Performance of An Energy Production System Consisting of Solar Collector, Biogas Dry Reforming Reactor and Solid Oxide Fuel Cell

Abstract

This paper aims to study the performance of solar collectors of various sizes under different weather conditions in different Japanese cities, i.e., Kofu City, Nagoya City and Yamagata City. The heat generated by the solar collector was used to conduct a biogas dry reforming reactor for producing H₂ to feed a solid oxide fuel cell (SOFC). This study revealed that the output temperature of a solar collector T_fb in April and July was higher than that in January and October irrespective of city. The optimum length of the absorber (dx) of the collector was 4 m irrespective of city. It was clarified that the T_fb in Yamagata City in January and October, i.e., winter and autumn, is lower than that in Kofu City and especially Nagoya City, which is strongly influenced by the tendency of solar intensity (I), not the velocity of the surrounding air (u_a). On the other hand, the T_fb is almost the same in April and July, i.e., spring and summer, irrespective of city. The amount of produced H₂ via the biogas dry reforming reactor and the power generated by the SOFC using H₂ in spring and summer were higher compared to the other seasons irrespective of city. This study revealed that the highest available household number per month was 4.7, according to the investigation in this study.

1. Introduction

Global warming is an important issue for the world. One of the promising approaches to it is renewable energy. According to the Energy White Paper [1], the ratio of the installment capacity of renewable energy excluding hydropower generation to all energy was 20.7% globally in 2020. In addition, the ratio of the power energy of renewable energy excluding hydropower generation to all energy was 12.2% globally in 2022. The World Energy Outlook 2022 forecasts that the ratio of the power energy of renewable energy to all energy will increase up to 49% by 2030 [2]. Therefore, it is necessary to promote renewable energy utilization more.

To reduce CO₂, which is the main chemical that causes global warming, H₂ is the focus of attention globally. The authors focus on H₂ production via the biogas dry reforming reaction process. Biogas consisting of CH₄ (ratio: 55–75 vol%) and CO₂ (ratio: 25–45 vol%) [3] is produced via fermentation by the action of anaerobic microorganisms on raw materials such as garbage, livestock and sewage sludge. According to the International Energy Agency (IEA) [4], biogas equivalent to 1.46 EJ was produced in 2020. The amount of energy of produced biogas in 2020 was approximately five times as large as that in 2000. It can be expected that the produced biogas will increase more. Therefore, biogas is a promising energy source. Though biogas is usually used as fuel for gas engines or microgas turbines [5], the efficiency of power generation decreases compared with using natural gas. Since biogas consists of CO₂ of approximately 40 vol%, the heating value of biogas is smaller compared to that of natural gas. In this study, biogas is proposed to be used as a feedstock to produce H₂ through a thermally powered biogas dry reforming process. The H₂ can be used as a fuel for solid oxide fuel cells (SOFCs) [6]. SOFCs can also utilize CO, which is a by-product of biogas dry reforming, as a fuel, resulting in an effective energy production system.

This study proposes a system combining the above-mentioned energy production system with a solar collector to supply the heat required since biogas dry reforming is an endothermic reaction. Some studies previously reported combined systems to produce H₂ using a solar collector to provide heat for the chemical reaction. The parabolic trough solar collector (PTC) was investigated to realize this purpose for CH₃OH steam reforming [7,8,9,10,11]. According to reference [12], a parabolic-dish solar collector (PDSC) uses technology that concentrates solar irradiation at a focal point, while the output of the PDSC is coupled with a number of useful applications. PDSCs have a higher concentration ratio (1000–3000). Such a concentrator is used to extract solar irradiation and concentrate it at a focal point. This concentration is in a parabolic shape, and it is made with a reflected material on the front face of its body. A receiver is used to convert the concentrated solar energy into the desired form of energy, like electrical energy or mechanical energy. Some research is being performed on different designs of receivers. According to the literature survey by the authors, Ruelas et al. [13] developed a mathematical model and applied it to estimating the intercept factor for Scheffler-type solar concentration based on the optical behavior and geometry of the concentrator in Cartesian coordinates. In addition, Azzouzi et al. [14] used heat equations to develop a model and predict the heat flux and the temperature distribution in the focal zone. Using SolTrace code, they noted that the predicted and experimental results were in good agreement. Pavlovic et al. [15] performed optical and thermal analyses to find the ideal position of the receiver in relation to the concentrator to maximize the optical efficiency and improve the flux distribution on the receiver. Comparing the mathematical modeling of a PDSC, such as that shown in reference [12], with that of the PTC in this study, the focal length of the parabolic-dish collector, focal point of the diameter and aperture area of the dish collector and concentration ratio are considered in the mathematical modeling of the PDSC. The numerical modeling of the PTC in this study can predict the temperature of fluid flowing through the absorber heated by the PTC without considering it, resulting in easy estimation. The authors think it is a merit of the numerical modeling of the PTC. According to reference [16], a PTC is the most appropriate method for providing thermal energy in an intermediate temperature range compared to the other types of concentrating solar collectors. Considering the temperature range of the biogas dry reforming process, the PTC is regarded as a proper candidate to supply the heat required for the reforming process [9]. According to reference [9], the combination of a PTC and a fuel cell is a promising system from the viewpoint of exergy. From the NEDO Renewable Energy Technology White Paper [17], the parabolic trough type, Fresnel type, tower type and dish type are actually installed in the world. The efficiency of the plant for the parabolic trough type, Fresnel type, tower type and dish type is 15%, 8–10%, 20–35% and 25–30%, respectively. In addition, the land utilization efficiency for the parabolic type, Fresnel type and tower type is 25–40%, 60–80% and 20–25%, respectively. The power generation cost of the parabolic trough type when using solar thermal power generation for a plant size below 250 MW and over 250 MW is approximately 0.2–0.3 USD/kWh and 0.22–0.27 USD/kWh, respectively. Although the power generation cost strongly depends on the sunlight illumination condition, this study thinks the PTC is one of the most effective kinds of energy technology. Numerical analysis using the commercial software COMSOL and Fluent was conducted to evaluate the H₂ production performance, the temperature distribution and the thermal efficiency of the combination system [7,8,10,11]. Regarding the numerical analysis using COMSOL, on a reflux solar CH₃OH steam reforming reactor (SMSRR) [7], the influence of the diameter of the reflux tube in an SMSRR on the performance of the SMSRR was studied, and the diameter of the reflux tube was selected according to comprehensive performance. This paper reports that the reflux SMSRR recycled the heat in the outlet fluid to heat the inlet fluid, so that the temperature at the inlet and the reaction rate increased rapidly. As for the other numerical analyses using COMSOL [8], a new H₂ production method allowing for a more uniform distribution of solar flux, temperature and deformation in the receiver/reactor by combining a linear Fresnel reflector, a compound parabolic concentrator, a mid- and low-temperature receiver/reactor and the CH₃OH steam reforming reaction was proposed. The solar light is concentrated on the surface of the receiver/reactor by the linear Fresnel reflector and the compound parabolic concentrator instead of the traditional PTC. A 3D model was established to study the performance of the mid-and-low temperature receiver/reactor, including solar flux distribution, fluid flux, mass diffusion, heat transfer, chemical reaction, and structural deformation. The results of numerical analysis showed that the temperature and reaction fields were highly influenced by the circumferential distribution of the solar flux. The linear Fresnel reflector can achieve a more uniform temperature distribution along the cross-section in the flow direction than the PTC due to the more uniform distribution of solar flux. On the other hand, the numerical analysis using FLUENT [10], a novel parabolic trough solar receiver–reactor, was proposed and investigated for continuous and efficient H₂ production via the CH₃OH-steam reforming reaction. A 3D model based on the finite volume method (FVM), which was combined with the Monte Carlo ray-tracing method (MCR), was carried out. The results showed that the proposed novel system had much better comprehensive characteristics and performance than that of the corresponding original system. In addition, this proposed novel system could have great potential to be improved by tuning corresponding key operating parameters such as the inlet temperature, the flow model and the concentric tube geometry. Regarding the numerical analysis using FLUENT [11], a novel parabolic trough solar receiver–reactor (PTSRR) of gradually varied porosity catalyst beds was proposed and investigated for cost-efficient H₂ production. A 3D comprehensive model was developed for PTSRRs of the CH₃OH-steam reforming reaction (MSRR) in porous Cu/ZnO/Al₂O₃ catalyst packed beds by combining FVM and MCR with an MSRR comprehensive kinetic model. The results showed that the non-uniform porosity catalyst bed gradually increased from the bottom to the top, matched non-uniform temperature distributions and made the operation of PTSRRs safer. The other numerical thermodynamic analysis was investigated on the solar CH₄ steam reforming with H₂ permeation membrane reactors [18]. In this study [18], the PTC was adopted in order to provide the heat for CH₄ steam reforming. The distribution of partial pressure of each gas, the conversion rate of CH₄ and H₂O and thermodynamic efficiency were calculated, changing the reaction temperature from 573 to 873 K, resulting in the largest increase in the amount of produced H₂ and thermodynamic efficiency at 873 K. The thermodynamic efficiency up to 70% could be obtained. Regarding the combination system to produce H₂ using the solar collector in order to provide the heat for CH₄ dry reforming including biogas dry reforming, several studies have been reported [19,20,21]. Zhao et al. [19] reported the analysis results on the thermodynamic performance, indicating that the conversion rate of CH₄ as well as the CO₂ emission reduction increase with the reaction temperature. According to the combination of thermodynamic analysis and regression analysis for steam and dry CH₄ reforming [20], the CH₄ conversion increased with the reaction temperature exponentially from 470 to 870 K. On the other hand, according to the experimental study on the combination system to produce H₂ using the solar collector in order to provide the heat for CH₄ dry reforming including biogas dry reforming, the volume percentage of produced H₂ increased with the reaction temperature from 623 to 1273 K. The volume percentage of H₂ attained 45% at 1273 K. It was reported that the lower heating value of produced syngas could exceed that of input biogas over 673 K.

However, to date, no study has investigated the impact of the size of solar collectors on the temperature of biogas, which flows through the solar collector, the performance regarding producing H₂ from a biogas dry reforming reactor, and the power generated by SOFCs, excluding the authors’ previous study [6]. In addition, the feasibility study using the weather data to investigate the performance of solar collectors as well as producing H₂ from a biogas dry reforming reactor and the power generated by SOFCs has not been reported, excluding the authors’ previous study [6]. However, the authors’ previous study did not investigate the influence of weather data for the different cities in Japan on the performance of the solar collector as well as H₂ production from a biogas dry reforming reactor and the power generated by SOFCs. Since the feasibility study to install the combination system which consists of a solar collector, biogas dry reforming reactor and SOFCs for the existing city is important, this study focuses on it.

The aim of this study is to understand the influence of the weather data in various Japanese cities on the performances of solar collectors with different sizes and thus the performances of the combined system as well. The cities studied were Kofu City, Nagoya City and Yamagata City. According to the annual ranking on the sunshine duration for the prefectural capital cities in Japan in 2021 [22], the ranking of Kofu City, Nagoya City and Yamagata City was 1, 24 and 47, respectively. Therefore, this study was thought to cover the most areas in Japan. This study refers to the previous study on the developed heat transfer model investigating the PTC [12]. The temperature of heat transfer fluid out of the PTC could range approximately 700–873 K [23,24]. The temperature of heat transfer fluid was calculated using the developed heat transfer model [12] with the weather data of Kofu City, Nagoya City and Yamagata City in Japan in 2021 [25]. We adopted the specific characteristics of a biogas dry reforming reactor developed by the authors to calculate the amount of produced H₂ [26,27] and the power generated by SOFCs using H₂ obtained from a biogas dry reforming reactor. In the energy production system with a solar collector proposed by this study, the heat transfer fluid consists of CH₄ and CO₂ flows into a solar collector. After being heated by solar collector, the heat transfer fluid flows into the biogas dry reforming reactor. H₂ is produced in the reactor through the biogas dry reforming process. The produced H₂ is supplied into SOFCs as a fuel, resulting in electricity being generated.

2. Simplified Heat Transfer Model for Proposed Solar Collector

2.1. Governing Equation

Figure 1 shows the schematic drawing for the simplified heat transfer model of the PTC proposed in this study. In this model, a solar radiation is mainly absorbed on the outer surface of the absorber tube [19]. Some absorbed heat transports to the heat transfer fluid via conduction through the tube wall and convection from the inner surface of the tube to the fluid (Q_h). Other heat transfers as a loss by radiation to the inner surface of the glass tube via the vacuum space (Q_r) and then by conduction from the inner surface of the glass tube to the outer surface of the glass tube (Q_c). The heat is transferred to ambient from the outlet surface of the glass tube by two mechanisms: (i) the convection to the surrounding air (Q_a) and (ii) the radiation to the sky (Q_s).

Figure 2 illustrates the thermal resistance diagram for the heat transfer process in the proposed model. In this model, R₁ indicates the thermal resistance due to convection from the heat transfer fluid to the absorber [(m·K)/W]. R₂ indicates the thermal resistance due to conduction through the absorber [(m·K)/W]. R₃ indicates the thermal resistance due to radiation through a vacuum [(m·K)/W]. R₄ indicates the thermal resistance due to conduction through the glass tube [(m·K)/W]. R₅ indicates the thermal resistance due to convection to the surrounding air [(m·K)/W]. R₆ indicates the thermal resistance due to radiation to the surrounding surfaces (sky) [(m·K)/W].

We assume the surrounding surface temperature is equal to the ambient air temperature. The model formula for a single glass tube can be expressed as follows [12].

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

(1)

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

(2)

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

(3)

where I is the solar intensity [W/m²], α is the absorptivity of the absorber tube [-], τ is the transmissivity of the glass tube [-], D is the diameter of the absorber [m], dx is the length of the absorber [m], m is the mass flow rate of the heat transfer fluid assumed to be a biogas [kg/s], c is the specific heat of the heat transfer fluid [J/(kg·K)], T_fb is the temperature of the heat transfer fluid [K], T_fb,out is the temperature of the heat transfer fluid at outlet [K] and T_fb,in is the temperature of the heat transfer fluid at inlet [K]. D, which is the diameter of the absorber, indicates that sunlight is caught from the whole direction since it is the surface that receives light with multiplying by πdx, as shown in Equation (1). In the actual case, the sunlight does not illuminate the surface of the absorber from the whole direction. If the sunlight illuminates half of the surface of the absorber, T_fb is changed. For example, in January in Nagoya city, T_fb calculated in the case of sunlight illumination on half of the surface of the absorber is larger than that in the case of sunlight illumination on the whole surface of the absorber by 1% to 36%, which depends on the time of day it was investigated. This study would like to investigate the impact of the condition of light absorbed on the surface of absorber in the near future.

Each thermal resistance is defined as follows:

$$R_1=\frac{1}{2\pi r_{ti}h}$$

(4)

$$R_2=\frac{1}{2\pi k_t}\ln \frac{r_{to}}{r_{ti}}$$

(5)

$$R_3=\frac{1}{2\pi \sigma r_{to}}\left[\frac{1}{{\epsilon }_t}+\frac{1-{\epsilon }_g}{{\epsilon }_g}\left(\frac{r_{to}}{r_{gi}}\right)\right]{\left[\left(T_{to}^2+T_{gi}^2\right)\left(T_{to}+T_{gi}\right)\right]}^{-1}$$

(6)

$$R_4=\frac{1}{2\pi k_g}\ln \frac{r_{go}}{r_{gi}}$$

(7)

$$R_5=\frac{1}{2\pi r_{go}{h}_o}$$

(8)

$$R_6=\frac{1}{{\epsilon }_g\sigma 2\pi r_{go}\left(T_{go}+T_s\right)\left(T_{go}^2+T_s^2\right)}$$

(9)

where r_ti is the inner radius of the absorber [m], r_to is the outer radius of the absorber [m], r_gi is the inner radius of the glass tube [m], r_go is the outer radius of the glass tube [m], σ is the Stefan–Boltzmann constant [W/(m²·K⁴)], h is the heat transfer coefficient between the heat transfer fluid and the inner surface of the absorber [W/(m²·K)], h_o is the heat transfer coefficient from the outer surface of the glass tube to the surrounding air [W/(m²·K)], k_t is the thermal conductivity of the absorber [W/(m·K)], k_g is the thermal conductivity of the glass tube [W/(m·K)], ε_t is the emissivity of the absorber [-], ε_g is the emissivity of the glass tube [-], T_to is the temperature of the outer surface of the absorber [K], T_gi is the temperature of the inner surface of the glass tube [K], T_go is the temperature of the outer surface of the glass tube [K], T_s is the temperature of the sky [K] and T_a is the temperature of the surrounding air (=293) [K]. This study assumes T_s≒ T_a.

2.2. Estimation Procedure of Heat Transfer Coefficient

The convective heat transfer coefficient of the turbulent flow in a tube was estimated by Dittus–Boelter correlations [28] in this study as follows:

$$Nu=0.023 {\mathrm{Re}}^{0.8} {\mathrm{Pr}}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$$

(10)

In addition, the above equation is summarized in detail, which is a well-known dimensionless number and formula as follows:

$$Nu=\frac{hD}{k_a}$$

(11)

$$\mathrm{Re}=\frac{{\rho }_a{u}_{a}D}{{\mu }_a}$$

(12)

$$\mathrm{Pr}=\frac{C_{p,a}{\mu }_a}{k_a}$$

(13)

$$h_o=0.0191+0.006608u_a$$

(14)

where C_p,a is the specific heat of the surrounding air [J/(kg·K)], μ_a is the viscosity [Pa·s], k_a is the thermal conductivity of the surrounding air [W/(m·K)], u_a is the velocity of the surrounding air [m/s] and ρ_a is the density of the surrounding air [m/s]. According to the reference [29], the temperature of fluid flowing through the absorber was estimated well using the h_o equation shown by Equation (14). Therefore, the authors think the h_o equation shown by Equation (14) can be applied.

2.3. Calculation Procedure

From Equations (1) and (2), the following formula can be drawn:

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

(15)

Moreover, R₃ is decided from Equation (3) as follows:

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

(16)

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

$$T_{to}={\left[\frac{\left(R_5+R_6\right)\left(-T_s+T_g\right)}{2\pi \sigma t_{to}{R}_5{R}_6}\times \frac{\left\{r_{gi}+r_{to}\left(1-{\epsilon }_g\right)\right\}}{{\epsilon }_t{r}_{gi}}+T_{gi}^4\right]}^{\frac{1}{4}}$$

(17)

T_fb is calculated by averaging T_fb,in and T_fb,out as follows:

$$T_{fb}=\frac{T_{fb,in}+T_{fb,out}}{2}$$

(18)

In this study, T_fb is calculated changing dx according to the above equations. This study set D = 1.5 m according to the optimization by the authors’ previous study [6]. The weather data, i.e., I, u_a and T_a in Kofu City, Nagoya City and Yamagata City are inputted [25]. The data of horizontal solar light intensity from the Japanese government [25] are used as I. Therefore, it is impossible to estimate the mirror and solar reflection as well as consider the variable angle of solar radiation. Therefore, this study assumes that they are ignored. The authors will investigate them in the new model in the near future. The heat transfer fluid is assumed as a mixture of CH₄ and CO₂. The molar ratio of CH₄: CO₂ is 1.5: 1, simulating the biogas. The following assumptions are considered in this study:

    (i).

The mass flow rate of the heat transfer fluid (m) is 0.05 kg/s.

   (ii).

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

  (iii).

T_fb,in is 283 K.

  (iv).

T_s ≒ T_a.

   (v).

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

  (vi).

R₂ and R₄ are ignored since they are very small compared with the other thermal resistances [22].

 (vii).

T_ti is equal to T_to.

(viii).

T_gi the equal to T_go, which is 373 K.

   (ix).

The mirror and solar reflection are ignored.

    (x).

The variable angle of solar radiation is ignored.

In addition, this study does not calculate the heat loss of transport pipelines. The authors would like to consider it as a future subject. In addition, this study investigates in order to clarify the feasibility of the proposed system consisting of a PTC, biogas dry reforming reactor and SOFCs referring the simplified heat transfer model developed by the previous study [29]. In the model developed by the previous study, the mirror’s reflectivity, manufacturing precision, intercept factor and edge losses were not considered. As to these factors, the authors would like to investigate the design and the performance evaluation of PTCs in detail in the near future. In addition, as to the variable angle of solar radiation, this study assumes the solar collector sets horizontally. In addition, this study uses the solar intensity according to the data base of horizontal solar intensity in Japan [25]. Therefore, in this study, the impact of change in the angle of solar radiation can be ignored. Table 1 lists the physical properties adopted 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 in physical properties with the temperature under an unsteady state condition, the calculation is too complex and huge. Although the physical properties listed in Table 1 depend on the temperature exactly, the authors assume that we can calculate T_fb using the initial values at 283 K shown in Table 1.

Comparting to the other heat transfer models, some recent papers reported on the heat transfer analysis using the Hottel–Whiller–Bliss model for a solar collector [30,31,32]. However, these papers investigated a flat plate solar collector [30,31,32], while this study investigates a PTC. In addition, the Hotel–Whiller–Bliss model considered thermal conduction only in these previous studies [30,31,32], while the model investigated in this study considers the thermal conduction, the thermal convection and the thermal radiation heat transfer; thus, the assessment of the whole heat transfer mechanism can be conducted in this study. Therefore, the authors think the model investigated in this study has merit and is superior to the Hottel–Whiller–Bliss model.

3. Proposed Combined Energy System

Figure 3 shows the proposed system which consists of a solar collector, biogas dry reforming reactor and SOFC [6]. In the proposed system, the heat transfer fluid consisting of CH₄ and CO₂ flows into the solar collector. After heated by the solar collector, the heat transfer fluid flows into a biogas dry reforming reactor. H₂ is produced in the reactor through a biogas dry reforming process. The produced H₂ is provided into the SOFC as a fuel. As a result, the electricity is generated. The by-product of the process, CO, was not considered in this study.

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

CH₄ + CO₂ → 2H₂ + 2CO

(19)

In this study, the molar flow rate of CO₂ and CH₄ is set 1.67 × 10⁻² mol/s and 2.51 × 10⁻² mol/s, respectively. This molar ratio represents CH₄: CO₂ of 1.5: 1 in the case of m = 0.05 kg/s. From Equation (19) and these molar flow rates, the molar flow rate of the produced H₂ can be estimated to be 3.34 × 10⁻² mol/s. According to the authors’ previous experimental studies changing the reaction temperature, which corresponds to T_fb in this study, from 673 to 873 K [26,27], the best performance of biogas dry reforming is obtained at 873 K. Therefore, we assume H₂ can be produced by biogas dry reforming at T_fb over 873 K. The conversion ratio of H₂ is assumed to be 100% and 10%, according to the authors’ previous experimental studies [26,27], respectively. This study assumes that the conversion ratio of H₂ is 100% as the ideal maximum performance case.

To calculate the power generated by SOFC, we consider the lower heating value of H₂ (=10.79 MJ/m³_N) and the power generation efficiency of a commercial SOFC of 55% [33]. In the case of the conversion ratio of H₂ = 100%, the power generated by an SOFC can be estimated as follows:

(3.34 × 10⁻² [mol/s] × 22.4 [L/mol]) ÷ (1000 [L/m³] × 0.55 × (10.79 [MJ/(m³N)]) = 4.44 [kW]

(20)

The amount of produced H₂ and the power generated by an SOFC which are estimated under several conditions are discussed in the following section.

4. Results and Discussion

4.1. Temperature of Heat Transfer Fluid, T_fb

The weather data of I, u_a and T_a in Kofu City, Nagoya City and Yamagata City in 2021 [25] which are adopted for the calculation of T_fb were collected and are shown in Table 2, Table 3 and Table 4. As representative data for each city, the data in January are shown in these tables. The monthly mean values of I, u_a and T_a are listed in these tables. In addition, Table 5, Table 6 and Table 7 list the amount of heat produced by a PTC which is IατDπdx as shown in Equation (1). As representative data for each city, the data in January are shown in these tables.

Figure 4, Figure 5, Figure 6 and Figure 7 show the changes of T_fb with time in different months and cities. The data in January, April, July and October are shown as representative data for winter, spring, summer and autumn, respectively. The monthly mean values are shown in Figure 4, Figure 5, Figure 6 and Figure 7.

It can be seen from Table 2, Table 3 and Table 4 and Figure 4, Figure 5, Figure 6 and Figure 7 that the change in T_fb with time follows the change in I mainly. In addition, T_fb in April and July is higher than that in January and October irrespective of city, since I in April and July is higher than that in January and October. It is found from Figure 4, Figure 5, Figure 6 and Figure 7 that T_fb increases with the increase in dx since the surface area of the absorber tube, i.e., the heat transfer area, is larger. Additionally, it can be seen that T_fb for dx = 5 m is higher than 2000 K in April and July irrespective of city, which is not suitable for actual application due to the safety issues of the material of the absorber tube. Therefore, this study decides that the optimum dx should be around 4 m irrespective of city to ensure the safety of stainless steel, which is the material used to make the absorber tube. For example, the melting point of SUS 405 is 1700 K [34]. In the following discussion of the analysis results, this study adopts the results using dx = 4 m. As to the comparison of the tendency of T_fb, it is seen that T_fb in Yamagata City in January and October, i.e., winter and autumn, is lower than that in Kofu City and Nagoya City especially, which is strongly influenced by the tendency of I, not u_a. On the other hand, T_fb is almost the same in April and July, i.e., spring and summer, irrespective of city. The difference of T_fb between Kofu City and Nagoya City is relatively small, resulting from the difference of sunshine duration for the ranking prefectural capital city being under 24 in Japan in 2021 [22]. As to the data of July shown in Figure 6, it is observed that that T_fb increases before noon, which is faster compared to the other months shown in this study. Since July is in the summer, the temperature rises after a sunrise quickly compared to the other seasons in Japan. In addition, July is the rainy season in Japan. The rain would usually occur in the afternoon in Japan. Therefore, we can find the lack of symmetry of T_fb in Figure 6. Regarding the system operation during off-sunshine hours, this study considers that the system does not operate during off-sunshine hours. However, this study thinks the energy can be saved as a state of H₂ during off-sunshine hours, resulting in the power generated by an SOFC being available for the energy demand during off-sunshine hours.

This study aimed to evaluate the comparison of the performance of a PTC installed in three cities in Japan. Comparing the analysis for the different cities, e.g., in the other countries, the difference among the three cities investigated in this study was small. However, the need to utilize renewable energy has been increasing rapidly in Japan due to the increase in the requests to develop the CO₂ reduction technology. Therefore, the authors think that this study investigating the performance of PTCs in the cities in Japan where they are installed is meaningful. In addition, this study has already conducted the analysis with a time step of 1 h. However, all data with a time step of 1 h are 24 h × 365 days × 3 cities = 26,280 data. There are too many data with a time step of 1 h to show all of it in the manuscript due to the space limitation of the manuscript.

4.2. Amount of H₂ Produced via Biogas Dry Reforming and Power Generated by SOFC

To calculate the amount of H₂ produced via the biogas dry reforming reactor, Table 8 shows the time when T_fb is over 873 K for Kofu City, Nagoya City and Yamagata City. In this table, the data in the case of dx = 4 m are shown. As we described before, this study assumes that H₂ can be produced at the conversion ratio of H₂ of 100% when T_fb is over 873 K. The time when T_fb is over 873 K is marked in this table.

According to Table 8, the time when T_fb is over 873 K in spring and summer is longer than that in winter and autumn irrespective of city. This is mainly due to the tendency of I, not u_a. In addition, the time when T_fb is over 873 K is 0 in January and December in Yamagata City is known. Therefore, other cities should be selected if the proposed system would be used all year around.

Table 9 shows the amount of H₂ produced via the biogas dry reforming reactor for Kofu City, Nagoya City and Yamagata City, respectively. It can be seen from Table 9 that the annual amount of H₂ produced via the biogas dry reforming reactor for Nagoya City is more than that for Kofu City. As described above, the difference in sunshine duration for the ranking prefectural capital city, which was under 24 in Japan in 2021 [22], was small.

It is observed from Table 9 that the amount of produced H₂ via the biogas dry reforming reactor in spring and summer is higher, as expected, compared to the other seasons irrespective of city. This could be explained by the time when T_fb is over 873 K shown in Table 8. When assuming the conversion ratio of H₂ is set at 10%, according to the authors’ previous experimental studies [26,27], the values listed in Table 6 become 1/10.

Table 10 lists the power generated by SOFCs with the H₂ generated via the biogas dry reforming reactor for Kofu City, Nagoya City and Yamagata City. The annual power generated by SOFCs for Kofu City, Nagoya City and Yamagata City is 10,809 kWh, 10,959 kWh and 8389 kWh, respectively. The annual power generated by SOFCs for Nagoya City was also higher than that for Kofu City. As described above, the difference of sunshine duration for the ranking prefectural capital city, which was under 24 in Japan in 2021 [22], was small.

It is observed from Table 10 that the power generated by SOFCs in spring and summer is higher compared to the other seasons irrespective of city, which can be explained by the time when T_fb is over 873 K in Table 8. Additionally, it is found from Table 10 that the power generated by SOFCs in January and December in Yamagata City is 0, because the reactor did not work as T_fb was lower than 873 K. Therefore, as claimed before, other cities should be selected if the proposed system would be used all year around. When assuming the conversion ratio of H₂ is set at 10% according to the authors’ previous experimental studies [25,26], the values listed in Table 10 become 1/10.

Table 11 lists the number of households whose power demand could be met by the combined system in each month for Kofu City, Nagoya City and Yamagata City. The number which was termed as “available households number per month” in this study was calculated by dividing the power generated by SOFCs by the electricity demand of a couple households in each season [35].

It can be seen from Table 11 that the highest available households number per month clarified in this study is 4.7 in June in Kofu. According to Table 11, this highest number can be also observed for Yamagata City. In spring and summer in Yamagata City, the Foehn phenomenon, which causes the sunny days with high temperature, seldom occurs [25]. Therefore, the highest available household number per month of 4.7 can be obtained even for Yamagata City. However, the highest available households number per month of 4.7 is still small. In this study, the analysis was conducted for the case of m = 0.05 kg/s. If m was larger, the amount of H₂ produced via the biogas dry reforming reactor would increase. The optimum dx and D would be changed when m was over 0.05 kg/s.

Compared with the previous studies [7,8,9,10,11,18,19,20,21], this study has exhibited the feasibility of the proposed system of PTCs with a biogas dry reforming reactor and SOFCs, since there is no previous report on this system. This study has revealed that the power generated by SOFCs using H₂ which is obtained via biogas dry reforming using PTCs can be supplied for households in Japan irrespective of city, especially for spring and summer.

When assuming the conversion ratio of H₂ is set at 10% according to the authors’ previous experimental studies [26,27], the values listed in Table 11 become 1/10. Although the available households number per month for each city was small in case of the conversion ratio of H₂ of 10% as well as that of 100%, this study proposes a multi-energy production system consisting of a solar collector, biogas dry reforming reactor and SOFC to provide the power for more households. Regarding the cost analysis, it is difficult to obtain the actual cost, the conversion cost and the installation cost and so on now for solar collectors. Therefore, the authors would like to investigate the cost analysis in the near future. Regarding the energy conversion ratio, there is heat loss when applying the heat from a solar collector to a biogas dry reforming reactor. In addition, the H₂ yield for the biogas dry reforming depends on the reaction temperature. Moreover, this study set the power generation efficiency of the SOFC at 55% following the reference [33]. However, the power generation efficiency of the SOFC would be improved in the near future due to the development of technology. Although the power generation efficiency of SOFCs was set based on using H₂ as a fuel, CO can also be used as a fuel for SOFCs. Even though the conversion ratio of H₂ is 10%, CO is also used a fuel for SOFCs, which would increase the power generated by SOFCs. These are the future research areas. To supply the energy for these seasons, the storage of H₂ after a biogas dry reforming is proposed and is being studied currently. The results of these subjects will be reported in the near future.

5. Conclusions

We have simulated the performances of PTCs and a proposed energy system with the weather data of different cities in Japan. The studied cities are Kofu City, Nagoya City and Yamagata City, which almost cover the whole climate zones of Japan. The temperature of the heat transfer fluid has been calculated using the simple but effective heat transfer model developed. The following conclusions are drawn from the study:

• T_fb in April and July is higher than that in January and October irrespective of city since I in April and July is higher than that in January and October.
• T_fb increases with the increase in dx. However, this study has decided that the optimum and the maximum dx should be 4 m irrespective of city, since this study assumed that stainless steel was used as the material to make the absorber tube.
• T_fb in Yamagata City in January and October, i.e., winter and autumn, was lower than that in Kofu City and Nagoya City especially, which is influenced by the tendency of I strongly, not u_a. On the other hand, T_fb was almost the same in April and July, i.e., spring and summer, irrespective of city.
• Not only the amount of produced H₂ but also the power generated by SOFCs in spring and summer were higher compared to the other seasons irrespective of city.
• The highest available households number per month found in this study was 4.7 in June in Kofu City as well as June and July in Yamagata City. To increase the households number, some measures, e.g., increasing m, should be further studied.
• In Japan, the productivity in summer is higher irrespective of investigated city. It depends on the weather characteristics, i.e., I, u_a and T_a of cities in Japan. Therefore, the authors think similar results would be obtained when adopting the existing PTC system.