Theoretical Analysis of Pressure Retarded Membrane Distillation

Article Cite This: Ind. Eng. Chem. Res. 2017, 56, 14888−14901

pubs.acs.org/IECR

Theoretical Analysis of Pressure Retarded Membrane Distillation (PRMD) Process for Simultaneous Production of Water and Electricity Kiho Park,† Do Yeon Kim,†,‡ and Dae Ryook Yang* Department of Chemical and Biological Engineering, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Republic of Korea ABSTRACT: This study proposed and investigated a new pressure-retarded membrane distillation (PRMD) for simultaneous production of water and electricity. The PRMD process was designed by combining the concepts of direct contact membrane distillation (DCMD) and pressure-retarded osmosis (PRO) processes in a single membrane module. A mathematical model for the PRMD process was developed, and the performances of energy generation and water production were estimated and compared to the results of the DCMD process. It was found that the PRMD process can save energy by producing electricity from a hydro-turbine, but the water production rate is slightly less than the DCMD process. Also, the effects of operating conditions and membrane properties were analyzed, and the best conditions were investigated. By applying the best available membrane technology, the PRMD process can save about 0.1738 kWh/m3 with about only 3% sacrifice of fresh water production compared to the DCMD process at the same basis. Thus, the PRMD process can be used as a multifunctional system for producing water as the DCMD process and electricity as the PRO process at the same time, so it can be a self-sustained process when low-grade heat energy could be supplied.

1. INTRODUCTION Membrane distillation (MD) is a thermal membrane separation process in which only vapor molecules are transported through porous hydrophobic membranes. The driving force of the MD process is supplied by the vapor pressure difference caused by temperature difference between two solutions. The MD has potential applications in many areas producing highly purified permeate and separating contaminants from liquid solutions. It has been tested in the treatment of thermally sensitive industrial products such as concentrating aqueous solution in fruit juices1 and in pharmaceutical industry.2 And also, it has been widely applied in wastewater treatment3,4 and seawater desalination.5−9 In seawater desalination fields, the potential advantages of the MD process compared with the conventional thermal desalination techniques, such as multistage flash (MSF) and multiple effect distillation (MED), are its lower operating temperature and its possibility for utilizing low-grade waste or alternative energy sources.2,10−12 Even though the energy consumption of the MD process is estimated more than 450 kWh/m3, a moderate temperature range (60−90 °C) enables one to utilize low-grade waste heat and concentrated solar energy.13−17 Recently, the interest of using MD process for desalination is increasing worldwide due to these attractive features, especially when coupled with solar energy or utilizing low-grade heat source.18−21 Among MD configurations, direct contact membrane distillation (DCMD) is considered in this study. The DCMD has several advantages compared with other MD configurations. The DCMD is the simplest MD process since it does not © 2017 American Chemical Society

require vacuum pump as in vacuum membrane distillation (VMD), nor condenser as in sweep gas membrane distillation (SGMD), or cooling surface as in air gap membrane distillation (AGMD).2,22,23 Moreover, the DCMD process can be utilized as any desired membrane configuration (flat sheet, spiral wound, capillaries, or hollow fibers).17,24−26 Thus, the DCMD can be conveniently used for diverse applications in which water is the major permeating component, such as desalination.12 The pressure-retarded osmosis (PRO) process was suggested by Loeb et al. for electricity generation through a turbine generator.27−30 In the PRO process, two aqueous solutions which have different concentrations are in contact with a semipermeable membrane placed between the solutions. Then, water molecules permeate from the low concentration solution to the high concentration solution by the chemical potential difference between the two solutions.31 In comparison with the forward osmosis (FO) process, hydraulic pressure which is lower than the osmotic pressure difference between the two solutions is applied on the high concentration side. The increase in volume of the pressurized solution is used to drive a hydro-turbine to generate electricity.32 Therefore, the amount of generated electric power is as much as the multiplication the applied pressure by the permeated water volume. By this mechanism, the PRO process converts the chemical potential Received: Revised: Accepted: Published: 14888

September 1, 2017 November 27, 2017 November 29, 2017 November 29, 2017 DOI: 10.1021/acs.iecr.7b03642 Ind. Eng. Chem. Res. 2017, 56, 14888−14901

Article

Industrial & Engineering Chemistry Research

Figure 1. A schematic illustration of the concept of the PRMD process.

the concepts of the DCMD and the PRO processes is suggested and analyzed theoretically. The proposed process has also two aqueous solution sides, which have cold and hot temperatures and separated by a porous hydrophobic membrane. Vapors permeate from hot temperature side to cold temperature side through the membrane as in the DCMD process. In the PRMD module, hydraulic pressure, which is limited by the membrane characteristics, is applied on the cold temperature solution. Consequently, electric power is generated through a turbine generator as in the PRO process. The proposed process can produce fresh water as well as electric power simultaneously in a single membrane module with low quality energy source such as waste energy or solar energy. Also, a mathematical model for the proposed process was developed, and power generation and water production rate in the PRMD process were analyzed using the developed model. The effects of operating conditions and membrane properties were investigated to identify which conditions would be favorable and how the membrane should be designed for an optimal operation of the PRMD process. In addition, the best available technology in membrane fields is applied to assess the potential of the PRMD process. The analyzed results were compared to the DCMD and PRO processes to confirm that the proposed process could be an attractive dual-purpose desalination process which produces fresh water as the DCMD process and electricity as the PRO process at the same time. The PRMD uses only one membrane module not like PRO-MD hybrid which used two modules in series. From the analyses, recommendable applications to utilize the PRMD process effectively were suggested.

(osmotic energy) of a high concentration solution into mechanical energy. The most attractive feature of the PRO system is that it could be a viable source of renewable energy without carbon emission.33 Also, the amount of global energy potential by utilizing the PRO system has been estimated about 2000 TWh per year, which is almost 20% of global energy production from all renewable energy sources.33,34 However, the required conditions to operate the PRO process efficiently are too limited to utilize the process widely. Although the extractable energy from the process is 0.256 kWh/m3 at the condition with seawater as draw solution and river water as feed solution, which is the maximum extractable energy calculated by Gibbs free energy of mixing, the energy requirement for operating the PRO process is about 0.17−0.55 kWh/m3.32 Thus, the energy-efficiency of the process is very low or even becomes a negative value. Moreover, the efficiency of energy extraction is reduced to 30% by concentration polarization and constant-pressure operation.31 For these reasons, the PRO process cannot be utilized solely in its current stage. Nowadays, hybrid systems that use the PRO process to reduce the energy of reverse osmosis (RO) desalination process have been investigated by many researchers.35−38 The RO-PRO hybrid system can reduce the specific energy consumption in the desalination process to approximately 1 kWh/m3 at 50% recovery.38 In addition, a PRO-MD hybrid process has been suggested to improve the efficiency of the PRO process.39,40 By applying MD process as a sequence process after the PRO system for draw solution regeneration, low-grade thermal energy can be utilized to drive the draw solution regeneration process, and working concentration of draw solution can increase to improve osmotic power generation. In this manner, the PRO system can be utilized by combining other processes to improve the energy efficiency. Thus, in the current stage, it would be a good solution for utilizing the PRO system appropriately to find a hybridizing concept with other processes. Recently, a thermo-osmotic energy conversion (TOEC) process has been suggested and analyzed.41−43 The TOEC process can convert thermal energy to electricity by utilizing the difference of vapor pressure between hot temperature aqueous solution and cold temperature aqueous solution. In this process, the membrane should be hydrophobic to avoid liquid flow across the membrane pore. Applying hydraulic pressure in cold reservoir, the amount of vapor flux from the hot reservoir to the cold reservoir can drive a hydro-turbine to produce mechanical work, which can generate electricity like the PRO system. Even though the TOEC process has an attractive opportunity to harvest some energy from waste heat, the process concept can be more extended and the applicability of the process promoted. In this study, a pressure-retarded membrane distillation (PRMD) with a single membrane module through combining

2. METHODS 2.1. Description of PRMD Process. Figure 1 illustrates the conceptual idea of the proposed PRMD process. The process is similar to the DCMD process in terms of its way of operation that water flux has occurred due to the vapor pressure gradient when two feed solutions with different temperatures are faced across a semipermeable membrane. In the DCMD process, the water permeate flux is produced for seawater desalination or wastewater treatment. However, in the PRMD process, the feed stream with cold temperature is pressurized under a certain pressure called liquid entry pressure (LEP). Then, the permeated water flux and the applied pressure could generate electricity by driving a hydro-turbine like the PRO process. The energy is produced in the magnitude of the applied pressure (Pci) multiplied by the permeate flux (ΔV). In the PRO process, the pressurized stream is a draw solution so the purpose of the PRO process is only to generate electricity. However, in the PRMD process, the pressurized stream can be a fresh water stream. Therefore, the PRMD can play both roles, production of fresh water as well as energy at the same time. That is the biggest advantage of the PRMD process and is the 14889

DOI: 10.1021/acs.iecr.7b03642 Ind. Eng. Chem. Res. 2017, 56, 14888−14901

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is the gas constant; pa is the partial pressure of the air entrapped in the pores; P is the total pressure inside the pores; T is the temperature; Dwk is the Knudsen diffusion coefficient of water vapor depending on the mean pore radius, r, and Dwa0 is the diffusion coefficient of water in air. 2.2.2. Heat Transfer. Similarly to the mass transfer, the heat transfer is generally described in terms of a set of serial and parallel resistances. There are two parts of heat transfer resistances: boundary layers of the membrane and the membrane itself. Figure 3 illustrates the situations in the

main difference from the PRO-MD hybrid process which can produce only electricity. 2.2. Theoretical Model. The DCMD and PRMD modules consist of porous hydrophobic hollow fiber membranes. The hot feed stream is a hot aqueous solution (for example, seawater) that is fed into the shell side and pure water which has cold temperature flows into the tube side. Vaporization takes place at the interface of the membrane on the hot feed solution and condensation on the permeate side of the membrane. The PRMD process is very similar to the DCMD process except the pressurization on the cold side. Thus, the PRMD model was developed by using the mechanisms which are already developed for the DCMD process. 2.2.1. Mass Transfer. In the DCMD and PRMD processes, the vapor pressure difference induced by the temperature difference between the two solutions is the driving force for water vapor transfer across the membrane. The resistances-inseries model is usually employed to describe the membrane distillation processes.44 Figure 2 shows the series and parallel

Figure 3. A schematic diagram of resistances-in-series model for heat transfer.

DCMD and PRMD processes. For describing the boundary layer resistances, empirical correlations to evaluate the boundary layer heat transfer coefficient, h, is usually employed. The tube side heat transfer coefficient is defined as11,17,49−52 hFd i

Nu F =

Figure 2. A schematic diagram of resistances-in-series model for mass transfer.

k

hFd i

Nu F =

arrangement of resistances to mass transfer. The model consists of boundary layer resistances (which occur between bulk solution and membrane surface) and resistances inside the membrane. The boundary layer resistances generally result in a negligible contribution to the overall mass transfer resistance, unlike resistances inside the membrane.2,11,45,46 In order to describe the mass transfer inside the membrane, the dusty-gas model is usually adopted. It establishes that the mass transfer can be affected by four mechanisms: viscous resistance, Knudsen diffusion resistance, molecular diffusion resistance, and surface diffusion resistance. Surface diffusion resistance is normally assumed negligible in the DCMD process,2,10−12,47,48 and viscous resistance is also neglected when considering the air trapped within the pores as a stagnant film.48 Therefore, vapor flux, J, can be expressed as48 1 J= (p F − pm P ) Rm m (1) Rm = Dw k =

pa ⎞ τδ RT ⎛ 1 ⎟⎟ ⎜⎜ k + ε M ⎝ Dw PDwa 0 ⎠ 2r 3

8RT πM

F

kF hFd i

Nu F =

kF

Re F =

Pr F =

0.33 ⎛ d⎞ = 1.62⎜Re F × Pr F × i ⎟ ⎝ L⎠

= 0.023(Re F)0.8 (Pr F)0.3 = 0.027(Re F)0.8 (Pr F)0.33

(Re F < 2100)

(2100 < Re F < 6000) (Re F > 6000)

(4) (5) (6)

d iv Fρ F μF

(7)

cp FμF kF

(8)

where k is the thermal conductivity, di is the inner diameter of hollow fiber, L is the hollow fiber length, v is the linear velocity, ρ is the density, μ is the viscosity, and Cp is the specific heat capacity. The shell side heat transfer coefficient is described as11,53 Nu P =

Re P = (2)

Pr P =

(3)

where Rm is the total membrane resistance which has the terms of Knudsen and molecular diffusion resistances; pm is the vapor pressure at the surface of the membrane, superscripts F and P are the hot feed side and the permeate side; ε, τ, and δ are the effective porosity, tortuosity, and thickness factors of the membrane, respectively; M is the molecular weight of water; R

dh =

hPdh kP

= 0.206(Re P × cos θy )0.63 (Pr P)0.36

(9)

dhv PρP μP

(10)

cp PμP kP

(11)

1−ϕ do ϕ

(12)

where dh is the hydraulic diameter of the shell side, θy is the yaw angle, which varies between 0° for cross flow and 90° for parallel flow, and 87° for shell-and-tube capillary membrane 14890


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Industrial & Engineering Chemistry Research module,53 φ is the packing density, and do is the outer diameter of the hollow fiber. Using the heat transfer coefficient, h, the heat transfer rates from bulk solution to membrane surfaces at both shell (hot feed) and tube (permeate) sides can be expressed as Q F = hFNfiberπdo(Tb F − Tm F)

(13)

Q P = hPNfiberπdi(Tm P − Tb P)

(14)

2.2.4. Mass, Energy, and Momentum Balance Equations. Under steady-state condition, the mass balance equations at shell and tube sides can be expressed as hot feed (shell side) dFw F = −J(Nfiberπdlm) dz dFs F =0 dz

where Q is the heat flux, Nfiber is the number of fibers, and subscripts b and m are the bulk solution and the membrane surface, respectively. The heat flux transferring across the membrane takes place by two mechanisms: conduction across the membrane material and latent heat associated with the vaporized solvent. Therefore, the heat transfer rate across the membrane is expressed as11,54,55 ⎡ ⎤ k Q = Nfiberπdlm⎢J ΔH + m (Tm F − Tm P)⎥ ⎣ ⎦ δ

F F = Fw F + Fs F ρF

−

Nfiberπdo 2 4

)

(19)

FP

vP = ρw

(

Nfiberπdi 2 4

)

(20)

where F is the mass flow rate, x is the mass fraction, v is the average velocity of solution, dsh is the shell diameter, and subscripts w and s represent the water and salt, respectively. In this study, seawater was used as hot feed solution. Therefore, it can be assumed that solute is nonvolatile. Consequently, the solute cannot permeate through the membrane (assuming 100% rejection).2,11,12,48 Energy balance equations can be expressed as

(16)

hot feed (shell side)

(17)

d[(Fw FCp ,w + Fs FCp ,s)Tb F]

2.2.3. Liquid Entry Pressure (LEP). In MD operations, the penetration of liquid through the pores of the membrane should be avoided. Normally, if a hydrophobic membrane is used, liquid water cannot pass through membrane pores as long as the operating pressure is kept below a critical threshold known as LEP. Young−Laplace equation offers a relationship for the critical pressure of solvent penetration. The LEP can be described as51 2Θσ cos θ rpore

πdsh2 4

dF P = ±J(Nfiberπdlm); (co‐: +, counter‐ : − ) dz

(15)

where, kg and kp are the thermal conductivities of gas and membrane material, respectively. At steady state, the amounts of heat transferring through the boundaries of both solutions (hot feed and permeate) are equal to that across the membrane. Therefore, the following equation should be satisfied.

LEP = −

(

permeate (tube side)

where ΔH is the enthalpy of vaporization and km is the conduction heat transfer coefficient for a two-phase composite material. The dlm is the log-mean fiber diameter which is calculated by (do − di)/ln(do/di). The km is generally calculated by isostrain model56

QF = QP = Q M

FF

vF =

M

k m = εkg + (1 − ε)k p

xs F = Fs F/F F

dz

= −Q F

(21)

permeate (tube side) d[F PCp ,wTb P] dz

= ±Q P; (co‐: +, counter‐ : − )

(22)

For the feed fluids under the steady-state operation, the incompressible fluid, the long narrow channels of the hollow fiber, and no component of velocity in the azimuthal direction were assumed for the sake of simple calculation. The governing equations that express the hot feed side velocity and pressure are obtained by solving the axial component of the Navier− Stokes equation. Therefore, average pressure over a crosssection of hollow fiber can be expressed as11

(18)

where rpore is the radius of membrane pore, σ is the interfacial tension, Θ is the geometric factor related to the pore structure, and θ is the liquid−solid contact angle. When it is assumed that the structure of pores is cylindrical, the geometric factor Θ is 1. Actually, the maximum operable pressure on the membrane is usually correlated to the membrane thickness and the membrane material. However, there is a lack of experimental data to derive a correlation equation for calculating the maximum operable pressure for MD process since the conventional MD process has not considered the pressurization on the cold feed side until quite recently. Therefore, in this study, it is assumed that the membrane can sustain the LEP, since a previous study revealed experimentally that the TOEC process can be operable under the pressure of 10.3 bar on the PTFE membrane.43

hot feed (shell side) 32μF dP F = − 2 vF dz dh

(23)

permeate (tube side) 32μP dP P = ± 2 v P; dz di 14891

(co‐: −, counter‐ : + ) (24) DOI: 10.1021/acs.iecr.7b03642 Ind. Eng. Chem. Res. 2017, 56, 14888−14901

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Figure 4. Algorithm for simulating the MD module.

2.2.5. Electricity Generation and Energy Consumptions. The electricity generation from the PRMD process can be expressed by considering the pressure drop in the membrane module and the efficiency of hydro-turbine Egen = ηHT(P P − ΔP)

requirement for circulation of the permeate stream in the membrane module. In this study, the heat energy to raise the temperature of the hot feed stream was not considered in the energy requirement calculation, since the heat energy requirements in the PRMD and DCMD are the same. And also, it was assumed that the heat energy could be freely utilized from low grade waste heat energy or concentrated solar energy. Then, the net energy generation in the PRMD process is expressed as

(Fout P − Fin P) ρP

(25)

where, ηHT is the efficiency of hydro-turbine, ΔP is the pressure drop in the membrane module, and subscripts in and out denote the inlet stream and outlet stream, respectively. In this study, the permeate pressure for the PRMD pressure was assumed same as the LEP. The energy requirement to pressurize the permeate side should be considered to analyze the amount of net energy generation. Concerning a situation that an energy recovery device (ERD) is applied to improve the energy efficiency of the PRMD process, the energy requirement in the PRMD process can be described as P

Ereq =

P

P

1 P Fin − ηERD(P − ΔP)Fin ηpump ρP

Enet = Egen − Ereq

(27)

To analyze how much the thermal energy in the hot feed side stream contributes to the evaporation of water molecules in the MD processes, the heat energy efficiency (EE) is defined as EE =

(Fout P − Fin P)ΔH Fin FCp ,in FTin F − Fout FCp ,out FTout F

(28)

2.3. Algorithm for Solving Equations. The performance of each MD module is simulated by using the above model equations. To identify the permeate water flux across the membrane, the partial pressures at the surface of the membrane should be known. To calculate the partial pressures, the temperatures at the surface of the membrane should be determined. It requires the amount of water flux as shown in eq 15. Thus, an iterative procedure should be utilized to simulate the MD module. In Figure 4, the detailed algorithm for solving

P

(26)

where ηERD is the efficiency of ERD and ηpump is the efficiency of high pressure pump. The energy requirement in the DCMD process was calculated in the same manner while setting the permeate pressure as 1.3 bar, which considers the pressure 14892


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Industrial & Engineering Chemistry Research Table 1. Membrane, Module Parameters, and Operating Conditions for the Simulation in This Study membrane parameters

module parameters

22291−50154 [#] 0.3 (mm)

hot feed concentration (CF)

3.5−17.5 (wt %)

hot feed temperature (TF) ERD efficiency (ηERD) pump efficiency (ηpump) hydro-turbine efficiency (ηHT)

50−90 [°C] 0.95 [−] 0.85 [−] 0.95 [−]

0.75 [−]

length (L)

0.5 (m)

tortuosity (τ)

1.5 [−]

0.1 (m)

thermal conductivity of the membrane (kp) pore radius (rpore)

0.25 [W/m/K]

shell side diameter (dsh) packing density (φ)

0.05−0.20 (μm)

membrane thickness (δ)

30−120 (μm)

membrane contact angle (θ)

130 (°)

number of fibers (Nfiber) fiber inner diameter (di)

the above developed model equations was depicted. For each iteration, a gain substitution method was used to update the guessed variable by multiplying the error between the guessed variable and the newly calculated variable and the gain. The ordinary differential equations (ode) were solved by using ode solver called “ode45”, which is a built-in function in MATLAB R2016a. With a counter-current flow configuration, the variables at the end of the permeate side were guessed initially. After solving the model equations, the calculated variables were compared with the inlet conditions of the permeate side. If there were some errors between the calculated variables and the inlet variables, the guessed variables at the end of the permeate side were updated by using the shooting method. Table 1 shows the parameters and operating conditions for this simulation. Those parameters were obtained from the refs 11 and 57. The number of hollow fibers is changed as increasing membrane thickness while the diameter of shell side and hollow fiber inner diameters are fixed. If the membrane thickness is assumed as 30 μm, the number of fibers becomes 50, 154, and 22291 for the membrane thickness of 120 μm.

operating conditions cold feed (permeate) flow rate (FP) cold feed (permeate) temperature (TP) cold feed (permeate) pressure (PP) hot feed flow rate (FF)

porosity (ε)

0.65 [−]

0.24 (kg/s) 20 (°C) 1.3−16 (bar) 0.25 (kg/s)

Figure 5. Comparison between the simulation results by using the developed model in this study and the experimental results from ref 58 for validation of the developed model.

3. RESULTS AND DISCUSSION 3.1. Model Validation. This study aims the theoretical analysis of the newly proposed process, and accordingly the accuracy of the theoretical model should be assured. Therefore, the developed model should be validated with experimental results from the literature in order to make sure that the developed model well describes the experimental results. Figure 5 shows the results simulated by the developed model in the present work and the experimental results from the literature.58 The simulation results were obtained by using the same parameters and operating conditions in the experimental data. It is shown that the simulation and experimental results are in a good agreement. The MD process is relatively mature and there have been much reliable research on the mathematical models which are widely accepted and have high reliability. And the PRMD process is almost similar to the DCMD process. Therefore, it can be believed that the simulation results from the developed model are reliable for the theoretical analysis of the PRMD process. 3.2. Effects of Operating Conditions on the Permeate Flux in the PRMD. Important operating conditions in the PRMD process are the temperature of the hot feed stream, the flow rates of the hot feed and permeate streams, the hydraulic pressure on the permeate stream, and the concentration of the hot feed stream. In order to investigate the effects of each

operating condition on the permeate flux in the PRMD process, simulations were conducted with varying operating conditions. At first, in order to identify the effect of feed and permeate flow rates, the membrane thickness and pore radius were fixed at 60 and 0.1 μm, respectively, which are the membrane properties from ref 11. The concentration of the hot feed solution was 3.5 wt % (seawater condition), and the permeate pressure was the LEP. Then, the simulations were conducted by changing the hot feed and permeate flow rates and the hot feed temperature. In Figure 6a, as the hot feed temperature increases, the permeate flux also increases. This is because the vapor pressure difference, namely, the driving force, increases due to the temperature elevation. Also, when the flow rates of the hot feed and permeate increase, the permeate flux increases. This can be explained by the mitigation of polarization phenomena, that is, temperature polarization. However, even though the average permeate flux increases as increasing the flow rates, the ratio of the amount of permeated water in the module to hot feed flow rate, which is called recovery, could decrease as shown in Figure 6b. There exists an optimal flow rate around 0.25 kg/s. Thus, high flow rates are not always desirable, and the flow rates should be chosen appropriately to obtain the maximum recovery. 14893


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Figure 6. Simulation results to investigate the effects of the hot feed and permeate flow rates (same values) and the hot feed temperature on the (a) permeate flux and (b) recovery.

Figure 7. Simulation results to investigate the effects of (a) the applied pressure on the permeate flux and (b) the hot feed concentration on the permeate flux as changing the hot feed temperature.

Then, the hot feed flow rate and the permeate flow rate were fixed as 0.25 kg/s and 0.24 kg/s, respectively. To reduce volume difference between the feed and permeate sides by water permeation in a module, the permeate side flow rate is determined slightly lower than the hot feed flow rate. The simulations to investigate the effects of permeate pressure and hot feed concentration were carried out. Figure 7a shows the effect of the applied pressure on the permeate flux. As shown in Figure 7a, the permeate flux reduces slightly as the pressure becomes higher, but the magnitude of changes is nearly insignificant. It revealed that the pressurization in the permeate side has little effect on the permeate flux. In other words, the PRMD process can be operated with a little loss of the permeate flux compared to the unpressurized DCMD process. In ref 7, the effect of total pressure on the water flux in the DCMD module was already measured experimentally. The results showed that there is an insignificant variation of water permeate flux on the total pressure. Thus, the permeate pressure could increase as much as possible to maximize the

power generation in the PRMD process. However, as already reported in recent literature, membrane deformation is one of the critical issues affecting the practical operation of the PRO process.59−61 The membrane deformation is due to a pressurization on the PRO membrane. Therefore, there would be a possibility for the membrane deformation to appear in the PRMD process. Even though it was assumed in this study that there is no membrane deformation in the PRMD module, the membrane deformation should be considered in the future work. Figure 7b illustrates the effects of the hot feed concentration on the permeate flux. As the hot feed concentration increases, the permeate flux decreases due to the reduction in the vapor pressure. The flux reduction caused by the concentration is lower than the effect of temperature but higher than the effect of pressure. Therefore, the most significant operating variable is the hot feed temperature. In addition, the hot feed temperature lower than 70 °C is too low to obtain the meaningful amount of 14894


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Industrial & Engineering Chemistry Research water flux from the PRMD process. After this section, the range of hot feed temperature is chosen as 70−90 °C. 3.3. Effects of Membrane Geometrical Properties on the Permeate Flux in the PRMD. In Figure 8, the permeate

energy produced under the normal operating conditions and membrane properties. Also, the proposed process is compared with the typical DCMD process. The PRMD process can produce the energy by applying an appropriately high pressure on the permeate side but reduce the permeate flux due to decreased driving force, compared to the DCMD process. Thus, in order to obtain the same amount of the permeate flow rate as the DCMD process, more membrane area is required in the PRMD process. In Figure 9 (panels a−c), average permeate flux, heat energy efficiency, and recovery are compared between the DCMD and the PRMD processes as changing the concentration and temperature of the hot feed solution. The range of hot feed concentration is selected to simulate how much water flux would be permeated in the PRMD process when utilizing a retentate stream from the RO process as the hot feed in the PRMD. The membrane properties in this study were fixed at the reference condition, where the membrane thickness and pore radius were 60 and 0.1 μm, respectively.11 With the operating conditions considered, the PRMD process showed slightly lower performance in water production than the DCMD process. Since the pressurization on the permeate stream in the PRMD process hinders the permeate flux slightly, the average permeate flux decreases, and consequently, the heat energy efficiency and recovery are also reduced. Thus, the slightly larger membrane area in the PRMD is required to obtain comparable permeate flux to the DCMD. Net specific energy generation from the PRMD process are shown in Figure 9d. To obtain a positive value of the net specific energy generation with the condition of 3.5 wt % hot feed concentration, the hot feed temperature should be higher than 80 °C. In Figure 9d, crossover points indicate which hot feed temperature should be chosen to obtain a positive net energy generation in the PRMD process at each hot feed concentration. Figure 10 illustrates the additional membrane area and saved energy (energy produced by the PRMD: energy consumed in the PRMD + energy consumed in the DCMD) in the PRMD process compared to the DCMD process as changing the temperature and concentration of the hot feed stream. When the hot feed concentration is 3.5 wt % (seawater concentration), 0.02−0.08 kWh/m3 can be saved at the temperature range of 75−90 °C. On the other hand, when the hot feed concentration is 14 wt % (the concentration after 75% of seawater is recovered), temperature should exceed 90 °C in order to operate favorably in terms of the energy production. Overall, the amount of energy production from the PRMD process is quite small. However, instead of consuming energy for circulating feed and permeate side solutions in the DCMD process, the PRMD process can produce electricity, and the permeate flux decrease is less than 5% compared to the DCMD process. 3.4.2. Effects of Membrane Thickness and Pore Radius. For the purpose of enhancing the efficiency of the PRMD process, the membrane properties are also important factors. Thus, the membrane properties are investigated in this section to identify the effects of membrane properties on the performance of energy production. The simulation conditions were fixed at 85 °C of the hot feed temperature, 3.5 wt % of the hot feed concentration. With regard to the pore radius, the permeate flux increases but the LEP decreases at the larger pore radius, and consequently, the possible applied pressure also decreases.

Figure 8. Effects of geometrical properties on the permeate flux and LEP.

flux and LEP were calculated as changing the properties of membranes, especially, the pore radius and the membrane thickness. The simulation conditions were 85 °C of the hot feed temperature, 0.25 kg/s of the hot feed flow rate, 3.5 wt % of the hot feed concentration, 0.24 kg/s of the permeate flow rate, and LEP of the permeate pressure. As the membrane becomes thicker, the average permeate flux becomes higher. That is because the reduction of heat conduction as increasing membrane thickness. However, when the membrane thickness increases, total number of fibers in the hollow fiber module are reduced. In other words, total permeate flux might be decreased as increasing membrane thickness. This result can be proved by the following section. In the case of LEP, the membrane thickness does not affect it and it can be explained by eq 18. For different pore sizes, the permeate flux increases as the pore size gets larger. As indicated in eq 3, Knudsen and molecular diffusion resistances decrease as the pore radius increases. Moreover, the LEP is also highly connected with the pore radius. As the pore radius decreases, the LEP increases. In the PRMD process, the pore radius can be regarded as one of the most important factors which determine the permeate flux and the produced amount of energy. The pore radius plays an important role to decide the LEP which cannot be exceeded by the applied pressure on the permeate side. The smaller pore radius enables the result in the higher LEP and higher applied pressure on the permeate side which leads to more energy production. However, the small pore radius makes the permeate flux decrease and consequently leads to the reduced energy production. In other words, the pore radius affects both the permeate flux and possible operating pressure, which are directly correlated to the energy production, respectively. Therefore, it is crucial to choose an optimal pore radius for the maximum energy production. 3.4. Analysis of Power Generation. 3.4.1. Effects of Hot Feed Concentration and Temperature. The proposed process aims to produce fresh water by MD and electricity by a hydroturbine at the same time. This section analyses the electrical 14895


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Figure 9. Performance comparison between the DCMD and the PRMD processes as changing the concentration and temperature of hot feed solution. (a) Average permeate flux, (b) heat energy efficiency, (c) recovery, and (d) net specific energy generation in the PRMD process.

regardless of the membrane pore radius. Even though the average permeate flux increases consistently within the given range of membrane thickness, the recovery shows a maximum point around 80 μm. The main reason for this is the changed number of fibers for a fixed module size as already mentioned. As increasing the membrane thickness, the number of fibers within the fixed size module is reduced, which induces the total permeate flux reduction despite the increased average permeate flux. With all these arguments, there is an optimal point of membrane thickness and pore radius with regard to the power generation. As shown in Figure 11d, the net specific energy generation in the PRMD process shows the maximum energy generation (0.04858 kWh/m3) at 90 μm of membrane thickness and 0.09 μm of pore radius. With the carefully designed membrane module, the amount of generated electricity in the PRMD process could be maximized. Figure 12 shows the additional membrane area requirement and saved energy compared to the DCMD process as changing the thickness and pore radius of the membrane. Using the optimized membrane properties, the amount of saved energy by replacing the DCMD process with the PRMD is about 0.07 kWh/m3 with slightly lower permeate flux by 4.396%.

Thus, the pore radius should be carefully chosen because it determines the permeate flow rate and applied pressure which finally decides the amount of the energy produced. With regard to the membrane thickness, the average flux increases for the thicker membrane as discussed later. However, the increased membrane thickness leads to the reduction of total number of fibers in the hollow fiber module. It could adversely affect the recovery. Therefore, the membrane thickness also should be carefully decided. In Figure 11 (panels a−c), the average permeate flux, the heat energy efficiency, and the recovery as changing the membrane properties are presented. As mentioned earlier, the difference in the permeate fluxes in the PRMD and the DCMD is not significant. Due to the results of lower heat energy efficiency, the permeate flux in the PRMD has a slightly lower value compared to the DCMD. In the considered ranges of membrane properties, the permeate flux increases at the larger pore size and thicker membrane. The reason why the average permeate flux increases with the thicker membrane is that the heat conduction between two sides of the membrane is reduced as mentioned above. From the graph showing recovery (Figure 11c), there is an optimal membrane thickness around 80 μm 14896


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Figure 10. (a) Saved specific energy and (b) additionally required membrane area by replacing the DCMD with the PRMD process as changing the hot feed temperature and concentration.

Figure 11. Performance comparison between the DCMD and the PRMD process as changing the membrane thickness and pore radius. (a) Average permeate flux, (b) heat energy efficiency, (c) recovery, and (d) net specific energy generation in the PRMD process.

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Figure 12. (a) Saved specific energy and (b) additionally required membrane area by replacing the DCMD with the PRMD process as changing the membrane and thickness pore radius.

Figure 13. (a) Saved specific energy and (b) additionally required membrane area by replacing the DCMD with the PRMD process as changing the membrane contact angle and conduction heat transfer coefficient.

3.4.3. Potential of the PRMD Process by Applying the Best Available Technology. As membrane technology has been developed, an improved membrane can be utilized in the PRMD process. To enhance the electricity generation in the PRMD process, the membrane should possess more hydrophobic surface and lower thermal conductivity. The larger hydrophobicity increases the LEP, and the lower thermal conductivity reduces the amount of heat transfer through the membrane matrix, which increases the temperature difference between both sides of the membrane. Thus, by applying the best available technology which has been reported by membrane developers and researchers,16,62−64 the potential of the PRMD process can be examined. The amount of saved specific energy and additional membrane requirement compared to the DCMD process as changing contact angle and conduction heat transfer coefficient are shown in Figure 13. The contact angle is directly correlated to the hydrophobicity of the membrane, and the conduction heat transfer coefficient is affected by the membrane thermal

conductivity and the membrane porosity as described in eq 16. As the contact angle increases, the saved specific energy and additional membrane area requirement also increase. Since the increased contact angle enables one to apply higher pressure in the permeate stream due to higher LEP, the larger amount of electricity generation becomes possible. However, the increased applied pressure slightly reduces the permeate water flux, and the additional membrane area is required. In addition, since low conductive heat transfer coefficient increases heat energy efficiency due to lower heat conduction, more electricity can be generated by the hydro-turbine consequently. The calculation results reveal that the amount of saved energy by replacing the DCMD with the PRMD is about 0.1738 kWh/m3 with 3% loss of permeate water flux if the best available membrane technology could be applied. Therefore, the PRMD process could become a more energy-efficient process than the DCMD without significant loss of water productivity. Figure 14 presents how much the net specific energy generation and power density in the PRMD could increase as 14898


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Figure 14. Net specific energy generation and power density in the PRMD process as changing the membrane contact angle and conduction heat transfer coefficient.

significantly as mentioned in the above section. The proposed theoretical analysis in this study could provide an insightful guideline for a novel dual-purpose desalination system. If the commercial MD membrane reaches the best available technology level, the PRMD process can be successfully implemented and subsequently compete with other processes.

changing the contact angle and conduction heat transfer coefficient. The maximum amount of electricity generation in the PRMD process is 0.1606 kWh/m3, which is more than three times the calculation results with the parameters in Table 1. In this condition, the power density in the PRMD process is shown as 2.034 W/m2, which is comparable to the power density of the PRO process with module-scale design (1.6 W/ m2).31,65 Unlike the PRO system, the PRMD process can produce fresh water and electricity simultaneously. Therefore, the PRMD process could become an attractive multifunctional system for producing water as the DCMD process and electricity as the PRO process at the same time if the lowgrade waste heat energy or concentrated solar energy could be utilized almost for free and the best available membrane technology could be applied. 3.4.4. Discussion of the Required Conditions for Successful Application of the PRMD Process. In order to utilize the PRMD process appropriately, the region with water and electricity scarcity would be most suitable. Many researchers have suggested smart grid system for efficient utilization of water and electricity resources.66 However, small islands far from land cannot receive support from the smart grid system. Since the PRMD process can be a self-sustained seawater desalination process due to the produced electricity through turbine, the PRMD process could be effectively utilized in the region with small remote islands (e.g., Southeast Asia), if the driving force of the PRMD process could be easily supplied by solar power with an intensive energy collector. Another advantage of the PRMD process is that it could reduce the carbon footprint by utilizing renewable energy as a driving force. Many desalination processes such as RO and MSF emit carbon dioxide (around 1.4−1.8 kg/m3 desalted water in RO and 1.96 kg/m3 desalted water in MSF) due to utilization of fossil fuel for power generation.67,68 However, there is no need to use fossil fuel in the PRMD process. Thus, the PRMD process can produce electricity and water without carbon emission. Actually, the membrane development status in this current stage is not enough to make the PRMD process suitable. However, as membrane technology evolves, the amount of electrical energy available through the PRMD increases

4. CONCLUSIONS In this study, pressure-retarded membrane distillation (PRMD) is proposed through combining the concepts of a direct contact membrane distillation (DCMD) and pressure-retarded osmosis (PRO) processes. A mathematical model for the proposed process was developed and power generation and additionally required area of the membrane were analyzed using the developed model. It was validated that the developed model is reliable by comparison with experimental data from the literature. On the basis of the developed model, a theoretical analysis was carried out by varying operating conditions and membrane properties to identify the effects of operating variables and parameters on the permeate flux. The most significant operating variable is the hot feed temperature. And, the effect of the applied pressure on the permeate side is very small. It revealed that the pressurization on the permeate side to operate the PRMD process has little effect on the permeate water flux. In other words, the PRMD process can be operated with only a little loss of permeate flux compared to the unpressurized typical DCMD process. The changes in the membrane thickness and pore radius affect the LEP and permeate water flux in opposite directions, thus the membrane properties should be carefully designed to maximize the amount of electricity generation. Since the proposed process aims to produce fresh water and electricity by a hydro-turbine simultaneously, the electrical energy production under the normal operating conditions and membrane properties were also analyzed and compared with the typical DCMD process at the same basis. In the considered range of the feed concentration, energy can be saved depending on the temperature conditions with a little loss of water production rate. And, to maximize the energy production in the PRMD process, the membrane properties were optimized. This 14899


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study found that the optimal thickness and pore radius for the PRMD process are about 90 μm and about 0.09 μm, respectively. With the membrane properties, the amount of saved energy by replacing the DCMD process with the PRMD is about 0.07 kWh/m3 with slightly lower permeate flux by 4.396%. As applying the best available technology in membrane fields, the amount of saved energy by replacing the DCMD with the PRMD increases to 0.1738 kWh/m3 with 3% loss of permeate water flux. The power density in the PRMD process is 2.034 W/m2, which is comparable to the power density of the PRO process. Since the PRMD process enables one to produce fresh water and electricity at the same time, it could be said that the availability of the PRMD process is higher compared to the DCMD process and the PRO process. If waste heat energy and concentrated solar energy could be utilized almost for free and the best available technology could be successfully applied in the commercial MD module, the PRMD process could become an attractive dual-purpose desalination process as an alternative to the DCMD process.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +82 2 3290 3298. Fax: +82 2 926 6102. E-mail: dryang@ korea.ac.kr. ORCID

Kiho Park: 0000-0002-8303-0461 Present Address ‡

D.Y.K.: Imperial College of London, Department of Chemical Engineering, South Kensington, London, SW7 2AZ, UK. Author Contributions †

K.P. and D.Y.K. contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the Korea Agency for Infrastructure Technology Advancement (KAIA) grant funded by the Ministry of Land, Infrastructure and Transport (Grant 17IFIP-B116952-02) and a Korea University grant.

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REFERENCES

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