Heat-Integration of Solar-Heated Membrane Distillation and Fuel Cell for Desalination System Based on the Dynamic Optimization Approach

Abstract

The heat integration feasibility of the proton exchange membrane fuel cell (PEMFC) coupled with the solar-heated direct contact membrane distillation (DCMD) module is evaluated in this study. The additional waste heat from the PEMFC increases the DCMD system’s ability to produce fresh water and electricity. Two systems units to be assessed mainly include a flat plate solar collector, a heat storage tank with an internal heat exchanger, and the DCMD module with and without the PEMFC module. The importance of daily operation continuity is emphasized through a preliminary dynamic simulation and proper sizing of the solar-heated DCMD distillation. Sensitivity analysis is implemented to analyze the relationship between the essential variables and the daily freshwater production. The design variables of both configurations are rigorously optimized in terms of minimum unit production cost (UPC). The proposed heat integration feasibility is evaluated to obtain critical insights on the design strategy of the hybrid systems.

1. Introduction

The desalination technology includes thermal distillation and membrane separation. Traditionally, the leading separation technologies are the multi-stage flash (MSF) and reverse osmosis (RO). Note that the separation methods above need high energy consumption and costs [1]. Membrane distillation (MD) is considered as the combination of the above technologies. Currently, there are many applications in MD technology for industrial and scientific fields, including the pharmaceutical industry, wastewater treatment, and desalination. MD technology is utilized mainly to separate the contaminants from liquid solutions and produce the high-purity permeates [2]. Therefore, MD gradually becomes an alternative to traditional distillation techniques. Its main advantages compared with conventional technology are (1) lower operating temperature and hydrostatic pressure, (2) non-volatile material removal rate is close to 100%, (3) low resistance for mass transfer between gas and liquid (high permeability), (4) low sensitivity to salt concentration, and (5) the membrane properties are not easily affected on the high osmotic pressure or concentration polarization [3].

MD is a non-isothermal separation process. By utilizing the microporous and hydrophobic surfaces, MD exploits the temperature gradient’s vapor pressure difference by the two sides of the membrane. Thus, it drives the vapor molecules to diffuse through the permeate side of the membrane. There are the potentials for MD systems to be combined with renewable energy such as solar energy [4,5,6] and/or industrial waste heat [7,8,9,10]. MD’s heat and mass transfer occurs from the feed side through its boundary layer across the membrane and then passes to the permeate side. As the heat and mass transfer happen simultaneously, the mass transfer affects the rate and heat transfer coefficient [11]. The design of MD must consider the flow state, structural uniformity, packing density, pressure drop, thermal stability, and recovery to ensure well flow conditions [12]. Significantly, the hollow fiber membrane module can achieve high permeation. At the same time, the structure is simple with good ductility, high packing density, and a large surface area per unit volume without any structural support. The feed can easily flow in the fiber’s pores, and the permeate is collected from the shell wall of the membrane. Thus, the hollow fiber membrane module is easier to use than those of frame or spiral one [13].

On the other hand, the fuel cell is an energy conversion device that generates electricity, heat, and water by electrochemical reaction. Hydrogen and oxygen are fed through an electrode without burning any fossil fuel. The proton exchange membrane fuel cell (PEMFC) has been widely applied due to its advantages: high power density, low operating temperature, fast power-up, and long life [14,15,16]. However, the PEMFC will produce almost equal waste heat and electricity during the steady-state operation, so its energy efficiency is usually limited to 50–60%. An additional cooling system is needed to remove the waste heat and maintain the PEMFC’s temperature uniformity [17]. Hasani and Rahbar [18] proposed an experimental study to evaluate the waste heat recovery system performance of the PEMFC. Lai et al. [9] proposed a hybrid PEMFC and direct contact membrane distillation (DCMD) module to simultaneously use the waste heat generated by a PEMFC for desalination. The operating parameters of the hybrid system were analyzed and optimized with a genetic algorithm. Unfortunately, the economic aspects were not addressed and there were no constraints implemented on maintaining the daily production continuity of the hybrid system.

There is the potential that the combination of a PEMFC with DCMD can be rigorously optimized to achieve the maximum energy gain. The combined hybrid system is also believed to be more efficient than a single PEMFC, although there is a concern about fuel cells as hydrogen is hazardous and flammable, thus sacrificing the safety of the desalination technology. Still, we are yet to see any failing industrial fuel cells due to the high safety standards. There is a lack of literature on PEMFC and DCMD design; however, many scholars explore the availability of renewable energy. Combining with renewable energy, i.e., solar power, its inherent disadvantage will depend on geographical location and environmental conditions. Therefore, the hybrid renewable energy system should be combined with an alternative continuous energy supply to provide stability [19].

In recent years, there has been very little literature on applying hybrid systems of PEMFC and DCMD instead of providing only electricity for a PEMFC. PEMFC and DCMD hybrid multi-generation systems can simultaneously produce freshwater and electricity. Ghobeity et al. [20] designed the solar electrothermic plant of combined heat and power generation system. The solar pond collects solar irradiation and is incorporated into the Rankine cycle. It has a turbine to generate electricity and uses reverse osmosis and efficient distillation for water production. The meteorological model is used to estimate the local solar irradiation for dynamic simulation. Subsequently, the heuristic global optimization method is used to obtain the maximum power and water production. Mohan et al. [21] proposed the solar generation system for cooling water, freshwater, and hot water production. Three different solar collectors, along with the local weather conditions, are considered for dynamic simulation. Note that the design of hybrid systems may be affected by environmental, energy availability, or technology. In this situation, it is necessary to optimize the combination size to improve its energy efficiency or decrease its cost. In addition, to conform with the actual operating conditions, that optimal design should also consider the ambient temperature, solar irradiation, or seawater temperature.

This work is intended to provide insights on improving traditional distillation technology with hybrid DCMD and PEMFC of a multi-generation system to produce freshwater and electricity. The heat integration feasibility of a proton exchange membrane fuel cell (PEMFC) coupled with solar-heated DCMD module will be studied in this work. It is expected that with the PEMFC integration, the overall system may benefit from higher throughput and some economic advantages. The novelty of rigorous dynamic optimization and daily production continuity constraints are introduced in the subsequent sections to ensure the operability of the optimal design.

This work is organized as follows: Section 2 is dedicated to the mathematical models and verifications of the corresponding unit operations in a PEMFC and DCMD. Section 3 describes the optimization procedure of the multi-generation systems. The case study and optimization results are discussed in Section 4. Finally, conclusions are given in the last section.

2. Mathematical Models of DCMD and PEMFC

2.1. System Description

In this study, the membrane distillation systems of two heating methods were discussed. The one is the solar-heated membrane distillation system, and the other is the PEMFC coupled solar-heated membrane distillation system, as shown in Figure 1. There are two loops in both systems. The primary closed-loop consists of circulating working fluid, i.e., pure water, to collect heat from solar irradiation. The secondary open-loop consists of the seawater heated by the heat storage tank with an internal heat exchanger. Then, the heated seawater will enter the DCMD module for freshwater production, and the remaining undistilled concentrated seawater will be discharged into the sea. The second system is an improved design of the original configuration that adds the PEMFC in the secondary open-loop of the system. Due to the unstable supply of solar radiation, the seawater sometimes cannot reach the required temperature for entering the membrane. Therefore, the waste heat of the PEMFC is used for preheating to increase seawater temperature and water production. The location of the PEMFC is particularly chosen to be right before the DCMD module to ensure the controllability and quick action for the DCMD feed water inlet temperature. The mathematical model of each system unit includes the solar flat plate collector, the heat storage tank with internal heat exchanger, the hollow fiber DCMD module, and the PEMFC module. The following subsections will establish the mass balance and energy balance for each module.

2.1.1. Solar Collector

The solar flat plate collector is the primary source of thermal energy in this study. The heat from the solar radiation is absorbed and then transferred to the working fluid. The working fluid loops continuously through the collector following the circulation pump direction. The surface of the collector uses a transparent glass cover for solar radiation absorption. In contrast, the other parts use adiabatic materials to reduce heat loss. This work refers to the theoretical model and the parameters by Farahat et al. [22]. The parameters are shown in

Table 1. Characteristics of two kinds of membrane distillation systems.

Parameter Description	Symbol	Value	Unit
SolarCollector [22]
Fluid specific heat (pure water)	Cpf	4180	J/(kg·K)
Collector efficiency factor	Fsc	0.9	-
Collector overall heat loss coefficient	Usc	4.7	W/(m2·K)
Optical efficiency coefficient	ηo	0.84	-
Heat Storage Tank with Internal Heat Exchanger [23]
Internal heat exchanger area	Ah	20	m2
Heat storage tank in the environment contact area	As	1.2	m2
Seawater specific heat	Cph	4080	J/(kg·K)
Internal heat exchanger overall loss coefficient	Uh	250	W/(m2·K)
Heat storage tank in the environment overall loss coefficient	Us	1.2	W/(m2·K)
Hollow Fiber DCMD Module [24]
Membrane area for heat transfer through feed side to membrane	Af	1	m2
Knudsen-diffusion coefficient	Ck	0.0015	-
Molecular-diffusion coefficient	Cm	5.1 × 103	1/m
Poiseuille-flow coefficient	Cp	1.297 × 10−10	M
The fiber inside diameter	di	0.3	Mm
The fiber outside diameter	do	0.424	Mm
Vapor conductive coefficient	kmg	0.028	W/(m·K)
Solid membrane conductive coefficient	kms	0.25	W/(m·K)
The fibers length	L	0.34	m
The fibers number	Nf	3000	-
Membrane thickness	δm	60	μm
Porosity	ε	75	%
Packing density	φ	60	%
The viscosity of water vapor within the membrane	μw	1.08 × 10−5	Pa·s
PEMFC [16]
Hydrogen specific heat	Cp,H2	28.944	J/(mol·K)
Gaseous water specific heat	Cpg,H2O	33.59	J/(mol·K)
Liquid water specific heat	Cpl,H2O	75.37	J/(mol·K)
Oxygen specific heat	Cp,O2	29.696	J/(mol·K)
The PEMFC specific heat	Cp,st	4000	J/(kg·K)
Faraday constant	F	96,484.6	sA/mol
The enthalpy of combustion for hydrogen	∆HH2	285,500	J/mol
The coolant inlet mass flow rate	m	0.1	kg/s
Cell number	Nfc	112	-
Anode inlet gases pressure	Pan	2.9	atm
Cathode inlet gases pressure	Pca	3	atm
Universal gas constant	R	8.314	J/(mol·K)
Thermal resistance	Rt	0.145	K/W
Anode inlet gases temperature	${\mathrm{T}}_{\mathrm{an}}^{\mathrm{in}}$	323	K
Cathode inlet gases temperature	${\mathrm{T}}_{\mathrm{ca}}^{\mathrm{in}}$	323	K
Membrane thickness	tm	0.0178	cm
Input hydrogen flow rate factor	λH2	1.5	-
Input oxygen flow rate factor	λO2	2	-
Membrane water content	λm	14	-

and follow the assumptions: (i) The pressure drop in the wall of the collector is negligible, (ii) the temperature of working fluid is maintained below 100 °C to avoid boiling, and (iii) steady-state operation in the collector.

The Hottel–Whillier equation for the heat absorbed (Q_sc) by the solar collector, considering the heat losses from the solar collector to the atmosphere, is

$${\mathrm{Q}}_{\mathrm{sc}}{=\mathrm{A}}_{\mathrm{sc}}{\mathrm{F}}_{\mathrm{r}}\left[\mathrm{S}-{ \mathrm{U}}_{\mathrm{sc}}\left({\mathrm{T}}_{\mathrm{fi}}-{ \mathrm{T}}_{\mathrm{a}}\right)\right]$$

(1)

where T_fi and T_a are the temperatures of fluid into the collector and the ambient temperature, respectively. S and F_r are the radiation flux absorbed by the absorber area of the collector and the heat removal factor, which are defined as

$${\mathrm{S}=\mathsf{\eta }}_{\mathrm{o}}\mathrm{I}$$

(2)

$${\mathrm{F}}_{\mathrm{r}}=\frac{{\mathrm{m}}_{\mathrm{f}}{ \mathrm{C}}_{\mathrm{pf}}}{{\mathrm{A}}_{\mathrm{sc}}{ \mathrm{U}}_{\mathrm{sc}}}\left[1 -\exp \left(-\frac{{\mathrm{F}}_{\mathrm{sc}}{ \mathrm{U}}_{\mathrm{sc}}{ \mathrm{A}}_{\mathrm{sc}}}{{\mathrm{m}}_{\mathrm{f}}{ \mathrm{C}}_{\mathrm{pf}}}\right)\right]$$

(3)

The Q_sc by the working fluid is

$${\mathrm{Q}}_{\mathrm{sc}}={ \mathrm{m}}_{\mathrm{f}}{\mathrm{C}}_{\mathrm{pf} }\left({\mathrm{T}}_{\mathrm{fo}}-{\mathrm{T}}_{\mathrm{fi}}\right)$$

(4)

2.1.2. Heat Storage Tank with Internal Heat Exchanger

In this study, the heat storage tank is used to store the obtained solar heat energy and prolong the operation due to the unstable supply of solar radiation. The heat storage tank temperature (T_s) and internal heat exchanger outlet temperature (T_ho) are computed according to the theoretical model and the parameters by Badescu [23]. Note that the corresponding parameters are shown in Table 1. It is assumed that the heat losses on the duct connecting the solar collector and the storage tank are neglected. The water is uniformly mixed in the closed-loop to simplify the model.

The energy balance of the water in the storage tank is

$${\mathrm{M}}_{\mathrm{s}}{\mathrm{C}}_{\mathrm{pf}}\frac{{\mathit{d}\mathrm{T}}_{\mathrm{s}}}{\mathit{d}\mathrm{t}}={\mathrm{Q}}_{\mathrm{sc}}-{\mathrm{Q}}_{\mathrm{s}}-{\mathrm{Q}}_{\mathrm{h}}$$

(5)

where Q_sc is the heat flux transferred from the solar collector to the heat storage tank, which can be divided into two cases:

(1)

The collector outlet temperature (T_fo) is higher than the heat storage tank temperature (T_s).

(2)

The collector outlet temperature (T_fo) is lower than the heat storage tank temperature (T_s), which means the collector does not obtain any energy.

$${\mathrm{Q}}_{\mathrm{sc}}=\left\{\begin{array}{c}{\mathrm{m}}_{\mathrm{f}}{ \mathrm{C}}_{\mathrm{pf} }\left({\mathrm{T}}_{\mathrm{fo}}-{\mathrm{T}}_{\mathrm{s}}\right){, \mathrm{T}}_{\mathrm{fo}} \ge { \mathrm{T}}_{\mathrm{s}}\\ {0, \mathrm{T}}_{\mathrm{fo}}{ < \mathrm{T}}_{\mathrm{s}}\end{array}\right.$$

(6)

Q_s is the heat flux lost through the storage tank walls, defined as

$${\mathrm{Q}}_{\mathrm{s}}={\mathrm{U}}_{\mathrm{s}}{\mathrm{A}}_{\mathrm{s}}\left({\mathrm{T}}_{\mathrm{s}}-{\mathrm{T}}_{\mathrm{a}}\right)$$

(7)

Q_h is the heat flux provided to the seawater in the secondary circuit, defined as

$${\mathrm{Q}}_{\mathrm{h}}={\mathrm{m}}_{\mathrm{h}}{\mathrm{C}}_{\mathrm{ph}}\left({\mathrm{T}}_{\mathrm{ho}}-{\mathrm{T}}_{\mathrm{hi}}\right)={\mathrm{U}}_{\mathrm{h}}{\mathrm{A}}_{\mathrm{h}}\left({\mathrm{T}}_{\mathrm{s}}-{\mathrm{T}}_{\mathrm{ho}}\right)$$

(8)

2.1.3. The Hollow Fiber DCMD Module

This work refers to the theoretical model and the unidimensional hollow fiber direct contact membrane distillation module parameters by Cheng et al. [24]. The model considers the heat transfer, mass transfer, and transport behavior between the feed side, across the membrane, and the permeate side that follows the assumptions: (i) steady incompressible flow, (ii) feed is Newtonian fluid and unidirectional flow, (iii) the fibers are distributed regularly within the shell of the module, (iv) axial diffusion is negligible, and (v) heat loss to the ambient environment is negligible. For brevity and to avoid repetitions with the previous literature, the model details, the computational procedures, and the model verification with experimental data are provided in the Supplementary Materials.

2.1.4. The PEMFC Module

Proton exchange membrane fuel cells (PEMFCs) are electrochemistry modules that directly convert chemical energy into electrical and thermal energy. This work is according to the theoretical model and the parameters established by Hu et al. [16]. The model can calculate the fluid outlet temperature of the PEMFC (T_st). The parameters are shown in Table 1 and follow the assumptions: (i) at steady-state operation, the temperature and pressure distribution in the PEMFC are consistent, (ii) the vapor is saturated in the PEMFC, (iii) the generated water is in a liquid state at PEMFC working temperature, and (iv) the outlet temperature of the fluid is equal to the operating temperature of the fuel cell. Again, for the sake of brevity, the model details and the computational procedures are provided in the Supplementary Materials.

2.2. Preliminary Simulation Results

In this study, a preliminary simulation test for the solar-heated membrane distillation system is carried out. To simulate realistic operation conditions, environmental data of Taichung, Taiwan, are adopted in this study from Ho and Huang [25]. The data for each hour are averaged from the whole year data, as shown in Figure 2. The ambient temperature (T_a) and solar irradiation data (I) in Figure 2 are substituted into the established mathematical formula. The equipment size is set as design variables. The values of the operating conditions for simulation are shown in

Table 2. The operating conditions of preliminary simulation for the solar-heated membrane distillation system.

Parameter Description	Symbol	Value	Unit
Solar collector area	Asc	50	m2
Membrane area	Am	1.2	m2
Heat storage tank size	Ms	500	kg
The primary circuit mass flow rate	mf	0.1	kg/s
Seawater mass flow rate	mh	0.01	kg/s
The initial water temperature of the heat storage tank	Ts(0)	25	°C
Seawater temperature	Thi	20	°C
MD feed side outlet pressure	Pf(L)	101.325	kPa
MD permeate side inlet pressure	Pp(0)	101.325	kPa
MD permeate side outlet temperature	Tp(L)	25	°C
MD feed side inlet velocity	vf(0)	0.457	m/s
MD permeate side outlet velocity	vp(L)	0.229	m/s
MD feed side inlet salt concentration	Xfs(0)	0.025	kg salt/kg water

. The variation of solar collector outlet temperature (T_fo), the heat storage tank temperature (T_s), and the heat exchanger outlet temperature (T_ho) are calculated at each time point in the day. The amount of water production in one day is estimated accordingly.

First, the initial water temperature of the heat storage tank is set to 25 °C at normal temperature, and T_fo is constrained to be less than 100 °C. The preliminary simulation results are shown in Figure 3a; T_fo can reach the highest temperature of 93 °C, and T_ho is 87 °C. When the MD feed side inlet temperature is lower than 40 °C, the calculated J is 0 kg/m²·h, and the TDP_h is 0 kg/h. When the MD feed side inlet temperature reaches the highest temperature, the calculated J is 35 kg/m²·h, and the TDP_h is about 48 kg/h. The water production per day will be estimated to be 372.2 kg/day. The permeate flux (J) and water production (TDP_h) results are shown in Figure 3b.

Note that the operating conditions for preliminary simulation are adopted arbitrarily. It is expected that the outlet water temperature of the heat storage tank cannot drop from the initial temperature at the beginning of the day to the temperature at the end of the day. Moreover, the solar collector outlet temperature should not be greater than 100 °C for successive days. Such unideal conditions may occur without the appropriate size of the corresponding units, as shown in Figure 4. Therefore, the following will describe the optimal design method of the system and verify with simulation to satisfy the operating temperature limits and continuity for day-to-day operation.

3. Design Optimization of PEMFC and DCMD Systems

In this study, the mathematical model of the two alternative systems is built for optimal design based on the previous unit models. The dynamic characteristics of solar irradiation are considered during different periods, and the ambient temperature is varied. The operational constraints are also embedded to achieve optimal results within a practical and operable design. The total distillate production (TDP) and the total annual cost (TAC) are subsequently calculated from the cost function of each unit. The unit production cost (UPC) is the objective function. The lowest UPC of the two systems using the Taichung area data will be evaluated.

3.1. Unit Cost Function

The economic cost analysis is estimated by the unit size of the system and the unit cost function. The TAC consists of the annual fixed cost (P_fixed) and the annual operating and maintenance cost (P_O&M) in Equation (9), and the details are shown in Figure 5. The cost equation calculation follows Macedonio et al. [26]. The model follows the assumptions: (i) The solar collector, the heat storage tank, and the pump life (n) is expected to be 20 years, the membrane is 7 years, the PEMFC is 2 years, and the annual interest rate (i) is 5%, (ii) land cost is negligible, (iii) the instrumentation control of system and labor costs are negligible, and (iv) the seawater preprocessing is negligible.

$${\mathrm{TAC}=\mathrm{p}}_{\mathrm{fixed}}+{\mathrm{p}}_{\mathrm{O}\&\mathrm{M}}$$

(9)

3.1.1. Annual Fixed Cost

Annual fixed cost (p_fixed) includes the purchase and installation cost of each unit. The cost is calculated by the total purchase cost (p_cc) and amortization factor of equipment (a is the solar collector, heat storage tank, and pump; b is the membrane; c is the PEMFC) as shown in Equations (10) and (11):

$${\mathrm{p}}_{\mathrm{fixed}}=\mathrm{a}\times \left({\mathrm{p}}_{\mathrm{sc} }{+\mathrm{p}}_{\mathrm{scr} }{+\mathrm{p}}_{\mathrm{te} }{+\mathrm{p}}_{\mathrm{pump}}\right)+\mathrm{b}\times \left({\mathrm{p}}_{\mathrm{mem}}{+\mathrm{p}}_{\mathrm{mema}}\right)+{\mathrm{c}\times \mathrm{p}}_{\mathrm{fc}}$$

(10)

$$\left\{\mathrm{a}\right., \mathrm{b}, \left.\mathrm{c}\right\}=\frac{\mathrm{i}{\left(1+\mathrm{i}\right)}^{\mathrm{n}}}{{\left(1+\mathrm{i}\right)}^{\mathrm{n}}-1}$$

(11)

The cost of each unit equipment purchase is based on the cost data (p₁) provided by the literature and adjusted with the cost index published by the Chemical Engineering Plant Cost Index (CEPCI) (p₂), as in Equation (12):

$${\mathrm{p}}_2{=\mathrm{p}}_1\left({\mathrm{I}}_2/{\mathrm{I}}_1\right)$$

(12)

where I₁ and I₂ are the cost index of referred literature at that time and nowadays. Note that the costs in the literature are adjusted to the current cost index (616 in February 2019) in this study for subsequent calculations.

Solar Collector

The cost is based on the estimated solar collector provided by Saffarini et al. [27], which is USD 160/m². The cost index noticed in 2012 is 584.6, and the cost is adjusted to USD 168/m² for February 2019, according to Equation (12). Due to that the systems are located in Taiwan, the subsidy method announced by the Ministry of Economic Affairs is implemented. The cover-type solar collector is subsidized for USD 75/m². Thus, the solar collector cost is corrected to USD 93/m². In addition, the installation cost of the solar collector is estimated to be 30% of the purchase cost, as calculated by Equations (13) and (14):

$${\mathrm{p}}_{\mathrm{sc}}{=93 \mathrm{A}}_{\mathrm{sc}}$$

(13)

$${\mathrm{p}}_{\mathrm{scr}}=0{.3 \mathrm{p}}_{\mathrm{sc}}$$

(14)

Heat Storage Tank with Internal Heat Exchanger

This unit is divided into two parts. Due to the fact that the working fluid is pure water, the general carbon steel material is selected for the heat storage tank. The cost is estimated to be USD 160/m² in February 2019.

The cost of the heat exchanger is based on the model provided by Turton et al. [28], considering its size, pressure, and material and estimation by cost index adjustment as shown in Equations (15)–(20). The size range is 10–1000 m², and the pressure is assumed less than 5 barg. The cost index noticed in 2014 is 521.9 for cheaper fixed shell and tube heat exchangers, which are also suitable for use at high temperatures. In terms of material, carbon steel is selected at the shell side for working fluid and titanium alloy at the tube side for seawater.

$${\mathrm{p}}_{\tan \mathrm{k}}{=160(\mathrm{M}}_{\mathrm{s}}/1000)$$

(15)

$${\mathrm{C}}_{\mathrm{BM}}{=\mathrm{C}}_{\mathrm{p}}^0\left({\mathrm{B}}_1{+\mathrm{B}}_2{\mathrm{F}}_{\mathrm{p}}{\mathrm{F}}_{\mathrm{M}}\right)$$

(16)

$${\mathrm{logC}}_{\mathrm{p}}^0{=\mathrm{k}}_1{+\mathrm{k}}_2\log \left({\mathrm{A}}_{\mathrm{h}}\right){+\mathrm{k}}_3{\left[\log \left({\mathrm{A}}_{\mathrm{h}}\right)\right]}^2$$

(17)

$${\mathrm{logF}}_{\mathrm{p}}{=\mathrm{C}}_1{+\mathrm{C}}_2\log \left(\mathrm{P}\right){+\mathrm{C}}_3{\left[\log \left(\mathrm{P}\right)\right]}^2$$

(18)

$${\mathrm{p}}_{\mathrm{n}}{=\mathrm{C}}_{\mathrm{BM}}\left(616/521.9\right)$$

(19)

$${\mathrm{p}}_{\mathrm{te}}{=\mathrm{p}}_{\mathrm{n}}{+\mathrm{p}}_{\tan \mathrm{k}}$$

(20)

where C_BM is the bare module cost defined as the direct and indirect costs of purchase and installation. F_p and F_M are the pressures and material factors. The constants in the formula are obtained from Turton et al. [28]. B₁ and B₂ are bare module cost factor constants; k₁, k_2, and k₃ are size factor constants; C₁, C_2, and C₃ are pressure factor constants. The constants are shown in

Table 3. The bare module cost constant factor of the heat exchanger.

Symbol	B1	B2	k1	k2	k3	c1, c2, c3	FM
Value	1.63	1.66	4.8306	−0.8509	0.3187	0	4.6

.

The DCMD Module

The cost is based on the estimated DCMD module provided by Al-Obaidani et al. [3], USD 90/m². The cost index noticed in 2008 is 575.4, and the cost is adjusted to USD 96/m² in February 2019. In addition, the installation cost of the DCMD module is estimated to be double the purchase cost, as calculated by Equations (21) and (22):

$${\mathrm{p}}_{\mathrm{mem}}{=96 \mathrm{A}}_{\mathrm{mem}}$$

(21)

$${\mathrm{p}}_{\mathrm{mema}}{=2 \mathrm{p}}_{\mathrm{mem}}$$

(22)

The PEMFC Module

The cost is based on the estimated PEMFC module provided by Bezmalinović et al. [29], which is USD 2000/kW. The cost index noticed in 2013 is 567.3, and the cost is USD 2172/kW nowadays. The total power of the designed fuel cell is estimated as shown in Equation (23):

$${\mathrm{p}}_{\mathrm{fc}}{=2172 \mathrm{Q}}_{\mathrm{tot}}$$

(23)

Pump

This study selects the centrifugal pump with a high delivery rate, low price, and low head to transport the primary closed-loop working fluid and seawater. The cost is based on the model provided by Turton et al. [28], considering its size, pressure, and material and estimating it by cost index adjustment, as shown in Equations (15)–(20). The constants in the formula are obtained from Turton et al. [28], and the constants are shown in

Table 4. The bare module cost constant factor of the pump.

Symbol	B1	B2	k1	k2	k3	c1, c2, c3	FMa	FMb
Value	1.89	1.35	3.3892	0.0536	0.1538	0	1	4.4

. The power range is 1–100 kW, and the pressure is assumed less than 10 barg. The power (W_pump) is estimated by the volume flow rate (Q_v) and head (H) of the operation in Equation (24), assuming the efficiency of each pump (η_pump) is 80% and the head is 20 m. According to Peters et al. [30], the volume flow rate of the operation is 0.6 m³/h. In terms of material, carbon steel is selected at the primary closed loop for the working fluid and nickel alloy for the seawater side (F_Mb) [31].

$${\mathrm{W}}_{\mathrm{pump}}=\frac{9{.8 \times \mathrm{Q}}_{\mathrm{v}} \times \mathrm{H}}{{\mathsf{\eta }}_{\mathrm{pump}} \times 3600}$$

(24)

3.1.2. Annual Operating and Maintenance Cost

The annual operating and maintenance costs (p_O&M) only consider the replacement of a DCMD and PEMFC module, system maintenance, and utility cost, as shown in Equation (25), and that refers to Saffarini et al. [27].

$${\mathrm{p}}_{\mathrm{O}\&\mathrm{M}}{=\mathrm{p}}_{\mathrm{memr} }{+\mathrm{p}}_{\mathrm{fcr} }{+\mathrm{p}}_{\mathrm{M} }{+\mathrm{p}}_{\mathrm{w}}{+\mathrm{p}}_{\mathrm{elec}}{+\mathrm{p}}_{{\mathrm{H}}_2}$$

(25)

The DCMD and PEMFC Replacement

The membrane replacement rate depends on seawater’s salt concentration. The annual replacement rate varies between 5% to 20% of the initial purchase cost. The membrane replacement rate is assumed 15% per year, as shown in Equation (26). The PEMFC needs to be replaced every three and a half years, where the annual replacement cost is estimated to be 0.3 times the initial purchase cost in Equation (27):

$${\mathrm{p}}_{\mathrm{memr}}=0{.15 \mathrm{p}}_{\mathrm{mem}}$$

(26)

$${\mathrm{p}}_{\mathrm{fcr}}=0{.3 \mathrm{p}}_{\mathrm{fc}}$$

(27)

Total Maintenance Cost

The annual maintenance cost of the system is estimated to be 0.5% of the annual fixed cost in Equation (28):

$${\mathrm{p}}_{\mathrm{M}}=0{.005 \mathrm{p}}_{\mathrm{fixed}}$$

(28)

Utility Cost

The utility cost includes the water, electricity, and gas costs that need to be calculated for the two systems in this study. In terms of water cost, the cooling water cost (p_w) of the primary closed loop is related to the heat storage tank size of the system. According to Taiwan Water Corporation’s basic charge, the unit price of the water is USD 0.39/m³, incorporated in Equation (29). The seawater in the secondary circuit is taken from the sea of nature, which is zero-cost. In terms of electricity cost, both systems use solar energy as the heat source that only needs to consider the electricity cost of the pump (p_elec). According to the Taiwan Power Company’s basic charge, the unit price of the electricity is USD 0.08/kWh. The calculation mode provided by Vogelesang [32] is based on its operating time (t_pump), power consumption (W_pump), and unit power price, as shown in Equation (30). The PEMFC coupled solar-heated membrane distillation system uses hydrogen and oxygen to generate electricity. Thus, the power generated from the PEMFC can be supplied into the hybrid system. If there is excess power, it is sold at the unit price of USD 0.08/kWh. In terms of gas cost, according to Bezmalinović et al. [29], the unit price of hydrogen is USD 5/kg, and the cost is adjusted to USD 5.4/kg nowadays. The cost depends on the amount of reaction (${\mathrm{N}}_{{\mathrm{an}, \mathrm{H}}_2}^{\mathrm{re}}$) and the operation time (t_fc), as formulated in Equation (31):

$${\mathrm{p}}_{\mathrm{w}}=0.39\times \left({\mathrm{M}}_{\mathrm{s}}/1000\right)$$

(29)

$${\mathrm{p}}_{\mathrm{elec}}=365\times 0{.08\times \mathrm{W}}_{\mathrm{pump}}{\times \mathrm{t}}_{\mathrm{pump}}$$

(30)

$${\mathrm{p}}_{{\mathrm{H}}_2}=5.4\left({\mathrm{N}}_{{\mathrm{an}, \mathrm{H}}_2}^{\mathrm{re}}{ \times \mathrm{t}}_{\mathrm{fc}}{ \times 2\times 10}^{-3}\right)$$

(31)

where 2 × 10⁻³ kg/mol is the unit conversion of hydrogen molecular weight.

3.2. Objective Function and Constraints

The objective function of the membrane distillation systems with two heating methods consists of the TAC and TDP, as shown in Equation (32). The optimized variables and the related constraints are shown in Equations (33)–(38). The operational constraints of a solar-heated membrane distillation system are as follows: (i) the solar collector outlet temperature (T_fo) must be lower than 100 °C at any time (n) to avoid boiling of the working fluid; (ii) the set temperature difference must be less than 1 °C; (iii) the temperature at the end of each day must be greater than the start of the day and the water production of the day must be greater than zero. The initial heat storage tank temperature cannot be fixed at the beginning and end of the day to ensure the continuity of day-to-day operation. The total operating time is H, and t ∈ [0, H]. In addition, the constraints of the PEMFC coupled solar-heated membrane distillation system include the above three conditions. The PEMFC temperature must be lower than 100 °C at any time period (n = 1, …, H) for safe working temperature.

$$\mathrm{UPC}=\mathrm{TAC}/\mathrm{TDP}$$

(32)

For the first solar-heated membrane distillation system optimization model, the TDP is computed according to Equations (1)–(8) and all of the equations in Supplementary Materials [33,34,35]. The TAC is calculated based on Equations (9)–(31). The UPC is minimized as follows:

$$\mathrm{Obj}=\underset{\mathrm{f}}{\min }\left(\mathrm{UPC}\right)$$

(33)

$${\mathrm{f}=\mathrm{A}}_{\mathrm{sc}}{, \mathrm{M}}_{\mathrm{s}}{, \mathrm{T}}_{\mathrm{s}}\left(0\right)$$

(34)

$$S.t.\left\{\begin{array}{c}\begin{array}{c}{\mathrm{T}}_{\mathrm{fo}}\left(\mathrm{n}\right) < 100 °\mathrm{C} \hfill \\ {\mathrm{T}}_{\mathrm{s}}\left(\mathrm{H}\right)\ge {\mathrm{T}}_{\mathrm{s}}\left(0\right)\\ {\mathrm{T}}_{\mathrm{s}}\left(\mathrm{H}\right)-{\mathrm{T}}_{\mathrm{s}}\left(0\right) \le 1 °\mathrm{C} \hfill \\ \mathrm{TDP} > 0 \hfill \end{array}\end{array}\right\}$$

(35)

As for the PEMFC coupled solar-heated membrane distillation system optimization model, it includes the same TDP and TAC calculations with the UPC is minimized as follows:

$$\mathrm{Obj}=\underset{\mathrm{f}}{\min }\left(\mathrm{UPC}\right)$$

(36)

$${\mathrm{f}=\mathrm{j}}_{\mathrm{fc}}{, \mathrm{A}}_{\mathrm{sc}}{, \mathrm{A}}_{\mathrm{fc}}{, \mathrm{M}}_{\mathrm{s}}{, \mathrm{T}}_{\mathrm{s}}\left(0\right)$$

(37)

$$S.t.\left\{\begin{array}{c}\begin{array}{c}{\mathrm{T}}_{\mathrm{fo}}\left(\mathrm{n}\right) < 100 °\mathrm{C} \hfill \\ {\mathrm{T}}_{\mathrm{s}}\left(\mathrm{H}\right)\ge {\mathrm{T}}_{\mathrm{s}}\left(0\right)\\ {\mathrm{T}}_{\mathrm{s}}\left(\mathrm{H}\right)-{\mathrm{T}}_{\mathrm{s}}\left(0\right) \le 1 °\mathrm{C} \hfill \\ {\mathrm{T}}_{\mathrm{st}}\left(\mathrm{n}\right) < 100 °\mathrm{C} \hfill \\ \mathrm{TDP} > 0 \hfill \end{array}\hfill \end{array}\right\}$$

(38)

3.3. Optimal Design Method and Computational Strategy

This study uses the fmincon function and the sequential quadratic programming (SQP) algorithm in MATLAB to execute the optimization. The dynamic model is built in the SIMULINK platform to compute TDP and TAC for each different design parameter. Note that the optimization process is shown in Figure 6. The MATLAB default parameters setting is used for fmincon function. The computational works were carried out in a desktop server platform with Intel^® Xeon^® Silver 4216 CPU @ 2.10 GHz (two processors) and 768 GB RAM. All of the mathematical models were solved with MATLAB R2019a.

Before the optimization analysis, the initial values of the optimization variables and their calculation ranges are set accordingly. The fmincon function will subsequently substitute the initial iteration values of design parameters in Equations (1)–(31) and all of the equations in Supplementary Materials into the established dynamic model in SIMULINK. The TDP and TAC are calculated within the SIMULINK platform. The fmincon function minimizes the UPC objective function, as shown in Equations (32)–(38). The next iteration is carried out after the calculation reaches convergence in the SIMULINK platform. The above steps are repeated within the fmincon routine until the iteration UDP value is less than the step tolerance and finish the iteration.

However, the operational constraints are set in this study in the fmincon solver layer. If the results violate the constraints as shown in Equations (36)–(38), the TDP computed from SIMULINK will be overridden with the algorithm shown in Algorithms 1. If any operational constraint is violated, the water production TDP is given with a small value. UPC will be minimized for optimal design variables different to the initial values as the optimization algorithm is carried out. Note that fmincon is a local solver. Therefore, to determine the globality of the solution, several initial values are implemented with a full-range scan method to scan all the possible solutions (f), as shown in Figure 7. By comparing all the local best solutions in these ranges, the global minimum of UPC can be computed accordingly.

Algorithm 1. Conditional algorithm for operational constraints.

if Ts(end) ≥ Ts(0) & Ts(end) − Ts(0) ≤ 1

if Tfo(n) < 100

if Tst(n) < 100

% Calculate the TDP from Equations (1)–(8) and all of the equations in Supplementary Materials.

TDP = TDP;

else

TDP = 1 * 10 ^ −5;

end

else

TDP = 1 * 10 ^ −5;

End

else

TDP = 1 * 10 ^ −5;

end

4. Results and Discussion

4.1. Sensitivity Analysis

A sensitivity analysis is implemented to rank the importance of the design variables and simultaneously reduce the dimensionality of the optimization procedure, as shown in

Table 5. Sensitivity analysis parameter of two systems.

The Solar-Heated Membrane Distillation System		The PEMFC Coupled Solar-Heated Membrane Distillation System
Sensitivity Analysis Parameter	Symbol	Sensitivity Analysis Parameter	Symbol
Solar collector area	Asc	The PEMFC active area	Afc
The primary circuit mass flow rate	mf	Solar collector area	Asc
Seawater mass flow rate	mh	The PEMFC current density	jfc
Heat storage tank size	Ms	The primary circuit mass flow rate	mf
The initial water temperature of the heat storage tank	Ts(0)	Seawater mass flow rate	mh
		Heat storage tank size	Ms
		The PEMFC mass	Mst
		The initial water temperature of the heat storage tank	Ts(0)

. The sensitivity analysis simulates the one-day operation systems and evaluates the water production TDP for each variable of interest. In contrast, the other variables are fixed at their nominal values.

The increase or decrease effects on TDP for each variable change are shown in Figure 8. In this study, each variable of interest is varied by four times the initial values shown in Table 2. The result shows that m_f has the most minor influence on water production compared with other solar-heated membrane distillation system parameters. Thus, m_f is not considered as the optimization design variable. The result for the PEMFC coupled solar-heated membrane distillation system shows that the most influential is j_fc and the least is M_st. Therefore, M_st is not considered as the optimization design variable. Note that m_h impacts the water production, as shown in the sensitivity analysis result for the latter system, which corresponds to the flow of the primary feed source. If the flow rate is too fast, the preheating of seawater may be insufficient and lead to water production decrease as the inlet membrane temperature decreases. If the flow rate is too low, the preheated seawater temperature can be higher. Still, since the flow rate is too low, the expected water production will also be impacted. Therefore, m_h is not considered as the optimization design variable. Thus, A_sc, T_s(0), and M_s are selected for the original configuration. As for the second system, j_fc, A_fc, A_sc, T_s(0), and M_s are chosen as the optimization variables for optimal design. The parameters excluded for optimization are shown in

Table 6. The excluded parameters and their fixed values.

Parameter Description	Symbol	Value	Unit
The primary circuit mass flow rate	mf	0.1	kg/s
Seawater mass flow rate	mh	0.01	kg/s
The PEMFC mass	Mst	20	kg

, and are fixed in the subsequent computation.

4.2. Optimization Results

In this study, the UPC is minimized and, subsequently, the corresponding TAC and TDP are analyzed. The operating conditions for the optimum design of the two systems in this study are shown in

Table 7. The operating conditions for both systems.

Parameter Description	Symbol	Value	Unit
Membrane area	Am	1.2	m2
The primary circuit mass flow rate	mf	0.1	kg/s
Seawater mass flow rate	mh	0.01	kg/s
Seawater temperature	Thi	20	°C
The PEMFC mass	Mst	20	kg
MD feed side outlet pressure	Pf(L)	101.325	kPa
MD permeate side inlet pressure	Pp(0)	101.325	kPa
MD permeate side outlet temperature	Tp L)	25	°C
MD feed side inlet velocity	vf(0)	0.457	m/s
MD permeate side outlet velocity	vp(L)	0.229	m/s
MD feed side inlet salt concentration	Xfs(0)	0.025	kg salt/kg water

. The environmental data of Taichung, Taiwan, are adopted, as shown in Figure 2. The optimization procedure above is then implemented to compute the optimum design for both systems. Before the optimization is carried out, the initial points and calculation range of the optimization variables are set according to

Table 8. The initial point and calculation range of optimization variable for both systems.

The Solar-Heated Membrane Distillation System
Optimal Variable	Initial Point	Variable Range (Upper-Lower Limit)
Asc	[10, 20, …, 110, 120] (10 steps)	10–120
Ts(0)	[25, 30, …, 70, 75] (5 steps)	25–80
Ms	[1145, 1395, …, 4645, 4895] (250 steps)	1000–5000
The PEMFC Coupled Solar-Heated Membrane Distillation System
Optimal Variable	Initial Point	Variable Range (Upper–Lower Limit)
jfc	[0.9, 1.2, 1.5] (0.3 steps)	0.8–1.6
Afc	[60, 90, 120, 150] (30 steps)	50–150
Asc	[10, 20, …, 110, 120] (10 steps)	10–120
Ts(0)	[25, 30, …, 70, 75] (5 steps)	25–80
Ms	[1145, 1395, …, 4645, 4895] (250 steps)	1000–5000

. Note that there are several initial points to ensure the globality of the solutions, as described in Figure 7.

The optimum result of the solar-heated membrane distillation system using fmincon is shown in Figure 9a. The initial variables set are as follows: A_sc is 80 m², M_s is 4145 kg, and T_s(0) is 70 °C. The lowest UPC is USD 118.55/m³, which corresponds to A_sc at 80.09 m², M_s of 4145 kg, and T_s(0) at 71.8 °C. The plane curve in Figure 9a is obtained from several runs of fmincon for visualization purposes, and, then, a full-range scan with fixed steps (see

Table 9. The optimal results with different methods for both systems.

System	The Solar-Heated Membrane Distillation System		The PEMFC Coupled Solar-Heated Membrane Distillation System
Symbol (Unit)	fmincon	Full-Range	fmincon	Full-Range
Asc (m2)	80.09	80	80.10	80
Ms (kg)	4145	2645	3145	3145
Ts(0) (°C)	71.8	71	71.6	70
Afc (cm2)	─	─	50.072	60
jfc (A/cm2)	─	─	1.87	1.8
UPC (USD/m3)	118.55	119.78	132.65	140.05
TAC (USD/y)	23,189	23,167	65,309	71,926
TDP (m3/y)	195.59	193.40	492.34	513.58

) is carried out to verify the fmincon result, and the results are shown in Figure 9b. Note that the blank area in the variable range means that the corresponding sizes cannot satisfy the operational constraints. M_s and A_sc have an impact on the UPC with the T_s(0) variation. When T_s(0) increases, M_s and A_sc are more significant and, consequently, the calculated UPC is lower. The optimum variable for A_sc is 80 m², M_s is 2645 kg, T_s(0) is 71 °C, and the lowest UPC is USD 119.78/m³ for the fixed steps approach. The optimum TAC is found to be USD 23,189/y using fmincon algorithm. It can be seen here that the lower TACs collocate with the low T_s(0). Thus, there is an optimum T_s(0) that can be suggested to design the corresponding hybrid system. The UPC results are similar to fmincon function and full-range scan method; however, the full-range scan method uses more significant calculation steps, hence less accuracy. It is noteworthy to mention that the UPC in this study is on the expensive side as the membrane area is fixed at 1.2 m², which is arguably out of the economic scale for large-scale production [36]. It is expected that the UPC will be lower for a larger membrane area. Still, in this study, the membrane area is deliberately fixed to be consistent with the previous literature values [24] and as a reference basis for the subsequent optimization of other design parameters. Moreover, this study is primarily aimed at showcasing rigorous dynamic optimization and, at the same time, simultaneously introducing the daily production continuity constraints, ensuring the operability of the optimal design.

The partial results of the PEMFC coupled solar-heated membrane distillation system for fmincon are shown in Figure 10. Since there are five optimization variables, the optimization results only can present partial data. The initial points of the variables set are as follows: A_sc is 80 m², M_s is 3145 kg, T_s(0) is 70 °C, A_fc is 30 cm², and j_fc is 1.8 A/cm². The result shows that the lowest UPC is USD 132.65/m³ for A_sc of 80.10 m², M_s at 3145 kg, T_s(0) value of 71.57 °C, A_fc of 50.07 cm², and j_fc of 1.87 A/cm². The higher T_s(0) collocates with more significant M_s and the smaller A_fc, potentially achieving the lowest UPC. The full-range scan result is omitted as the conclusion is similar to the first system. The TAC result of the PEMFC coupled solar-heated membrane distillation system with fmincon corresponds to USD 65,309/y.

On the other hand, one may want to find the extent of the throughput from both systems. The TDP result of the solar-heated membrane distillation system with fmincon is shown in Figure 11a. The TDP increases as the T_s(0) and M_s increases to a certain point at the similar A_sc. If the M_s is too large, the downstream temperature from the internal heat exchanger would struggle to rise due to the heat storage tank’s heat capacity. This situation will lead to a lower TDP at the larger size of M_s. The TDP optimum is 195.59 m³/y.

The partial TDP results of the PEMFC coupled solar-heated membrane distillation system with fmincon are shown in Figure 11b, where A_sc and j_fc data are considered at 80 m² and 1.8 A/cm². Similar to the previous results, the higher T_s(0) collocates with the larger A_fc. The TDP increases as the generated heat increases. The optimal TDP with fmincon algorithm is computed to be 492.34 m³/y.

The optimal results with fmincon and full-range scan methods are summarized in Table 9. Although the results of fmincon and full-range scans are similar, the fmincon can potentially find the lower UPC. By introducing the PEMFC, the required size of the heat storage tank is reduced as the waste heat from the PEMFC plays a role in increasing the TDP of the system, and the dependency on the solar loop is reduced.

The systems are simulated for a one-day operation to verify the operating temperature limits and continuity for day-to-day operation. The simulation results of both systems using different methods are shown in Figure 12a. Note that the T_s difference must be less than 1 °C, and the temperature at the end of each day (T_s(H)) must be greater than the start of the day (T_s(0)). Based on the simulation results in Figure 12a, each optimum result obviously has continuity for day-to-day operation. In addition, by comparing the minimum UPC of the two systems, the UPC of adding the fuel cell system is USD 14.15/m³ higher than the original configuration. The T_s profiles are almost similar for both systems, as T_s is related to the first loop, as shown in Figure 1. The waste heat of the PEMFC only affects the downstream temperature out of the heat storage tank. Hence, the TDP of adding the fuel cell system is 297.1 m³/y, more increased than the original configuration (2.5 times the original value, as shown in Figure 12b). This is the most apparent impact of the PEMFC addition, benefitting its stable heat supply for the entire operation. The TAC is USD 42,120/y higher than the original configuration (2.8 times the original value). The cost details from each unit of the two systems are shown in

Table 10. The unit cost details of both systems with different methods.

System		The Solar-Heated Membrane Distillation System		The PEMFC Coupled Solar-Heated Membrane Distillation System
Units Cost Symbol)		The Cost with fmincon (USD)	The Cost with Full-Range (USD)	The Cost with fmincon (USD)	The Cost with Full-Range (USD)
Solar collector (psc & pscr)		9684.1	9672	9683.7	9672
Heat storage tank with internal heat (pte)		201,011	200,350	200,851	200,851
DCMD module (pmem & pmemr)		345.6	345.6	345.6	345.6
PEMFC (pfc)		─	─	33,616	38,870
Pump (ppump)		63,717	63,717	63,717	63,717
Annual fixed cost (pfixed)		23,002.5	22,981	40,152	42,988
Unit replacement cost	DCMD (pmemr)	17.28	17.28	17.28	17.28
	PEMFC (pfcr)	─	─	10,085	11,661
System maintenance cost (pM)		115	114.9	200.42	214.9
Utility cost	Cooling water (pw)	1.6	1	1.3	1.3
	Electricity (pelec)	52.6	52.6	(−)3610	(−)4306
	Hydrogen (pH2)	─	─	18,463	21,349
Operating and Maintenance cost (pO&M)		186.5	185.8	25,157	28,938
Total annual cost (TAC)		23,189	23,167	65,309	71,926

. The PEMFC cost is USD 17,149/y, and the hydrogen price is USD 18,463/y higher than the original configuration. With the addition of the PEMFC, it can supply the power of the pump in the system. Still, the excess electricity can be sold to increase revenue from the power production of the PEMFC.

Based on the cost breakdown in Table 10, the hydrogen price is the main reason behind the higher value of TAC than the original configuration. If the hydrogen price can be decreased, the UPC of the PEMFC coupled solar-heated membrane distillation system will also potentially be reduced. Consequently, the UPC and TAC of the PEMFC coupled solar-heated membrane distillation system are recalculated based on the different hydrogen prices, as shown in Figure 13. The result shows when the hydrogen price decreases from USD 5.4/kg to USD 3/kg, the UPC is USD 116/m³. Thus, if the hydrogen price decreases below USD 3/kg, the UPC of the PEMFC coupled solar-heated membrane distillation system will be more competitive than the original configuration.

5. Conclusions

In this work, the models of PEMFC and DCMD systems have been built and verified with the experimental data. The rigorous optimization procedure of the hybrid systems has been proposed accordingly. The feasibility of solar-heated membrane distillation and PEMFC coupled solar-heated membrane distillation systems is evaluated according to their UPC, TAC, and TDP. The PEMFC coupled with a solar-heated DCMD module system fails to effectively reduce its UPC due to the high price of hydrogen. Still, it shows that it can have a more sustainable heat source and increase the TDP from the original configuration. With the addition of the PEMFC, the required size for heat storage tanks could be smaller. According to TAC analysis, the PEMFC coupled solar-heated membrane distillation system is 2.8 times higher than the original system. If the hydrogen price can be less than USD 3/kg, the UPC of the PEMFC coupled solar-heated membrane distillation system will be more competitive than the original system. The potential exists to combine with the electrolytic cell to produce hydrogen independently from any waste/excess energy in the future. Hence, more costs can be saved for desalination with a multi-generation hybrid system.