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

1. Introduction

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

To reduce CO₂ which is a main chemical to cause the global warming, H₂ is paid attention in the world. This study focuses on the H₂ production from biogas dry reforming reaction process. Biogas consisting of CH₄ (55 - 75 vol%) and CO₂ (25 – 45 vol%) [3] is produced from fermentation by the action of anaerobic micro-organisms on raw materials such as garbage, livestock and sewage sludge. According to the International Energy Agency (IEA) [4], 1.46 EJ equivalent biogas has been produced in 2020. The amount of energy of produced biogas in 2020 is approximately five times as large as that in 2000. It can be expected that the produced biogas will increase more. Therefore, the biogas is a promising energy source. Though the biogas is used as a fuel for gas engine or micro gas turbine generally [5], the efficiency of power generation decreases compared to using a natural gas. Since a biogas contains 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 feedstock to produce H₂ through thermally powered biogas dry reforming process. The H₂ can be used as a fuel for solid oxide fuel cell (SOFC) [6]. SOFC can also use CO which is a by-product from biogas dry reforming as a fuel, resulting that the effective energy production system can be realized.

This study proposes the system combining the above mentioned energy production system with a solar collector to supply the heat required since the biogas dry reforming is an endothermic reaction. Some studies previously reported the combined system to produce H₂ using the solar collector in order to provide the heat for the chemical reaction. The parabolic trough solar collector (PTC) has been investigated for this purpose for CH₃OH steam reforming [7,8,9,10,11]. Numerical analysis using the commercial software COMSOL and Fluent has been conducted to evaluate the H₂ production performance, the temperature distribution and the thermal efficiency of the combination system [7,8,10,11]. The other numerical thermodynamic analysis has been investigated on the solar CH₄ steam reforming with H₂ permeation membrane reactors [12]. In this study [12], the PTC was adopted to provide the heat for CH₄ steam reforming. The distribution of partial pressure of each gas, conversion rate of CH₄ and H₂O and thermodynamic efficiency were calculated changing the reaction temperature from 573 K to 873 K, resulting that the amount of produced H₂ and the thermodynamic efficiency are the largest 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 [13,14,15]. Zhao et al. [13] has reported the analysis results of 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 [14], the CH₄ conversion increased with the reaction temperature exponentially from 470 K 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 K 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, there is no study to investigate the impact of size of solar collector on the temperature of biogas which flows through the solar collector and the performance to produce H₂ from biogas dry reforming reactor and the power generated by SOFC excluding the authors’ previous study [6]. In addition, the feasibility study using the weather data to investigate the performance of solar collector as well as producing H₂ from biogas dry reforming reactor and the power generated by SOFC was not reported excluding the authors’ previous study [6]. However, the authors’ previous study has not investigated the impact of weather data for the different cities in Japan on the performance of solar collector as well as producing H₂ from biogas dry reforming reactor and the power generated by SOFC. Since the feasibility study to install the combination system consisting of solar collector, biogas dry reforming reactor and SOFC for the existing city is important, this study focuses on it.

The purpose of this study is to understand the impact of the weather data in various Japanese cities on the performances of solar collector with different sizes, thus the performances of combined system. The cities studied were Kofu city, Nagoya city and Yamagata city. According to the annual ranking on the duration of sunshine for the prefectural capital cities in Japan in 2021 [16], 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 the developed heat transfer model investigating PTC [17]. PTC is the most appropriate collector to provide the solar thermal energy at an intermediate temperature range among the several types of concentrating solar collector [18]. The temperature of heat transfer fluid out of the PTC could range approximately 700 K - 873 K [19,20]. The temperature of heat transfer fluid was calculated by the developed heat transfer model [17] with the weather data of Kofu city, Nagoya city and Yamagata city in Japan in 2021 [21]. This study adopted the specific characteristics of a biogas dry reforming reactor developed by authors to estimate the amount of produced H₂ [22,23] and the power generated by SOFC with H₂ obtained from biogas dry reforming reactor.

2. Heat Transfer Model for Solar Collector Proposed

2.1. Govering Equation

Figure 1 illustrates the schematic drawing for 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 [17]. Some absorbed heat transports to the heat transfer fluid by 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 through 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 transferred to ambient from the outlet surface of the glass tube by two mechanisms as follows: (i) the convection to the surrounding air (Q_a), (ii) the radiation to the surrounding surfaces (Q_s), e.g. building and sky.

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

This study assumes that the surrounding surface temperature is equal to the ambient air temperature. The model equation for a single glass tube can be expressed as follows [17].

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

(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 absorber tube [-], τ is the transmissivity of glass tube [-], D is the diameter of absorber [m], dx is the length of absorber [m], m is the mass flow rate of heat transfer fluid which is assumed to be a biogas [kg/s], c is the specific heat of heat transfer fluid [J/(kg・K)], T_fb is the temperature of heat transfer fluid [K], T_{fb, out} is the temperature of heat transfer fluid at outlet [K] and T_{fb, in} is the temperature of heat transfer fluid at inlet [K]. Each thermal resistance is defined as following:

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

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

2.2. Estimation of Heat Transfer Coefficient

The convective heat transfer coefficient for the turbulent flow in a tube was estimated by Dittus-Boelter correlations [24] in this study as follows:

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

(10)

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

(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 surrounding air [J/(kg・K)], μ_a is the viscosity [Pa・s], k_a is the thermal conductivity of surrounding air [W/(m・K)], u_a is the velocity of surrounding air [m/s] and ρ_a is the density of surrounding air [m/s].1.3. Calculation procedure

According to Equations (1) and (2), the following equation 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 [21]. The heat transfer fluid is assumed as the mixture of CH₄ and CO₂. The molar ratio of CH₄ : CO₂ is 1.5 : 1, which simulates 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 absorber and glass tube is 1/10 D.

(iii)

T_{fb, in} is 283 K.

(iv)

T_s equals to T_a.

(v)

The thickness of 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 to the other thermal resistances [17].

(vii)

T_ti equals to T_to.

(viii)

T_gi equals to T_go, which is 373 K.

Table 1 lists the values of physical properties adopted in this study.

3. Proposed Combined Energy System

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

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

CH₄ + CO₂ → 2H₂ + 2CO

(19)

In this study, the molar flow rate of CO₂ and CH₄ is 1.67×10^-2 mol/s and 2.51×10^-2 mol/s, respectively. This molar ratio represents CH₄ : CO₂ of 1.5 : 1 when m is 0.05 kg/s. According to Equation (19) and these molar flow rates, the molar flow rate of produced H₂ can be calculated to be 3.34×10^-2 mol/s. From the authors’ previous experimental studies changing the reaction temperature, which corresponds to T_fb in this study, from 673 K to 873 K [22,23], the performance of biogas dry reforming is the best at 873 K. Therefore, this study assumes that H₂ can be produced by biogas dry reforming at T_fb over 873 K. The conversion ratio of H₂ is assumed to be 100 %. Though the highest conversion ratio of H₂ was approximately 10 % according to the authors’ previous experimental studies [22,23], this study assumes that the conversion ratio of H₂ is 100 % as the ideal maximum performance case.

To estimate the power generated by SOFC, this study considers the lower heating value of H₂ (= 10.79 MJ/m³_N) and the power generation efficiency of commercial SOFC of 55 % [25]. When the conversion ratio of H₂ is 100 %, the power generated by SOFC can be calculated 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 SOFC which are estimated by this study under several conditions are discussed in the next section.

4.1. Temperature of Heat Transfer Fluid

The weather data of I, u_a and T_a in Kofu city, Nagoya city and Yamagata city in 2021 [21] 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 value of I, u_a and T_a are listed 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 a representative data for Winter, Spring, Summer and Autumn, respectively. The monthly mean values are shown in these figures.

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 of T_fb with time follows the change of 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 absorber tube, i.e. heat transfer area is larger. Additionally, it can be seen that T_fb for dx = 5 m is higher than 2,000 K in April and July irrespective of city, which is not suitable for actual application due to the safety issues of the material of 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 that is the material used to make the absorber tube. For example, the melt point of SUS 405 is 1,700 K [26]. In the following discussion on 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 influenced by the tendency of I strongly, 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 that the difference of duration of sunshine for the ranking prefectural capital city which was under 24 in Japan in 2021 [16].

3.2. Amount of H₂ Produced from Biogas Dry Reforming and Power Generated by SOFC

To calculate the amount of H₂ produced from the biogas dry reforming reactor, Table 5 lists 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 5, 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, it is known the time when T_fb is over 873 K is 0 in January and December in Yamagata city. Therefore, other cities should be selected if the proposed system would be used all year around.

Table 6 lists the amount of H₂ produced from the biogas dry reforming reactor for Kofu city, Nagoya city and Yamagata city, respectively. It can be seen form Table 6 that the annual amount of H₂ produced from the biogas dry reforming reactor for Nagoya city is over than that for Kofu city. As described above, the difference of duration of sunshine for the ranking prefectural capital city which was under 24 in Japan in 2021 [16] was small.

It is seen from Table 6 that the amount of produced H₂ from 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 listed in Table 5.

Table 7 lists the power generated by SOFC with the H₂ generated from the biogas dry reforming reactor for Kofu city, Nagoya city and Yamagata city. The annual power generated by SOFC for Kofu city, Nagoya city and Yamagata city is 10,809 kWh, 10,959 kWh and 8,389 kWh, respectively. The annual power generated by SOFC for Nagoya city was also higher than that for Kofu city. As described above, the difference of duration of sunshine for the ranking prefectural capital city which was under 24 in Japan in 2021 [16] was small.

It is seen from Table 7 that the power generated by SOFC 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 5. In addition, it is found from Table 7 that the power generated by SOFC 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.

Table 8 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 that was termed as “available households number per month” in this study, was calculated by dividing the power generated by SOFC by the electricity demand of couple households in each season [27].

It can be seen from Table 8 that the highest available households number per month clarified in this study is 4.7 in June in Kofu. According to Table 8, 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 [21]. 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 from the biogas dry reforming reactor would increase. The optimum dx and D would be changed when m was over 0.05 kg/s. In addition, the available households number per month was small in autumn and winter. 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 on these subjects will be reported in the near future.