Thermodynamic and Economic Analysis of a Phosphoric Acid Fuel Cell Combined Heating Cooling and Power System

Abstract

This study proposes an innovative hybrid system that integrates a phosphoric acid fuel cell (PAFC) with an absorption refrigeration system (ARS) to enhance overall exergy efficiency. Waste heat from the PAFC is used in ARS generation. An evaluation is made of the energy efficiency, economic aspects, and the influence of the operating pressures of the two working fluid pairs, LiBr/H₂O and R134a/DMF. In the combined PAFC-ARS, the absorption refrigeration unit incurs the highest exergy loss: 157 kW (R134a/DMF) and 146 kW (LiBr/H₂O). The second-largest loss is experienced by the pure electrical generation PAFC unit at 117 kW. From an economic perspective, PAFC-ARS (LiBr/H₂O) systems incur costs of USD 2.4/t for both hot water and cooling water, and USD 0.13 kW/h for electricity, with an 8 year payback period. In comparison, the R134a/DMF system entails costs of USD 2.1/t for hot water and cooling water and USD 0.16 kW/h for electricity. The PAFC exhibits a net output power of 434 kW, considering both energy and exergy perspectives. The corresponding maximum net electric energy efficiency (η_I) of the PAFC is 52%, while the overall exergy efficiency of the cooling model (η_II,dc) of the PAFC-ARS peaks at 56%, and the overall exergy efficiency of the heating model (η_II,dh) reaches its maximum at 61%. In conclusion, the PAFC-ARS (LiBr/H₂O) demonstrates superior economic viability.

1. Introduction

As society and the economy expand rapidly, the consumption of fossil energy has surged accordingly. The carbon dioxide emitted from this energy source poses a significant environmental threat [1]. Hydrogen is considered to be a potential energy carrier utilized in fuel cells and combustion processes [2]. Hydrogen is a clean energy source that falls within the category of green energy sources [3]. Fuel cells are anticipated to serve as a superior carbon-free option [4]. Due to the absence of greenhouse gasses (like carbon dioxide and nitrogen oxides) and their ability to produce electricity using only water and heat as byproducts, hydrogen fuel cells are considered to be an environmentally friendly energy source [5].

PAFCs are highly preferred for addressing diverse electricity demands in buildings due to their exceptional durability and reliability [6]. These fuel cells can consistently perform even in challenging conditions. Utilized for supplying power to large buildings, supporting small distributed generation, and propelling vehicles, PAFCs contribute to emission reduction and the promotion of sustainable development. The capability to manage fuel impurities enhances their reliability and reduces pre-processing requirements [7].

Yurong [8] conducted a detailed study on a comprehensive system that integrates compressed air energy storage, the organic Rankine cycle (ORC), and an absorption refrigeration system (ARS). The study focused on multi-objective optimization to improve round-trip efficiency while minimizing the investment cost per unit of output power. After integrating the ORC with the PAFC system, Seunghun achieved a maximum exergy efficiency of 52.70% for this hybrid system by efficiently harnessing the waste heat [9]. Xinru [10] developed a hybrid ORC and PAFC system using a numerical simulation, with a focus on energy efficiency, utility, and the environmental impacts. Similarly, incorporating an ARS with a PAFC system can yield substantial efficiency improvements, as ARSs are commonly employed to recycle various low-grade heat energies [11]. Past research has explored the integration of PAFC with ORC [9,10] and ARS [12].

ARSs offer numerous advantages over ORC systems, especially when used with low-temperature heat sources, thereby expanding their applicability. Conversely, ORC systems demonstrate superior energy conversion performance at elevated temperatures [13]. Furthermore, the versatility of absorption refrigeration systems extends to their customization for combined cooling and storage heating [14], thereby enhancing adaptability across diverse scenarios. Most importantly, the efficiency of a single-effect ORC system is approximately 25% [15], representing a significant energy wastage. In contrast, single-effect ARSs typically achieve an efficiency of around 60% to 80% [16].

The efficacy of ARSs in energy utilization is notably due to their proficiency in harnessing surplus or low-quality energy. It is important to note, however, that this advantage comes with the trade-off of higher equipment investment and operational costs [17]. On the other hand, ORC systems prove to be efficient in both low-temperature and small-scale equipment, demonstrating adaptability to various working fluids and conditions [9,13], albeit with potential concerns such as the generation of toxic substances. Lastly, Puqing [12] developed a hybrid system integrating an ARS and a PAFC through numerical simulations using MATLAB Simulink. His study thoroughly examined various parameters affecting the hybrid system’s performance; however, his analysis did not cover the energy efficiency, exergy efficiency, economic, or exergy aspects of the system. Demonstrably, the PAFC-ARS has not been thermodynamic and economically evaluated before.

It is evident that there is a need to carry out efficiency and economic analyses of PAFC-ARS systems. This study addresses this gap with a comprehensive analysis of a 440 kW PAFC system integrated with an ARS, considering its energetic, exergetic, and economic dimensions. The evaluation of the system entails adjusting the operating pressure of the PAFC and the working fluid in the ARS. This equipment can be applied around hydrogen production plants because the costs associated with storing and transporting hydrogen are relatively higher than those for electricity.

2. System Configuration

2.1. PAFC-ARS Description

Figure 1 presents a schematic diagram of the hybrid system that combines a PAFC and an ARS. The PAFC system, as illustrated in this study, has a power capacity of 440 kW and operates on pure hydrogen as its fuel source. The system’s design facilitates the recycling of unreacted hydrogen from the PAFC anode. Simultaneously, air and water from the PAFC cathode preheats both incoming fuel gas and air. Within the PAFC stack, an isothermal phase transition occurs, transferring the generated heat to the cooling plate. During this process, the cooling plate absorbs the heat and transforms water into saturated vapor. A portion of this vapor preheats the air supplied to the PAFC system, while another segment preheats the incoming hydrogen and air. The residual vapor is directed towards the ARS, contributing to additional energy generation.

The generator in the ARS extracts heat from the PAFC, separating gaseous refrigerant from its liquid counterpart and yielding a more concentrated liquid solution. The gaseous refrigerant undergoes condensation within the condenser, transforming into a saturated liquid. Subsequently, through a sequence of heating and expansion, evaporation is achieved, facilitating the extraction of a significant amount of heat and enabling the refrigeration process. Simultaneously, the absorber and condenser generate substantial heat. The efficiencies of the various components are shown in

Table 1. System operating parameters under nominal circumstances.

Component	Value
Temperature of the environment	25 °C
Operating pressure	1 bar
Fuel utilization	80%
Air utilization	70%
Pump efficiency	0.95
SHE efficiency	0.7
HEX efficiency	0.85

.

In Figure 1, the term HEX stands for Heat Exchanger. SHE is an abbreviation for Solution Heat Exchanger. RefV refers to Refrigerant Valve, and SolV denotes the Solution Valve.

2.2. ARS Working Fluid Pairs

The ARS working fluid profoundly influences absorption refrigeration efficiency. LiBr/H₂O and NH₃/H₂O are commonly used working fluids [18]. Despite offering advantages such as high efficiency and low cost, these pairs encounter limitations: LiBr/H₂O faces crystallization and corrosion, while NH₃/H₂O deals with NH₃ separation and toxicity issues [19].

LiBr/H₂O is known for its efficiency, environmental friendliness, longevity, and flexibility, but it is plagued by corrosion risk, high initial cost, and safety concerns related to lithium bromide. In contrast, NH₃/H₂O excels in cooling capacity, operating cost, and efficiency; however, it faces challenges such as ammonia’s toxicity and flammability, maintenance requirements, and potential environmental impact.

For R134a/DMF, compared to R22, R141b, and R142b, it is not ozone-depleting and is less corrosive than NH₃, making it environmentally preferable [20]. Simulations by Suresh [21] models the absorption of R134a in a liquid R134a/DMF solution, calculating thermophysical properties. Zehioua [22] identifies optimal R134a/DMF pairs within the temperature range of 30.15 to 79.09 °C, while Han et al. [23] experimentally determine solubility within the temperature range of −10 to 90 °C. He [24] ranks R134a/DMF as suitable for solar absorption refrigeration, in alignment with Chunhua’s [25] study on enhancing performance. The choice of working fluid pairs significantly influences the appropriateness and efficiency of an ARS. The LiBr/H₂O system demonstrates superior performance at lower temperatures, especially in applications such as air conditioning and industrial cooling. In contrast, R134a/DMF exhibits versatility across a broader temperature range, albeit with reduced efficacy at lower temperatures. Consequently, this study selects two working fluid pairs, LiBr/H₂O and R134a/DMF, for further investigation.

3. Modeling Description

3.1. PAFC Model

The accurate modeling and simulation of PAFC is important to ensure reliable operation and optimize system performance. Cells are a class of electrochemical devices that serve as energy converters. Specifically, PAFCs fall into the category of hydroxyl cells. The anode reaction of hydroxyl fuel cells can be described by the following equations (Equations (1) and (2)):

$${\mathrm{H}}_2\to 2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}$$

(1)

The cathodic reaction is:

$$1/2{\mathrm{O}}_2+2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}\to {\mathrm{H}}_2\mathrm{O}$$

(2)

In order to construct the PAFC system with Aspen Plus V12^®, precise calculations of voltage and power are needed. The expression for the voltage of the PAFC in degrees Celsius is given by Equations (3) and (4) [26].

$$V_{net}=E_{Nernst}-V_{act}-V_{ohm}-V_{conc}$$

(3)

The variables in question are defined as follows: E_Nernst represents the Nernst voltage, V_act denotes the activation polarization loss, V_ohm represents the ohmic polarization loss, and V_conc represents the concentration polarization loss.

$$E_{Nernst}=E_0+{\displaystyle \frac{RT}{2F}}{\displaystyle \frac{RT}{2F}}ln({\displaystyle \frac{p_{(H_2)}\cdot p_{(O_2)}^{0.5}}{p_{(H_{2}O)}}})ln({\displaystyle \frac{p_{(H_2)}\cdot p_{(O_2)}^{0.5}}{p_{(H_{2}O)}}})$$

(4)

where E₀ is the ideal voltage at standard pressure; R is the ideal gas constant; F is the Faraday constant; T is the operating temperature of the PAFC; and p_H2, p_O2, and p_H2O are the partial pressures of H₂, O₂, and H₂O, respectively.

The activation polarization loss occurs at the anode and cathode. The modified Butler–Volmer equation is used in the calculation and is expressed as follows in Equations (5)–(7):

$$V_{act}=V_{act,a}+V_{act,c}$$

(5)

$$V_{act,a}={\displaystyle \frac{RT}{2F}}ln({\displaystyle \frac{p_{(H_2)}\cdot p_{(O_2)}^{0.5}}{2{\lambda }_a{\alpha }_{a}F}})sin{h}^{-1}({\displaystyle \frac{i}{(i_{(0,a)}·p_{(H_2)})}})$$

(6)

$$V_{act,c}={\displaystyle \frac{RT}{2F}}ln({\displaystyle \frac{p_{(H_2)}\cdot p_{(O_2)}^{0.5}}{4{\lambda }_c{\alpha }_{c}F}})sin{h}^{-1}({\displaystyle \frac{0.2li}{(i_{(0,c)}·p_{(H_2)})}})$$

(7)

The activation polarization losses occurring at battery terminals are represented by the symbols V_act,a and V_act,c, respectively. The exchange current densities at battery terminals are denoted as i_(0,a) and i_(0,c₎, respectively. The charge transfer coefficients associated with battery terminals are denoted as α_a and α_c, respectively. Finally, the battery terminals’ constants are represented by the symbols λ_a and λ_c, correspondingly. The current density is dependent on temperature and may be mathematically expressed as follows in Equations (8)–(10):

$$i_{(0,a)}={\lambda }_r{i}_{r,a}{e}^{\delta ({\displaystyle \frac{1}{T_r}}-{\displaystyle \frac{1}{T}})}$$

(8)

$$i_{(0,c)}={\lambda }_r{i}_{r,c}{e}^{\delta ({\displaystyle \frac{1}{T_r}}-{\displaystyle \frac{1}{T}})}$$

(9)

$$V_{ohm}=j{\displaystyle \frac{t_{ele}}{{\sigma }_{ele}}}$$

(10)

where tele is the thickness of the electrolyte and σ is the specific conductivity of the aqueous phosphoric acid solution. The specific conductivity can be determined by the temperature, viscosity, and concentration [26] in Equation (11):

$$\sigma ={\displaystyle \frac{(702.7X^{1.5}-1734.2X^2+1446.5X^{2.5}-350.7X^3)}{10\mu }}{e}^{(-0.010163+0.011634X-0.08313X^2)T}$$

(11)

The mole percentage of phosphoric acid in the electrolyte is denoted by X, while the viscosity is represented by μ. Equation (12) determines the conductivity and has been modified to accommodate the specific units employed in the model discussed in this study. The expression for concentration polarization loss is provided as follows in Equation (11):

$$V_{conc}=\begin{array}{c}{\displaystyle \frac{RT}{2F}}(1+{\displaystyle \frac{1}{{\lambda }_c{\alpha }_c}})\end{array}\ln {\displaystyle \frac{{\dot{l}}_L}{{\dot{l}}_L-i}}$$

(12)

3.2. Absorption Refrigeration Model

Absorption refrigeration, distinct from conventional vapor compression, employs heat absorption and evaporation for diverse cooling applications. The essential components are the working fluids, acting as a refrigerant and an absorbent. This study specifically focuses on the LiBr/H₂O and R134a/DMF working pairs. To create the thermodynamic model of ARS, it is necessary to consider two governing equations: one for mass conservation and one for energy conservation. The mass balance, concentration balance, and energy balance equations [27] can be expressed as follows (Equations (13)–(15)):

$${\displaystyle \sum _{in}(\dot{m}x}{)}_{in}={\displaystyle \sum _{out}(\dot{m}}x{)}_{out}$$

(13)

$${\displaystyle \sum \dot{Q}}+{\displaystyle \sum _{in}(\dot{m}h}{)}_{in}={\displaystyle \sum _{out}(\dot{m}}h{)}_{out}+{\displaystyle \sum \dot{W}}$$

(14)

$$x={\displaystyle \frac{{\dot{m}}_{Absorbant}}{{\dot{m}}_{Solution}}}$$

(15)

The symbol $\dot{m}$ represents the mass flow, where $\dot{Q}$ and $\dot{W}$ are heat and work transfer rates, respectively, crossing the system boundary. x represents the concentration. In the LiBr/H₂O system, water serves as the refrigerant and LiBr servers as an absorbent. For the R134a/DMF system, R134a, a common vapor-compression refrigerant, evaporates in the evaporator, absorbing heat for cooling. Mixing with DMF in the absorber releases heat, raising the temperature. The refrigerant condenses in the condenser’s post-generator heat, restarting the cycle as the liquid refrigerant enters the evaporator.

3.3. Exergy Modeling

In this study, energy reduction is a key parameter affected by thermodynamic irreversibility [28]. To determine the total exergy of a system, it is necessary to combine its chemical and physical exergy and neglect other exergy [29] using Equation (16).

$$\dot{E}=m(e{x}_{ph}+e{x}_{ch})$$

(16)

In this specific context, “physical exergy” pertains to the utmost amount of work that can be accomplished when transitioning a singular unit mass of a substance solely through physical methods from its initial state to its ambient conditions. The subsequent equation illustrates the computational procedure [30] using Equations (17) and (18).

$$e{x}_{ph}={\displaystyle \sum _{\mathrm{i}}(h_i-h_0)}-T_0(s_i-s_0)$$

(17)

$$e{x}_{ch}={\displaystyle \sum x_{i}e{x}_{ch,i}+R{T}_0}{\displaystyle \sum x_i\ln (x_i)}$$

(18)

The symbol m represents the mole flow. Specific enthalpy and entropy are denoted by the variables h and s, respectively. Reference [31] in the literature provides data on the traditional chemical exergy of various gasses. The concept of chemical exergy is discussed without considering potential and kinetic exergy [9]. The calculation of exergy utilizes the equation labeled as Equation (18).

Inside

Table 2. Exergy equations for system components.

Component	Fuel Exergy	Product Exergy	Exergy Destruction
Fuel Blower	$W_{FB}$	${\dot{E}}_2-{\dot{E}}_1$	$W_{FB}-({\dot{E}}_2-{\dot{E}}_1)$
Air Blower	$W_{\mathrm{A}B}$	${\dot{E}}_7-{\dot{E}}_6$	$W_{\mathrm{A}B}-({\dot{E}}_7-{\dot{E}}_6)$
HEX-1	${\dot{E}}_{10}-{\dot{E}}_{11}$	${\dot{E}}_3-{\dot{E}}_2$	${\dot{E}}_{10}-{\dot{E}}_{11}-({\dot{E}}_3-{\dot{E}}_2)$
HEX-2	${\dot{E}}_{11}-{\dot{E}}_{12}$	${\dot{E}}_8-{\dot{E}}_7$	${\dot{E}}_{11}-{\dot{E}}_{12}-({\dot{E}}_8-{\dot{E}}_7)$
HEX-3	${\dot{E}}_{16}-{\dot{E}}_{17}$	${\dot{E}}_9-{\dot{E}}_8$	${\dot{E}}_{16}-{\dot{E}}_{17}-({\dot{E}}_9-{\dot{E}}_8)$
Mixer1	${\dot{E}}_3+{\dot{E}}_5$	${\dot{E}}_4$	${\dot{E}}_3+{\dot{E}}_5-{\dot{E}}_4$
PAFC	${\dot{E}}_4+{\dot{E}}_9+{\dot{E}}_{14}$	${\dot{E}}_5+{\dot{E}}_{10}+{\dot{E}}_{15}+W_{PAFC}$	${\dot{E}}_4+{\dot{E}}_9+{\dot{E}}_{14}-({\dot{E}}_5+{\dot{E}}_{10}+{\dot{E}}_{15}+W_{PAFC})$
Pump1	$W_{PUMP}$	${\dot{E}}_{14}-{\dot{E}}_{13}$	$W_{PUMP}-({\dot{E}}_{14}-{\dot{E}}_{13})$
AH/AC	${\dot{E}}_{18}-{\dot{E}}_{19}$	${\dot{E}}_{23}-{\dot{E}}_{24}+{\dot{E}}_{22}-{\dot{E}}_{20}$	${\dot{E}}_{18}-{\dot{E}}_{19}-({\dot{E}}_{23}-{\dot{E}}_{24}+{\dot{E}}_{22}-{\dot{E}}_{20})$

, several components related to exergy parameters are included within the system. For the calculation of exergy efficiency (${\eta }_{II,i}$) and exergy destruction (${\dot{E}}_{D,i}$) for every component, Equations (19) and (20) are employed. Equation (21) contains the remaining relevant variables.

$${\dot{E}}_{D,i}={\displaystyle \sum {\dot{E}}_{in,i}}-{\displaystyle \sum {\dot{E}}_{out,i}}$$

(19)

$${\eta }_{II,i}={\displaystyle \frac{{\dot{E}}_{out,i}}{{\dot{E}}_{in,i}}}=1-{\displaystyle \frac{{\dot{E}}_{D,i}}{{\dot{E}}_{in,i}}}$$

(20)

$${\eta }_{II,tol}={\displaystyle \frac{{\dot{E}}_{out,tol}}{{\dot{E}}_{in,tol}}}$$

(21)

The net electric energy efficiency (${\eta }_I$) for the PAFC, exergetic efficiencies for the PAFC-ARS (${\eta }_{II}$), domestic hot water exergetic efficiencies for the PAFC-ARS (${\eta }_{II,dh}$), and domestic cooling water exergetic efficiencies for the PAFC-ARS (${\eta }_{II,dc}$) are calculated using Equations (22)–(26), respectively.

$$P_{fuel}={\dot{m}}_{fuel,in}\cdot LH{V}_{fuel}$$

(22)

The variable $LH{V}_{fuel}$ denotes the Lower Heating Value (LHV) corresponding to the quantity of syngas introduced into the anode of the PAFC stack. Regarding the PAFC-ARS subsystem, Equations (24) and (25) are used to compute the power inputs and outputs, while Equation (25) is employed to determine the ${\eta }_I$.

$${\eta }_I={\displaystyle \frac{W_e}{P_{fuel}}}$$

(23)

$${\eta }_{П}={\displaystyle \frac{W_e}{{\dot{E}}_{fuel}}}$$

(24)

$${\eta }_{П,dh}={\displaystyle \frac{W_e+(1-\frac{T_0}{T_{dh}})Q_{dh}}{{\dot{E}}_{fuel}}}$$

(25)

$${\eta }_{П,dc}={\displaystyle \frac{W_e+(1-\frac{T_0}{T_{dc}})Q_{dc}}{{\dot{E}}_{fuel}}}$$

(26)

The variable W_e represents the net power of the PAFC system. The variable $T_{dh}$ represents the temperature of domestic hot water, whereas $T_{dc}$ represents the temperature of domestic cooling water.

3.4. Economic Modeling

A technique used in the economic analysis of the PAFC-ARS hybrid system involves the categorization of the chemical engineering plant cost index (CAPEX) into five distinct groupings. The categories included in this study are total project cost (Tp), total overnight cost (To), total as-spent cost (Tas), bare erected cost (Be), engineering, procurement, and construction cost (Ep), and total project cost (Tp). The calculations for each of these categories are performed using the corresponding Equations (27)–(30), as presented in

Table 3. Original equipment cost and cost conversion.

Component	Equation	Unit of Parameter	Reference Year	CEPCI
PAFC	$2000\times {\dot{\mathrm{W}}}_{\mathrm{P}\mathrm{A}\mathrm{F}\mathrm{C}}$	${\dot{\mathrm{W}}}_{\mathrm{P}\mathrm{A}\mathrm{F}\mathrm{C}}$ (kW)	2009 [6]	521.9
Blower	$91562\times {\left({\dot{\mathrm{W}}}_{\mathrm{B}\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}}\right)}^{0.67}$	${\dot{\mathrm{W}}}_{\mathrm{B}\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}}$ (kW)	2009 [7]	521.9
Pump-1	$16800\times {\left({\displaystyle \frac{{\dot{\mathrm{W}}}_{\mathrm{P}\mathrm{u}\mathrm{m}\mathrm{p}}}{200}}\right)}^{0.67}$	${\dot{W}}_{\mathrm{Pump}}$ (kW)	2014 [9]	556.8
Heat exchange	$235\times {\left({\dot{\mathbf{Q}}}_{\mathrm{H}\mathrm{E}\mathrm{X}}\right)}^{0.75}$	${\dot{Q}}_{HEX}$(kW)	2014 [18]	556.8
Absorption chiller	$585\times {\dot{\mathrm{Q}}}_{\mathrm{A}\mathrm{C}\mathrm{H}}$	${\dot{\mathrm{Q}}}_{\mathrm{A}\mathrm{C}\mathrm{H}}$ (kW)	2017 [32]	567.5

.

$$Be=C_{equ,actual}+ISC$$

(27)

$$Epc=Be+IdC$$

(28)

$$\mathrm{Tp}=Epc+CONS$$

(29)

$$\mathrm{To}=\mathrm{Tp}+\mathrm{Oc}$$

(30)

The original equipment cost ${{\mathrm{Z}}_{\mathrm{K}}}^{\mathrm{o}}$ is summarized in Table 3. It should be noted that the cost estimation has to be converted to the year 2023, or the present year, by using the CEPCI. The detailed conversion equation of component cost in different years was estimated using Equation (31), the details of which can be found in [31].

$${\displaystyle \frac{{\mathrm{Z}}_K}{{\mathrm{Z}}_K^0}}={\displaystyle \frac{CEPCI}{CEPC{I}^0}}$$

(31)

Finally, the economics of the power plant over its lifespan was assessed using net present values (NPV). To ascertain the current value, all forthcoming cash flows are evaluated using a discount factor (i). The acceptability of the electricity system is contingent upon the positive NPV found using Equation (32) [31].

$$NPV=-Tas+{\displaystyle {\sum }_{n=1}^t\frac{{(Net cash flow)}_n}{{(1+i)}^n}}$$

(32)

The value of each component was determined by adding the installation expenses to the cost of the component. The concept of the EPC encompasses both the direct costs and the expenses related to indirect costs. The total price (Tp) includes both the estimated project cost (EPC) and expenses associated with contingencies. The “To” refers to the total cost, which includes the total project cost (TPC), additional night-time expenses, and the owner’s cost.

Table 4. Primary premise of CAPEX and OPEX estimate and economic assumptions.

Installation Cost Parameter	Value	Unit
Interest (discount) rate (i)	4.35	%
Owner’s cost	5	%
Construction	2	Year
Insurance cost	1	%
Contingency	0.02	%
OPEX
Average nominal escalation rate of hydrogen cost	−4.5	%
Hydrogen prices	2.85	USD/kg
Depreciation cost of equipment	1	%
The variable O&M costs	3.0	%
Cost of installation	5	%
Economic
Average inflation rate	2.0	%
System lifetime	20	Year
PAFC Annual plant operating hours	6000	h/year

provides a summary of the parameters used to estimate capital expenditures (CAPEX), operating expenditures (OPEX), and the economic assumptions required to evaluate the economic analysis.

4. Result and Discussion

4.1. Validation and Model Comparison

In this section, exploration is conducted on the validation and comparison of models developed for the PAFC-ARS.

The PAFC model developed in this study is compared with the model proposed in related research [9]. The results, as summarized in

Table 5. Validation of PAFC model with reference data.

Operating Parameters	This Study	Oh, Seunghun	Errors (%)
Operating pressure (bar)	1	1	0
Operating temperature (°C)	150	150	0
Hydrogen volumetric flow rate (kg/h)	24.89	24.88	0.04
Air flow rate (kg/h)	6.22	6.14	1.30
Power (kW)	441	440	0.23

, indicate a discrepancy of less than 2%. The assessment involved comparing the current–voltage polarization curve of the PAFC model with existing experimental data [33], as shown in Figure 2. Simulation outputs, demonstrating a mere 1.51% (red circle maker) error, affirm the validity of this model.

Table 6. Validation of LiBr/H₂O absorption refrigeration model.

Steam	Blanco-Marigorta		Present Study
	T (°C)	P (kPa)	T (°C)	P (kPa)
25	32.7	0.676	32.7	0.67
26	32.7	7.406	32.7	7.46
27	63.61	7.406	65.7	7.46
28	76.76	7.406	78.4	7.46
29	40.06	7.406	40.1	7.46
30	1.39	0.676	1.2	0.67
31	1.39	0.676	1.3	0.67
32	89.36	7.406	89.9	7.46
33	53.11	7.406	53.3	7.46
34	44.96	0.676	43.1	0.67
COP	0.72		0.74

is dedicated to presenting the results of the LiBr/H₂O model alongside simulation outcomes and experimental data derived from Blanco-Marigorta [34]. This comparison serves to validate the lithium bromide absorption refrigeration model. Similar to the lithium bromide absorption chillers, the data for the R134/DMF chillers are around 5% of the published findings [35] for all errors in

Table 7. Validation of R134a/DMF absorption refrigeration model.

Parameters	A. Yokozeki [35]		Present Study
	T (°C)	P (bar)	T (°C)	P (bar)
Generator	100	10.15	100	10.15
evaporator	10	4.14	10.58	4.14
Absorber	30	4.14	26	4.14
condensers	40	10.15	40.04	10.15
COP	0.47		0.46

; thus, the two model are valid.

Figure 3 presents a comprehensive evaluation of the overall efficiencies of the two fluid pairings employed in the PAFC-ARS composite structure. More precisely, 4 bar corresponds to a temperature of 140 °C, and 5 bar corresponds to a temperature of 150 °C. This parameter is linked to the physical properties of saturated steam water. Comparing the assessments of ${\eta }_I$ and ${\eta }_{II}$ with ${\eta }_{II,dh}$ and ${\eta }_{II,dc}$ in the following four cases (each color) clearly shows that integrating the PAFC structure with the ARS enhances overall system efficiency. The enhancement is attributed to the ARS utilizing the waste heat from the PAFC. In comparing all efficiency sets at 4 and 5 bar, the LiBr/H₂O working fluid demonstrate greater efficiency than the R134a/DMF working fluid, as evidenced by the former’s higher COP. At 5 bar, the ARS using LiBr/H₂O achieves a maximum overall exergy efficiency of heating model (${\eta }_{II,dh}$) 61% higher than that of ARS employing R134a/DMF (59%). Additionally, ARS with LiBr/H₂O attains a maximum overall exergy efficiency cooling model (${\eta }_{II,dc}$) that is higher than ARS with R134a/DMF 0.2%.

4.2. Exergy and Economic Analysis

Figure 4 illustrates the initial design and subsequent modifications made to a 440 kW PAFC system. This study delineates a hybrid system incorporating an ARS. The ARS integrates two distinct working fluids, and the assessment of energy efficiency relies on factors like combustion efficiency and heat loss. Additionally, this study conducts an economic analysis encompassing CAPEX, operational costs, NPV, and other relevant factors. Ultimately, a thorough evaluation of the two working fluids is conducted, yielding definitive recommendations.

Figure 4. Flowchart outlining the model and procedures of the PAFC-ARS.

Figure 4. Flowchart outlining the model and procedures of the PAFC-ARS.

Following the deduction of energy consumption,

Table 8. Simulation results of the energy system.

PAFC-ARS	Parameter (Units)	Energy	Exergy
Input	Hydrogen kW	829	806
	Mass flow, kg/h	25	25
Output	PAFC power, kW	441	441
	Net power, kW	434	434
	Cooling, kW(LH)	281	17
	Cooling, kW(RD)	277	11
performance	Net power efficiency, %	52%	54%
	${\eta }_{II,dc}$, % (LH)	86%	56%
	${\eta }_{II,dc}$, % (RD)	86%	55%

illustrates the highest overall energy efficiency, with the PAFC generating a net power of 434 kW. When utilizing aqueous lithium bromide solutions, absorption chillers discharge 71 kW of energy, with 54 kW designated as heat, and the remaining portion constituting cooling energy. In the case of R134a/DMF utilization, 56 kW of energy is released, with 45 kW attributed to heat, and the remaining portion allocated to cooling energy. (LH is the abbreviation for LiBr/H₂O, and RD stands for 134a/DMF in Table 8).

The exergy-related parameter formulas can be found in Table 2, while the corresponding results are presented in Figure 5. This comprehensive analysis explores the exergy loss of each component, disclosing that the absorption refrigeration unit constitutes the highest exergy loss, approximately 50%, followed by the PAFC unit, which contributes nearly 40%. This indicates a direction for future system optimization.

Figure 5 illustrates a Sankey diagram depicting the energy flow in the broader PAFC system employing the LiBr/H₂O working fluid (the numerical values have been rounded to whole numbers). When the R134a/DMF working fluid pairs are utilized for the ARS, the system’s exergy loss rises to 157 kW, slightly surpassing that of the LiBr/H₂O (146 kW). The reason for this lies in the release of some energy during the heat transfer process, and the portion of exergy losses in absorption refrigeration is also considered. This diagram provides a comprehensive overview of exergy distribution and transformation, emphasizing the absorption refrigeration unit and PAFC unit as the primary sources of exergy losses. Please refer to Appendix A:

Table A1. Thermodynamic property for the PAFC-ARS hybrid system.

State	Temperature (°C)	Pressure (kPa)	H (kJ/kg−1)	s (kJ/kg−1K−1)	MassFlow (kg/h)
1	25.00	100.00	0.49	0.05	24.89
2	41.43	120.00	235.54	0.07	24.89
3	165.00	120.00	2020.71	4.85	24.89
4	170.01	100.00	2093.32	5.77	31.12
5	190.00	100.00	2383.74	6.41	6.22
6	25.00	100.00	−0.23	0.15	1102.66
7	41.23	120.00	16.17	0.15	1102.66
8	137.45	120.00	114.05	0.42	1102.66
9	163.62	120.00	140.85	0.49	1102.66
10	172.86	100.00	−2470.48	0.25	1127.55
11	140.42	100.00	−2509.89	0.16	1127.55
12	67.00	100.00	−2605.62	−0.10	1127.55
13	150.00	500.00	−15,339.28	−7.59	720.61
14	150.00	505.00	−15,339.28	−7.59	720.61
15	150.00	475.29	−13,386.57	−2.98	720.61
16	150.00	475.29	−13,386.57	−2.98	15.13
17	150.00	500.00	−15,339.28	−7.59	15.13
18	150.00	475.29	−13,386.57	−2.98	705.48
19	150.00	500.00	−15,339.28	−7.59	705.48
LH	Temperature (°C)	Pressure (kPa)	h (kJ/kg−1)	s (kJ/kg−1K−1)	MassFlow (kg/h)
20	25.00	101.33	−15,875.73	−9.06	16,308
21	44.32	101.325	−15,795.02	−8.79	16,308
22	60.06	100.00	−15,729.19	−8.59	16,308
23	15.00	101.33	−15,917.55	−9.20	30,600
24	7.10	101.33	−15,950.63	−9.32	30,600
25	32.70	0.67	−9305.68	−4.25	5248.80
26	32.71	7.46	−9305.67	−3.86	5248.80
27	65.71	7.46	−9240.84	−3.9	5248.80
28	78.40	7.46	−13,332.90	−0.95	433.55
29	40.13	7.46	−15,812.60	−8.85	433.55
30	1.23	0.67	−15,812.60	−8.81	433.55
31	1.30	0.67	−13,477.13	−0.30	433.55
32	89.90	7.46	−8587.68	−3.49	4815.25
33	53.30	7.46	−8656.43	−3.41	4815.25
34	43.15	0.67	−8656.41	−3.73	4815.25
RD	Temperature (°C)	Pressure(bar)	h (kJ/ kg−1)	s (kJ/kg−1K−1)	MassFlow (kg/h)
20	25.00	1.00	−15,972.08	−9.32	12,816
21	42.82	1.00	−15,891.49	−9.06	12,816
22	60.04	1.00	−15,813.47	−8.82	12,816
23	15.00	1.00	−16,017.34	−9.48	17,640
24	7.01	1.00	−16,053.55	−9.61	17,640
25	26.00	4.14	−6679.14	−4.28	12,190.00
26	26.55	10.15	−6677.90	−4.27	12,190.00
27	53.00	10.15	−6636.06	−4.14	12,190.00
28	85.00	10.15	−8680.52	−2.33	4539.72
29	37.00	10.15	−8900.78	−3.02	4539.72
30	10.58	4.14	−8900.78	−3.01	4539.72
31	40.04	4.14	−6594.42	−4.00	12,190.00
32	85.00	10.15	−5242.64	−4.69	7650.28
33	45.10	4.14	−5309.30	−4.88	7650.28
34	45.10	4.14	−5309.30	−4.88	7650.28

for detailed parameter information.

In Figure 6, depicting the relationship between the system efficiency and the net system output efficiency of PAFC at different operating pressures, the maximum system power output point (437 kW) is observed to be around 4 bar, while the highest net electric energy efficiency (52%) is observed around 5 bar.

On the premise that the price of water, as well as the price of cooling and heating, are based on the references [36,37], Figure 7 and Figure 8 provides an extensive analysis of the NPV parameters for the system, taking into account different electricity, hot water, and chilled water prices in order to examine financial dynamics. The study unveiled an important finding: the use of lithium bromide as the working fluid resulted in a more favorable electricity cost of USD 0.13/kWh, whereas the cost of hot and chilled water was relatively high at USD 2.4/t. In contrast, with R134a/DMF as the working fluid, the cost of electricity is USD 0.16/kWh, and the cost of hot and chilled water is USD 2.1/t. Therefore, the payback period for selecting R134a/DMF is shorter in areas with lower electricity costs. Conversely, in areas with lower electricity prices, the choice of LiBr/H₂O proves to be cost effective. These findings empower decision-makers to make choices aligning with their financial objectives while adhering to the 8-year design payback limit for the system.

5. Conclusions

This paper presents the PAFC-ARS, which is environmentally friendly and does not emit greenhouse gasses. This system can be applied in commercial sectors to meet diverse energy demands and reduce operating costs. The PAFC-ARS demonstrated a notable overall exergy efficiency in its heating model, reaching 61.0% when employing LiBr/H₂O as the working fluid pairs. Moreover, the PAFC-ARS hybrid system showcased a peak net electric energy efficiency (${\eta }_I$) of 52% when utilizing LiBr/H₂O as the working fluid, underscoring its capacity to convert a substantial fraction of incoming energy into practical output efficiently.

The economic viability of the PAFC-ARS indicates a payback period of 8 years. This assessment operates under the assumption that LiBr/H₂O will be used as the operational medium and also assumes an energy cost of up to 2.4 USD/t hot water, cooling water, as well as 0.13 USD/kWh for electricity. Conversely, under comparable conditions, the use of R134a/DMF resulted in the same payback period with 2.1 USD/t for hot water, cooling water, and 0.16 USD/kWh. Price comparisons reveal that the former charges are slightly higher than market prices for both heat and cold energy, while the latter charges are slightly above market prices for electricity.