Analysis of Dynamic Biogas Consumption in Chinese Rural Areas at Village, Township, and County Levels

Abstract

Understanding the characteristics of biogas demand in rural areas is essential for on-demand biogas production and fossil fuel offsetting. However, the spatiotemporal features of rural household energy consumption are unclear. This paper developed a rural biogas demand forecasting model (RBDM) based on the hourly loads of different energy types in rural China. The model requires only a small amount of publicly available input data. The model was verified using household energy survey data collected from five Chinese provinces and one year’s data from a village-scale biogas plant. The results showed that the predicted and measured biogas consumption and dynamic load were consistent. The relative error of village biogas consumption was 11.45%, and the dynamic load showed seasonal fluctuations. Seasonal correction factors were incorporated to improve the model’s accuracy and practicality. The accuracy of the RBDM was 19.27% higher than that of a static energy prediction model. Future research should verify the model using additional cases to guide the design of accurate biogas production and distribution systems.

1. Introduction

1.1. Background

More than 90,000 biogas projects were operating in China in 2020, and the number of new projects is increasing [1]. With an efficient production and supply system, the local residents’ energy needs can be met in rural areas, and significant carbon emission reductions (CERs) can be achieved [2]. However, the production and supply system does not always operate optimally due to the uncertain demand for rural energy and the limited gas storage capacity [3]. Therefore, a large proportion of biogas (55–65% CH₄) is released, resulting in low energy efficiency and insufficient climate change mitigation [4,5].

Biogas is an efficient, clean, and renewable energy source. Its appropriate use minimizes methane emissions during energy conversion and distribution [6]. Biogas can be used for cooking, heating, and power generation after dehydration and desulfuration [7,8]. Biogas boilers generate steam to create electricity for manufacturing or agricultural use [9]. Chinese rural areas have many potential customers for biogas usage, with a consumption potential of 134.9 billion m³/a in households and 24.8 billion m³/a in the small-scale industry. The amount of biogas used could result in CERs of 193 million t/a [10]. Therefore, rural areas have significant potential for biogas development.

Numerous forecast models have been developed to estimate urban natural gas consumption [11]. For example, Yu and Xu developed a combined method based on a backpropagation (BP) neural network and an optimized genetic algorithm and evaluated the model using natural gas consumption data in Shanghai, with the mean absolute error (MAE) ranging from 7857.5 to 8739.2 [12]. Yin et al. used survey data from 13 households in Baoding, Hebei, China, and logistic regression (LR) and ordinary least squares (OLS) tests to determine the heating demand [13]. The large amount of natural gas consumption data from high-density buildings and urban gas network facilities provides sufficient information for these studies [14]. However, the prediction results still have a non-negligible error. In addition, Chinese rural areas have low natural gas utilization and a decentralized household distribution. Thus, forecasting models for urban natural gas consumption are unsuitable for rural areas due to a lack of field survey data [15].

Most research on rural energy consumption in China has focused on energy use and clean energy transition, whereas few studies have analyzed the rural energy demand. Most researchers utilized statistical data [16], average energy consumption (AEC) [17], and linear equations [18] for energy analysis. However, these data only reflect energy demand or static hourly load in a given region. Energy consumption is volatile; thus, energy shortages exist even if sufficient energy is produced [19]. In addition, significant differences exist in the economic conditions in China’s rural areas, such as villages, townships, and counties, resulting in large differences in energy use [20]. Using the above method to predict the rural energy demand results in prediction errors. Therefore, establishing a biogas demand forecasting model for Chinese rural areas is essential.

This paper develops a rural biogas demand forecasting model (RBDM) for villages, townships, and counties, considering the energy requirements for cooking, heating, and small-scale industries. The RBDM is developed using hourly load data for different energy types and by considering the energy consumption of villages, townships, and counties. The RBDM is optimized and validated using household survey data and operating data from a biogas plant. Biogas production and supply scenarios are constructed to analyze the dynamic load characteristics of villages, townships, and counties.

1.2. Literature Review

Biogas, a clean energy, is generated through the anaerobic fermentation of organic materials, such as straw, animal manure, and domestic waste. Anaerobic fermentation requires a closed environment, a suitable temperature, and Pondus Hydrogenii. The main components are methane (50–70%) and carbon dioxide (30–40%). In 2019, the total amount of organic waste (dry weight) in China was about 1.311 billion tons, and the proportions of straw and animal manure were 63.1% and 27.0%, respectively. These provided sufficient raw material supply for biogas production [21]. In addition, biogas has lower carbon emissions in the production, transport, and utilization processes than other utilization methods of raw materials, such as burning and open stacking [22]. It is predicted that, on the premise of effectively developing biogas, the production potential of biogas will reach 169 billion m³ by 2030, with CERs of about 300 million tCO₂; by 2060, it will reach 371 billion m³, with CERs that could reach 660 million tCO₂ [23]. Therefore, biogas has considerable development potential and prospects in Chinese rural areas.

Biogas can be consumed in many ways, such as power generation, direct combustion nearby, and integration into the gas pipeline, and its demand forecasting methods are different. Biogas power generation is the conversion of biogas into other energy types, so the biogas demand can be obtained by the forecasting electricity demand. The power demand forecast model often uses an autoregressive integrated moving average (ARIMA) and a long short-term memory network (LSTM). For example, Dittmer et al. [24] evaluated the LSTM suitable for power demand forecasting in rural areas and used the historical power data of experimental stations provided by operators. The results showed that the absolute percentage error (APE) of the selected model was 13–16%, which was suitable for the production guidance of biogas power plants. After desulfurization, decarbonization, and dehydration, the biogas methane content can reach 80%, and the fuel performance was the same as that of natural gas, which could be incorporated into the natural gas pipeline. However, the penetration rate of natural gas pipelines in China’s rural areas was only 39.93% [25], so most of the biogas incorporated into pipelines was supplied for urban use. Therefore, the data used in the forecasting model were mainly from cities. The forecasting model was consistent with that of power systems. For instance, Qin et al. [26] proposed a combined model of federated learning, deep contrastive learning, and clustering approaches. They assessed the model using historical urban gas data provided by gas companies, and the results showed an average improvement of 25.30% in the mean squared error (MSE). The above methods were mostly used in large-scale biogas projects. However, in the rural areas of China, villages are widely dispersed. When the transportation distance of organic waste exceeds 15 km, the economic cost increases significantly, losing the value of producing energy [27]. Therefore, it was necessary to process it within a suitable distance as close as possible. However, most of the nearby waste treatment used small-scale biogas projects. These projects, when installing equipment for biogas upgrading or generating electricity, will significantly increase the expected investment or even lose economic value. Therefore, the biogas from small-scale biogas projects directly supplied to the nearest consumption was the most effective way. But existing studies on the biogas demand forecast model mainly focus on large time scales. For example, Senol et al. [28] estimated Turkey’s biogas demand for 2035 by using an artificial neural network (ANN), ARIMA of time series, and linear regression models. Models such as ARMA and LSTM need to be driven by historical data, but it was difficult to obtain historical energy consumption data in Chinese rural areas, so their prediction models were not suitable for rural areas, or they need to use the per capita energy consumption data from the National Bureau of Statistics [29], such as the per capita energy consumption of 0.5 tce (ton of standard coal equivalent) in 2022. But such data were difficult to capture changes in energy demand over time scales.

According to the existing literature, the research on biogas demand forecasting models in China’s rural areas mainly focuses on other energy types, and some biogas forecast models only focus on static energy consumption, failing to show the fluctuation on a short time scale. In addition, the accuracy of the forecast model in rural areas was affected by demographic, economic, and seasonal factors. Among them, family size was closely related to household energy consumption, and some studies have pointed out that an increase in family size will be accompanied by an increase in household energy consumption [30], but some scholars have pointed out that energy consumption has a scale effect and that an increase in family size has a negative impact on the per capita energy consumption [31]. Seasonal changes will lead to fluctuations in temperature, and residents’ heating demand will increase significantly when the ambient temperature is lower than the comfortable temperature of the human body [32]. In order to ensure the usability of the forecast model, it is necessary to consider the impact of these factors on the model.

2. Methodology

2.1. Database

The RBDM was established using an Access database and data from Science Direct, Google Scholar, the Web of Science, and the China National Knowledge Infrastructure. We utilized different data sources to replace missing data. The following datasets were used:

Dataset 1: the China Statistical Yearbook [33] and the China Population and Employment Statistical Yearbook [34], published by the National Bureau of Statistics (NBS) of China, are used for setting scenario-scale parameters;

Dataset 2: survey data on household cooking and heating energy consumption in Nanjing, Hefei, and Henan [35,36] are used to set parameters for cooking and heating times;

Dataset 3: energy consumption data from a small food-processing factory in China [37] are used for parameter setting in small-scale industries;

Dataset 4: data on residential cooking energy loads in Chinese rural areas [1,38,39] are used to obtain the cooking dynamic curve;

Dataset 5: data on residential heating energy loads in Chinese rural areas [38,40,41] are used to obtain the heating dynamic curve;

Dataset 6: energy consumption load data of small-scale industries in Chinese rural areas [42] are used to obtain the small-scale industry dynamic curve.

2.2. Scenario Configuration

Due to different population sizes and economic conditions in different administrative regions, many combinations of energy types are used in villages, townships, and counties [43]. We focused on the energy demand for cooking, heating, and small-scale industries and created energy consumption scenarios for villages, townships, and counties. The number of energy users for cooking purposes has increased steadily in villages, townships, and counties, with a significant shift in scale. Township and county residents use gas-heating equipment for heating, whereas village residents mostly use small electrical appliances [44]. Due to the scattered distribution of small-scale industries in villages and townships, we analyzed industrial energy consumption at the county level [39,45]. In summary, we analyzed the cooking energy demand in villages, townships, and counties, the heating demand in townships and counties, and the energy demand of small-scale rural industries in counties. The scenarios are described in

Table 1. The scenarios for analyzing the energy demand in villages, townships, and counties.

Type		Villages		Townships		Counties
		Autumn and Winter	Spring and Summer	Autumn and Winter	Spring and Summer	Autumn and Winter	Spring and Summer
Number of households		312	312	9328	9328	152,985	152,985
Cooking		✓	✓	✓	✓	✓	✓
	Cooking time (h)	1.47	1.47	1.47	1.47	1.47	1.47
Heating		✗	✗	✓	✗	✓	✗
	Living space (m2)			111.92		111.92
	Heating time (h)			3.67		3.67
Small-scale industry		✗	✗	✗	✗	✓	✓
	Number of					24	24
	Single-unit biogas consumption (m3)					364,283.33	364,283.33

✓: Included; ✗: Not included.

.

Dataset 2 shows that rural residents cooked on average for 88.2 min [35] per day and spent 3.67 h daily heating their homes during the 120-day [36] winter period. Dataset 1 indicates that the average population in villages, townships, and counties was 836, 25,000, and 410,000, respectively [33], with an average family size of 2.68 people [34] and a per capita living space of 41.76 m² [33]. According to 2021 statistics, the urbanization rate was 64.72%, resulting in urban populations of 16,180 in townships and 265,352 in counties [46].

The annual industrial energy consumption is related to the rated energy consumption of equipment and production output. A small food-processing industry was used as an example to calculate the energy consumption of small-scale rural industries [37]. According to Dataset 3, the industry’s annual energy consumption was 1,994,600 kWh of electricity, 1.16 tone (t) of natural gas, and 30 t of diesel fuel [37]. According to Dataset 1, each county has an average of 12 townships [33]. Since each township has two small-scale industries, 24 industries exist in the county. We assumed a 60% methane content of the biogas.

2.3. Model Establishment

Since cooking, heating, and small-scale industries have different energy consumption requirements, a mathematical model can be established to analyze the total energy consumption. The cooking energy consumption was calculated using the rated flow and duty cycle (Equation (1)):

$$q_1=Q{t}_1$$

(1)

where q₁ represents the daily cooking gas consumption of a single household, Q is the rated flow of the gas equipment (0.425 m³/h) [47], and t₁ is the daily operating time of the cooking equipment.

The heating gas consumption q₂ was calculated based on the heating space, the heating area heat index, and the heating time [48].

$$q_2={\displaystyle \frac{3.5\beta A_0{t}_2}{H\eta }}$$

(2)

where β is the heat index for residential buildings, H is the lower calorific value of the gas, A₀ is the building’s heating space, t₂ is the equipment operating time for heating, η is the thermal efficiency of a gas boiler, and 3.5 is the conversion factor that takes into account the calorific value of the gas and the efficiency of the heating equipment.

The industrial biogas consumption was calculated by converting the energy usage of different energy types into biogas usage, considering the thermal efficiency of different energy equipment [48]. The daily biogas energy consumption of an industry q₃ can be expressed as Equation (3):

$$q_3={\displaystyle \frac{\alpha H^{\prime }{\eta }^{\prime }}{365H\eta }}$$

(3)

where $H^{\prime }$ is the low calorific value of other energy sources, ${\eta }^{\prime }$ is the thermal efficiency of other equipment, and the other equipment represents small rural processing equipment, such as drying equipment or packaging equipment, and α is the annual usage of other fuels.

Thus, the rural biogas demand S_n can be calculated using Equation (4):

$$S_n=\left\{\begin{array}{c}{\displaystyle \frac{N\ast \sum q_n}{14.4}},n=\mathrm{1,2}\\ {\displaystyle \frac{N\ast \left(q_1+q_2\right)+N_0\ast q_3}{14.4}},n=3\end{array}\right.$$

(4)

where N is the number of residential households, N₀ is the number of industries, and 14.4 is the conversion factor that takes into account the methane content of biogas and the hourly load.

Table A1. Proportion of hourly energy consumption for cooking, heating, and small-scale industries.

Time (h)	Cooking (%)			Heating (%)			Small-Scale Industry (%)
	A1	A2	A3	B1	B2	B3	C1
1	0	0.07	0.34	4.78	2.83	8.87	0
2	0	0.07	0.17	4.48	2.83	8.09	0
3	0	0	0.43	4.56	2.66	7.05	0
4	0	0	0.35	4.48	2.39	6.09	0
5	0.74	0	3.03	4.48	0.53	5.81	0
6	10.09	0	6.62	4.78	0.35	6.06	0
7	9.79	0.20	2.11	4.71	0.62	5.52	0
8	3.41	4.03	0.36	4.54	1.95	3.35	10
9	0.45	7.46	0.37	4.36	1.33	0.96	10
10	0.59	5.21	2.04	3.48	1.77	0.39	10
11	16.77	4.42	21.27	3.90	1.77	0.36	10
12	18.40	16.57	11.66	3.80	2.83	0.57	10
13	2.82	13.80	0.63	3.13	3.28	0.61	10
14	0.89	5.28	0.63	3.10	2.83	1.10	10
15	0	2.77	0.14	2.29	2.48	1.25	10
16	0.89	1.98	0.47	2.74	2.83	0.78	10
17	12.46	4.16	3.74	3.90	2.66	0.50	10
18	18.84	16.37	11.85	4.12	7.09	0.89	0
19	3.26	12.34	23.13	4.82	10.19	1.43	0
20	0.59	2.11	9.51	4.85	14.08	4.31	0
21	0	1.58	0.74	4.54	14.44	5.88	0
22	0	1.06	0.24	4.78	9.12	9.58	0
23	0	0.40	0	4.78	6.29	10.37	0
24	0	0.13	0.17	4.57	2.83	10.19	0
Reference	[1]	[38]	[39]	[40]	[38]	[41]	[42]

lists the proportion of hourly energy consumption for cooking, heating, and small-scale industries. The biogas consumption rate under different scenarios was divided into several stages, and the relationship between biogas production and consumption was analyzed using the average consumption in these stages [49]. The data of hourly load of household cooking in different regions of China [1,38,39] and the data of hourly load of heating in different regions of China are used [38,40,41]. Assuming that a small-scale industry, once started, operates at and maintains a full load. Then, the energy consumption rate of the industry was related to the equipment’s operating hours [42]. Gaussian regression was used to describe the spatiotemporal distribution of the biogas consumption rates [50] (Equation (5)):

$$y_{\left(t\right)}=y_0+{\displaystyle \frac{A}{w\ast sqrt\left(pi/2\right)}}\ast exp\left(-2\ast {\left({\displaystyle \frac{x-x_c}{w}}\right)}^2\right)$$

(5)

where y₀ indicates the offset, A denotes the area, x_c denotes the center, w denotes the standard deviation, and y_(t) denotes the probability density of the Gaussian distribution.

In summary, the hourly dynamic demand for biogas in rural areas can be expressed as follows (Equation (6)):

$$Q\left(t_0\right)={\displaystyle \frac{24\ast S_n\ast y\left(t_0\right)}{{\sum }_{t=1}^{\infty }y\left(t\right)}}$$

(6)

where y(t₀) indicates the offset at t₀, and Q(t₀) denotes the hourly demand rate of biogas at t₀.

2.4. Model Validation Using Survey and Monitoring Results

2.4.1. Household Survey

To verify the accuracy of the model’s prediction of the total demand amount, field survey data from Chinese rural areas in five provinces were used. A questionnaire on rural energy consumption was designed to determine the energy consumption of Chinese rural households. It included questions on household information, types of energy sources, and annual energy consumption. Household energy consumption data were collected using face-to-face interviews with respondents. The survey sites were located in representative villages in five provinces (Sichuan, Jilin, Guangdong, Hubei, and Jiangxi), and the respondents were randomly selected. They had lived in the villages for more than 6 months a year. The geographic and economic conditions of the surveyed areas are presented in

Table 2. Geographical and economic conditions of surveyed areas.

Area	Location	Climate	Terrain	GDP per Capita (RMB)
Sichuan	Southwest inland	Subtropical monsoon climate	Mountain, Hilly, Plain, Plateau	30,679
Jilin	Northeast region	Temperate monsoon climate	Mountain, Plain	27,975
Guangdong	Southern China	Subtropical monsoon climate	Mountain, Hilly, Plain, Terrace	47,065
Hubei	Central China	Subtropical monsoon climate	Mountain, Hilly, Plain, Downland	32,914
Jiangxi	Eastern China	Subtropical monsoon humid climate	Mountain, Hilly	32,419

Data from [33].

. After the questionnaire collection, the Z-score was used for outlier detection. After data cleaning, the remaining valid questionnaires were 107 in Sichuan, 20 in Jiangxi, 97 in Jilin, and 119 in Hubei.

2.4.2. Biogas System Monitoring

The hourly consumption rate of biogas was verified with one year’s data of a village-scale biogas plant operating in a field. A village biogas plant located in Guangping, Deyang, Sichuan, southwestern China, was selected for the experiment. The plant was established on 25 February 2015 and began supplying gas on 6 April 2015. It has operated continuously and stably for 9 years. The biogas digester is a continuously stirred tank reactor with a fermenter volume of 80 m³ and a gas tank capacity of 30 m³. It supplies biogas to 52 rural households. The experiment was conducted after the system was operating stably and reliably. Fermentation feedstock was sourced from a pig farm adjacent to the biogas plant, consisting of manure and groundwater. The feedstock has been described in a previous study [51]. A semi-continuous feed was used, with 8 m³ (8% of total solids) of feedstock added to the digester for each feeding. A continuous stirred tank reactor (CSTR) is used in the project. The gas storage system adopts a low-pressure floating drum storage tank. When the gas capacity of the tank drops to a certain level, the feed is started.

Biogas production and supply data were recorded at 30-minute intervals using a root flow meter (QJYL-A-DN50S, Qianjia, Chengdu, China) synchronized with a volume adjustment meter. The data were transmitted to the information management system through remote measurement and control terminals. Regular monthly checks at the biogas plant ensured the consistent functionality of the data collection system.

2.5. Design of Production and Supply Scenarios

In order to analyze the regular change in the production and supply loads on a time scale, we assumed the direct combustion of biogas and created production and supply scenarios for villages, townships, and counties. We utilized the RBDM and the production data from case studies.

The procedure for developing the scenarios was as follows: To maximize the benefits of the biogas system, the amount of biogas consumed by users should be equal to or close to the amount produced by the plant, achieving a consumption-to-production ratio of 1. Therefore, we assume that the total amount of biogas produced is equal to that consumed. Based on the hourly load ratio of the RBDM, we derive the biogas consumption hourly load curve to analyze the production and supply dynamic load patterns at an hourly time scale. The representative production data for a feeding cycle (7 days) were selected from the case studies for the construction of the production and supply scenarios.

3. Results and Discussion

3.1. Results of the Demand Forecasting Model

Figure 1 shows the dynamic loads of rural biogas for village, township, and county scenarios. The regression coefficients of biogas demand in the stages are listed in

Table A2. Regression coefficients of biogas demand in different stages.

Type	Stage	Range	x	Regression Coefficient	Adjusted r2
Rural	I	22.00–3.00	22–24, 0–3	0	-
	II	3.00–9.00	3–9	y0 = 0.72 ± 0.52, xc = 6.64 ± 0.2, w = 2.28 ± 0.44, A = 24.69 ± 4.86	0.974
	III	9.00–15.00	9–15	y0 = 0.72 ± 0.52, xc = 11.63 ± 0.05, w = 1.79 ± 0.1, A = 69.82 ± 4.14	0.974
	IV	15.00–22.00	15–22	y0 = 0.72 ± 0.52, xc = 18.32 ± 0.05, w = 1.94 ± 0.12, A = 71.92 ± 4.42	0.974
Township	I	0.00–9.00	0–9	y0 = 850.01 ± 106.47, xc = 11.95 ± 0.2, w = 2.05 ± 0.55, A = 1950.16 ± 922.65	0.891
	II	9.00–14.30	9–14.5	y0 = 850.01 ± 106.47, xc = 13.91 ± 4.88, w = 8.76 ± 7.44, A = −7217.04 ± 7747.33	0.891
	III	14.30–24.00	14.5–24	y0 = 850.01 ± 106.47, xc = 19.73 ± 0.52, w = 4.6 ± 1.52, A = 5176.78 ± 6033.73	0.891
County	I	0.00–9.30	0–9.5	y0 = 12,515.38 ± 669, xc = 9.62 ± 0.17, w = 1.24 ± 0.75, A = −13,521.5 ± 7222.09	0.909
	II	9.30–15.00	9.5–15	y0 = 12,515.38 ± 669, xc = 15.53 ± 0.23, w = 4 ± 0.77, A = −110,999.32 ± 58,891.75	0.909
	III	15.00–24.00	15–24	y0 = 12,515.38 ± 669, xc = 16.85 ± 0.89, w = 8.12 ± 1.14, A = 186,157.88 ± 65,981.55	0.909

. The predicted annual biogas demand in the villages was 380.06 m³/household. The heating demand for biogas was 1.68 times higher during the heating season than during the non-heating season. The biogas demand for the small-scale industries was 0.15 times higher in the non-heating season and 0.06 times higher in the heating season. Consequently, heating was the dominant rural biogas demand, and seasonal changes significantly increased the biogas demand. The small-scale industry biogas demand increased slightly over time, which might have been due to the few small industries.

The distribution of hourly biogas demand during one day in the heating season in the township scenario is illustrated in Figure 1b. The biogas demand was divided into three intervals: Part A (0:00–9:30), Part B (9:30–14:00), and Part C (14:00–24:00). Parts B and C were the peak periods, accounting for 19.2% and 52.6% of the daily gas demand, respectively. The peak period of heating demand was from 18:00 to 8:00. The curve had a normal distribution, and the total demand accounted for 80.33% of the total daily heating demand. The heating demand increased in the evening and peaked at 21:00. Subsequently, it declined until 08:00 the next day, followed by a 9-hour period of low biogas demand. The proportions of biogas demand for heating and cooking in the three stages were 5.81, 0.73, and 3.3. Therefore, heating significantly increased the hourly biogas load in the townships and dominated the dynamic load curve, whereas cooking only affected the peak in Part B.

Townships had different energy demand characteristics in the heating and non-heating seasons; therefore, a seasonal analysis was required. During the non-heating season, the townships required energy only for cooking, and the energy demand characteristics were similar to the village scenario. Thus, the same biogas production strategy could be adopted. Due to the high heating demand in the heating season, the production strategy should be flexible in the stages. Part A had a low biogas demand for 9 h; thus, surplus biogas can be stored to meet the peak demand. Part B was a shoulder period, during which the hourly biogas production rate cannot be lower than the demand rate to ensure sufficient energy supply during peak periods. Part C exhibited a peak. Flexible adjustment and gas storage in tanks are required to meet the peak load.

Figure 1c shows the hourly gas demand for one day in the county scenario. The biogas demand was divided into three intervals: Part A (0:00–9:00), Part B (9:00–14:00), and Part C (14:00–24:00), with biogas demand proportions of 28.43%, 23.41%, and 48.16%, respectively. Parts B and C were the peak intervals of the day, with an average peak value of 35,670.82 m³. The dominant impact of the small-scale industry on the county load occurred in Part B. The demand increased by 5.31% when the number of industries doubled and by 47.78% when it increased by 10. As a result, a large increase in small-scale industries can exacerbate the midday peak, reducing the stability of the county’s biogas production strategy. Counties should provide a reasonable amount of biogas to small industries according to the output and utilize time-sharing pricing to ensure that small industries consume the biogas surplus.

3.2. Model Validation and Optimization

3.2.1. Validation and Optimization of Total Biogas Consumption

Figure 2a shows the energy types used by residents. LPG has been widely used in rural areas without gas pipelines because of convenient transportation [52]. In contrast, natural gas is only used in areas with higher economic development because of the high investment in laying pipe networks. The proportions of LPG use were 93.04%, 80%, and 63.87% in Guangdong, Jiangxi, and Hubei, respectively. In contrast, the proportions were low in Sichuan (19%) and Jilin (26.8%). Natural gas is commonly used in Sichuan and Guangdong, which have high economic development. The natural gas penetration rate was 51% in Sichuan and 2.61% in Guangdong. Biomass resources are a common source of energy for rural residents due to easy access [53]. However, since commercial energy is superior to biomass resources in terms of cleanliness, safety, and calorific value, the use of biomass has decreased rapidly in rural areas. Despite this, the use of biomass energy is approximately 70% in Jilin and Hubei. As shown in Table 2, the per capita income of Jilin and Hubei was generally lower than that of other regions. This economic factor may be the reason for the high proportion of biomass energy use in Jilin and Hubei. Due to China’s low-carbon energy development goals, the use of heavily polluting coal in rural areas has been nearly eliminated [54]. Coal use in Jilin and Hubei was only about 20%. These areas have low economic development. When biogas is utilized by direct combustion, it primarily replaces gaseous energy sources, such as LPG and natural gas. Among the five surveyed regions, Sichuan and Guangdong have the highest usage of gaseous energy, with an average share reaching 82%. Thus, the gas consumption data from Sichuan and Guangdong can be used to verify the accuracy of the total demand amount of RBDM.

As shown in Figure 2b, the predicted and actual biogas energy demands were highly consistent. The average relative error was only 11.45%. The reason why the predicted value was lower than the actual value may be that the forecast model only considers cooking energy. However, energy is used for many other purposes, such as heating and hot water. This additional energy demand was not adequately considered in the forecasts, resulting in low projections.

It was assumed that household energy consumption would double with an increase in family size. We analyzed the energy consumption of different family sizes in Sichuan and Guangdong to assess the potential relationship between the prediction accuracy of biogas and the family size. The results are listed in

Table 3. Relative error in the relationship between biogas consumption and family size in Sichuan and Guangdong.

Family Size	Biogas Consumption (m3)			Relative Error (%)
	Max	Min	Mean
2	864.35	108.04	413.52	8.09
3	1273.95	72.03	458.57	17.12
4	1176.47	20.17	394.90	3.76
5	864.35	36.01	370.11	2.69
6	864.35	15.13	376.68	0.90
7	1296.53	108.04	404.27	5.98
8	432.18	180.07	378.15	0.50

. As the family size increased from two to eight people, the energy consumption did not increase linearly. The amount of energy consumed in households with three persons exceeded that of households with four to eight persons. The likely reason is that the field survey did not distinguish between the number of people in a household and the permanent resident population. However, the predicted value of biogas did not differ significantly for different family sizes, and the average relative error was low (5.58%). In summary, the effect of family size on the accuracy of predicting biogas demand was negligible.

3.2.2. Dynamic Load Validation and Optimization

The comparison of the predicted and actual 1-year biogas loads for villages is shown in Figure 3. The actual and predicted values were highly consistent. On a typical day, the actual and predicted biogas load showed three peaks: morning (8:00), midday (12:00), and evening (20:00). As the temperature changed seasonally, the dynamic load fluctuated significantly. The predicted and actual loads were similar in spring and summer, but the actual load exhibited significant peak variations during the evening, with the peak-to-valley difference decreasing by 44.58%. The predicted and actual loads were consistent in the autumn and winter, but the predicted load lagged 2 h behind the actual load.

Many factors cause RBDM errors in different seasons. For instance, the busy season in farming increased the time people spent on agricultural production, reducing the use of gas equipment, which was one reason for the seasonal errors in spring and summer [55]. Additionally, the fewer daylight hours in winter increase the time residents spend at home, resulting in seasonal errors in autumn and winter [56]. The actual peak loads occurred at 6:00, 12:00, and 18:00 in spring and summer and 8:00, 12:00, and 19:00 in autumn and winter. The corrected proportions of the peak load during the entire day were 9.48%, 17.63%, and 9.9% in spring and summer and 7.14%, 13.84%, and 10.84% in autumn and winter. It is difficult to obtain data in rural areas, which are required to adjust seasonal factors. Therefore, we incorporated seasonal correction factors to improve the model’s accuracy and practicability. The factors are listed in

Table 4. Seasonal correction factors.

Month	Correction Factor
Spring	1.1223
Summer	0.8431
Autumn	0.9375
Winter	1.0972

.

3.3. Biogas Production and Supply Scenarios

The production and supply scenarios for villages, townships, and counties for one week are illustrated in Figure 4. Energy loss and insufficient gas supply occurred daily in the villages, townships, and counties. The average daily unutilized biogas values in these regions were 43.48 m³, 21.9 m³, and 21.93 m³, and the average daily gas shortage values were 8.43 h, 14.71 h, and 14.57 h, respectively. Previous studies used static data due to the lack of dynamic data on the hourly gas load in rural areas, as shown in Figure 4a. The unutilized biogas volume was 22.15 m³, and the gas shortage was 15.57 h. This scenario does not consider energy consumption characteristics in different rural areas, resulting in significant deviations from the actual data. This deviation may result in longer gas shortages and inappropriate strategies for biogas production. The adjustment strategy based on the RBDM significantly improved the stability of biogas production and supply compared to the static method. It increased the biogas production and supply stability by 64.81%, 11.11%, and 24.07% in villages, towns, and counties, respectively.

However, achieving a real-time balance between biogas production and supply is difficult in practice because it requires high technical and technological standards [57]. Therefore, using storage tanks is inexpensive and effective to reduce energy loss and gas shortage [58]. The stability of biogas consumption increased significantly by 67.85%, 53.37%, and 59.78%, and the energy utilization increased by 78.13%, 72.83%, and 73.87% when a 30 m³ gas storage tank was added to the production and supply systems of the villages, townships, and counties, respectively. As shown in Figure 4b, periods of gas shortage and long-term gas interruption occurred in the villages. Thus, storing the gas is an efficient measure. The rate of increase in biogas stability after adding a storage tank was higher in villages than in townships and counties. However, energy consumption in townships and counties was complex, resulting in an uneven distribution of gas storage or interruptions, as shown in Figure 4c,d. This imbalance may result in insufficient storage space or no storage. Therefore, it is difficult to obtain the optimal balance between production and supply using only storage tanks. It is also necessary to optimize biogas production (such as the feeding interval and amount) according to the energy demand to improve biogas production and supply stability.

Multiple factors affect biogas production, including temperature and the fermentation potential of raw materials. Therefore, biogas production may not match the predicted values, and residents may be unable to obtain sufficient biogas in the short term. Alternative energy sources, such as LPG, could be used to ensure a stable energy supply.

4. Conclusions

We proposed a novel dynamic biogas demand forecasting model with multiple variables (RBDM) to increase the accuracy of biogas load forecasts in rural areas where energy consumption data are lacking. A coupled analysis method was used for an efficient variable selection, and Gaussian functions were utilized to determine time-dependent variables and reduce the number of equations. The main conclusions are summarized as follows:

(i)

The predicted average biogas demand for villages, townships, and counties was 380.06 m³/a·household, 1019.28 m³/a·household, and 1076.43 m³/a·household, respectively. The peak consumption periods were 09:00–15:00, 14:30–24:00, and 15:00–24:00, respectively.

(ii)

The prediction error was 19.27% lower than that of the static model. The predicted gas consumption and dynamic loads were consistent with the actual values, and the relative error of gas consumption in villages was 11.45%. The model was optimized by incorporating seasonal correction factors to improve the load prediction accuracy. The seasonal correction factors were 1.1223, 0.8431, 0.9375, and 1.0972, respectively.

(iii)

The reasonable parameters of the RBDM increased the stability of production and supply of villages, townships, and counties by 64.81%, 11.11%, and 24.07%, respectively, significantly improving the reliability of biogas supply and energy utilization rate.

This study developed a novel framework for forecasting biogas dynamic loads in rural areas. More regional surveys and measurements are necessary to improve the accuracy of predicting biogas demands. Additionally, the collaboration between the RBDM and production models and the application of the RBDM in specific regions were not considered, indicating areas for further research.