ H ; H ; þ DH ; þ H ; H ; GOR is a criterion widely used to evaluate the heat ¼ d ÂÃd i d sat fg d d sat d o _ þ D þ utilization efficiency of thermal desalination system ms Hs;i Hs;sat Hfg;s Hs;sat Hs;o including MD. For the desalination process in which (102) the heat input is by externally supplied steam that gives its heat by condensation, it is typically used as where Hd,i is specific enthalpy of the superheated dis- the second term on the right-hand side of Eq. (101) tillate (J/kg), Hd,sat—specific enthalpy of the saturated A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20113

distillate (J/kg), Hd,o—specific enthalpy of the superheat utilization efficiency of the system is achieved. It cooled distillate (J/kg), Hs,i—specific enthalpy of the is noteworthy that increase of the heat recovery factor superheated steam (J/kg), Hs,sat—specific enthalpy of requires a more complex system and raises other the saturated steam (J/kg), Hs,o—specific enthalpy of energy consumption such as pump work. Further- the supercooled steam (J/kg). more, since heat recovery is typically implemented by GOR is a criterion for how well the heat input is employing multi-stage operation, the driving forces utilized to produce distillate on the system level. For (temperature and pressure differences) in each stage MD systems in which the product is the distillate, are proportionally lowered, resulting in lower product GOR is directly related to SHC: mass fluxes in each stage. þ D þ ¼ Hd;i Hd;sat Hfg;d Hd;sat Hd;o GOR (103) 3.5.6. Performance ratio (PR) SHCm Rooted in the past overwhelming use of thermal Besides the above-discussed constraints, the definition distillation, for which the needed heat was supplied in of any performance criterion that is based on heat most cases by steam from boilers or back-pressure only is incomplete and could be very misleading if the steam turbines, this widely used PR is defined as the amount of associated work input is not negligible rela- ratio of the mass flow rate of the produced distillate tive to the associated amounts of heat. As one extreme to the mass flow rate of the input steam used to gen- example in which a criterion based on heat only is erate the distillate. In MD the heat input is typically _ completely correct, is when only heat is used where not steam, so the Qin appeared in the Eq. (102) needs even the pumping is, say, buoyancy driven, and the to be modified to the equivalent weight of steam to system does not use any mechanically or electrically calculate PR. This performance criterion is used to driven pumps. The other extreme is where no heat is evaluate the heat utilization performance of the MD used and all the energy input/output is by mechanical on the system level (Fig. 14). work, such as in RO processes. An intermediated example are various thermal distillation processes m_ including MD where the dominant energy is heat but PR ¼ d (105) m_ work for pumping is not negligible relative to it. s _ where PR is performance ratio (dimensionless), md— _ 3.5.5. Heat recovery factor (Hr) mass flow rate of the distillate (kg/s), ms—mass flow rate of the input steam (kg/s). The heat recovery factor is defined as the ratio of While this definition is very practical because it is the heat rate recovery (rate of heat gain by the feed easy to measure and also reflects a partially relevant stream in the heat recovery device as shown in Fig. 8 income-to-energy expense economic ratio, it does not and can be calculated by Eq. (52)) for reuse in the pro- represent correctly an energy ratio like the GOR (Eq. cess, to the total heat transfer rate across the mem- (102)) and lacks scientific generality. Further com- brane. We have chosen this denominator because it ments are shown in the above discussion of the GOR. represents the fundamentally maximal amount of heat Since the latent heat of evaporation for the distil- that can be recovered. This performance criterion is late is almost the same as the condensation latent heat used to evaluate the heat utilization performance of of the heating steam, PR can be regarded as an the MD on the system level (Fig. 14). approximation of GOR without considering the sensible heat change in the process which expressed in the _ ratio of mass flow rate. ¼ Qr Hr 00 (104) Since PR and GOR evaluate the same characteris- qt A tics of the process, PR has the same advantages and _ limitations mentioned in the discussion of GOR. where Hr is heat recovery factor (dimensionless), Qr— 00 heat recovery rate (W), qv—heat flux across the membrane by evaporation (W/m2), A—membrane area 2 3.5.7. Flow pressure drop (ΔP) (m ). Hr evaluates the internal heat recovery extent in This is a ubiquitous criterion, defined as the pres- the MD system. A higher Hr means more heat is sure change of a flow stream from a defined inlet to a recovered and less heat input is needed, thus a higher defined outlet: 20114 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

D ¼ water and power plants, and its FESR, applying at the P Pin Pout (106) system level (Fig. 9) is: where ΔP is flow pressure drop (Pa), P —flow pres- in _ þ _ _ sure at the defined flow inlet (Pa), P —flow pressure Qpow Qwat Qdual out FESR ¼ (107) _ þ _ at the defined flow outlet (Pa). Qpow Qwat ΔP is an important criterion for all processes involving fluid flow including MD. One role is to where FESR is fuel energy saving ratio (dimension- determine pumping work (proportionally affecting _ less), Qpow—heat consumption rate of the reference system energy efficiency) and pressure, as well as power-only system with same electrical energy output module and entire system design parameters such as rate as the dual-purpose desalination system (W), flow cross sections of conduits and their needed _ Qwat—heat consumption rate of the reference water- strength to withstand the pressures. Another role is in only system with same water production rate as the determining distillate transport thermodynamics _ dual-purpose desalination system (W), Qdual—heat including vapor transport rate, such as between MSF consumption rate of the dual-purpose desalination stages or across MD membranes. plant (W). In MD, the membranes are thin, can be mechani- For such a dual-purpose desalination system with cally breached if excessive pressure is applied across _ electrical energy generation rate We;dual and water pro- them, and must be supported by a sufficiently strong _ _ duction rate md;dual, Q can be calculated by: backing mesh that consequently also reduces the pow membrane effective transport area and even promotes _ fouling. Excessive pressure drop across the hydropho- _ ¼ We;dual Qpow (108) bic membrane will also result in membrane wetting ge;ref and impairment of the distillate quality, as well as _ membrane compacting that reduces the mass transport where We;dual is electrical energy production rate of across it. the dual-purpose desalination plant (W), ge;ref —heat to In typical DCMD and SGMD modules with a electrical energy conversion factor for the reference counter-flow arrangement, the feed stream pressure power plant (dimensionless). decreases along the flow path while the pressure at _ Similarly, Qwat is calculated by: other side across the membrane increases, so the maximal pressure difference occurs at the inlet or outlet of _ _ md;dual the feed stream. For AGMD and VMD modules, the Q ¼ (109) wat g feed stream pressure decreases along the flow path w;ref while pressure is constant at other side across the _ membrane, so maximum pressure difference arises at where md;dual is water production rate of the dual-pur- inlet of the feed stream. pose desalination plant (kg/s), gw;ref —heat to water conversion factor for the reference desalination plant (kg/J). This criterion can also be modified in the similar 3.5.8. Fuel energy saving ratio (FESR) manner to evaluate the energy saving performance for As described in Section 2.5, properly designed MD coupled with other processes. dual- or multi-purpose desalination plants use less energy as compared with separate power-only and _ þ _ _ Qoth QMD Qcoup water-only systems with same loads of outputs, and FESR ¼ (110) _ þ _ the fuel energy saving ratio [23] is used to evaluate Qoth QMD the energy saving performance of multi-purpose _ desalination plants. The fuel energy saving ratio is where Qoth is heat consumption rate of the reference defined as the ratio of heat consumption saving by system performs only the “other process” with same using the multi-purpose desalination plant compared output rate of the other product as the couple system _ with using separate reference single-purpose-only sys- (W), QMD—heat consumption rate of the reference MD system with the same product output rate as the cou- tems having the same outputs as the multi-purpose _ plant, to the total heat consumption of these separate pled system (W), Qcoup—heat consumption rate of the reference systems. Most common is the dual purpose, coupled system (W). A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20115

3.5.9. Specific equivalent electrical energy consumption 3.6. Exergy performance criteria (EEEC) Definitions of the various forms of exergy effi- For dual-purpose desalination plants, the specific ciency are available in many publications (e.g. [43,44]) equivalent electrical energy consumption is defined as and are summarized in [45]. Those most applicable to the ratio of the reduction of the electrical energy pro- MD follow. duction of the dual-purpose desalination plant com- Exergy analyses have been conducted for MD pro- pared with the reference power-only system for the cesses [46–48], but various different expressions are same total heat input, to the mass flow rate of the used in different papers to calculate the exergy and water produced by the dual-purpose desalination most of them are based on significant simplifications. plant. This performance criterion can be used to evalu- Comparisons and clarifications of some of these ate the energy performance of a dual-purpose MD expressions are in [15]. The general expressions for plant at the system level (Fig. 9). exergy are discussed in Section 2.6. _ ψ _ _ Q g ; g ; 3.6.1. Overall exergy efficiency ( t) ¼ We;ref We;dual ¼ in e ref e dual EEECm _ _ (111) md;dual md;dual The overall exergy efficiency is defined as the ratio of the exergy output to the exergy input for the con- where EEECm is specific equivalent electrical energy trol volume of interest. This performance criterion is consumption per unit mass of the product (J/kg), used to evaluate the exergy performance of MD on _ We;ref —electrical energy output rate of the reference the system level (Fig. 14), or of a specific component power-only system with the same total heat input as of the system (such as the membrane module (B in _ the dual-purpose desalination plant (W), We;dual— Fig. 15)). electrical energy output rate of the dual-purpose _ _ _ desalination plant (W), md;dual—water production rate E E _ w ¼ output ¼ des of the dual-purpose desalination plant (kg/s), Q — t _ 1 _ (113) in Einput Einput total heat input rate (W), ge;ref —heat to electrical energy conversion factor for the reference power plant ψ where t is overall exergy efficiency (dimensionless), (dimensionless), g ; —heat to electrical energy con- _ _ e dual E —exergy input rate (W), E —exergy output version factor for the dual-purpose desalination plant input _ output rate (W), E —exergy destruction rate (W). (dimensionless). des The calculation of the exergy input and output of a It can also be expressed based on the volume of simple MD system are discussed in Section 2.6. This the water produced. criterion can also be used to analysis the subprocess within the system which often takes place in a single _ _ _ Q g ; g ; component (such as the membrane module (B in ¼ We;ref We;dual ¼ in e ref e dual EEECV _ _ (112) Fig. 15)). Vd;dual Vd;dual Overall exergy efficiency evaluates the effectiveness of the energy use and the irreversibility in the where EEECV is specific equivalent electrical energy process. It is especially useful if there is intent to use 3 consumption per unit volume of the product (J/m ), the exergy potential of output streams and energy out- _ 3 Vd;dual—volumetric water production rate (m /s). puts other than that of the intended separation prod- Though a dual-purpose desalination plant saves uct. This also leads to its limitation: it does not focus energy compared with separate power-only and on the typically most wanted separation (e.g. desalina- water-only systems, it produces less electrical energy tion) system product (e.g. the desalted water), but compared with power-only system with same includes all system outputs, most of which are usually amount of heat input. The production of the water not useful; furthermore, although they are an integral is thus at the expense of this electrical energy reduc- part of the selected process, most of them are undesir- tion and the EEEC evaluates this equivalent electri- able for practical purposes, since they are wastes such cal energy consumption of the dual-purpose as hot concentrated brines that contain various addi- desalination plant. This criterion provides a metric tives such as anti-foaming and anti-scaling chemicals, to compare the heat utilization efficiency of the etc., heat emissions, streams with kinetic energy that dual-purpose desalination plant to the separate disturb the biota, etc., which have negative environ- power-only and water-only systems. mental and economic impacts. 20116 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

ψ 3.6.2. Utilitarian exergy efficiency ( u) _ ¼ Einput The utilitarian exergy efficiency of a chosen control SXCm _ (116) mpro volume is defined as the ratio of the exergy output useful to the owner, to the exergy input paid by the where SXC is specific exergy consumption per unit owner. This performance criterion is used to evaluate m _ mass of the product (J/kg), E —total exergy input the exergy performance of the MD on the system level input rate (W), m_ —mass flow rate of the product (kg/s). (Fig. 14), or of a specific component of the system pro It can also be expressed as the amount of exergy (such as the membrane module (B in Fig. 15)). supplied to produce a unit volume of the product. _ E w ¼ u _ u _ (114) ¼ Einput Ep SXCV _ (117) Vpro ψ where u is utilitarian exergy efficiency (dimension- _ _ where SXCV is specific exergy consumption per unit less), Eu—paid exergy input rate (W), Ep—useful 3 _ volume of the product (J/m ), Vpro—volumetric flow exergy output rate (W). 3 The paid and useful exergies are defined depend- rate of the product (m /s). ing on the need of the user, and thus somewhat arbi- SXC evaluates how well the exergy input is used trarily. For the MD process in which we focus on the to produce the product. It provides a metric to com- product (distillate and/or concentrated feed solution) bine the thermal and electrical energy consumption in of the separation, the useful exergy output can be MD based on the second law of thermodynamics. ψ taken as the exergy contained in the product, and u thus becomes: 3.6.4. Exergy consumption ratio (XCR)

_ The exergy consumption ratio is defined as the ¼ Epro ratio of the minimal specific exergy consumption wu _ (115) Ep needed for the separation (SXCmin) to the specific exergy consumption of the system (SXC). This perfor- _ where Epro is product exergy output rate (W). mance criterion is used to evaluate the exergy perfor- It should be noted that this product (in Eq. (115)) mance of the MD on the system level (Fig. 14). may be not only the desired product that is valuable to the user, but also the undesired product which the SXC XCR ¼ min (118) user must remediate. SXC For the paid exergy, consider a simple DCMD, AGMD, SGMD, VMD system as Figs. 10–13 show. where XCR is exergy consumption ratio (dimension- Generally, the paid exergy input of these systems less), SXCmin—minimal specific exergy consumption includes exergy of the electrical energy consumption per unit mass of the product (J/kg), SXC—specific of the electrical devices such as pumps and blowers _ _ _ _ _ exergy consumption per unit mass of the product (J/ (W ; , W ; , W ; , W ; , W ; ) and the exergy of the heat e f e p e b e b e v _ kg). consumption of the heater (Qin). SXC (which is same the minimum work of sepa- ψ min Compared with overall exergy efficiency t, the ration (W )) can be calculated from the separation ψ min utilitarian exergy efficiency u, is more oriented to the exergy needed for a thermodynamically reversible desire of the user to evaluate the potential economic separation process. Since the exergy destruction equals value of the process and for guidance for economic to 0 in a reversible process, the exergy balance (Eq. system improvement. (65)) yields:

_ þ _ ¼ _ þ _ 3.6.3. Specific exergy consumption (SXC) mproSXCmin Eflow;f Eflow;d Eflow;cf (119) The specific exergy consumption is defined as the where m_ is mass flow rate of the product (kg/s), amount of exergy supplied to produce a unit mass of _ pro E ; —flow exergy of the inlet feed solution (W), the product. This performance criterion is used to _ flow f _ evaluate the exergy performance of the MD on the Eflow;d—flow exergy of the distillate (W), Eflow;cf —flow system level (Fig. 14). exergy of the concentrated feed solution (W). A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20117

According to Eq. (119), SXCmin can be calculated by: to electrical energy conversion factor for the reference power plant (dimensionless). _ _ _ E ; þ E ; E ; _ ¼ ¼ flow d flow cf flow f Similarly, Ewat is calculated by: SXCmin Wmin _ (120) mpro _ _ md;dual E ¼ (123) where Wmin is minimal work of separation (J/kg). wat nw;ref The calculation of the flow exergy is discussed in Section 2.6. A detail calculation of the SXCmin for the where m_ ; is water production rate of the dual-pur- saline water can be found in [21]. d dual pose desalination plant (W), n ; —exergy to water SXC evaluates how well the exergy input is uti- w ref conversion factor for the reference desalination plant lized to produce product and the extent to which the (kg/J). practical MD separation process approaches the ideal This criterion is used to evaluate the exergy saving reversible process. performance of the dual-purpose desalination plants. It can also be modified in a similar manner to evaluate 3.6.5. Multi-purpose plant exergy saving ratio (XSR) the exergy saving performance for MD coupled with other processes. For multi-purpose desalination plants, the exergy saving ratio can be defined as the ratio of the exergy _ þ _ _ Eoth EMD Ecoup consumption saved by using the multil-purpose XSR ¼ (124) _ þ _ desalination plant compared with using separate refer- Eoth EMD ence single-purpose-only systems having the same _ outputs as the multi-purpose plant, to the total exergy where Eoth is exergy consumption rate of the reference consumption of these separate reference single-pur- system that performs only the “other process” with pose-only systems. This performance criterion can be the same product output rate as the coupled system _ used to evaluate the exergy performance of such an (W), EMD—exergy consumption rate of the reference MD plant at the system level (Fig. 9), and is defined MD system with same product output rate as the cou- _ for the most commonly used type, the water produc- pled system (W), Ecoup—exergy consumption rate of tion and power generation one, by: the coupled system (W).

_ þ _ _ ¼ Epow Ewat Edual XSR _ _ (121) Epow þ Ewat 3.6.6. Relative exergy destruction ratio (XDR) The relative exergy destruction ratio is deﬁned as where XSR is exergy saving ratio (dimensionless), _ the ratio of the exergy destruction in a subsystem or Epow—exergy consumption rate of the reference subprocess (e.g. taking place in one of the system power-only plant with the same electrical energy out- components) to the total exergy input of the system. put rate as the dual-purpose desalination plant (W), _ E —exergy consumption rate of the reference water- wat _ only plant with the same water production rate as the ¼ Edes;sub _ XDR _ (125) dual-purpose desalination plant (W), Edual—exergy Einput consumption rate of the dual-purpose desalination plant (W). where XDR is relative exergy destruction ratio (di- Considering a dual-purpose desalination system _ _ mensionless), Edes;sub—exergy destruction in the sub- whose exergy consumption rate is E , having an elec- _ _ dual system or subprocess (W), Einput—total exergy input of trical energy production rate We;dual and desalted water the system (W). _ _ production rate md;dual. Epow can be calculated by: Since the total exergy destruction of the system _ equals to the sum of the exergy destructions of each ; ψ _ We dual of its subsystems, the overall exergy efﬁciency ( t) Epow ¼ (122) ne;ref (Eq. (113)) and XDR are:

_ X where We;dual is electrical energy production rate of ¼ XDRj 1 wt (126) n ; the dual-purpose desalination plant (W), e ref —exergy j 20118 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

where XDRj is relative exergy destruction ratio of the condenser constitutes internal heat recovery and thus ψ subsystem or subprocess j (dimensionless), t—overall a reduction of heat demand by the process. No exergy efficiency (dimensionless). backup heat or thermal storage was used. XDR evaluates the extent of the exergy destruction The properties of the fluid at each state point in within a subsystem and its thermodynamic perfor- Fig. 16 are reported in [48] and summarized in Table 1. mance. Knowledge of the exergy destruction share of Since the pressures in the system were not reported, the system components gives guidance about the ben- we calculated them as explained in the below-pre- efits of improving each of them. Detailed exergy anal- sented discussion about the PV module and pump, ysis of coupled MD systems can be found in [47,48]. with the assumption that 35% of the total pressure drop is incurred from state 1 to 2 and from state 5 to 6, each, and the remaining 30% of the total pressure 3.6.7. Example of calculation of the energy and exergy drop is incurred from state 3 to 4. criteria The method used to calculate the flow exergy in [48] is replaced here by the method proposed in [49], While energy analysis is common knowledge, using Eqs. (58), (59), (61) and thermodynamic property exergy analysis and the comparison between them is correlations for sea water [34], which applies to the less so, and a simple but explicit analysis and calcula- salinity range in this example. The dead state is tion example is therefore shown here. The example is chosen to be the condition of the feed solution input based on data from the paper by Banat et al. [48] that (state 0) at its ambient conditions, T0 = 308.15 K, shows an exergy analysis of a solar-powered mem- p0 = 101.325 kPa, and ws,0 = 3,000 ppm. The flow brane distillation system for 3,000 ppm brackish water. enthalpy is calculated by: The system was designed and tested to generate process parameters and design data for larger MD sys- _ ¼ _ tem. Our analysis is based on their data collected on Hi miHi (127) 12 June 2006, at 13:00 pm. _ _ In the example we show the method and results where Hi is flow enthalpy of stream i (kW), mi—mass for calculating most of the energy and exergy perfor- flow rate of stream i (kg/s), Hi—specific enthalpy of mance parameters and the properties needed for their stream i (kJ/kg). determination. Not all are necessary for each analysis, Similarly, the flow exergy is calculated by: and readers can of course select those they need. Fig. 16 shows the system flow sheet on which our _ _ exergy analysis is based. The system consists of three Ei ¼ miei (128) subsystems: a solar collector with a 6 m2 solar collec- _ tion area to provide the heat for the MD process, a PV where Ei is flow exergy of stream i (kW), ei—specific 2 module with a 0.86 m area to provide the electricity flow exergy of stream i (kJ/kg). for driving the MD process pump, and the MD mod- Our calculation results are summarized in Table 1. ule for desalting the brackish water feed. All of the The performance of the solar collector is also input energy is thus solar radiation. Since the paper reported in [48] and varies with time due to the varia- [48] did not present complete data about the PV mod- tion in solar irradiation intensity and ambient temper- ule, pump and related pressure change, we added ature. The solar intensity (I) here was 970 W/m2 on 12 these data based on the given related information and June 2006, at 13:00 pm. sound technical assumptions. The energy efficiency of the solar collector is The MD process described in [48] is Permeate Gap defined as the ratio of the heat gain by the fluid to the Membrane Distillation (PGMD), a version of AGMD total energy of the solar irradiation. where the air gap is removed and the coolant fluid is the feed solution itself. The process flow diagram is _ _ shown in Fig. 17. The saline cold feed stream first ¼ H4 H3 gsc (129) enters the distillate vapor condenser channel to con- IAsc dense the vapor and at the same time gets pre-heated where η is energy efficiency of the solar collector (di- by the latent heat released by the condensing vapor. sc _ mensionless), H —enthalpy of the collector outlet Then this pre-heated feed stream enters the heater 4 _ (here the solar collector) to raise its temperature to the stream, state 4 (W), H3—enthalpy of the collector inlet 2 level needed for the MD process, after which it enters stream, state 3 (W), I—solar irradiation (W/m ), Asc— 2 the MD evaporator. The preheat process in the absorption area of the solar collector (m ). A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20119

Fig. 16. Schematic of the solar-powered membrane distillation system [48]. The dashed-line boxes enclose the system subprocesses: (A) solar collector subprocess, (B) MD separation subprocess, (C) PV module subprocess, (D) pump subprocess, and (E) discharge subprocess.

the PV module (W), I—solar irradiation (W/m2), 2 _ APV—absorption area of the PV panel (m ), we—electrical power generated by the PV module per unit area (W/m2). The exergy efficiency of the PV module is defined as the ratio of the electrical power generated by the PV panel to the total exergy of the solar irradiation: Fig. 17. Module channel arrangement for PGMD [57]. _ _ ¼ We ¼ we The exergy efficiency of the solar collector is wPV _ _ (132) E esun defined as the ratio of the exergy gain by the sun collector-heated fluid to the total exergy of the solar where ψ is exergy efficiency of the solar collector irradiation. PV _ (dimensionless), W —electrical power generated by e _ the PV module (W), E —exergy of the solar irradia- _ _ _ _ sun E E E E _ w ¼ 4 3 ¼ 4 3 tion (W), we—electrical power generated by the PV sc _ _ (130) 2 _ Esun esunAsc module per unit area (W/m ), esun—exergy of the solar irradiation per unit area (W/m2). ψ where sc is exergy efficiency of the solar collector (di- To conduct the energy and exergy analyses, a typi- _ η mensionless), E4—low exergy at the collector outlet, cal energy efficiency ( PV) of 17.5% is assumed for the state 4 (W). PV module, thus 145.5 W electrical power is gener- For the PV module, the energy efficiency is defined ated. All the electrical energy is assumed to drive the here as the ratio of the electrical power generated by pump. This small pump’s efficiency is assumed to be this 0.86 m2 PV panel to the total energy of the solar 12%. Eq. (133) is used with this data to calculate the irradiation, liquid pressure at state 1, found to be 237.0 kPa, by:

_ _ _ qW g ¼ We ¼ we D ¼ e pump gPV (131) P _ (133) IAPV I m where η is energy efﬁciency of the PV module where ΔP is pressure increase of the ﬂuid in the pump PV _ _ (dimensionless), We—electrical power generated by (Pa), We—electrical power supplied to the pump (W),

20120 .LoadN ir/Dslnto n ae ramn 7(06 20093–20140 (2016) 57 Treatment Water and Desalination / Lior N. and Luo A.

Table 1 Properties of the liquids at the various locations in the system

Mass flow Specific Specific Specific chemical Specific chemical Specific flow Flow Flow Temperature, Salinity, Pressure, rate, m_ enthalpy, H entropy, s potential of water, potential of salts, μ exergy, e enthalpy, exergy, s _ _ Stream T (K) S (ppm) P (kPa) (kg/min) (kJ/kg) (kJ/kg) μw (kJ/kg) (kJ/kg) (kJ/kg) H (kW) E (W) 0 308.15 3,000 101.33 7.69 146.12 0.50 −8.97 −90.71 0.00 18.73 0.00 1 308.15 3,000 237.04 7.69 146.26 0.50 −8.97 −90.71 0.14 18.75 17.46 2 335.15 3,000 189.54 7.69 258.63 0.85 −27.43 −92.21 4.73 33.15 606.72 3 335.15 3,000 189.54 7.69 258.63 0.85 −27.43 −92.21 4.73 33.15 606.72 4 339.15 3,000 148.83 7.69 275.27 0.90 −30.96 −92.16 6.12 35.28 784.62 5 339.15 3,000 148.83 7.69 275.27 0.90 −30.96 −92.16 6.12 35.28 784.62 6 310.15 3,085 101.33 7.47 154.42 0.53 −10.01 −90.37 0.03 19.24 3.29 7 308.15 3,085 101.33 7.47 146.10 0.50 −8.97 −90.05 0.00 18.20 0.00 8 310.15 45 101.33 0.22 155.08 0.53 −9.97 −115.24 0.06 0.56 0.22 9 308.15 45 101.33 0.22 146.72 0.51 −8.93 −114.77 0.04 0.53 0.13 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20121

η ρ pump—pump efficiency (dimensionless), —density of calculated results are summarized in Table 2, demon- the fluid (kg/m3), m_ —mass flow rate of the fluid strating an order-of magnitude differences between (kg/m3). the exergy values when calculated by the 2 methods. There is no commonly agreed method for defining Both methods are fundamentally correct and their the solar exergy input because: (1) some assume that choice depends on the user’s objective, and it is the exergy should be based on the radiation at the sun important to recognize their differences when compar- surface and thus at this temperature, of about 5,800 K, ing such results. or just assuming that this electromagnetic radiation is The total energy input for this system is consid- pure exergy, and then some take into consideration ered to be the total solar irradiation I(Asc + APV) the effects of the radiation cone solid angle between = 6,654.2 W. The solar irradiation supplied to the solar the sun and earth, and the incidence angle on the col- collector IAsc = 5,820.0 W is considered as the heat lector, and the solar radiation extinction by the atmo- input for the system, and the electrical power gener- _ sphere, all of which vary with time, or (2) others ated by the PV module We = 145.5 W is considered as assume that the solar exergy input is just that of the the electrical power consumption for the system. The solar heat at its input point to the system, for example latent heat of the feed solution used in the calculation the exergy of the solar-heated fluid at state 4 in Fig. 16 is the average of the latent heats of states 5 and 6 Δ [50]. Banat et al. [48] used the commonly used expres- ( Hfg = 2,370.8 kJ/kg). sion based on the sun surface temperature: The energy performance criteria applied and calculated for this system are: the Specific heat consump- "# 4 tion SHC (Eq. (96)); the Specific electrical energy _ _ 1 T0 4 T0 Esun ¼ Aesun ¼ AI 1 þ (134) consumption SEEC (Eq. (98)); the Membrane thermal 3 Tsun 3 Tsun efficiency η (Eqs. (50), (87) and (100)); the GOR (Eq. (102)); and the Heat recovery factor Hr (Eqs. (50), (52) _ where esun is exergy of the solar irradiation per unit and (104)). The GOR and heat recovery factor are cal- 2 area (W/m ), T0—dead state temperature (K), Tsun— culated neglecting supercooling and superheating in temperature of the sun surface (K), which is consid- the heat exchanger, because they weren’t reported in ered in [48] to be 6,000 K. [48]. The results are summarized in Table 3. An alternate expression for calculating the solar The solar collector heats the brackish water (state 3 irradiation exergy, based on the temperature of the to 4) for the MD process, and the solar irradiation is solar-heated fluid is [50]: also used to generate electrical power by a PV module to drive the pump bringing the brackish water from state 0 to 1, the useful product is the distilled water _ _ T0 Esun ¼ Aesun ¼ AI 1 (135) (state 9), and the main byproduct is the concentrated T4 brackish water effluent (state 7). It is obvious for this solar-driven system that reduction of the energy input where T4 is fluid temperature at the solar collector per unit produced water is useful for reducing system outlet, state 4 (K). and product cost, but energy analysis alone does not The solar exergy associated with the solar thermal provide sufficient guidance for system improvement collector can be calculated by using either Eqs. (134) because the system uses and outputs different types of or (135), so as to demonstrate the difference in the energy, which have different qualities, characterized results in using these two solar heat exergy definition by exergy. Starting with the solar irradiation input to methods, the exergy analysis is once done using the thermal and PV collectors, it consists of electro- Eq. (134) and repeated by using Eq. (135). Eq. (134) is magnetic waves and is thus pure exergy and is a func- used to calculate the exergy efficiency of the PV mod- tion of the sun surface temperature (Eq. (134)) [50]. ule in both approaches. We named the exergy of the The electrical power generated by the PV module is solar irradiation calculated using Eq. (134) and its cor- also pure exergy (Eq. (57)). The heat produced in the _ sun responding exergy efficiency of the solar collector Esun solar collector has an exergy that is a function of the sun and wsc when based on the sun temperature, respec- heated fluid temperature and pressure (Eqs. (58)–(61)). tively. The exergy of the solar irradiation calculated The distillate, saline feed, and concentrated brackish using Eq. (135) and its corresponding exergy efficiency water discharge have exergies that are a function of _ flu flu of the solar collector are named Esun and wsc , respec- their temperatures, pressures, and compositions (Eqs. tively, based on the solar-heated fluid temperature. (58)–(61)). Energy analysis does not account for the Based on Table 1, the solar irradiation I, solar collector energy flows’ quality, and therefore, for example, one area Asc, PV panel area APV and Eqs. (129)–(135), the Watt of electrical power is assigned the same value as 20122 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

Table 2 Energy and exergy performance of the PV module and solar collector

PV module Solar collector Equation or its Equation or its Symbol number Value Symbol number Value

I (W/m2) 970.0 I (W/m2) 970.0 A (W/m2) 0.9 A (W/m2) 6.0 _PV _ sc _ We (W) 145.5 H4 H3 2,132.8 (W) _ 2 _ _ _ we (W/m ) We/APV 169.8 E4 E3 (W) 177.9 _ _ sun Esun (W) (134) 777.1 E (W) (134) 5,421.6 _ sc Eflu (W) (135) 532.0 _ 2 _ _sun 2 _ sun esun (W/m ) Esun/APV 903.6 esc (W/m ) Esc /Asc 903.6 _flu 2 _ sc esc (W/m ) Eflu/Asc 150.6 η η PV (%) (131) 17.5 sc (%) (129) 36.6 ψ sun PV (%) (132) 18.8 wsc (%) (130) 3.3 flu wsc (%) (130) 33.4

Table 3 _ sun _ flu solar collector (E = 5,421.6 W or E = 532.0 W), and Energy performance of the system sc sc the total exergy output is the ﬂow exergy of distillate _ Performance criterion Equation number Value (E9 = 0.13 W) and concentrated brackish water _ (E = 0.00 W). As discussed further below, the solar SHC (kJ/kg) (96) 1,587.3 7 collector and PV module are the main exergy destruc-

SEEC (kJ/kg) (98) 39.7 η (%) (50), (87), and (100) 54.2 tion subprocesses of the system, so this system has GOR (dimensionless) (102) 1.5 lower overall exergy efficiency than the system con- Hr (%) (50), (52), and (104) 89.8 sider MD separation subprocess only reported in [48]. To compare our results with the exergy analysis done in [48], we make the same assumptions as they one Watt of low temperature heat while the work did, but replace the method used to calculate the flow potential of one Watt of electrical power has one Watt exergy by the method proposed in [49], since some of exergy while the Watt of the heat energy has an negative flow exergy values were given in [48], indi- exergy value much lower than one Watt as deter- cating that their method may have some errors. Their mined by Eq. (56). analysis did not consider the PV module and the flow Based on the data in Tables 1 and 2, an exergy system pressure changes, and unlike here, they analysis of this system was conducted, including the assumed that the exergy input for the system equals calculation of the irreversibilities of the system, and to the flow exergy difference of state 3 and 4. Based thereby examined the potential for its improvement. on these assumptions and our calculation of the flow As discussed above, two expressions for calculating exergy, our result is that the exergy input is 183.19 W ψ ψ the solar irradiation exergy were used. The total and t = 0.072%, t = 0.070%, XCR = 0.072%. Ref. [48] ψ exergy input for this system is considered to be the reported that t = 0.3%, different from our result since exergy of the solar irradiation to the solar collector a different method was used to calculate the flow and PV module. exergy. The exergy performance criteria applied and calcu- When calculating the utilitarian exergy efficiency ψ ψ lated for this system were: Overall exergy efficiency t ( u), the solar irradiation exergy input to the solar col- ψ (Eq. (113)); Utilitarian exergy efficiency u (Eq. (114)); lector and PV module is considered as the valuable Specific exergy consumption SXC (Eq. (116)); Exergy exergy input, and the flow exergy of the desired dis- consumption ratio XCR (based on the thermodynami- tilled water product is considered to be the valuable cally minimal separation exergy to the actual used, exergy output. When calculating the Exergy consump- Eq. (118)). When calculating the overall exergy effi- tion ratio, SXCmin is calculated by Eq. (120) with ther- ciency, the total exergy input is the sum of the solar modynamic property correlations reported in [34] and _ exergy input to the PV module (Esun = 777.1 W) and thus SXCmin = 0.036 kJ/kg. A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20123

The results are summarized in Table 4, showing _ ¼ _ _ that the results for the exergy performance are signifi- Eloss;sub Ein;sub Eout;sub (137) cantly different, depending on the expressions used to _ calculate the solar irradiation exergy to the solar col- where Eloss;sub is subprocess energy loss to the environ- _ lector. In both expressions used in this paper, a negli- ment (W), Eout;sub—subprocess energy output (W), _ gible portion of the input exergy is carried out by the Ein;sub—subprocess energy input (W). desired product. The relative energy loss to the environment is Next, energy and exergy analyses are conducted defined as energy loss to the environment of the sub- on the five subprocesses of the system: first considered process to the total energy input and is calculated by: is the solar collector subprocess (dashed rectangle denoted by A in Fig. 16) where the feed stream is _ ¼ Eloss;sub heated by the solar irradiation, second is the MD sepa- lrsub _ (138) E ration subprocess (dashed rectangle denoted by B in input Fig. 16), third is the PV module subprocess (dashed where lr is subprocess relative energy loss to the rectangle denoted by C in Fig. 16) where solar irradia- sub _ environment (dimensionless), E ; —subprocess tion is used to generate electrical power, fourth is the loss sub _ pump subprocess (dashed rectangle denoted by D in energy loss to the environment (W), Einput—total Fig. 16) where electrical power is supplied to drive the energy input (W). pump, fifth is the discharge subprocess (dashed rect- The total energy input to the system are the solar irradiation (I(A + A ) = 6,654.2 W) plus the enthalpy angle denoted by E in Fig. 16) where the distilled and sc PV _ concentrated brackish water streams leave the MD of the feed solution input (H0), while the energy out- module and are cooled to ambient temperature. put of the system are the enthalpy of the distilled The energy analysis results of these subprocesses water and concentrated brackish water. It was found are summarized in Table 5. Process energy efficiency is that about 73.8% of the energy input is carried out by the product and byproduct liquids. The flow enthalpy defined as the ratio of the energy output to the energy _ input. It should be noted this process energy efficiency of the distillate (H9) amounts to 2.1% of the total energy input and the flow enthalpy of the concen- for the solar collector is different from the commonly _ η trated brackish water (H ) amounts to 71.7% of the defined energy efficiency of the solar collector, sc. The 7 process energy efficiency is calculated by: total energy input. According to the fluid properties in Table 1, it is noteworthy that in this example the com- _ bined enthalpy of the output distilled water ¼ Eout;sub (146.72 kJ/kg) and of the concentrated brackish water gsub _ (136) Ein;sub (146.10 kJ/kg) have nearly the same enthalpy as the input feed solution (146.12 kJ/kg), so the heat loss of the system to the environment equals to the input where η —process energy efficiency of the subpro- energy from the solar irradiation. In these energy sub _ cess (dimensionless), E ; —energy output of the losses to environment, the solar collector process con- _ out sub subprocess (W), Ein;sub—energy input of the subprocess sists of 55.4% of the total heat loss to the environment, (W). which is the major energy loss process of this system. The energy loss to the environment of the subpro- The distribution for the total energy input among the cess is defined as the energy difference between subprocesses is shown in Fig. 18. energy input and output of the subprocess and it is Based on the fluid properties in Table 1 and per- calculated by: formance of the PV module and solar collector in

Table 4 Exergy performance of the system

Solar exergy calculated based on Performance criterion Equation number Sun temperature Fluid temperature ψ t (%) (113) 0.0021 0.010 ψ u (%) (114) 0.0021 0.0098 SXC (kJ/kg) (116) 1,690.5 357.0 XCR (%) (118) 0.0021 0.010

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Table 5 Energy analysis of the subprocess

_ _ _ η Energy input, Ein;sub Energy output, Eout;sub Energy loss to environment, Eloss;sub Process energy efﬁciency, sub Relative energy loss to environment, lrsub

Value Value Value Value Value Process Equation (kW) Equation (kW) Equation (kW) Equation (%) Equation (%) _ _ _ − _ _ _ _ − _ Solar collector IAsc + H2 39.0 H5 35.3 IAsc + H2 H5 3.7 H5/(IAsc + H2) 90.5 (IAsc + H2 H5)/[I 14.5 _ (Asc + APV )+H2] ______MD separation H1 + H5 54.0 H2 + H6 + H8 52.9 H1 + H5 − H2 − H6 − H8 1.1 (H2 + H6 + H8)/(H1 + H5) 98.0 (H1 + H5 − H2 − H6 − H8)/[I 4.3 _ (Asc + APV )+H2] _ − _ _ − _ _ PV module IAPV 0.8 We 0.1 IAPV We 0.7 We/IAPV 17.4 (IAPV We)/[I(Asc + APV )+H2] 2.7 ______Pump H0 + We 18.9 H1 18.7 H0 + We − H1 0.1 H1/(H0 + We) 99.3 (H0 + We − H1)/[I 0.5 _ (Asc + APV )+H2] ______Discharge H6 + H8 19.8 H7 + H9 18.7 H6 + H8 − H7 − H9 1.1 (H7 + H9)/(H6 + H8) 94.6 (H6 + H8 − H7 − H9)/[I 4.2 _ (Asc + APV )+H2] _ _ _ _ _ − _ − _ Total I 25.4 H7 + H9 18.7 I 6.7 (H7 + H9)/[(I 73.8 [I(Asc + APV )+H2 H7 H9]/[I 1.2 _ _ − _ − _ _ _ (Asc + APV )+H2 (Asc + APV )+H2 H7 H9 (Asc + APV )+H2)] (Asc + APV )+H2] A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20125

Table 2, the exergy analysis of these subprocesses, while when it is calculated based on the fluid based separately on the two expressions for calculat- temperature, the exergy destruction in the PV module ing the solar irradiation exergy are summarized in process amounts to only 48.3% of the total exergy Tables 6 and 7. The exergy efficiency is defined here destruction, but is still the main exergy destruction in as the ratio of the exergy input to the exergy output of the system. The calculation thus demonstrates that the the subprocess and is calculated by: expressions used to calculate the solar exergy strongly influence the exergy analysis results. Figs. 19 and 20 _ show the exergy destruction shares when using these ¼ Eout;sub wsub _ (139) two expressions of the solar irradiation exergy. Ein;sub Keeping in mind that the main purpose of this example is to show how exergy analyses are made and how they and their results differ from energy ψ where sub is exergy efficiency of the subprocess analyses, some key conclusions about the exergy and _ (dimensionless), Eout;sub—exergy output of the subpro- energy performance of this sample system can also be _ cess (W), Ein;sub—exergy input of the subprocess (W). drawn: The exergy destruction by a subprocess is defined as the exergy difference between exergy input and (1) 73.8% of the input energy is carried out by the exergy output of the subprocess and is calculated by: distillate and concentrated brackish water, and. 26.2% of the total energy is lost to the environ- _ ¼ _ _ ment. Edes;sub Ein;sub Eout;sub (140) (2) The exergy analysis shows, however, that a _ negligible amount of exergy is carried out by where E ; is exergy destruction of the subprocess _ des sub the product and byproducts, mainly because (W), E ; —exergy input of the subprocess (W), _ in sub they are near the dead state temperature. E ; —exergy output of the subprocess (W). out sub (3) The solar collector energy conversion process The relative exergy destruction ratio is calculated is responsible for 55.4% of the total energy loss

by Eq. (125). to the environment. It can be seen from Tables 6 and 7 that a negligible (4) The exergy analysis results depend strongly on portion of the input exergy is carried out by the prod- the choice of the expression for calculating the ucts, which is contrary to the result of the energy anal- solar exergy input: ysis and is one demonstration of the of their differences. When the solar exergy supplied to the (a) If the solar exergy supplied to the solar col- solar collector is calculated based on the sun tempera- lector is calculated based on the sun temper- ture, the exergy destruction in the solar collector pro- ature, Eq. (134), the exergy destruction in cess amounts to 84.6% of the total exergy destruction, the solar collector amounts to 84.6% of the total exergy destruction in the system. One of the conclusions from this result is that the use of solar radiation generated at the sun temperature for producing low temperature heat is thermodynamically very inefficient. (b) If the solar exergy supplied to the solar collector is calculated based on the inlet fluid temperature, Eq. (135), the PV module process causes 48.3% of the total exergy destruction, which is also the largest component exergy destruction in the system. The second largest exergy destroyer in this approach is the solar collector, which accounts for 27.1% of the total exergy destruction. (5) The energy analysis, which points thus to the suggestion that increasing the energy efficiency Fig. 18. System energy input distribution with % break- of the solar collector would contribute most to down by the system subprocesses (percentage). the overall system energy efficiency.

20126 .LoadN ir/Dslnto n ae ramn 7(06 20093–20140 (2016) 57 Treatment Water and Desalination / Lior N. and Luo A.

Table 6 Exergy analysis of the subprocesses, with the solar irradiation exergy to the solar collector calculated based on the sun temperature (Eq. (134))

_ _ _ ψ Exergy input, Ein;sub Energy output, Eout;sub Exergy destruction, Eloss;sub Exergy efﬁciency, sub Relative exergy destruction ratio, XDR

Value Value Value Value Value Process Equation (W) Equation (W) Equation (W Equation (%) Equation (%)

_sun _ _ _sun _ − _ _ _sun _ _sun _ − _ _sun _ _ Solar collector esc Asc + E2 6,028.2 E5 784.6 esc Asc + E2 E5 5,243.6 E5/(esc Asc + E2) 13.0 (esc Asc + E2 E5)/(esc Asc + esunAPV + E2)84.6 ______− _ − _ − ______− _ − _ − _ _sun _ _ MD separation E1 + E5 802.1 E2 + E6 + E8 610.2 E1 + E5 E2 E6 E8 191.8 (E2 + E6 + E8)/(E1 + E5) 76.1 (E1 + E5 E2 E6 E8)/(esc Asc + esunAPV + E2) 3.1 _ _ _ − _ _ _ _ − _ _sun _ _ PV module esunAPV 777.1 We 145.5 esunAPV We 631.6 We/esunAPV 18.7 (esunAPV We)/(esc Asc + esunAPV + E2)10.2 _ _ _ _ _ − ______− _ _sun _ _ Pump E0 + We 145.5 E1 17.5 E0 + We E1 128.0 E1/(E0 + We) 12.0 (E0 + We E1)/(esc Asc + esunAPV + E2) 2.1 ______− _ − ______− _ − _ _sun _ _ Discharge E6 + E8 3.5 E7 + E9 0.1 E6 + E8 E7 E9 3.4 (E7 + E9)/(E6 + E8) 3.7 (E6 + E8 E7 E9)/(esc Asc + esunAPV + E2) 0.0 _sun _ _ _ _ _sun _ _ − _ − _ _ _ _sun _ _ _sun _ _ − _ − _ Total esc Asc + esunAPV + E2 6,198.6 E7 + E9 0.1 esc Asc + esunAPV + E2 E7 E9 6,198.4 (E7 + E9)/[(esc Asc + esunAPV + E2)] 0.0 [esc Asc + esunAPV + E2 E7 E9]/ 100.0 _sun _ _ (esc Asc + esunAPV + E2)

.LoadN ir/Dslnto n ae ramn 7(06 20093–20140 (2016) 57 Treatment Water and Desalination / Lior N. and Luo A.

Table 7 Exergy analysis of the subprocesses, with the solar irradiation exergy to the solar collector calculated based on the ﬂuid temperature (Eq. (135))

Energy output, _ _ _ ψ Exergy input, Ein;sub Eout;sub Exergy destruction, Eloss;sub Exergy efﬁciency, sub Relative exergy destruction ratio, XDR

Value Value Value Value Value Process Equation (W) Equation (W) Equation (W) Equation (%) Equation (%)

_flu _ _ _flu _ − _ _ _flu _ _flu _ − _ _flu _ _ Solar collector esc Asc + E2 1,138.7 E5 784.6 esc Asc + E2 E5 354.1 E5/(esc Asc + E2) 68.9 (esc Asc + E2 E5)/(esc Asc + esunAPV + E2)27.0 ______− _ − _ − ______− _ − _ − _ _flu _ _ MD separation E1 + E5 802.1 E2 + E6 + E8 610.2 E1 + E5 E2 E6 E8 191.8 (E2 + E6 + E8)/(E1 + E5) 76.1 (E1 + E5 E2 E6 E8)/(esc Asc + esunAPV + E2)14.7 _ _ _ − _ _ _ _ − _ _flu _ _ PV module esunAPV 777.1 We 145.5 esunAPV We 631.6 We/esunAPV 18.7 (esunAPV We)/(esc Asc + esunAPV + E2)48.2 _ _ _ _ _ − ______− _ _flu _ _ Pump E0 + We 145.5 E1 17.5 E0 + We E1 128.0 E1/(E0 + We) 12.0 (E0 + We E1)/(esc Asc + esunAPV + E2) 9.8 ______− _ − ______− _ − _ _flu _ _ Discharge E6 + E8 3.5 E7 + E9 0.1 E6 + E8 E7 E9 3.4 (E7 + E9)/(E6 + E8) 3.7 (E6 + E8 E7 E9)/(esc Asc + esunAPV + E2) 0.3 _flu _ _ _ _ _flu _ _ − _ − _ _ _ _flu _ _ _flu _ _ − _ − _ Total esc Asc + esunAPV + E2 1,309.1 E7 + E9 0.1 esc Asc + esunAPV + E2 E7 E9 1,308.9 (E7 + E9)/[(esc Asc + esunAPV + E2)] 0.0 [esc Asc + esunAPV + E2 E7 E9]/ 100.0 _flu _ _ (esc Asc + esunAPV + E2) 20127 20128 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

Many constructive guidelines for improving system efﬁciency can thus be drawn from the exergy analysis, which are not revealed by energy analysis alone or at all. We note that this example in Section 3.6.7 is primarily intended to demonstrate the exergy analysis method, and the conclusions from the analyses results are left to the user.

3.7. Heat and mass transport analysis The performance criteria used to characterize the transport process in MD are discussed in this section. These criteria are generally about the membrane module, where the coupled mass and heat transfer for the separation takes place. For an MD system shown in Fig. 8, the control volume of the membrane module Fig. 19. System exergy destruction including % breakdown by its subprocesses (percentage) with the solar irradiation considered in the deﬁnitions of the transport analysis exergy of the solar collector is calculated based on sun performance criteria is outlined by the dashed line of temperature Eq. (134). B in Fig. 15.

3.7.1. The convective heat transfer coefficient for fluid flow (h) Here the well-known convective heat transfer coefficient, defined as the ratio of the total heat flux to the

temperature difference between two points or surfaces in a fluid or between a point or surface in the fluid and another point or surface on a solid-fluid interface. In MD that interface is the membrane or the solid planes (such cooling plane) and the fluid could be the feed stream, the permeate stream, or the coolant stream. It is defined as follow:

00 ¼ qt h (141) Tb Tinter Fig. 20. System exergy destruction including % breakdown where h is convective heat transfer coefficient between by its subprocesses (percentage) with the solar irradiation 2 00 exergy of the solar collector calculated based on the fluid defined points and/or surfaces (W/(m K)), qt —total 2 temperature Eq. (135). heat flux there (W/m ), Tb—temperature at a chosen location in the bulk flow (K), Tinter—temperature at the chosen heat transfer boundary (K). (6) The exergy analysis shows that the solar collec- On the membrane module level (B in Fig. 15), as tor is also the major exergy destruction subpro- discussed in Section 2.2, heat transfer in the fluid cess. Increasing the exergy efficiency of the solar streams are essential components of the overall heat collector would require increasing of the flow transfer process in MD and the thermal boundary exergy of the heated fluid according to Eq. (130), layer of the fluid stream imposes an important portion _ ¼ _ where E4 m4e4. Thus, for example, a solar col- of the total heat transfer resistance [4], in large part lector delivering a fixed amount of heat: characterized by h. Increasing h reduces the overall _ − IAsc = m4Cp(T4 T3) can have different exergy heat transfer resistance in the membrane module, ψ efficiencies sc that depend ((Eq. (60)) on the col- which can be achieved through methods such as lector outflow temperature T4, which, in turn increasing the feed and the distillate stream flow _ would depend on the collector flow rate m4. velocities or the use of flow inserts (“spacers”) [11]. A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20129

On the MD system level (Fig. 14), h also plays a where Tv is saturation temperature of the vacuum side key role in all other heat transfer related components vapor pressure (K). in the system, such as the heat input and the recovery Noted that Tv is the actual temperature at the vac- heat exchangers. uum side membrane surface, and Tv is not the actual temperature as shown in Fig. 21. In SGMD, the vapor is condensed by an external 3.7.2. Nusselt number (Nu) condenser and the vapor pressure of sweeping gas The well-known Nusselt number is defined as the stream can be below its saturated pressure, so similar ratio of the convective to conductive heat transfer fluxes as TPC is defined in VMD, the TPC in SGMD is across the chosen boundaries of the fluid stream. defined as:

T ; T h d ¼ f m p;m ¼ TPC (145) Nu (142) Tf T kf p

where Nu is Nusselt number (dimensionless), h—con- where Tp;m is saturation temperature of the vapor 2 pressure at the membrane surface of the sweeping gas vective heat transfer coefficient (W/(m K)), d—stream side (K), T —saturation temperature of the vapor pres- hydraulic diameter (m), kf—thermal conductivity of p fluid (W/(m K)). sure at the bulk of the sweeping gas side (K). Correlations exist to relate Nu to easily measurable Fig. 22 illustrates the definition of TPC in SGMD. dimensionless number such as the flow Reynolds Noted that Tp,m is the actual temperature at the sweep- number (Re) and the fluid Prandtl number (Pr), allow- ing gas side membrane surface. ing the determination of h [11,51,52]. TPC can be a local value at any position typically used in transport process analysis and modeling or an average value of the whole MD membrane module. 3.7.3. Temperature polarization coefficient (TPC) The driving force for separation in MD is the

cross-membrane vapor pressure difference generally The temperature polarization coefficient is defined generated by the temperature difference, so (T − T )is as the ratio of the temperature difference across the f p the theoretical maximal driving force. The heat transmembrane surfaces to the temperature difference fer rate from the feed to the coolant between these between the feed and the permeate bulk streams: temperatures is limited by the resistances due to convection and conduction phenomena in the intervening ¼ Tf;m Tp;m media. These resistances cause corresponding drops in TPC (143) Tf Tp temperatures, as shown in Figs. 4 and 6, and as quan- tified by Eqs. (7) and (8). TPC is thus the ratio of the where TPC is temperature polarization coefficient (di- actual temperature driving force for the process to the mensionless), Tf,m—temperature at the membrane maximal present driving force. According to the heat feed-side surface (K), Tp,m—temperature at the mem- transfer resistance analog, TPC can also be evaluated brane permeate-side surface (K), Tf—temperature of by the heat transfer resistance of the membrane the feed bulk (K), Tp—temperature of the permeate together with the other heat transfer resistance in the bulk (K). transport process. So as discussed in Section 2.2, TPC The related temperature used to calculate the TPC in DCMD can be calculated by: for DCMD and AGMD are shown in Figs. 3 and 5. = TPC is the ratio of the actual temperature driving ¼ Tf;m Tp;m ¼ 1 Hm TPC = þ = þ = (146) force across the membrane to the present theoretical Tf Tp 1 hf 1 Hm 1 hp maximal temperature driving force across it. To keep the coherent physical meaning and standardizing the In AGMD, additional heat transfer resistances are pre- TPC value among all MD configurations, Alsaadi et al. sent due to the air gap (Rg), the condensate liquid film [53] proposed that the most appropriate definition for (Rf), and the cooling plate (Rc) are presented (Fig. 6) so: TPC in VMD is: Tf;m Tp;m 1=Hm TPC ¼ ¼ ; T T 1=h þ 1=H þ R þ R þ R þ 1=h ¼ Tf m Tv f p f m g f c p TPC (144) Tf Tv (147) 20130 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

molar concentration difference between their molar concentrations in the feed and the permeate bulk streams.

¼ cf;m cp;m CPC (148) cf cp

where CPC is molar concentration polarization coefficient (dimensionless), cf,m—molar concentration at the 3 membrane feed-side surface (mol/m ), cp,m—molar concentration at the membrane permeate-side surface 3 (mol/m ), cf—molar concentration of the feed bulk 3 (mol/m ), cp—molar concentration of the permeate bulk (mol/m3). Typically, for non-volatile solutes, cf,m and cf are equal to 0 for ideal MD process, since they are pure Fig. 21. Polarization definition-related temperature profiles distillate, so then the equation is reduced to: in VMD.

cf;m CPC ¼ (149) In VMD and SGMD, the vapor is condensed by the cf external condenser as stated before, so this heat transfer resistance analysis cannot be simply applied to Typically in MD, volatile solvent flows across the these processes. membrane as vapor and non-volatile solutes are TPC is often used as a criterion that evaluates the rejected at the membrane feed-side surface. As the sol- effects of heat transfer resistance of the thermal vent evaporates at the membrane feed-side surface, boundary layers relative to total heat transfer resis- the concentration of the solutes increases and becomes tance. TPC rising to approach 1 indicates an increasing higher at the membrane feed-side surface than in the convective heat transfer coefficient and small heat bulk stream. This phenomenon is called concentration transfer resistance of the intervening media, and the polarization. Similarly, the concentration polarization opposite is for TPC approaching zero. could also develop at the permeate side when the solute is volatile as Fig. 23 shows. Similar to TPC, CPC quantifies the concentration 3.7.4. Concentration polarization coefficient (CPC) polarization phenomenon exists in MD membrane The concentration polarization coefficient is module, and CPC was calculated from a film model defined as the ratio of the molar concentration differ- [11]. ence between the two membrane surfaces, to the cf;m J CPC ¼ ¼ exp (150) cf qdkso

2 ρ where J is mass flux (kg/(m s)), d—density of the 3 distillate (kg/m ), kso—mass transfer coefficient of the solutes (m/s). Due to the concentration polarization, the mole fraction of solutes is higher at the feed/membrane interface, which decrease the vapor pressure compared to bulk condition and consequently reduces the distillation driving force. Moreover, higher concentration at the membrane may promote the scaling formed on the membrane and cause loss of hydrophobicity. Analogy of the heat and mass transport processes indicates that methods that enhance heat transfer in Fig. 22. Polarization definition-related temperature profiles in SGMD. fluid flow, such as increase of the flow velocity, and A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20131 use of flow inserts, will also enhance the species trans- 3.8. Long-time performance criteria fer and thus reduce the concentration polarization MD productivity and energy/exergy efficiency [54,55]. deteriorate with operating time, mainly due to mem- CPC is a criterion used to evaluate the transport brane properties changes and fouling. Long-time per- process in MD, which is related to the product pro- formance of MD thus must be evaluated, especially duction rate, the energy efficiency, and the product when for commercial applicability. Performance crite- quality. ria used to evaluate the long-time performance of MD are discussed in this section. 3.7.5. Vapor pressure polarization coefficient (PPC) The vapor pressure polarization coefficient is 3.8.1. Mass flux change rate (MCR) defined as the ratio of the vapor pressure difference The mass flux change rate is defined as the rate of between the two membrane surfaces to the vapor the mass flux change as a percentage of the initial pressure difference in the feed and the permeate bulk mass flux: streams. Jinitial Jfinal 1 pf;m pp;m ¼ PPC ¼ (151) MCR (152) Jinitial t pf pp

− where MCR is mass flux change rate (s 1), J — where PPC is vapor pressure polarization coefficient initial initial mass flux (kg/(m2 s)), J —final mass flux (dimensionless), p —vapor pressure at the membrane final f,m (kg/(m2 s)), t—time period (s). feed-side surface (Pa), p —vapor pressure at the p,m Many studies reported mass flux changes with membrane permeate-side surface (Pa), p —vapor pres- f time [57–65] due to deterioration of membrane materi- sure of the feed bulk (K), p —vapor pressure of the p als, fouling, or the instability of the energy source permeate bulk (K). (such as solar heat). Stability of membrane materials MD is a thermally driven process utilizes vapor and fouling are an important aspect of MD system pressure difference at different temperature, and the distillation rate, product quality, and energy efficiency. mass flux is driven by vapor pressure difference as This criterion provides a comparative metric to evalu- Eq. (9) indicates. So PPC is the ratio of the actual ate MD performance in long-time operation with vapor pressure driving force for the process to the respect to the distillate production rate and factors present maximal vapor pressure driving force, consid- that will influence MD distillate production rate in ering both the temperature polarization and the con- long-time operation. centration polarization. PPC is applicable for all the four membrane module configurations, and was used, for example, to investigate MD in [56]. 3.8.2. Energy efficiency change rate (ECR) Similar to changes in distillation rate, the energy efficiency may change with time too, so a criterion named “energy efficiency change rate” that evaluates the long-time operation effect on energy efficiency of the MD process is proposed here and is defined as the rate of SHC change as a percentage of the initial SHC.

SHCinitial SHCfinal 1 ECR ¼ (153) SHCinitial t

− where ECR is energy efficiency change rate (s 1), SHCinitial—initial specific heat consumption (J/kg), SHCfinal—final specific heat consumption (J/kg), t—time period (s). MD energy efficiency changes with time have been Fig. 23. Concentration polarization-definition related con- reported in [48,57]. This criterion provides a compara- centration profile. tive metric to evaluate MD performance in long-time 20132 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

Table 8 Summary of the MD performance criteria with their utility

Equation Index Name Symbol Units number Utility; evaluates the: 1 Basic membrane – – – Membrane’s basic properties affect its performance in properties MD 2 Liquid entry pressure LEP Pa (77) Membrane’s ability to prevent pore wetting 3 Membrane permeability C kg/(m2 s Pa) (79) Membrane’s ability to produce mass flux − 4 Mass transport pre- PF m 1 or (80) Membrane’s ability to produce mass flux just from factor dimensionless membrane properties or m 2 5 Conduction heat hm W/(m K) (84) Membrane’s ability for the conduction heat loss transfer coefficient of the membrane _ 6 Product mass flow rate mpro kg/s (85) Product production rate 7 Mass flux J kg/(m2 s) (87) Transmembrane mass transfer rate per unit membrane area − 8 Relative concentration CR s 1 (89) Concentration rate of the solution change rate 9 Volumetric molar c mol/m3 (91) Species concentration of the solution concentration 10 Rejection factor R Dimensionless (93) Ratio of the solutes concentration difference between the feed solution and the distillate 11 Concentration factor CF Dimensionless (94) Concentration of the feed solution being concentrated or of the volatile solutes being removed 12 Separation factor α Dimensionless (95) Ability to separate the desired component 13 Specific heat SHC J/kg or J/m3 (96), (97) Heat consumption to produce a unit mass or volume of consumption the distillate 14 Specific electrical energy SEEC J/kg or J/m3 (98), (99) Electrical energy consumption to produce a unit mass consumption or volume of the distillate 15 Membrane thermal η Dimensionless (100) Heat utilization efficiency for distillation of the heat efficiency transport across the membrane 16 Gain output ratio GOR Dimensionless (102) Ratio of the transmembrane latent heat transfer rate to the heat input rate 17 Heat recovery factor Hr Dimensionless (104) Internal heat recovery extent in the MD system 18 Performance ratio PR Dimensionless (105) Ratio of the mass flow rate of the distillate to the mass flow rate of the input steam 19 Flow pressure drop ΔP Pa (106) pressure drop of the flow influencing the pump work and system operating conditions 20 Fuel energy saving ratio FESR Dimensionless (107) Ratio of the energy saved for dual-purpose desalination plant compare with separate power-only and water- only systems 21 Specific equivalent EEEC J/kg (111), Electrical energy reduction of the dual-purpose electrical energy (112) desalination plant per unit mass or volume of the consumption water produced ψ 22 Overall exergy t Dimensionless (113) Overall thermodynamic irreversibility of the process efficiency ψ 23 Utilitarian exergy u Dimensionless (114) Process exergy input and output based on user’s need efficiency 24 Specific exergy SXC J/kg (116), Exergy consumption to produce a unit mass or volume consumption (117) of the product 25 Exergy consumption XCR Dimensionless (118) Ratio of the minimum specific exergy consumption to ratio the specific exergy consumption

(Continued) A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20133

Table 8 (Continued) Equation Index Name Symbol Units number Utility; evaluates the: 26 Exergy saving ratio XSR Dimensionless (121) Ratio of the exergy saved for dual-purpose desalination plant compare with separate power-only and water- only systems 27 Relative exergy XDR Dimensionless (125) Extent of the exergy destruction within the subsystem destruction ratio 0 28 Temperature driven L11 W/(m K) (46) Contribution of unit temperature gradient to the heat heat flux kinetic flux coefficient 0 2 29 Concentration driven L12 (W m )/mol (46) Contribution of unit concentration gradient to the heat heat flux kinetic flux coefficient 0 30 Temperature driven L21 (kg K)/(m s) (47) Contribution of unit temperature gradient to the mass mass flux kinetic flux coefficient 0 2 31 Concentration driven L22 (kg m )/ (47) Contribution of unit concentration gradient to the mass mass flux kinetic (mol s) flux coefficient 32 Convective heat transfer h W/(m2 K) (141) Convective heat transfer ability of the fluid streams in coefficient for fluid flow MD 33 Nusselt number Nu Dimensionless (142) Ratio of the convective to conductive heat transfer ability of the fluid streams in MD 34 Temperature TPC Dimensionless (143), Driving temperature difference reduction across polarization Coefficient (144), membrane due to heat transfer resistances in the (145) module

35 Concentration CPC Dimensionless (148) Concentration difference increase across membrane due polarization coefficient to species transfer resistances in the module 36 Vapor pressure PPC Dimensionless (151) Driving vapor pressure difference reduction across polarization coefficient membrane due to heat and species transfer resistances in the module − 37 Mass flux change rate MCR s 1 (152) Distillation production rate change in the long-time operation − 38 Energy efficiency ECR s 1 (153) Heat utilization efficiency change in the long-time change rate operation − 39 Product quality change PCR s 1 (154) Product quality change in the long-time operation rate − 40 Fouling rate FR s 1 (155), Fouling in the long-time operation and its impact on (156) membrane properties

operation with respect to the heat utilization efficiency change of the product as a percentage of the initial and factors that will influence MD energy perfor- solutes molar concentration of the product. mance in long-time operation. cinitial cfinal 1 PCR ¼ (154) c t 3.8.3. Product quality change rate (PRC) initial − The product quality may also change with time, so where PCR is product quality change rate (s 1), a criterion named “product quality change rate” that cinitial—initial molar concentration of the solutes in 3 evaluates the long-time operation effect on the quality product (mol/m ), cfinal—final molar concentration of the product of MD process is proposed here and is of the solutes in product (mol/m3), t—time defined as the rate of the solutes molar concentration period (s). 20134 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

Table 9 Summary of the performance criteria in MD classiﬁed by category of use in the MD system and by distinction between scientiﬁc and commercial types of application

Categories Application Long Index Name Symbol Membrane Module System operation Scientific Commercial 1 Basic membrane properties – √√√ 2 Liquid entry pressure LEP √√√ 3 Membrane permeability C √√√ 4 Mass transport pre-factor PF √√ √√√ 5 Conduction heat transfer coefficient of the hm membrane _ 6 Product mass flow rate mpro √√ √ √ 7 Mass flux J √√√ √√ 8 Relative concentration change rate CR √√ √ √ 9 Volumetric molar concentration c √√√ √√ 10 Rejection factor R √√√ √√ 11 Concentration factor CF √√ √ √ 12 Separation factor α √√ √ √ 13 Specific heat consumption SHC √√√ 14 Specific electrical energy consumption SEEC √√√ 15 Membrane thermal efficiency η √√ √ 16 Gain output ratio GOR √√√ √√ 17 Heat recovery factor Hr 18 Performance ratio PR √√ 19 Flow pressure drop ΔP √√ √ √ √√ 20 Fuel energy saving ratio FESR 21 Specific equivalent electrical energy EEEC √√ consumption ψ √√ √ √ 22 Overall exergy efficiency t ψ √√ √ √ 23 Utilitarian exergy efficiency u 24 Specific exergy consumption SXC √√√ 25 Exergy consumption ratio XCR √√√ 26 Exergy saving ratio XSR √√ 27 Relative exergy destruction ratio XDR √√√ 0 √√ 28 Temperature driven heat flux kinetic L11 coefficient 0 √√ 29 Concentration driven heat flux kinetic L12 coefficient 0 √√ 30 Temperature driven mass flux kinetic L21 coefficient 0 √√ 31 Concentration driven mass flux kinetic L22 coefficient 32 Convective heat transfer coefficient for h √√ fluid flow 33 Nusselt number Nu √√ 34 Temperature polarization coefficient TPC √√ 35 Concentration polarization coefficient CPC √√ 36 Vapor pressure polarization coefficient PPC √√ 37 Mass flux change rate MCR √√√ 38 Energy efficiency change rate ECR √√√ 39 Product quality change rate PCR √√√ 40 Fouling rate FR √√√ A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20135

− The product quality change with time has been where TCR is membrane thickness change rate (s 1), δ δ reported in MD [57,60,62,66]. This criterion provides a initial—initial membrane thickness (m), final—final comparative metric to evaluate MD performance in membrane thickness (m), t—time period (s). long-time operation with respect to product quality Direct visual comparison also serves as a method and factors that will influence MD performance in to evaluate the fouling. More information about physi- long-time operation in that respect. cal, chemical, and biological characterization techniques on fouling can be found in [67–69]. 3.8.4. Fouling rate (FR) Fouling in MD can be evaluated indirectly by the 4. Conclusions change rate of the operation performance (criteria MCR, ECR, PCR). It can also be evaluated and charac- Table 8 summarizes the performance criteria terized more directly and specifically by the fouling reviewed in this paper with their units, definition itself and its impact on the membrane. equation numbers, and utilities. Table 9 summarizes these performance criteria, by category and applica- (1) The fouling rate can be evaluated by the tion (scientific or commercial). change rate of the surface concentration of the This report summarizes the technical/scientific foulants. So the foulants change rate can be performance criteria used in MD, on the component, defined as the rate of the foulants surface con- module, and systems levels. It thus offers clarity and centration change as a percentage of the initial uniformity in their use. foulants surface concentration. While most of the surveyed performance criteria are in common use, some, especially those related to exergy analysis and criteria about long-time operation, cinitial cfinal 1 FR ¼ (155) are basically new. c t initial Most of the performance criteria are based on uni-

−1 versal scientific principles and widely used, but some where FR is foulants change rate (s ), cinitial—initial have evolved with the technology for simplicity and foulants surface concentration (mol/m2), c —final final convenience and may lack correct scientific principles foulants surface concentration (mol/m2), t—time per- and lack unique definitions. While it is not our objec- iod (s). tive to restrict their use, we pointed to their limita- It should be noticed that if the foulants are tions. Furthermore, unnecessary duplicative microorganisms, the foulants surface concentration is multiplicity of performance criteria obfuscates the replaced in Eq. (155) by the number of the microor- field, prevents scientific uniformity, and creates ganisms per unit area: misunderstandings and misrepresentations. It is highly recommended to choose and use only the nec- ninitial nfinal 1 FR ¼ (156) essary minimum of performance criteria, based on ninitial t uniform scientific criteria. A full characterization of the membrane itself where ninitial is initial number of the microorganisms should include all the basic membrane properties −2 per unit area (m ), nfinal—final number of the microor- listed. In MD, it is at least needed to include −2 ganisms per unit area (m ), t—time period (s). the LEP, the membrane permeability (C), and the conduction heat transfer coefficient of the (2) The fouling rate can also be evaluated by the membrane (hm). change rate of the membrane properties such A comprehensive evaluation of the membrane as membrane thickness, porosity, contact angle, module (and for research focused on the membrane and tensile strength. Taking membrane thick- when the evaluation is done with it installed in a ness as an example, its change rate can be module) and of the MD system should at least include defined as the rate of the membrane thickness evaluation of the production rate (Section 3.3), the pro- change as a percentage of the initial membrane duct quality (Section 3.4) and the energy efficiency thickness. (Sections 3.5 and 3.6). Other criteria were introduced to evaluate the transport process and the long-time operation, of spe- dinitial dfinal 1 TCR ¼ (157) cial interest for commercial and industrial use. dinitial t 20136 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

Nomenclatures Hd,sat — specific enthalpy of the saturated distillate (J/kg) A — membrane area (m2) Hd,o — specific enthalpy of the supercooled distillate a — activity of the solvent (dimensionless) (J/kg) B — geometric factor (dimensionless) 2 Hs,i — specific enthalpy of the superheated steam C — membrane permeability (kg/(m s Pa)) (J/kg) c — volumetric molar concentration (mol/m3)or Hs,sat — specific enthalpy of the saturated steam (J/kg) foulants surface concentration (mol/m2) Hs,o — specific enthalpy of the supercooled steam CF — concentration factor (dimensionless) (J/kg) Cp — specific heat capacity at constant pressure hm — conduction heat transfer coefficient of the (J/(K kg)) membrane (W/(m2 K)) CPC — concentration polarization coefficient Hm — total heat transfer coefficient of the membrane, (dimensionless) 2 − defined in Eq. (4) (W/(m K)) CR — relative concentration change rate (s 1) Hr — heat recovery factor (dimensionless) Cv — specific heat capacity at constant volume _ Hin;f — enthalpy of the feed inflow (W) (J/(K kg)) _ Hin;p — enthalpy of the permeate inflow (W) D — diffusion coefficient for vapor (m2/s) _ Hout;f — enthalpy of the feed outflow (W) d — flow hydraulic diameter (m) _ Hout;p — enthalpy of the permeate outflow (W) dp — membrane pore size (m) 2 −1 I — solar irradiation (W/m ) ECR — energy efficiency change rate (s ) J — mass flux (kg/(m2 s)) EEECm — specific equivalent electrical energy Jj — fluxes consumption per unit mass of the product Jv — volumetric flux (m/s) (J/kg) Jv — average volumetric flux (m/s) EEECV — specific equivalent electrical energy kB — Boltzman constant(J/K) consumption per unit volume of the product kf — thermal conductivity of the fluid (J/m3) _ (W/(m K)) E — rate of the exergy transferred (W) _ C kg — thermal conductivity of the gas present in the E — rate of the chemical exergy transferred (W) _ pores (W/(m K))

Edes — exergy destruction rate (W) _ km — effective membrane thermal conductivity E — rate of the electrical exergy transferred (W) _ electrical (W/(m K)) E — rate of the flow exergy transferred (W) _ flow Kn — Knudsen number (dimensionless) Ein;c — flow exergy of the coolant inflow (W) _ ks — membrane material thermal conductivity E ; — flow exergy of the feed inflow (W) 2 _ in f (W/(m K)) Ein;g — flow exergy of the sweeping gas inflow (W) _ kso — mass transfer coefficient of the solutes E ; — flow exergy of the permeate inflow (W) _ in p (m/s) Einput — exergy input rate (W) 0 _ L11 — temperature driven heat flux kinetic coefficient E ; — flow exergy of the coolant outflow (W) _ out c (W/(m K)) Eout;d — flow exergy of the distillate (W) 0 _ L12 — concentration driven heat flux kinetic E ; — flow exergy of the feed outflow (W) 2 _ out f coefficient ((W m )/mol) Eout;g — flow exergy of the sweeping gas outflow (W) 0 _ L21 — temperature driven mass flux kinetic E ; — flow exergy of the permeate outflow (W) _ out p coefficient ((kg K)/(m s)) Eoutput — exergy output rate (W) L0 — concentration driven mass flux kinetic _ P 22 E — rate of the physical exergy transferred (W) coefficient ((kg m2)/(mol s)) _ Ep — useful exergy output rate (W) L — inverse temperature driven heat flux kinetic _ 11 Ethermal — rate of the thermal exergy transferred (W) coefficient ((K W)/m) _ Eu — paid exergy input rate (W) L12 — chemical potential driven heat flux kinetic ei — specific flow exergy of stream i (kJ/kg) coefficient ((K kg)/(m s)) _ esun — exergy of the solar irradiation per unit area L21 — inverse temperature driven mass flux kinetic 2 (W/m ) coefficient ((K kg)/(m s)) FESR — fuel energy saving ratio (dimensionless) L — chemical potential driven mass flux kinetic − 22 FR — foulants rate (s 1) coefficient ((K kg2)/(m s J)) 2 g — gravitational acceleration (m/s ) LEP — liquid entry pressure (Pa) GOR — gain output ratio (dimensionless) Ljk — kinetic (phenomenological) coefficients h — convective heat transfer coefficient for fluid lp — average length of the pores (m) 2 flow (W/(m K)) lrsub — subprocess relative energy loss to the H — specific enthalpy (J/kg) environment (dimensionless) Hd,i — specific enthalpy of the superheated distillate M — molecular weight of vapor material (kg/mol) − (J/kg) MCR — mass flux change rate (h 1) A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140 20137

mt — mass of the solution (kg) SEECv — specific electrical energy consumption per unit 3 msp — mass of the species (kg) volume of the distillate (J/m ) m˙ — mass flow rate (kg/s) SHCm — specific heat consumption per unit mass of the _ min;f — mass inflow rate of the feed solution (kg/s) distillate (J/kg) _ min;p — mass inflow rate of the permeate (kg/s) SHCV — specific heat consumption per unit volume of _ 3 mout;f — the mass outflow rate of the feed solution the distillate (J/m ) (kg/s) SXCm — specific exergy consumption per unit mass of _ mout;p — the mass outflow rate of the permeate (kg/s) the product (J/kg) n — number of the microorganisms per unit area SXCmin — minimum specific exergy consumption per − (m 2) unit mass of the product (J/kg) N — mole number of the species (mol) SXCV — specific exergy consumption per unit volume 3 Nso — mole number of the solutes (mol) of the product (J/m ) Nu — Nusselt number (dimensionless) T — temperature (K) nsol — solvent concentration (mol/kg) Tin — temperature of the heat input (K) P — pressure (Pa) Tv — saturation temperature of the vacuum side’s p — vapor pressure (Pa) vapor pressure (K) p* — vapor pressure of pure solvent (Pa) t — time period (s) pair — average partial pressure of the non- Tb — temperature in the bulk of the flow (K) − condensable gas in the membrane (Pa) TCR — membrane thickness change rate (s 1) −1 PCR — product quality change rate (s ) Tinter — temperature of the flow at the heat transfer − PF — mass transport pre-factor ((m 1) for β =0, boundary (K) β β (dimensionless) for = 1, (m) for =2) Tout — temperature of the heat output (K) Pin — flow pressure at the defined flow inlet (Pa) Tp — saturation temperature of vapor pressure at Pout — flow pressure at the defined flow outlet (Pa) bulk of the sweeping gas side (K) PPC — vapor pressure polarization coefficient Tp;m — saturation temperature of vapor pressure at (dimensionless) the membrane surface of the sweeping gas PR — performance ratio (dimensionless) side (K) _ Q — rate of the heat transferred (W) TPC — temperature polarization coefficient

_ Q — heat exchange rate in the condenser (W) (dimensionless) _ e Q — heat input rate by the fuel (W) v — velocity of the fluid flow _ fuel Qin — heat input rate (W) (m/s) _ 3 Qout — heat output rate (W) V — volume of the solution (m ) _ 3 Qr — heat recovery rate (W) Vmem — total volume of the membrane (m ) 00 2 3 q — heat flux (W/m ) Vp — volume of the pores (m ) 00 _ 3 qc — heat flux across the membrane by conduction V — volumetric flow rate (m /s) 2 _ (W/m ) We — rate of the electrical energy transferred (W) 00 2 _ qt — total heat flux (W/m ) We;b — the electrical energy consumption of the 00 qv — heat flux across the membrane by evaporation sweeping gas blower (W) 2 _ (W/m ) We;c — electrical energy consumption of the coolant r — average pore radius (m) flow pump (W) _ R — rejection factor (dimensionless) or the ideal gas We;f — electrical energy consumption of the feed flow constant (J/(mol K)) pump (W) _ Rc — heat transfer resistances of the cooling plate We;in — total electrical energy input (W) 2 _ ((m K)/W) We;p — electrical energy consumption of the permeate Rf — heat transfer resistances of the condensate flow pump (W) 2 _ liquid film ((m K)/W) We;t — electrical energy output of the vapor power Rg — heat transfer resistances of the air gap system (W) 2 _ ((m K)/W) We;v — electrical energy consumption of the vacuum R — the gas constant of vapor, defined in Eq. (37) pump (W) v _ (J/(kg K)) We;w — electrical energy consumption of the water rmax — largest pore radius (m) pump (W) S — salinity (%) Wmin — minimum work of separation (J/kg) s — specific entropy of the solution (J/(kg K)) w — mass fraction (dimensionless) s_ — entropy production rate (W/(K m3)) x — mole fraction (dimensionless) SEECm — specific electrical energy consumption per unit XDR — relative exergy destruction ratio mass of the distillate (J/kg) (dimensionless) 20138 A. Luo and N. Lior / Desalination and Water Treatment 57 (2016) 20093–20140

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