Performance of a Combined Energy System Consisting of Solar Collector, Biogas Dry Reforming and Solid Oxide Fuel Cell: An Indian Case Study

Akira Nishimura¹, Ryotaro Sato¹, Ryota Nakajima¹, Eric Hu²

¹Division of Mechanical Engineering, Graduate School of Engineering, Mie University, Tsu, Japan.
²School of Electrical Mechanical Engineering, the University of Adelaide, Adelaide, Australia.

DOI: 10.4236/sgre.2024.1510013                

Abstract

An energy production system consisting of a solar collector, biogas dry reforming reactor and solid oxide fuel cell (SOFC) was assumed to be installed in Kolkata, India. This study aims to understand the impact of climate conditions on the performance of solar collectors with different lengths of parabolic trough solar collector (dx) and mass flow rate of heat transfer fluid (m). In addition, this study has evaluated the amount of H₂ produced by biogas dry reforming (G_H2), the amount of power generated by SOFC (P_SOFC) and the maximum number of possible households (N) whose electricity demand could be met by the energy system proposed, considering the performance of solar collector with the different dx and m. As a result, the optimum dx was found to be 4 m. This study revealed that the temperature of heat transfer fluid (T_fb) decreased with the increase in m. T_fb in March, April and May was higher than that in other months, while T_fb from June to December was the lowest. G_H2, P_SOFC and N in March, April and May were higher than those in other months, irrespective of m. The optimum m was 0.030 kg/s.

Keywords

Solar Collector, Temperature of Simulated Biogas, Case Study of Installation in India, H₂ Production by Dry Reforming, Power Generated by SOFC

1. Introduction

Energy consumption has been increasing rapidly with the rapid economic development. According to the Energy White Paper [1], the energy consumption was 14.4 billion ton based on equivalent of oil in 2022. On the other hand, renewable energy is being paid attention to in order to introduce a mode to meet the increase in energy consumption as well as to solve the global warming problem. According to the data base [1], the ratio of renewable energy including hydro to total energy consumption was 14.2% in 2022 [1]. It is expected that renewable energy will increase worldwide.

Using renewable energy to produce H₂ is a promising way to utilize renewable energy. There are several approaches to produce H₂, including producing H₂ from biogas dry reforming. Biogas, which consists of CH₄ (ratio: 55 - 75 vol%) and CO₂ (ratio: 25 - 45 vol%) [2] can be produced by fermentation of the action of anaerobic microorganisms on raw materials such as garbage, livestock and sewage sludge. It is known from the International Energy Agency [3] that the biogas equivalent to 1.46 EJ was produced in 2020. According to the International Energy Agency [3], the amount of produced biogas based on energy value was approximately five times as large as that in 2000. We can expect that the produced biogas will increase more and more. Biogas is usually used as a fuel for gas engine and micro gas turbine [4]. However, the power generation is smaller than using a natural gas due to consisting of CO₂ of approximately 40 vol%. In this study, a biogas is proposed to be used as a feedstock to produce H₂ via a thermally powered biogas dry reforming process. The produced H₂ can be used as a fuel for solid oxide fuel cell (SOFC) [5]. CO, which is a by-product of biogas dry reforming can also be used as a fuel for SOFC, resulting a more effective energy production system.

This study proposes a system combining the above described energy production system with a solar collector to supply the heat, which is needed for a biogas dry reforming, because it is an endothermic reaction. There are some studies reporting the combined system with a solar collector to produce H₂ using a heat for the chemical reaction [6]-[14]. The numerical investigation of the effect of peak heat flux, inlet flow rate and CH₄/CO₂ feed ratio on reaction temperature, reaction rates, conversion of syngas, syngas yield, carbon deposition, and other thermochemical characteristics of the porous material filled in solar collector under high-flux concentrated irradiation was reported [6]. The peak heat flux over 0.734 MW/m² would decrease CH₄ conversion and H₂ yield, resulting in the reduction of the syngas yield. The experimental study using solar scheffler collector for biogas dry reforming was conducted [7]. The parabolic solar collector which could increase the temperature of biogas from 383 K to 773 K performed H₂ yield of 16% and CO yield of 10%. The solar thermochemical system including a parabolic trough solar collector and a membrane reactor was proposed and investigated experimentally to decrease the reaction temperature of dry reforming to a mid/low temperature range (573 K - 773 K) [8]. The conversion ratio of CH₄ at 673 K and 698 K reached 20.27% and 30.00%, respectively. The thermodynamic analysis on solar CH₄ system reforming with H₂ permeation membrane reactor at mid/low temperature was carried out numerically [9]. A solar trough collector was assumed to provide heat for the CH₄ system reforming. An optimal conversion ratio range of CH₄ for efficient solar CH₄ membrane reforming was calculated, resulting that the net solar-to-fuel efficiency reached 38.25% at 673 K which was lower temperature than normal operation temperature due to non-equilibrium state of CH₄ steam reforming by means of membrane. A reflux solar CH₃OH steam reforming reactor system was proposed and investigated numerically [10]. Parabolic solar collector was adopted to provide the heat for CH₃OH steam reforming. The energy conversion efficiency varied slightly with the inlet mass flow rate. The parabolic trough solar receiver-reactor was proposed and investigated numerically using the CFD software ANSYS Fluent for continuous and efficient H₂ production via CH₃OH steam reforming reaction [11]. A higher working temperature provided a relatively larger energy fraction of thermal loss. The parabolic trough solar receiver reactors of gradually varied porosity catalyst beds were proposed and investigated for cost-efficient H₂ production [12]. A 3D comprehension model was developed for the parabolic trough solar receiver-reactors of CH₃OH steam reforming reaction in porous Cu/ZnO/Al₂O₃ catalyst-packed beds, by combining the finite volume method with a comprehensive kinetic model. According to NEDO Renewable Energy Technology White Paper [13], parabolic trough type, Fresnel type, tower type and dish type are main type of concentration solar collectors installed in the world. The efficiency of parabolic trough type, Fresnel type, tower type and dish type is 15%, 8% - 10%, 20% - 35% and 25% - 30%, respectively. Additionally, the land utilization efficiency for parabolic trough type, Fresnel type and tower type is 25% - 40%, 60% - 80% and 20% - 25%, respectively. When using the solar thermal power generation for the plant size below 250 MW and over 250 MW, the power generation cost of parabolic trough type is approximately 0.2 USD/kWh - 0.3 USD/kWh and 0.22 USD/kWh - 0.27 USD/kWh, respectively. Although the power generation cost depends strongly on the sunlight illumination condition in this study, the parabolic trough solar collector was selected for study.

Considering the system proposed by this study, the location where the system is installed is important since the solar intensity influences the performance of solar collector [5]. In addition, the energy consumption and the CO₂ emission in Asia, e.g. China, India, Japan and so on increase rapidly [1]. The average global horizontal solar irradiance in India is 5.0 kWh/(m²·day) - 5.5 kWh/(m²·day), which is much larger than that in China and Japan, e.g. 3.0 kWh/(m²·day) - 4.5 kWh/(m²·day) and 3.0 kWh/(m²·day) - 3.5 kWh/(m²·day), respectively [14]. Therefore, this paper conducted a hypothetical case study by assuming to install the proposed system in Kolkata, India.

However, there is no study on assessment of performance of solar collector as well as the energy production system which is assumed to be installed in India. Therefore, the aim of this study is to understand the influence of the climate data in India on the performance of solar collectors with different sizes and heat mass flow rate of transfer fluid, e.g. the simulated biogas as well as the performance of the combination system proposed. The weather data of Kolkata was from METPV-ASIA [15]. This study used the developed heat transfer model of the parabolic trough solar collector in previous studies [16]. The temperature of heat transfer fluid out of the parabolic trough solar collector could range from approximately 700 K - 873 K [17] [18]. Since the biogas dry reforming could happen in the temperature range from 673 K to 873 K as per the previous experimental studies conducted by authors [19] [20], this study thinks that the parabolic trough solar collector is suitable. The authors have also adopted the specific characteristics of a biogas dry reforming reactor developed previously to calculate the amount of H₂ produced [19] [20] and the power generated by SOFC using H₂ obtained from a biogas dry reforming reactor. The heat transfer fluid which consists of CH₄ and CO₂ flows into the solar collector. After the heat transfer fluid is heated by solar collector, it flows into the biogas dry reforming reactor. H₂ will then be produced in the reactor via the biogas dry reforming process. The produced H₂ is provided to SOFC as a fuel, resulting that the electricity is generated. In this study, the impact of the climate condition of Kolkata in India on the performance of solar collectors with different lengths of parabolic trough solar collector (dx) and mass flow rate of heat transfer fluid (m) has been investigated. In addition, the amount of H₂ produced by biogas dry reforming (G_H2), the amount of power generated by SOFC (P_SOFC) and the maximum possible households (N) whose electricity demand could be met by the energy system proposed have been also evaluated considering the performance of solar collector with the different dx and m.

2. Heat Transfer Model

2.1. Governing Equations

Figure 1 illustrates the schematic drawing for the simplified heat transfer model of the solar collector proposed in this study. Solar radiation is mainly absorbed on the outer surface of the absorber tube in this model [8]. The absorbed heat transports to the heat transfer fluid by conduction through the tube wall and

Figure 1. Schematic drawing of heat transfer model of solar collector investigated in this study.

convection from the inner surface of the tube to the fluid (Q_h). Other heat transfers as a radiation loss to the inner surface of the glass tube through the vacuum space (Q_r) and then by conduction from the inner surface of the glass tube to the outer surface of it (Q_c). The heat is transferred to the ambient from the outlet surface of the glass tube via two mechanisms as follows: 1) the convection to the surrounding air (Q_a), 2) the radiation to the sky (Q_s).

Figure 2 exhibits the thermal resistance diagram of the heat transfer process in the model proposed by this study [21]. In this model, R₁ means the thermal resistance because of convection from the heat transfer fluid to the absorber [(m·K)/K]. R₂ means the thermal resistance because of conduction via the absorber [(m·K)/K]. R₃ means the thermal resistance because of radiation via vacuum [(m·K)/K]. R₄ means the thermal resistance because of conduction via the glass tube [(m·K)/K]. R₅ means the thermal resistance because of convection to the surrounding air [(m·K)/K]. R₆ means the thermal resistance because of radiation to the surrounding surfaces (sky) [(m·K)/K].

Figure 2. A thermal resistance diagram of the heat transfer model is proposed by this study.

This study assumes the surrounding surface temperature is equal to the ambient air temperature. The model equation for a single glass tube can be expressed as following:

$I\alpha \tau D\pi dx=\frac{T_{\text{to}}-T_{\text{fb}}}{R_1}+\frac{T_{\text{to}}-T_{\text{s}}}{{\left(R_5^{-1}+R_6^{-1}\right)}^{-1}}$ (1)

$mc\frac{d{T}_{\text{fb}}}{dx}=mc\frac{T_{\text{fb},\text{out}}-T_{\text{fb},\text{in}}}{dx}=\frac{T_{\text{to}}-T_{\text{fb}}}{R_1}$ (2)

$\frac{T_{\text{to}}-T_{\text{gi}}}{R_3}=\frac{T_{\text{to}}-T_{\text{s}}}{R_3+{\left(R_5^{-1}+R_6^{-1}\right)}^{-1}}$ (3)

where I means the solar intensity [W/m²], α means the absorptivity of absorber tube [−], τ means the transmissivity of glass tube [−], D means the diameter of absorber [m], dx means the length of absorber [m], m means the mass flow rate of heat transfer fluid assumed to be a biogas [kg/s], c means the specific heat of heat transfer fluid [J/(kg·K)], T_fb means the temperature of heat transfer fluid [K], T_fb,out and T_fb,in mean the temperature of heat transfer fluid at outlet [K] and inlet [K], respectively.

Each thermal resistance is defined as the following [16]:

$R_1=\frac{1}{2\pi r_{\text{ti}}h}$ (4)

$R_2=\frac{1}{2\pi k_{\text{t}}}\ln \frac{r_{\text{to}}}{r_{\text{ti}}}$ (5)

$R_3=\frac{1}{2\pi \sigma r_{\text{to}}}\left[\frac{1}{{\epsilon }_{\text{t}}}+\frac{1-{\epsilon }_{\text{g}}}{{\epsilon }_{\text{g}}}\left(\frac{r_{\text{to}}}{r_{\text{gi}}}\right)\right]{\left[\left(T_{\text{to}}^2+T_{\text{gi}}^2\right)\left(T_{\text{to}}+T_{\text{gi}}\right)\right]}^{-1}$ (6)

$R_4=\frac{1}{2\pi k_{\text{g}}}\ln \frac{r_{\text{go}}}{r_{\text{gi}}}$ (7)

$R_5=\frac{1}{2\pi r_{\text{go}}{h}_{\text{o}}}$ (8)

$R_6=\frac{1}{{\epsilon }_{\text{g}}\sigma 2\pi r_{\text{go}}\left(T_{\text{go}}+T_{\text{s}}\right)\left(T_{\text{go}}^2+T_{\text{s}}^2\right)}$ (9)

where r_ti means the inner radius of absorber [m], r_to means the outlet radius of absorber [m], r_gi means the inner radius of glass tube [m], r_go means the outlet of glass tube [m], σ means Stefan-Boltzmann constant [W/(m²·K⁴)], h means the heat transfer coefficient between the heat transfer fluid and the inner surface of absorber [W/(m²·K)], h_o means the heat transfer coefficient from the outer surface of glass tube to the surrounding air [W/(m²·K)], k_t means the thermal conductivity of absorber [W/(m·K)], k_g means the thermal conductivity of glass tube [W/(m·K)], ε_t means the emissivity of absorber [−], ε_g means the emissivity of glass tube [−], T_to means the temperature of outer surface of absorber [−], T_gi means the temperature of inner surface of glass tube [K], T_go means the temperature of outer surface of glass tube [K], T_s means the temperature of sky [K] and T_a means the temperature surrounding air (=293) [K]. We assume $T_{\text{s}}\fallingdotseq T_{\text{a}}$ .

2.2. Calculation Procedure of Heat Transfer Coefficient

The convective heat transfer coefficient of the turbulent flow in a tube was calculated by Dittus-Boelter correlations [22] in this study as following:

$Nu=0.023R{e}^{0.8}P{r}^{1/3}$ (10)

Additionally, the above equation is summarized in detail which is well known dimensionless number and equation as following:

$Nu=\frac{hD}{k_{\text{a}}}$ (11)

$Re=\frac{{\rho }_{\text{a}}{u}_{\text{a}}D}{{\mu }_{\text{a}}}$ (12)

$Pr=\frac{C_{\text{p},\text{a}}{\mu }_{\text{a}}}{k_{\text{a}}}$ (13)

$h_{\text{o}}=0.0191+0.006608u_{\text{a}}$ (14)

where C_p,a means the specific heat of surrounding air [J/(kg·K)], μ_a means the viscosity [Pa·s], k_a means the thermal conductivity of surrounding air [W/(m·K)], u_a means the velocity of surrounding air [m/s] and ρ_a means the density of surrounding air [m/s]. From the reference [16], the temperature of fluid flowing through the absorber was calculated well using the h_o equation shown in Equation (14). Consequently, the authors think the h_o equation shown by Equation (14) can be applied.

2.3. Calculation Procedure of T_fb

According to Equations (1) and (2), the following equation can be drawn:

$T_{\text{fb},\text{out}}=\frac{dx}{mc}\left\{I\alpha \tau D\pi dx-\frac{\left(T_{\text{to}}-T_{\text{s}}\right)\left(R_5+R_6\right)}{R_3\left(R_5+R_6\right)+R_5{R}_6}\right\}+T_{\text{fb},\text{in}}$ (15)

Moreover, R₃ can be decided from Equation (3) as following:

$R_3=\frac{\left(T_{\text{to}}-T_{\text{gi}}\right)R_5{R}_6}{\left(R_5+R_6\right)\left(-T_{\text{s}}+T_{\text{gi}}\right)}$ (16)

According to Equations (6) and (16), T_to can be obtained as following:

$T_{\text{to}}={\left[\frac{\left(R_5+R_6\right)\left(-T_{\text{s}}+T_{\text{g}}\right)}{2\pi \sigma t_{\text{to}}{R}_5{R}_6}\times \frac{r_{\text{gi}}+r_{\text{to}}\left(1-{\epsilon }_{\text{g}}\right)}{{\epsilon }_{\text{t}}{r}_{\text{gi}}}+T_{\text{gi}}^4\right]}^{\frac{1}{4}}$ (17)

T_fb can be calculated by averaging T_{fb, in} and T_{fb, out} as following:

$T_{\text{fb}}=\frac{T_{\text{fb},\text{in}}+T_{\text{fb},\text{out}}}{2}$ (18)

T_fb is calculated with changing dx according to the above equations in this study. D was set to be 1.5 m, according to the previous study [5]. The weather data, i.e. I, u_a and T_a in Kolkata from METPV-ASIA [15] were used. In this study, the mirror and solar reflection as well as to consider the variable angle and solar radiation were ignored [21]. The heat transfer fluid was a mixture of CH₄ and CO₂. The molar ratio of CH₄:CO₂ was 1.5:1. The following assumptions were made in this study [21]:

1) The distance between the absorber and glass tube is 1/10 D.

2) T_{fb, in} is 283 K.

3) $T_{\text{s}}\fallingdotseq T_{\text{a}}$ .

4) The thickness of absorber and glass tube is 0.005 m and 0.010 m, respectively.

5) R₂ and R₄ are ignored since they are very small compared with the other thermal resistances.

6) T_ti equals to T_to.

7) T_gi equals to T_go, which is 373 K.

8) The mirror and solar reflection is ignored.

9) The variable angle of solar radiation is ignored.

Table 1 lists the physical properties which were used in this study. Before the calculation of T_fb, we could not predict the exact value of it. If we calculate T_fb considering the change of physical properties with the temperature under an unsteady state condition, the calculation is too complex and huge. The physical properties listed in Table 1 were assumed to be temperature-independent, and the values of 283 K were listed and used.

Comparing the other heat transfer models, a few papers reported on the heat transfer analysis using Hottel-Whiller-Bliss model for a solar collector recently [23]-[25]. However, these papers investigated on a flat plate solar collector [23]-[25], while this study investigates a parabolic trough solar collector. Moreover, the Hotel-Whiller-Bliss model considered thermal conduction only in these previous studies [23]-[25], while this model investigated in this study considers the thermal conduction, the thermal convection and the thermal radiation heat transfer, resulting in the assessment of the whole heat transfer mechanism in this study. Consequently, the authors think the model investigated in this study has the merit and the superiority to Hottel-Whiller-Bliss model.

Table 1. The physical properties adopted in this study are [5] [16] [21].

Property	Value	Information
α [−]	0.94	-
τ [−]	0.94	-
εt [−]	0.9	-
c [J/(kg·K)]	1.335	for CH4:CO2 = 1.5:1
σ [W/(m2·K4)]	5.67 × 10−8	Stefan-Boltzmann coefficient
εg [−]	0.94	Glass smooth surface
ka [W/(m·K)]	0.0257	Surrounding air
ρa [kg/m3]	1.166	Surrounding air
μa [Pa·s]	1.82 × 10−5	Surrounding air
Cp, a [J/(kg·K)]	1006	Surrounding air
kt [W/(m·K)]	16	Stainless steel
Kg [W/(m·K)]	1.3	Quartz glass

3. Combined Energy Production System

Figure 3 illustrates the proposed systems consisting of solar collector, biogas dry reforming reactor and SOFC. In the proposed system, the heat transfer fluid which consists of CH₄ and CO₂ flows into solar collector. After being heated by solar collector, the heat transfer fluid flows into biogas dry reforming reactor. H₂ is produced in the reactor via biogas dry reforming process. The produced H₂ is supplied as fuel for SOFC. As a result, the electricity and heat is generated (In this study, only the electricity is considered). The by-product of the process, CO was not considered in this study. Generally, a biogas is used as a fuel for a micro gas turbine and a gas engine [4]. The power generation efficiency of micro gas turbine and gas engine is 33% [26], and approximately 30% [27], respectively. On the other hand, as to the combination system proposed by this study, the power generation efficiency of SOFC is 55% [28]. In addition, SOFC can be used as a co-generation system whose energy conversion efficiency is 87% [29]. Therefore, the system proposed by this study has a superiority to the existing system using a biogas as a fuel.

Figure 3. Combined energy production system consisting of solar collector, biogas dry reforming reactor and SOFC proposed by this study.

To calculate the amount of H₂ produced through the biogas dry reforming reactor, this study follows the reaction scheme of biogas dry reforming as follows:

${\text{CH}}_{\text{4}}+{\text{CO}}_{\text{2}}\to 2{\text{H}}_2+2\text{CO}$ (19)

We set the molar ratio of CH₄ and CO₂ is 2.51 × 10³ mol/s and 1.67 × 10³ mol/s, respectively when m = 0.005 kg/s. In this study, m is changed by 0.005, 0.010, 0.015 and 0.030 kg/s. According to Equation (19) and the molar flow rate when m = 0.005 kg/s, the molar flow rate of produced H₂ can be estimated to be 3.34 × 10⁻³ mol/s. According to the authors’ previous experimental studies investigating the impact of the reaction temperature on the performance of biogas dry reforming corresponding to T_fb in this study from 673 K to 873 K [19] [20], the best performance of biogas dry reforming was obtained at 873 K. The conversion ratio of H₂ is assumed to be 100% and 10% respectively [19] [20].

To calculate the power generated by SOFC, the lower heating value of H₂ (=10.79 MJ/m³N) and the power generation efficiency commercial SOFC of 55% [28] were used. The power generated by SOFC in the case of the conversion ratio of H₂ = 100% can be estimated as follows:

$\begin{array}{l}\left(3.34\times {10}^{-3}\left[\text{mol}/\text{s}\right]\times 22.4\left[\text{L}/\text{mol}\right]\right)\\ ÷\left(1000\left[\text{L}/{\text{m}}^3\right]\times 0.55\times 10.79\left[\text{MJ}/\left({\text{m}}^{\text{3}}\cdot \text{N}\right)\right]\right)=0.444\left[\text{kW}\right]\end{array}$

In addition, this study estimated the number of maximum possible households whose electricity demand could be met by the power generated by SOFC. The monthly data for the electricity demand of a couple households was used in this study [30].

4. Results and Discussion

4.1. Change of T_fb through Year with Different dx and m

The climate data, I, u_a and T_a in Kolkata, India according to METPV-ASIA [15] were used for the calculation of T_fb, and are shown in Tables 2-14.

Figures 4-15 show the changes of T_fb with time in different months. In these

Table 2. Climate data of I, u_a and T_a in Kolkata, India in January.

Time	I [MJ/m2]	ua [m/s]	Ta [K]
7:00	0.087	0.258	287.02
8:00	0.498	0.323	287.02
9:00	0.877	1.000	294.94
10:00	1.271	1.000	294.94
11:00	1.576	1.000	294.94
12:00	1.725	1.000	294.94
13:00	1.666	1.000	294.94
14:00	1.413	0.935	294.94
15:00	1.134	0.194	293.85
16:00	0.935	0.194	293.85
17:00	0.389	0.194	293.85
18:00	0.003	0.194	293.85

Table 3. Climate data of I, u_a and T_a in Kolkata, India in February.

Time	I [MJ/m2]	ua [m/s]	Ta [K]
7:00	0.162	0.214	289.65
8:00	0.700	0.214	289.65
9:00	1.173	0.214	299.87
10:00	1.674	0.964	299.87
11:00	1.966	0.964	299.87
12:00	2.124	0.964	299.87
13:00	2.085	0.964	299.87
14:00	1.830	0.964	299.87
15:00	1.508	0.214	298.80
16:00	1.282	0.214	298.80
17:00	0.660	0.214	298.80
18:00	0.090	0.214	298.80

Table 4. Climate data of I, u_a and T_a in Kolkata, India in March.

Time	I [MJ/m2]	ua [m/s]	Ta [K]
7:00	0.406	0.548	295.34
8:00	1.000	0.548	295.34
9:00	1.534	1.065	304.23
10:00	2.012	1.065	304.23
11:00	2.364	1.065	304.23
12:00	2.565	1.065	304.23
13:00	2.505	1.065	304.23
14:00	2.255	1.065	304.23
15:00	1.816	0.581	303.07
16:00	1.199	0.581	303.07
17:00	0.681	0.581	303.07
18:00	0.108	0.581	303.07

Table 5. Climate data of I, u_a and T_a in Kolkata, India in April.

Time	I [MJ/m2]	ua [m/s]	Ta [K]
7:00	0.643	0.867	298.37
8:00	1.163	0.867	298.37
9:00	1.657	1.600	305.65
10:00	2.092	1.600	305.65
11:00	2.433	1.600	305.65
12:00	2.672	1.600	305.65
13:00	2.581	1.600	305.65
14:00	2.323	1.600	305.65
15:00	1.844	1.333	304.17
16:00	1.239	1.333	304.17
17:00	0.744	1.333	304.17
18:00	0.158	1.333	304.17

Table 6. Climate data of I, u_a and T_a in Kolkata, India in May.

Time	I [MJ/m2]	ua [m/s]	Ta [K]
7:00	0.744	0.355	299.41
8:00	1.266	0.355	299.41
9:00	1.771	1.290	306.59
10:00	2.223	1.290	306.59
11:00	2.555	1.290	306.59
12:00	2.684	1.290	306.59
13:00	2.555	1.290	306.59
14:00	2.241	1.290	306.59
15:00	1.786	1.613	304.59
16:00	1.150	1.613	304.49
17:00	0.517	1.613	304.49
18:00	0.184	1.613	304.49

Table 7. Climate data of I, u_a and T_a in Kolkata, India in June.

Time	I [MJ/m2]	ua [m/s]	Ta [K]
7:00	0.651	1.033	300.15
8:00	1.029	1.033	300.15
9:00	1.552	1.367	305.26
10:00	1.939	1.367	305.26
11:00	2.191	1.367	305.26
12:00	2.187	1.367	305.26
13:00	2.046	1.367	305.26
14:00	1.729	1.367	305.26
15:00	1.138	1.200	302.89
16:00	0.722	1.200	302.89
17:00	0.302	1.200	302.89
18:00	0.133	1.200	302.89

Table 8. Climate data of I, u_a and T_a in Kolkata, India in July.

Time	I [MJ/m2]	ua [m/s]	Ta [K]
7:00	0.556	0.484	300.25
8:00	0.926	0.484	300.25
9:00	1.260	1.452	304.60
10:00	1.579	1.452	304.60
11:00	1.796	1.452	304.60
12:00	1.828	1.452	304.60
13:00	1.792	1.452	304.60
14:00	1.538	1.452	304.60
15:00	1.390	1.097	303.29
16:00	1.504	1.097	303.29
17:00	0.997	1.097	303.29
18:00	0.454	1.097	303.29

Table 9. Climate data of I, u_a and T_a in Kolkata, India in August.

Time	I [MJ/m2]	ua [m/s]	Ta [K]
7:00	0.586	0.645	300.31
8:00	1.037	2.032	300.31
9:00	1.434	2.032	305.28
10:00	1.871	2.032	305.28
11:00	2.133	2.032	305.28
12:00	2.155	2.032	305.28
13:00	1.874	2.032	305.28
14:00	1.614	2.032	305.28
15:00	1.346	1.323	302.75
16:00	0.844	1.323	302.75
17:00	0.444	1.323	302.75
18:00	0.143	1.323	302.75

Table 10. Climate data of I, u_a and T_a in Kolkata, India in September.

Time	I [MJ/m2]	ua [m/s]	Ta [K]
7:00	0.518	0.333	299.56
8:00	0.972	0.333	299.56
9:00	1.409	1.267	304.88
10:00	1.775	1.267	304.88
11:00	1.981	1.267	304.88
12:00	2.019	1.267	304.88
13:00	1.901	1.267	304.88
14:00	1.645	1.267	304.88
15:00	1.178	1.033	302.16
16:00	0.622	1.033	302.16
17:00	0.338	1.033	302.16
18:00	0.040	1.033	302.16

Table 11. Climate data of I, u_a and T_a in Kolkata, India in October.

Time	I [MJ/m2]	ua [m/s]	Ta [K]
7:00	0.476	0.290	298.05
8:00	0.968	0.290	298.05
9:00	1.404	1.097	303.70
10:00	1.773	1.097	303.70
11:00	2.025	1.097	303.70
12:00	2.100	1.097	303.70
13:00	1.924	1.097	303.70
14:00	1.594	1.097	307.70
15:00	1.203	0.613	300.89
16:00	0.621	0.613	300.89
17:00	0.221	0.613	300.89
18:00	6.452 × 10−4	0.613	300.89

Table 12. Climate data of I, u_a and T_a in Kolkata, India in November.

Time	I [MJ/m2]	ua [m/s]	Ta [K]
7:00	0.340	0.333	292.90
8:00	0.863	0.367	292.90
9:00	1.345	1.133	301.10
10:00	1.749	1.133	301.10
11:00	2.038	1.133	301.10
12:00	2.075	1.133	301.10
13:00	1.942	1.133	301.10
14:00	1.613	1.100	301.10
15:00	1.119	0.267	297.87
16:00	0.680	0.267	297.87
17:00	0.158	0.267	297.87
18:00	0	3.597	297.87

Table 13. Climate data of I, u_a and T_a in Kolkata, India in December.

Time	I [MJ/m2]	ua [m/s]	Ta [K]
7:00	0.170	0.168	287.07
8:00	0.676	0.181	287.07
9:00	1.118	0.945	298.35
10:00	1.502	0.971	298.35
11:00	1.760	1.087	298.35
12:00	1.850	1.023	298.35
13:00	1.755	1.003	298.35
14:00	1.504	0.977	298.35
15:00	1.085	0.094	294.41
16:00	0.668	0.071	294.41
17:00	0.163	0.097	294.41
18:00	0	0.142	294.41

Figure 4. Comparison of change of T_fb with time among different dx and m in January ((a): m = 0.005 kg/s, (b): m = 0.010 kg/s, (c): m = 0.015 kg/s, (d): m = 0.030 kg/s).

Figure 5. Comparison of change of T_fb with time among different dx and m in February ((a): m = 0.005 kg/s, (b): m = 0.010 kg/s, (c): m = 0.015 kg/s, (d): m = 0.030 kg/s).

Figure 6. Comparison of change of T_fb with time among different dx and m in March ((a): m = 0.005 kg/s, (b): m = 0.010 kg/s, (c): m = 0.015 kg/s, (d): m = 0.030 kg/s).

Figure 7. Comparison of change of T_fb with time among different dx and m in April ((a): m = 0.005 kg/s, (b): m = 0.010 kg/s, (c): m = 0.015 kg/s, (d): m = 0.030 kg/s).

Figure 8. Comparison of change of T_fb with time among different dx and m in May ((a): m = 0.005 kg/s, (b): m = 0.010 kg/s, (c): m = 0.015 kg/s, (d): m = 0.030 kg/s).

Figure 9. Comparison of change of T_fb with time among different dx and m in June ((a): m = 0.005 kg/s, (b): m = 0.010 kg/s, (c): m = 0.015 kg/s, (d): m = 0.030 kg/s).

Figure 10. Comparison of change of T_fb with time among different dx and m in July ((a): m = 0.005 kg/s, (b): m = 0.010 kg/s, (c): m = 0.015 kg/s, (d): m = 0.030 kg/s).

Figure 11. Comparison of change of T_fb with time among different dx and m in August ((a): m = 0.005 kg/s, (b): m = 0.010 kg/s, (c): m = 0.015 kg/s, (d): m = 0.030 kg/s).

Figure 12. Comparison of change of T_fb with time among different dx and m in September ((a): m = 0.005 kg/s, (b): m = 0.010 kg/s, (c): m = 0.015 kg/s, (d): m = 0.030 kg/s).

Figure 13. Comparison of change of T_fb with time among different dx and m in October ((a): m = 0.005 kg/s, (b): m = 0.010 kg/s, (c): m = 0.015 kg/s, (d): m = 0.030 kg/s).

Figure 14. Comparison of change of T_fb with time among different dx and m in November ((a): m = 0.005 kg/s, (b): m = 0.010 kg/s, (c): m = 0.015 kg/s, (d): m = 0.030 kg/s).

Figure 15. Comparison of change of T_fb with time among different dx and m in December ((a): m = 0.005 kg/s, (b): m = 0.010 kg/s, (c): m = 0.015 kg/s, (d): m = 0.030 kg/s).

figures, dx and m were also changed. The monthly mean values are shown in these figures. According to Tables 2-13 and Figures 4-15, the change in T_fb followed the change in I mainly. Additionally, it can also be seen from Figures 4-15 that T_fb rises with the increase in dx. This is due to the increase in heat transfer area for receiving the solar heat, which can be understood from Equation (15) [21]. However, some conditions exhibited T_fb over 2000 K in the case of dx = 5 m, indicating that it was not practically possible due to the durability of material of solar collector. For example, the melting point of SUS 405 is 1700 K [31]. In the following discussion, the results were based on dx = 4 m. In addition, it is shown from Figures 4-15 that T_fb decreases with the increase in m. Since the heat capacity is larger with the increase in m as shown in Equation (15), T_fb decreases with the increase in m. It can be found that T_fb is below 1000 K even dx = 5 m for some months. Moreover, it can be seen that T_fb in March, April and May is higher than the other months. In India, March, April and May belongs to a summer season which exhibits longer sunshine duration and higher I, resulting from Tables 2-13. On the other hand, it can be seen from Figures 4-15 that T_fb from June to December is lower than the other months. Since June to December is the rainy season in Kolkata, T_fb is lower due to lower I. Therefore, it can be revealed that T_fb is determined by the climate characteristics.

4.2. Estimation of H₂ Produced by Biogas Dry Reforming and Power Generation by SOFC

This study assumed that H₂ can be produced by biogas dry reforming when T_fb is over 873 K. Tables 14-17 list G_H2, P_SOFC and N per month changing m at dx = 4 m according to the duration when T_fb is over 873 K shown in Figures 4-15.

Table 14. Comparison of G_H2, P_SOFC and N among different months for m = 0.005 kg/s at dx = 4 m.

	GH2 [kg]	PSOFC [Wh]	N [-]
January	4.48	82,639	0.5
February	5.39	99,522	0.7
March	5.97	110,185	0.7
April	6.50	119,959	0.8
May	6.71	123,958	0.8
June	5.78	106,631	0.7
July	5.97	110,185	0.7
August	5.97	110,185	0.7
September	5.05	93,302	0.6
October	5.22	96,412	0.6
November	5.05	93,302	0.6
December	5.22	96,412	0.6
Total	67.31	1,242,691	8.04

Table 15. Comparison of G_H2, P_SOFC and N among different months for m = 0.010 kg/s at dx = 4 m.

	GH2 [kg]	PSOFC [Wh]	N [-]
January	7.46	137,731	0.9
February	9.43	174,163	1.2
March	11.94	220,370	1.4
April	11.55	213,261	1.4
May	11.94	220,370	1.4
June	8.66	159,946	1.0
July	11.94	220,370	1.4
August	10.44	192,824	1.2
September	8.66	159,946	1.0
October	10.44	192,824	1.2
November	8.66	159,946	1.0
December	7.46	137,731	0.9
Total	118.59	2,189,481	14.2

Table 16. Comparison of G_H2, P_SOFC and N among different months for m = 0.015 kg/s at dx = 4 m.

	GH2 [kg]	PSOFC [Wh]	N [-]
January	6.71	123,958	0.8
February	12.13	223,924	1.6
March	15.67	289,235	1.8
April	15.16	279,905	1.8
May	15.67	289,235	1.8
June	12.99	239,919	1.6
July	13.43	247,916	1.6
August	13.43	247,916	1.6
September	12.99	239,919	1.6
October	13.43	247,916	1.6
November	10.83	199,932	1.3
December	11.19	206,597	1.3
Total	153.63	2,836,374	18.35

It can be seen from Tables 14-17 that G_H2, P_SOFC and N in March, April and May were higher than that in the other months irrespective of m. The durations when T_fb was over 873 K in March, April and May were longer than that in the other months since I_s in March, April and May were higher. In addition, G_H2, P_SOFC and N increased when m mas larger. Since the mass of simulated biogas, e.g. heat transfer fluid increased, G_H2 was larger, causing larger P_SOFC and N. However, G_H2, P_SOFC and N decreased if m was set over 0.05 kg/s. This was due to the increase in heat capacity with the increase in m as shown in Equation (15). Therefore, this

Table 17. Comparison of G_H2, P_SOFC and N among different months for m = 0.030 kg/s at dx = 4 m.

	GH2 [kg]	PSOFC [Wh]	N [-]
January	0	0	0
February	4.04	74,611	0.5
March	17.90	330,555	2.1
April	21.66	399,865	2.6
May	22.38	413,194	2.6
June	8.66	159,946	1.0
July	0	0	0
August	8.95	165,277	1.0
September	0	0	0
October	4.48	82,639	0.5
November	0	0	0
December	0	0	0
Total	88.07	1,626,116	10.48

study has concluded that the optimum m should be 0.03 kg/s. If the conversion ratio of H₂ is assumed to be 10%, G_H2, P_SOFC and N become one-tenth compared to each value shown in Tables 14-17.

Considering N, it is not sufficient to cover the citizen living in Kolkata. However, this study thinks the following approach is efficient:

1) Increase the number of proposed system

2) Increase D and re-optimize the size of solar collector

3) Concentrate the solar light with installing the equipment in order to increase the solar intensity

This study would like to investigate these subjects in the near future.

4.3. Discussion of Result Obtained by This Study and Comparison of It with the Other Researches

This study has revealed that the optimal dx is 4 m due to the durability of the material of solar collector if we install the proposed system in India. In addition, this study has also revealed that the optimal m is 0.03 kg/s. If we can develop a material that can be used over 1700 K, the larger solar collector can be available. In addition, this study has assumed H₂ can be produced by biogas dry reforming when T_fb is over 873 K. If the heat with T_fb over 873 K can be stored and used in the time or the day with T_fb below 873 K, H₂ can be produced more, resulting that P_SOFC and N become larger. This study proposes that the biogas heated over 873 K is stored in an adiabatic tank and used for the time when the heat is needed. If this proposal can be realized, the system proposed by this study would be available for wider area and climate conditions.

On the other hand, there is no study on assessment of performance of solar collector as well as the energy production system which is assumed to be installed in India. According to the other researches investigating the solar collector which utilized the obtained for a chemical reaction, the relationship between the conversion ratio of CH₄ and CO₂ and the temperature of heated biogas was reported [7]-[9]. However, this study has assumed that the conversion ratio of H₂, which is similar to the conversion ratio of CH₄, is constant. In addition, this study has revealed that P_SOFC and N, which have not been reported in the other researches. Moreover, this finding as well as the performance of solar collector are available for India, which has also not been reported in the other researches. Consequently, the results obtained by this study is meaningful.

5. Conclusions

This study simulated the performances of solar collectors with different dx and m and the energy system proposed with the weather condition in Kolkata, India. In addition, this study evaluated G_H2, P_SOFC, and N. As a result, the optimum dx was founded to be 4 m considering the melting point of material of solar collector. It is revealed that T_fb decreases with the increase in m. In addition, T_fb in March, April and May are higher than that in other months since March, April and May are summer in India. On the other hand, T_fb from June to December were lower due to the rainy season. As to G_H2, P_SOFC and N, they were all higher in March, April and May than in other months irrespective of m. Finally, this study reveals that the optimum m is around 0.030 kg/s.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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