Strategic Resource Planning for Sustainable Biogas Integration in Hybrid Renewable Energy Systems

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Rural communities and energy planners can directly apply the methodology developed in this study to optimize biogas production from locally available biomass resources. By implementing optimization strategies for biomass input and reactor sizing, communities can enhance the efficiency of their hybrid renewable energy systems, ensuring a stable and reliable energy supply.

Abstract

In response to the growing demand for sustainable energy and the environmental impacts of fossil fuels, renewable sources like biomass have become crucial, especially in regions rich in agricultural and animal waste. This study focuses on a real-life project in Aras de los Olmos, Spain, where solar, wind, and biogas from biomass serve as primary energy sources, supplemented by a hydro-based storage system to stabilize supply. Central to the research is optimizing biomass inflow to the biogas reactor—the primary controllable variable—to effectively manage the supply chain, maximize energy output, and minimize logistical costs. The study addresses practical challenges by utilizing real data on demand, truck capacities, and costs and employing robust optimization tools like Gurobi. It demonstrates how optimized biomass flow can secure energy needs during high demand or when other renewables are unavailable. Integrating technical and economic aspects, it offers a comprehensive and practical model for sustainable and economically viable energy production in rural communities. It provides a foundational framework for future renewable energy and optimized energy storage system studies.

1. Introduction

The transition to sustainable energy has spurred extensive research into renewable resources like biomass due to its environmental and economic advantages, especially in rural and off-grid areas. Studies have shown that integrating biogas production into renewable energy systems, particularly hybrid microgrids, can reduce reliance on diesel fuel, lower overall costs, and support sustainable rural electrification by effectively managing technical and economic factors [1,2,3,4,5,6,7].

For instance, ref. [1] investigated a hybrid microgrid for rural regions that integrates photovoltaic (PV), biogas, diesel generators, and battery storage. Their study analyzed technical and economic factors to optimize system configurations, demonstrating that higher biogas availability reduces reliance on diesel generators. This reduction reduces overall costs and emissions, supporting sustainable rural electrification through renewable integration. Similarly, ref. [2] proposed a distributed energy management framework for multi-microgrid systems integrating biogas, solar, and wind energy. They introduced an energy hub model that optimizes energy exchange between microgrids to enhance system efficiency. The research emphasizes biogas’s flexible role in meeting variable demands, especially during low solar and wind output periods.

Significant advancements in microgrid energy systems and biogas technology have been made in recent years, addressing technical and economic challenges highlighted in previous studies. For instance, ref. [8] introduced a method to optimize the size and location of renewable resources, including biogas, within electricity grids, emphasizing economic and environmental impacts and highlighting biogas’s role in balancing solar and wind fluctuations. Similarly, ref. [9] optimized a hybrid energy system combining biogas and photovoltaic plants for a rural Spanish community, achieving notable cost reductions and demonstrating the practical benefits of integrated systems. Moreover, by analyzing individual end uses and external factors, ref. [10] proposed a forecasting method that enhances microgrid energy management by aligning demand with generation.

These studies collectively showcase the potential of biogas as a critical component in resilient and efficient energy systems while highlighting areas for further exploration. However, these studies often focus primarily on the outputs—specifically the generated energy from biogas and its role in hybrid energy systems—while overlooking the biogas production process. This oversight neglects crucial factors such as enhancing the efficiency of biomass conversion into biogas, which is essential for a comprehensive understanding of biogas integration into renewable energy systems.

To address this gap, researchers have shifted toward optimizing biomass utilization, particularly animal manure and agricultural residues, as sustainable feedstocks for bioenergy production. Studies in this area [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25] explore technological advancements like gasification and anaerobic digestion to efficiently convert biomass into renewable energy. They highlight the significant role of manure and crop residues in achieving environmental goals within a circular bioeconomy framework by reducing greenhouse gas emissions and supporting sustainable agricultural practices.

For example, ref. [12] introduced a simplified model for optimizing biogas plants to supply energy based on demand, addressing challenges in renewable energy integration. Traditional biogas plants often operate at a constant full load, limiting their flexibility. They proposed a simplified model that uses only four parameters to address this, replacing the more complex standard anaerobic process model. This streamlined approach enables faster simulations and allows biogas plants to adapt more readily to fluctuations in energy demand. Experimental validation shows that this model maintains accuracy while significantly enhancing computational efficiency, making it suitable for real-time optimization in the renewable energy market.

Similarly, ref. [13] reviewed the life cycle assessment of biogas production from manure, highlighting both environmental benefits and challenges. Despite manure’s low energy potential and limited biogas conversion efficiency compared to other biomass sources, it remains an environmentally viable feedstock, especially when co-digested with other organic materials. They examined stages such as feedstock management, anaerobic digestion, and combined heat and power integration, noting that regional factors significantly influence environmental impacts. The study emphasizes that while manure-based biogas production has global potential, regional adaptations are necessary to maximize sustainability outcomes.

Furthermore, ref. [18] analyzed the technical challenges facing biogas plants in agriculture-heavy countries like Pakistan, noting that sector growth still needs improvement despite the substantial organic waste available for biogas production. Key issues include inadequate infrastructure, gas leakages, digestate management, and corrosion, which affect the sustainability and efficiency of biogas operations. The authors recommend design improvements, such as leak-proof piping, optimized digestate removal, corrosion-resistant materials, and government support, as essential for realizing biogas’s potential as a reliable renewable energy source in Pakistan and similar regions.

Additionally, ref. [22] optimized biogas production through co-digestion of canola residues and cattle manure, using the response surface methodology to enhance methane yield. Key factors—temperature, total solids concentration, stirring time, and inoculum ratio—were identified as crucial for biogas productivity. In different lab experiments, thermophilic conditions produced the highest methane yield, generating 403.63 l/kg of organic material. The study highlights the response surface methodology as an effective tool for optimizing anaerobic digestion parameters. It demonstrates that co-digestion under controlled conditions significantly boosts methane production, making it advantageous for renewable energy applications.

Despite these advancements, a common shortcoming remains the need for further integration of logistical challenges within a holistic system. While these studies advance the technological aspects of biogas production, they often need to fully address practical issues related to biomass sourcing, transportation, and storage. Handling perishable and bulky materials like manure presents significant difficulties that can affect the feasibility and sustainability of biogas projects. Many rely on simulations or controlled conditions without incorporating actual data, failing to account for the complexities of biomass logistics.

Recognizing these gaps, some research has focused on biomass logistics and supply chain optimization [26,27,28,29,30,31]. These studies address crucial operations such as harvesting, storage, pre-processing, and transportation, highlighting that logistics can account for a significant portion of biomass supply costs. For instance, ref. [27] developed a multi-objective optimization model for designing a sustainable biomass supply chain network, focusing on poultry waste. Their model integrates geographic information systems and the analytic hierarchy process to identify suitable biogas facility locations. The model demonstrates significant cost-effectiveness and environmental benefits by balancing profit maximization with minimizing transportation distances.

Similarly, ref. [28] developed a regional optimization model for biomass transportation, considering economic, social, and environmental costs. Using a mixed integer linear programming framework, they evaluated sustainable transportation costs for potential bioenergy plant locations, incorporating region-specific data on emissions, pavement damage, and traffic congestion. Their findings emphasize the importance of multimodal transport options (truck and rail) to reduce emissions and cost, highlighting the need for comprehensive cost evaluations to support sustainable biomass logistics.

Moreover, ref. [30] comprehensively reviewed biomass transportation and logistics, emphasizing its critical role in the bioenergy supply chain. They categorized research findings across multiple criteria, including logistics cost, transport distance, plant capacity, and system efficiency. The review highlights research gaps, such as the need for sustainable cost models that incorporate economic, environmental, and social factors and better alignment of logistics frameworks with the specific challenges of biomass supply chains.

However, existing efforts often operate in isolation from the technical optimization of energy system components, neglecting to comprehensively integrate biomass logistics and storage with biogas production’s economic and operational dimensions—especially under real-world constraints. Factors such as fluctuating biomass supply, transportation challenges, storage limitations, and variable demand profiles affect biogas-based systems’ viability and sustainability. As a result, it remains unclear how best to synchronize biomass procurement, reactor operation, and energy generation in practice.

To address this research gap, the present study develops a comprehensive model that tightly integrates biomass logistics—including transportation and storage management—with the technical and economic optimization of an existing hybrid energy system. Drawing on real-world data from a project in Aras de los Olmos (Valencia, Spain), this approach systematically accounts for transport distances, scheduling, and storage capacities along with their associated costs, captures real-life factors such as fluctuating biomass availability, generator downtimes, and infrastructural constraints, and balances biogas production with other renewables like solar, wind, and hydropower to mitigate intermittency.

The model enhances logistical efficiency, reduces biogas release, and improves energy reliability by uniting these upstream (biomass supply chain) and downstream (energy generation) processes. This holistic approach brings the framework closer to operational applicability, making it more robust and adaptable to varied conditions. Ultimately, the study bridges previous shortcomings by providing a resilient and integrated hybrid energy system better equipped to meet demand under realistic constraints, thereby advancing renewable energy solutions.

This paper is organized as follows. Section 2 presents the materials and methods employed in the study. In Section 3, the results for various scenarios are discussed. Following this, Section 4 discusses the impact of changes, variable sensitivity, and method limitations. Finally, Section 5 concludes the paper with key findings and implications.

2. Materials and Methods

In this section, the established renewable energy system designed to support the energy needs of a specific region is introduced. The system integrates sustainable resources such as biomass, solar, and wind energy. Biomass, sourced from local supplies, is the primary feedstock in biogas production for electricity generation, enhancing environmental sustainability.

The mathematical framework governing biogas production is then delineated, including the fundamental equations and constraints that define the system’s operational limits. This encompasses modeling the biogas production process, reactor dynamics, and the conversion efficiency of biomass to biogas, along with constraints imposed by reactor capacity and operational conditions.

Attention is subsequently focused on the biomass supply chain, highlighting strategies to ensure a consistent and cost-effective biomass flow to the reactor. This includes logistical considerations for transportation, storage, and feedstock management—all essential to maintaining system efficiency and sustainability through efficient supply chain management.

Finally, the problem is formally defined to address optimizing biomass input and reactor capacity, ensuring that energy demands are met reliably. Various scenarios are presented to evaluate the system’s performance under different conditions, such as fluctuations in biomass availability and energy demand. These scenarios provide insights into the system’s resilience and effectiveness in diverse operational contexts, comprehensively analyzing the renewable energy system’s capabilities and potential challenges.

2.1. Area and System Study

Aras de los Olmos is a small rural municipality in the Valencian Community of Spain, with fewer than 400 residents. Located at the end of a 20 kV power line, the area has experienced frequent outages and issues with electricity reliability. The municipality offers ideal conditions for renewable energy implementation, with available land for constructing wind, solar, and biogas plants, supported by its economy, which heavily relies on livestock farming, providing ample biogas feedstock. With a drop of over 100 m, the nearby river also creates a suitable location for a hydroelectric plant. These factors make Aras de los Olmos an excellent candidate for developing a hybrid renewable energy system that combines PV, wind, hydro, and biogas to ensure a reliable and sustainable energy supply.

The energy demand in Aras de los Olmos, along with Losilla, has been carefully tracked to improve the quality and reliability of the electricity supply. Data on the municipality’s energy consumption has been recorded over several years to identify patterns. On average, the city uses about 150 kWh of electricity per day, with peaks reaching 250 kWh during the busiest times. Weekly data show that most energy is consumed during daylight hours, with a noticeable drop around midday. Monthly consumption varies significantly, peaking in the summer months like August and dropping during the early part of the year, with an average of 120 MWh per month. Annual trends from 2019 to 2022 indicate a steady rise in energy use, with a projected growth rate of 1.4% per year. This gradual increase reflects the shift towards greater electrification and the community’s growing reliance on renewable energy sources.

The energy system established in Aras de los Olmos integrates multiple renewable energy technologies to create an autonomous and sustainable energy supply for the region. Figure 1 presents the designed system incorporating key components [32].

PV Power Plant (700 kW): A solar power plant equipped with a tracking system is a central component of the renewable energy mix. This PV installation captures and converts solar energy into electricity, contributing significantly to the local energy supply. The tracking system ensures that the solar panels are always positioned optimally to capture maximum sunlight throughout the day. The 700 kW capacity was chosen to account for future growth in energy demand as the minimum required power for the next 30 years, considering a 1.4% annual increase in consumption.

Wind Power Plant (200 kW): A wind power facility located in an elevated area captures wind energy and converts it into electricity. This plant diversifies the energy supply and ensures a stable flow of electricity even when other renewable sources may not be as effective.

Hydroelectric Power Plant (200 kW): A small-scale hydroelectric plant is integrated into the system, harnessing the power of flowing water to generate electricity. This facility adds a reliable, consistent energy source, especially during lower solar and wind availability.

The system includes two water tanks: an upper tank with a capacity of 20,000 m³ and a lower tank with a capacity of 4000 m³. These tanks are part of a pumped hydro storage system that stores excess energy. Water can be pumped from the lower to the upper tank when excess renewable energy is available, and it can then be released through turbines to generate electricity when demand is higher or other energy sources are insufficient.

A dedicated pumping station manages water movement between the upper and lower tanks. This station ensures the efficient operation of the hydroelectric component of the system, facilitating energy storage and release as needed.

Biomass Power Plant (200 kW): The biomass and biogas plant is another vital energy source. Local biomass is processed to produce biogas, which is then used to generate electricity. This facility adds to the overall sustainability of the energy system by utilizing organic waste and other renewable feedstocks available in the region.

Main Grid: The energy system in Aras de los Olmos is designed with the flexibility to operate autonomously or be connected to the general energy grid. This setup allows for energy independence during outages or low external supply while still being integrated into the broader network when necessary. Four 20 kV evacuation lines have been constructed to handle the high-voltage power transmission generated from renewable sources. These lines, capable of carrying up to 2.5 times the maximum power generated by the renewable plants, connect to the existing distribution infrastructure, which has sufficient capacity to accommodate the new power without extension. Additionally, three new transformer substations will be built to ensure proper voltage levels for local consumption, stepping down the electricity for homes and businesses. This dual functionality of regional autonomy and connection to the broader grid offers both resilience and efficiency to the system.

2.2. Biogas Production and Management

In this renewable energy system, the only controllable parameter is the biomass input to the biogas reactor, which is crucial for biogas production. This is because other energy sources, such as solar and wind, inherently depend on environmental conditions and are not directly controllable. Solar energy generation varies based on sunlight availability, which changes throughout the day and is influenced by weather conditions and seasonal patterns. Similarly, wind power generation depends on wind speed and is subject to fluctuations that cannot be regulated.

The system incorporates a hydroelectric component as an energy storage mechanism to balance these fluctuations. When solar panels or wind turbines generate excess energy, this surplus pumps water from a lower reservoir to an upper reservoir. During higher energy demand, or when solar and wind resources are insufficient, the stored water is released from the upper to the lower reservoir, driving turbines to generate electricity. This energy storage capability helps smooth out the variability of renewable energy sources, reducing reliance on the external grid and ensuring that energy needs can be met consistently.

However, the biomass input remains the most flexible and directly controllable parameter. By adjusting the amount of biomass fed into the biogas reactor, the system can ensure a steady production of biogas, producing electricity. This controllability allows for continuous energy generation even when solar and wind resources and hydroelectric storage are insufficient to meet demand. Biomass, therefore, plays a crucial role in maintaining the overall system’s stability and reducing dependence on the grid.

Since biogas production can be controlled by adjusting the biomass flow entering the digester, a more detailed analysis of the governing relationships is required. Understanding the dynamics between biomass input and biogas output is crucial for optimizing the system’s performance, ensuring consistent energy generation, and maintaining the efficiency of the overall process.

Biogas production in an anaerobic digestion system relies heavily on the quantity and characteristics of the biomass fed into the reactor. The total biomass input ($m_{Biomass}$) is a key factor, and only a fraction of that, known as volatile solids ($f_{VS}$), can be broken down by microbes to produce biogas. The percentage of $f_{VS}$ in the biomass is 80%, indicating that 80% can be converted into biogas.

Additionally, the conversion efficiency (${\eta }_{Conversation}$), which is 75%, represents the proportion of volatile solids converted into biogas during digestion. The mass of volatile solids that are converted into biogas each day ($m_{VS}$) can be calculated using Equation (1):

$$m_{VS}=m_{Biomass}\times f_{VS}\times {\eta }_{Conversation}$$

(1)

From this, the daily biogas production rate is calculated by considering the methanogenic capacity ($k_{Methanogenic}$), representing the volume of biogas produced per kilogram of volatile solids. In this case, $k_{Methanogenic}$ is estimated to be $0.228 {\mathrm{Nm}}^3/\mathrm{kg}$, meaning that 0.228 cubic meters of biogas is produced for every kilogram of volatile solids. The maximum potential biogas production rate can be calculated using Equation (2):

$$Q_{max}=m_{VS}\times k_{Methanogenic}$$

(2)

This gives the maximum potential biogas production rate at the start of the process on Day 1 ($Q_{max}$), reflecting the energy output when the system runs at full capacity.

However, biogas production does not remain constant over time. As the microbes digest biomass, the rate of biogas production gradually decreases. This time-dependent decay in biogas production is often modeled using an exponential decay function. The biogas production at any given time t can be described using Equation (3):

$$Q\left(t\right)=Q_{max}\times exp\left(-k\times \left(t-1\right)\right)$$

(3)

Here, $Q\left(t\right)$ is the biogas production at time t, $Q_{max}$ is the initial production rate (calculated previously), and k is a decay constant that governs how quickly biogas production declines. This exponential decay is essential because it reflects the actual behavior of anaerobic digesters: biogas production peaks shortly after the biomass is introduced and slowly tapers off as digestion continues. Therefore, understanding the time dynamics of biogas production is crucial for ensuring a consistent energy supply, especially when the system is integrated with other renewable energy sources, like solar and wind, which are less controllable.

Due to the use of animal waste from local farms, including rabbits, pigs, and chickens, the decay constant for biogas production is estimated to be around 0.135 [33]. This value reflects the relatively fast degradation of organic material in animal waste, leading to a quicker process than other biomass types.

Figure 2 shows the biogas production process for 1 kg of biomass over 30 days. The top graph illustrates the biogas production rate (${\mathrm{m}}^3/\mathrm{day}$), which starts high and gradually decreases following an exponential decay as the available biomass is consumed. By the end of the period, the production rate approaches zero. The bottom graph presents the cumulative biogas production (${\mathrm{m}}^3$), which steadily increases over time before flattening out as production slows. This indicates that most of the biogas is generated in the early days of the process, with diminishing returns as the digestion process progresses.

As seen in Figure 2, the retention time of the biomass is estimated to be 30 days. Retention time refers to the period during which the biomass remains in the digester for biogas production. The 30-day period ensures that most biodegradable material is fully broken down, maximizing biogas yield. This duration allows optimal digestion while preventing excess accumulation of undegraded material, ensuring efficient system operation.

As has been shown in Figure 2, the representation of cumulative biogas production over a given period is calculated using Equation (4):

$$Q_{Cumulative}={\displaystyle \sum }_{t_i}^{t_i+T}Q\left(t\right)$$

(4)

In this case, $Q_{Cumulative}$ represents the cumulative biogas produced between the starting time $t_i$ and the end time $t_i+T$. $T$ corresponds to retention time.

Converting daily biogas production equations into hourly values provides a more detailed and precise understanding of the system’s dynamics. Using hourly rates makes monitoring and managing fluctuations in biogas production throughout the day easier, especially when integrating biogas generation with other renewable energy sources like solar and wind. This allows for better matching energy supply with real-time demand, optimizing generator operation, and ensuring more efficient use of biogas, particularly during peak energy consumption or reduced availability of other energy sources. The hourly biogas production is analyzed with greater granularity, providing insights into the fluctuations in generation rates across different hours. This detailed perspective is crucial for optimizing energy supply and ensuring that demand is met consistently throughout the day, as described in Equation (5):

$$Q\left(t\right)={\displaystyle \frac{m_{Biomass}\times f_{VS}\times {\eta }_{Conversation}\times k_{Methanogenic}\times exp\left(\frac{-k}{730}\times \left(t-1\right)\right)}{24}}$$

(5)

The cumulative biogas production must account for each input over its retention time if there are different biomass inputs at various times. In this case, the equation would sum the biogas production from each input separately over the relevant hourly period. The generalized form of the cumulative biogas production is represented in Equation (6):

$$Q_{Cumulative}={\displaystyle \sum }_1^n{\displaystyle \sum }_{t_i}^{t_i+T}Q\left(t\right)$$

(6)

Figure 3 illustrates the biogas production over time for two biomass inputs: 20 tons at hour 1 and 10 tons at hour 400. The top graph shows the biogas production rate (${\mathrm{m}}^3/\mathrm{h}$), with two distinct peaks corresponding to the two biomass inputs. The first peak, larger in magnitude, reflects the higher input of 20 tons, while the second, smaller peak represents the 10-ton input at hour 400. After each peak, the production rate decreases exponentially as the volatile solids in the biomass are consumed. The bottom graph depicts the cumulative biogas production (${\mathrm{m}}^3$), showing a steady increase as the biogas is produced following each biomass input. As production slows down after both inputs, the cumulative production curve flattens, reflecting the complete digestion of the biomass over time. This highlights how the amount and timing of biomass inputs affect the production rate and the cumulative output of biogas.

Based on the daily biogas requirement, the total biogas needed for a year is calculated using Equation (7):

$$Q_{Total}=365\times Q_{Daily}$$

(7)

To ensure stable and continuous biogas production, Equation (8) must always hold:

$$Q_{Total}\le Q_{Cumulative}$$

(8)

By maintaining this balance, the system can consistently meet energy needs without falling short, ensuring a reliable and sustainable energy supply throughout the operation.

It is important to note that the available volume of waste is limited. According to data provided by the municipality, this volume is 9880 tons per year. To achieve optimal biogas production, exceeding this amount will not be possible. Therefore, the system must be designed to operate efficiently within this biomass availability limit, as expressed using Equation (9):

$${\displaystyle \sum }_{i=1}^N{m}_i\le M_{Available}$$

(9)

where $m_i$ is the mass of each biomass input, $N$ is the total number of biomass inputs, and $M_{Available}$ is the total biomass available annually (9880 tons).

Also, it is crucial to ensure that, at any given moment, the total volume of biomass in the reactor does not exceed the maximum capacity. This can be expressed using Equation (10):

$${\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^N{m}_i}{\rho }}\le V_{Reactor}$$

(10)

where $\rho$ is the density of the biomass, which is approximately $1000 \mathrm{kg}/{\mathrm{m}}^3$, and $V_{Reactor}$ is the maximum volume capacity of the reactor, supposed to be $812 {\mathrm{m}}^3$.

Now that we are familiar with the constraints of available biomass and the reactor’s capacity, it is necessary to explain the logic of biomass input and output in the reactor, which is why Figure 4 is referenced. After biomass enters the reactor, it remains throughout the retention time until all biogas is produced. As seen with the 250-ton input at hour 1, the biomass stays in the reactor until hour 730, when it is fully digested and then discharged, marking the end of the biogas production for that batch.

If additional biomass is added before the retention time of the previous input is complete, all inputs remain in the reactor until the final retention period is finished, as the different inputs cannot be separated. As shown in Figure 4, the second wave of inputs starts at hour 1460 with 250 tons, followed by additional inputs of 250 tons at hours 1610 and 1760. This causes the reactor’s mass to increase stepwise, reaching 750 tons after the last input. The mass remains constant until hour 2490 when 730 h have passed since the previous input; at this point, all biomass is discharged from the reactor.

It is important to note that at no point should the volume of biomass in the reactor exceed its maximum capacity. For example, in Figure 4, during the third wave of inputs, four entries of 250 tons are added at hours 3650, 3800, 3950, and 4100. However, only 62 tons from the last input at hour 4100 can be added to the reactor to stay within the reactor’s maximum capacity, and the remaining 188 tons are considered excess and are prevented from entering the reactor. The total biomass of 812 tons is then fully discharged from the reactor at hour 4830.

Corresponding to the input masses, the lower sections of Figure 4 display both the real-time biogas production and cumulative biogas production.

In the biogas production system, a storage tank with a capacity of $400 {\mathrm{m}}^3$ has been designed to store the biogas produced. Additionally, a minimum capacity of $50 {\mathrm{m}}^3$ must always be maintained to ensure that biogas is available in emergencies. Therefore, the storage capacity must always follow Equation (11) to ensure proper operation:

$$V_{Min}\le V_{Storage}\le V_{Max}$$

(11)

The biogas process involves managing supply and demand hourly, ensuring efficient utilization of biogas to meet all energy needs. Here’s the overall process:

The system compares biogas production with demand each hour. If production exceeds demand, the excess biogas is stored, provided the storage capacity is not exceeded; otherwise, the excess is released. When demand exceeds production, the system checks if stored biogas can cover the shortfall. It is used if sufficient storage is available; otherwise, unmet demand is logged. The storage system maintains a minimum level to ensure continuous availability.

The system continuously monitors key parameters to ensure efficient biogas production management, balancing supply and demand. Two indices are defined to measure performance. The first, the Unmet Demand Ratio (UDR), represents the ratio of total unmet demand to total demand. The second, the Released Gas Ratio (RGR), measures the ratio of total released gas to total biogas produced. These indices provide insight into the system’s efficiency in managing unmet demand and excess gas.

The closer the UDR is to one, the larger the portion of unmet demand. Conversely, as it approaches zero, it indicates that most of the demand has been successfully met.

For RGR, the closer it is to one, the more biogas has been released without being used to meet demand or stored. As it gets closer to zero, it indicates that most of the biogas has either been used to meet demand directly or stored efficiently.

2.3. Biomass Logistics and Transportation

Another key aspect of this research is the examination of the economic factors involved in biomass logistics. The cost model accounts for various expenses, including the cost of the biomass itself and the transportation costs associated with moving the biomass from local farms to the biogas reactor. These costs are critical in assessing the overall feasibility and efficiency of the system, as both the availability and cost of biomass and transportation logistics directly impact the sustainability and economic viability of the biogas production process.

All cost calculations are directly linked to the biomass input, incorporating both the cost of the biomass and the transportation expenses required for its delivery, as outlined in Equation (12):

$$Total Cost=\sum Biomass Amount\times Biomass Cost+\sum {\displaystyle \lceil \frac{Biomass Amount}{Truck Capacity}\rceil }\times Trip Cost$$

(12)

where Biomass Amount refers to the total biomass delivered to the reactor in each entry and Biomass Cost reflects the local availability of agricultural by-products, such as animal waste from nearby farms. It is set at USD 0.033 per kg due to its low market value. This cost is based on inquiries from local farmers, which aligns with other references [29]. Truck Capacity is the maximum amount of biomass a truck can transport per trip, and Trip Cost covers transportation expenses per trip, including fuel, labor, etc.

To simplify calculations and reduce computational load, the biomass input amounts are discretized to match standard truck capacities of 5, 10, 15, 20, and 25 tons. This ensures the model is easier to manage and simulates realistic logistics more accurately. The approach reflects practical transportation from farms to the reactor by aligning biomass inputs with full truckloads. It prevents the added cost of making trips for loads smaller than the truck’s capacity, optimizing transportation efficiency and reducing unnecessary costs.

In this case, Equation (12) is modified to Equation (13), which is now based on truck capacity. This equation also allows combining different truck types for a single biomass input, optimizing transportation by incorporating trucks with various capacities:

$$Total Cost=\sum Trip{s}_i\times Capacit{y}_i\times Biomass Cost+\sum \left(Trip{s}_i\times Trip Cos{t}_i\right)$$

(13)

where $Trip{s}_i$, $Capacit{y}_i$, and $Trip Cos{t}_i$ are the number of trips, the capacity of the truck, and the transportation cost per trip for truck $i$, respectively.

To calculate transportation costs, the general assumptions include a travel distance of 120 km (about 75 miles) and a driver’s wage of USD 25 per hour. Each trip, including loading, unloading, and driving, takes 4 h, resulting in a fixed driver’s wage of USD 100 per trip across all truck capacities. Insurance costs vary based on the truck’s capacity, reflecting the higher value and responsibility associated with larger trucks. Insurance costs are USD 50 for a 5-ton truck, USD 60 for a 10-ton truck, USD 70 for a 15-ton truck, USD 80 for a 20-ton truck, and USD 90 for a 25-ton truck. Additionally, permits and tolls are fixed at USD 35 per trip, while miscellaneous costs, covering communication and parking, are set at USD 30 per trip, regardless of truck size.

Thus, the total cost for transporting biomass varies by truck size, with a 5-ton truck costing USD 215, a 10-ton truck costing USD 225, a 15-ton truck costing USD 235, a 20-ton truck costing USD 245, and a 25-ton truck costing USD 255. These amounts represent the full transportation costs, ensuring efficient biomass delivery based on the capacity of each truck, and were provided based on inquiries from local transportation companies.

2.4. Optimization Approach

The objective function and subject constraints are established with the problem’s dimensions defined.

$O.F.=Min\left(Total Cost\right)$: The goal is to minimize the total cost, including the cost of biomass and transportation.

$Q_{Total}\le Q_{Cumulative}$: The constraint should ensure that the total biogas produced equals the required gas demand for the year. This guarantees that the cumulative biogas production meets or exceeds the energy needs, ensuring no shortfall in supply over the annual period. Naturally, the closer the total output is to the total demand, the less waste or gas will be released, minimizing losses and improving overall efficiency.

To address the potential gaps in the production schedule, it is essential to highlight that the first condition does not fully cover all the technical requirements. This is because, while the total biogas produced over the year might be more than the total demand, there could still be shortfalls during specific periods where production does not align with immediate demand. Therefore, another condition is necessary to ensure the energy demand is fully met without any unmet need.

$UDR=0$: This condition ensures that all energy demand is fully met without a shortfall. Essentially, this aligns with the first condition, which guarantees that the total biogas produced is sufficient to meet the annual gas demand.

${\displaystyle \sum }_{i=1}^N{m}_i\le M_{Available}$: This constraint represents the limitation on biomass availability. The total biomass used cannot exceed the available biomass defined by the municipality’s resources.

${\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^N{m}_i}{\rho }}\le V_{Reactor}$: This constraint refers to the reactor’s volume limitation. The total volume of biomass inside the reactor must not exceed the reactor’s maximum capacity to ensure efficient and stable biogas production.

$V_{Min}\le V_{Storage}\le V_{Max}$: This ensures that the biogas storage volume remains within the defined limits, between the minimum and maximum capacities. This maintains a buffer of stored gas for emergencies while preventing overflow from exceeding the maximum capacity.

In this study, the optimization problem is classified as a Mixed-Integer Nonlinear Programming (MINLP) model due to its distinct characteristics. The discrete nature of the problem arises from the use of fixed truck capacities (5, 10, 15, 20, and 25 tons), where the logistics of biomass transportation are discretized based on these specific truck sizes. Furthermore, the biogas production process follows an exponential decay pattern, introducing nonlinearity into the model. As a result, we are dealing with a MINLP problem where both the discrete logistics decisions and the nonlinear dynamics of biogas generation must be considered.

Given the complexity of the search space and the large number of potential scenarios, stochastic optimization methods such as genetic algorithms or particle swarm optimization may not be reliable or guaranteed to find the optimal solution. While these methods are effective in some contexts, they can struggle with the precision required for problems like this, where discrete and nonlinear elements are intertwined. To address this, numerical and computational methods, like those provided by the Gurobi optimizer, are preferred.

Gurobi efficiently solves the MINLP by optimizing the balance between transportation costs, biomass input, and biogas production to meet the energy demand while minimizing total costs. By leveraging Gurobi’s capabilities, the model accounts for the truck capacities’ discrete nature and biogas generation’s nonlinearity, resulting in a robust and accurate solution. This approach ensures that the optimization process is reliable and practical, meeting field-based constraints such as fixed truck sizes and the nonlinear production curve of biogas over time.

2.5. Considered Scenarios

Two scenarios have been considered to thoroughly examine the system’s performance, governing conditions, and equations. The first represents normal conditions, where the system supplies a fixed daily power demand. The second scenario addresses an emergency condition, simulating a situation where, for one month, other renewable sources are offline, leaving biogas as the only energy provider. This setup allows for a comprehensive evaluation of the system’s resilience under both standard and high-demand conditions.

Scenario 1: As mentioned, a 200 kW generator has been designated to produce biogas electrical energy. It has been planned for this generator to operate at its maximum capacity for 12 h each day, specifically during solar energy production from PV panels, which is not available due to the absence of sunlight. This ensures a continuous energy supply even during non-sunlight hours. In this situation, the needed electrical energy is calculated using Equation (14):

$$E_{Electrical}=P_{Electrical}\times t=200 \mathrm{kW}\times 12{\displaystyle \frac{\mathrm{h}}{\mathrm{day}}}=2400{\displaystyle \frac{\mathrm{kWh}}{\mathrm{day}}}$$

(14)

This is the total electrical energy needed per day. However, the generator’s efficiency requires more biogas energy input than electrical output. With an internal combustion engine coupled to a generator with an efficiency of 29%, the energy of biogas needed is calculated using Equation (15):

$$E_{Biogas}={\displaystyle \frac{E_{Electrical}}{{\eta }_{Engine}}}={\displaystyle \frac{2400\frac{\mathrm{kWh}}{\mathrm{day}}}{0.29}}=8276{\displaystyle \frac{\mathrm{kWh}}{\mathrm{day}}}$$

(15)

This is the actual energy that needs to be produced from biogas to supply the daily $2400 \mathrm{kWh}$ of electrical energy. To calculate how much biogas is needed, it has been assumed that the biogas contains 60% methane and has a lower heating value (LHV) of $5.6 \mathrm{kWh}$ per normal cubic meter $\left({\mathrm{Nm}}^3\right)$. The total biogas volume required is calculated using Equation (16):

$$Q_{Daily}={\displaystyle \frac{\%C{H}_4\times E_{Biogas}}{LHV}}={\displaystyle \frac{0.6\times 8276\frac{\mathrm{kWh}}{\mathrm{day}}}{5.6\frac{\mathrm{kWh}}{{\mathrm{Nm}}^3}}}=887{\displaystyle \frac{{\mathrm{Nm}}^3}{\mathrm{day}}}$$

(16)

This means that the system needs to produce 887 cubic meters of biogas per day to meet the energy demand. Based on this daily biogas requirement, all the requirements for optimizing the problem will be met.

Scenario 2: In the second scenario, it is assumed that other energy generators will be out of service in July, and the biogas system must operate continuously for 24 h a day to meet the energy demand. This scenario represents a significant increase in biogas consumption compared to the standard operation, where biogas only requires 12 h daily. The additional demand necessitates adjusting the system to maintain a constant energy supply.

The electrical energy required per day under this condition is calculated using Equation (17):

$$E_{Electrical}=P_{Electrical}\times t=200 \mathrm{kW}\times 24{\displaystyle \frac{\mathrm{h}}{\mathrm{day}}}=4800{\displaystyle \frac{\mathrm{kWh}}{\mathrm{day}}}$$

(17)

To generate this amount of electricity, the required biogas energy, considering the generator efficiency of 29%, is calculated using Equation (18):

$$E_{Biogas}={\displaystyle \frac{E_{Electrical}}{{\eta }_{Engine}}}={\displaystyle \frac{4800\frac{\mathrm{kWh}}{\mathrm{day}}}{0.29}}=16552{\displaystyle \frac{\mathrm{kWh}}{\mathrm{day}}}$$

(18)

Considering that biogas contains 60% methane and has an LHV of $5.6 \mathrm{kWh}/{\mathrm{Nm}}^3$, the daily biogas volume required is calculated using Equation (19):

$$Q_{Daily}={\displaystyle \frac{\%C{H}_4\times E_{Biogas}}{LHV}}={\displaystyle \frac{0.6\times 16552\frac{\mathrm{kWh}}{\mathrm{day}}}{5.6\frac{\mathrm{kWh}}{{\mathrm{Nm}}^3}}}=1774{\displaystyle \frac{{\mathrm{Nm}}^3}{\mathrm{day}}}$$

(19)

3. Results

After running the optimization process,

Table 1. Optimal results for Scenario 1.

No.	Trips (Tons)	Supply Step (h)	Bio. (Tons)	Generation (m3)	Released (m3)	Release (%)	Bio. Cost (USD)	Trans. Cost (USD)	Total Cost (USD)
1	1 × 15 + 97 × 5	90	500	500,312	175,969	35.17	16,500	21,090	37,590
2	1 × 20 + 59 × 10	146	610	611,893	287,543	46.99	20,130	13,520	33,650
3	1 × 25 + 44 × 15	195	685	688,431	364,092	52.89	22,605	10,595	33,200
4	1 × 25 + 39 × 20	219	805	809,658	809,658	59.94	26,565	9810	36,375

presents some of the top-performing cases from Scenario 1. These cases highlight the most efficient combinations of biomass transportation and biogas production, providing insights into how the system can meet energy demands at minimal cost.

From the results in Table 1, several key insights can be drawn:

In all cases, the total biogas generation exceeds the annual demand while ensuring zero UDR.

Different combinations of trips and truck capacities are used in each case. For example, the first case uses smaller trucks (5 tons) more frequently, whereas larger trucks (20 and 25 tons) are used in fewer trips in other cases. This indicates the trade-off between truck size and the number of trips required for biomass delivery. In each case, the first truckload arrives at the first hour to meet immediate demand and ensure proper storage levels.

The supply steps, ranging from 90 to 219 h, indicate the intervals between consecutive biomass feedings into the reactor. Each supply step remains shorter than the retention time, ensuring that the reactor does not need to be emptied within the study period. This allows for continuous production without disruption. Additionally, the first truckload is always larger than subsequent ones to fulfill initial demand and maintain the minimum storage threshold.

The release rate, which represents the percentage of biogas released rather than stored or consumed, increases as the total biomass and generation grow. For instance, the release rate goes from 35.17% in the first case to 59.94% in the fourth, highlighting that higher generation tends to release more surplus biogas. Moreover, the reactor’s maximum capacity is not reached in any case, indicating that the reactor operates below full capacity.

Table 1 provides a detailed breakdown of biomass and transportation costs for each case. While the biomass cost increases with the total biomass supplied, transportation costs decrease as the number of trips reduces with larger truck capacities. For example, the third case has the lowest total cost (USD 33,200) despite the slightly higher biomass cost due to reduced transportation costs.

A clear trade-off between truck capacity, number of trips, and total costs is observed. Cases with larger truck capacities require fewer trips, resulting in lower transportation costs, whereas smaller trucks have higher transportation costs but offer more flexibility in scheduling and logistics. This structure is because each case starts with a larger truck to ensure early demand is met, followed by smaller trucks to optimize the cost and logistics.

Figure 5 illustrates the process of meeting biogas demand over 48 h, showcasing how the system handles energy generation, storage, and release. The two cases (Case 1 and Case 3 from Table 1) demonstrate different supply patterns, charging, and releasing dynamics based on the available biomass input and storage capacity. In both cases, the system is designed to ensure that all demand is met, with any surplus biogas either stored or released when storage reaches its maximum capacity.

In both cases, biogas production, demand, and storage capacity balance are carefully managed through charging and releasing biogas when necessary.

Charging (green bars) begins when biogas production exceeds demand and the storage has available capacity. In both cases, the charging process starts around the same time (approximately hour 8). However, the difference lies in the storage and release patterns. In Case 1, storage fills up quickly, leading to earlier and more frequent releases of excess biogas (blue bars). On the other hand, in Case 3, the storage period is longer before releasing excess biogas due to the larger total biomass input, resulting in fewer but larger releases.

As the system works to meet demand, discharging (red bars) ensures the energy requirements are met when production is insufficient. In both cases, the storage never falls below the minimum reserve level, ensuring that the system can handle fluctuations in demand. The dashed line shows that the system consistently meets demand, only drawing from storage when necessary.

The release rates in both cases are linked to how quickly the storage fills up. In Case 1, the release rate is lower (35.17%) because the system manages storage effectively with the smaller biomass input. In Case 3, the release rate is higher (52.89%) due to the larger biomass input, causing the storage to fill up faster and leading to more frequent releases of surplus gas.

The supply step is crucial. In Case 3, with a longer supply step (195 h), the system can operate for extended periods without restocking biomass, resulting in more stable charging and releasing patterns. Conversely, Case 1, with shorter supply intervals (90 h), requires more frequent interventions, potentially increasing operational complexity.

Figure 5 demonstrates how the system effectively balances biogas production, charge, and release to meet demand and efficiently manage storage. The system is designed to prevent wastage while ensuring a stable and reliable energy supply.

A new optimization was performed for Scenario 2, where other energy generators are assumed to be offline during July, necessitating a 24 h biogas supply. This adjustment led to changes in the biomass supply intervals to meet the increased demand. The optimized results for this analysis are presented in

Table 2. Optimal results for Scenario 2.

No.	Trips (Tons)	Supply Step (h)	Bio. (Tons)	Generation (m3)	Released (m3)	Release (%)	Bio. Cost (USD)	Trans. Cost (USD)	Total Cost (USD)
1	1 × 15 + 100 × 5	90/60	515	515,450	163,576	31.73	16,995	21,735	38,730
2	1 × 20 + 62 × 10	146/99	640	635,708	283,660	44.62	21,120	14,195	35,315
3	1 × 25 + 45 × 15	195/160	700	703,062	351,175	49.95	23,100	10,830	33,930
4	1 × 25 + 40 × 20	219/181	825	818,594	466,797	57.02	27,225	10,055	37,280

, showing the impact on biomass inputs, costs, and biogas generation efficiency.

The comparison between Table 1 (Scenario 1) and Table 2 (Scenario 2) highlights key differences that emerge under the distinct conditions of each scenario.

In Scenario 2 (Table 2), the biomass input is slightly higher across all cases compared to Scenario 1. For instance, in Case 1, the total biomass increases from 500 to 515 tons. This increased biomass reflects the need to meet the 24 h continuous demand during the one month when solar panels are out of service in Scenario 2.

The dual numbers in the supply step (e.g., 90/60 h in Case 1) indicate that biomass is supplied every 90 h throughout the year. Still, during the month when solar panels are offline, the supply must be increased to every 60 h to ensure continuous biogas production. This adjustment in Scenario 2 is necessary to maintain a steady biogas supply during the 24 h demand period.

The release rate in Scenario 2 is consistently lower than in Scenario 1, indicating that more biogas is utilized or stored rather than released. For example, in Case 1, the release rate decreases from 35.17% to 31.73%. This suggests that Scenario 2, with the extended demand period, results in more efficient use of biogas, as more of it is required to meet the continuous demand.

The biomass cost increases slightly in Scenario 2 due to the higher total biomass input. For example, in Case 1, the biomass cost rises from USD 16,500 to USD 16,995. Similarly, transportation costs increase in Scenario 2 because of the more frequent biomass deliveries required during the 24 h demand period.

The total cost in Scenario 2 is generally higher across all cases due to the increased biomass input and more frequent trips required to supply the reactor. For example, in Case 1, the total cost rises from USD 37,590 in Scenario 1 to USD 38,730 in Scenario 2. The higher costs reflect the need to maintain continuous biogas availability during the extended operational period.

Generally, Scenario 2 results in higher costs due to increased biomass input and more frequent deliveries. However, it also leads to lower release rates, indicating more efficient use of the biogas to meet the continuous 24 h demand during the solar panel outage period. While Scenario 2 incurs higher costs, it ensures that biogas is available for longer, maintaining a stable energy supply during the critical month.

A comparative examination of the biogas release rates and overall costs in Scenarios 1 and 2 reveals distinct efficiency patterns. Although both scenarios ensure adequate energy supply, Scenario 2′s continuous demand schedule leads to more effective use of biogas, as evidenced by its lower release rates (see Table 2). In contrast, Scenario 1′s intermittent demand cycle generally results in higher release percentages, indicating that excess biogas is vented to maintain safe reactor conditions. Despite the additional costs incurred in Scenario 2 to handle more frequent deliveries and increased biomass input, the net benefit of reduced venting translates into a more efficient energy utilization profile. These findings underscore the interplay between cost factors (transportation, biomass procurement) and operational outcomes (biogas usage versus release), offering a holistic view of how system design influences practical performance.

To evaluate the system’s performance during the high-demand month of July, where biogas is required continuously for 24 h daily, the generated and released biogas for Scenario 1 and 2 (focusing on Case 3 in each scenario) have been plotted in Figure 6. It demonstrates how the system responds to the demand in both scenarios. It highlights key differences in biogas generation and release patterns under these distinct operational conditions, noting that the demand has increased in one of the scenarios.

Figure 6 illustrates the generated and released biogas over time for Scenario 1 and 2; both focused on Case 3 during the high-demand period of July. In Scenario 2, where the biogas demand is continuous for 24 h, the system generates biogas at a higher and more frequent rate than in Scenario 1. The sharper declines in the generated biogas curves for Scenario 2 indicate a quicker depletion of biogas as the system tries to meet the constant demand. In contrast, Scenario 1 shows a more gradual usage of biogas due to the 12 h demand window.

In both cases, when production exceeds demand, biogas is released. However, in Scenario 2, the reduced amount of released gas highlights the system’s efficiency in utilizing more biogas to meet demand. Conversely, Scenario 1 shows higher release volumes, as surplus gas accumulates during the lower-demand periods, leading to more frequent releases. Overall, the comparison between these two scenarios demonstrates that during the high-demand month of July, the system in Scenario 2 can more effectively use biogas to meet the 24 h demand, with less surplus gas released.

4. Discussion

A detailed examination of biomass input and demand variations is essential to understand how fluctuations in biomass availability affect energy security and supply reliability. Increased biomass input leads to more stable biogas production, reducing strain on storage facilities and ensuring a consistent energy supply. Conversely, decreased biomass input may increase reliance on stored biogas, potentially leading to unmet demand if storage capacity is inadequate. These dynamics highlight the system’s resilience and adaptability to changing biomass availability.

Integrating renewable sources like solar and wind is crucial in managing energy supply fluctuations. During high solar or wind availability periods, dependence on biogas decreases, allowing excess biogas to be stored for future use. When solar or wind resources are limited, reliance on biogas intensifies, necessitating a robust supply chain and adequate storage. This variability underscores biogas’s vital role in offsetting the intermittency of solar and wind energy to maintain a balanced energy mix.

Addressing key variables such as biomass input, storage capacity, and demand levels provides insights into the system’s sensitivity to different factors. Varying biomass input directly impacts biogas availability: increased input stabilizes energy production, while decreased input heightens reliance on storage. Storage capacity is critical; extensive storage buffers against demand fluctuations, whereas limited storage may lead to unmet demand. High demand levels can stretch resources, requiring reliable biomass input and ample storage to ensure continuous energy supply.

Scenario analysis deepens our understanding of system resilience by testing conditions like unexpected outages in renewable sources due to severe weather conditions or technical issues. Seasonal changes may reduce biomass availability during certain months, increasing dependency on storage. Analyzing these cases helps identify periods when the system remains robust and when enhancements in storage capacity or alternative energy inputs are necessary to prevent shortages. This approach highlights potential vulnerabilities and guides investment decisions for capacity improvements or operational adjustments to ensure year-round performance.

Consideration of methodological limitations is also essential. Simplifications and assumptions within the model, such as fixed biomass input and ideal storage conditions, affect the accuracy of results. Biomass supply can vary due to seasonal changes, transportation delays, or availability constraints, impacting biogas production and storage levels. Assuming ideal storage conditions may overlook issues like degradation or leakage, affecting the actual volume of biogas. While necessary for model manageability, these simplifications could lead to differences between simulated results and real-world performance.

In addition to addressing seasonal and logistical constraints, several technological interventions can enhance the resilience and efficiency of biogas systems. Real-time monitoring and predictive analytics, using Internet of Things (IoT) sensors and machine learning algorithms, enable continuous tracking of biomass availability and demand fluctuations, allowing operators to optimize storage and schedule transportation proactively. Advanced pre-treatment techniques—such as enzymatic or thermal methods—can improve biomass degradability, thereby shortening retention times in the reactor and moderating the impact of seasonal shifts in feedstock quality. Meanwhile, adaptive energy management systems integrate real-time data from solar, wind, or other renewable sources and adjust biogas production dynamically to meet fluctuating demand. This seamless coordination ensures a stable supply of energy across peaks and troughs. Finally, logistics optimization tools, leveraging geographic information systems (GISs) and advanced routing algorithms, minimize transport costs and emissions while guaranteeing timely biomass delivery. By incorporating these strategies, biogas facilities can reduce waste, stabilize operations, and meet evolving energy needs despite seasonal and logistical hurdles.

The proposed model demonstrates significant scalability and adaptability, making it suitable for use in settings beyond Aras de los Olmos by incorporating real-world data and flexible constraints—such as biomass availability, reactor capacity, and transportation costs. For larger communities, scaling up reactor and storage capacities, optimizing transportation routes for higher volumes of biomass, and integrating additional renewable sources can enhance its effectiveness. At the same time, the modular nature of the framework readily accommodates regional variations in energy consumption patterns. For instance, the model can prioritize those energy sources in areas with abundant solar or wind resources and use biogas as a stabilizing component. In contrast, regions with extensive agricultural or livestock activities may maximize locally available biomass. However, numerical optimization methods like Gurobi can face challenges when dealing with extensive systems or real-time data inputs—particularly in discrete, nonlinear problems requiring substantial computational resources. Consequently, alternative computational approaches or model simplifications may be necessary to maintain performance as the system scales up. Future research could validate the model’s adaptability by applying it to diverse regions, including urban areas with higher energy demands and rural communities with varied resource availability. This balanced emphasis on technical feasibility and computational considerations underscores the model’s potential to facilitate broader adoption of hybrid renewable energy systems tailored to local conditions.

A key avenue for broader impact lies in aligning the proposed biomass logistics and hybrid energy framework with existing renewable energy programs and policies. Policymakers and energy agencies can be pivotal in fostering integrated energy systems by supporting infrastructure development that ensures a reliable biomass supply and stable biogas production. Policies promoting collaboration with renewable energy initiatives, such as integrating biogas with solar and wind systems, can enhance energy stability by addressing intermittency issues. Furthermore, incentivizing partnerships with agricultural sectors—particularly in regions rich in biomass residues or manure—can advance circular economy principles by transforming agricultural waste into valuable energy resources while reducing environmental footprints. Policy frameworks can encourage sustainable development and foster energy resilience by embedding biogas as a central component of broader renewable energy strategies.

In parallel, targeted economic policies are essential to making biogas projects more financially viable. Subsidies, tax credits, and grants can offset the high transportation, storage, and infrastructure costs, enabling wider adoption of biogas technologies. Coordinated financial strategies between energy providers, agricultural industries, and government bodies can also secure consistent feedstock supply and operational sustainability. Regulatory frameworks that reward reduced greenhouse gas emissions or offer preferential energy pricing for renewable sources further enhance the economic appeal of biogas. By emphasizing these economic incentives and reducing operational barriers, policymakers can align logistical efficiency with long-term profitability. This synergy between economic strategies and model-based optimization drives the adoption of hybrid energy systems, stabilizes rural economies and strengthens long-term energy resilience.

Practical considerations for real-world implementation are critical to ensuring the system’s reliability and efficiency. Variability in biomass availability—caused by seasonal harvest cycles, weather conditions, or transportation delays—can lead to fluctuations in biogas production and strain energy supply chains. Additionally, variations in biomass quality, such as differences in feedstock composition or moisture content, directly impact conversion efficiency and energy output. Effective storage management further complicates these dynamics, as issues like degradation or maintenance can reduce the usable volume of biogas, potentially affecting system performance.

While this study relied on real-world data from an actual project—limiting the scope for testing extensive variations—it recognized the importance of assessing the impact of fluctuating input variables. A comprehensive sensitivity analysis could address seasonal changes in biomass composition, generator efficiency variations, and storage limitations. Incorporating these analyses in future work would improve the model’s robustness, offering more profound insights into its adaptability across diverse operational contexts. Such refinements would help ensure the system’s resilience under real-world challenges and enhance its scalability for broader applications.

Moreover, increasing storage volume could significantly reduce gas venting and associated greenhouse gas emissions. Such an expansion, however, involves added construction costs and must be evaluated alongside the potential savings in fuel losses and environmental benefits. Optimizing reactor, generator, and storage dimensions from the outset—based on forecast demand and the potential for excess biogas production—can lead to a more integrated and cost-effective system design. In addition to sizing the biogas-related equipment, other system components, such as generators and storage units, must also be precisely sized. Only with all components operating at their best capacities can the system achieve maximum efficiency and resilience, effectively accommodating operational challenges in supply, storage, and energy generation. These practical insights highlight the importance of a comprehensive approach to system optimization, considering all components within the framework of real-world challenges.

In closing, this discussion of parameter sensitivity, methodological limitations, and practical implications provides a comprehensive understanding of the model’s strengths and areas for improvement. By addressing these aspects, the study underscores the potential of biogas as a stabilizing energy source. It outlines strategies for refining the model to enhance its applicability and reliability in diverse practical scenarios.

5. Conclusions

This study highlights the critical role of biogas production in hybrid renewable energy systems, emphasizing the importance of optimizing biomass logistics and storage management. By examining variations in biomass input, storage capacity, and energy demand, the research demonstrates how strategic resource planning can stabilize supply, minimize unmet demand, and reduce dependence on supplementary energy sources. Biogas proves essential in balancing the intermittency of solar and wind energy, ensuring a steady energy supply under varying conditions. The analysis also underscores the significance of biomass availability and storage capacity in enhancing system resilience, particularly during seasonal fluctuations and demand surges. Scenario testing reveals the system’s ability to address regular and emergency conditions, allowing operators to anticipate shortfalls and proactively adjust resource utilization. However, challenges such as inconsistent biomass supply and suboptimal storage conditions highlight the need for practical solutions in real-world applications.

Future research should expand optimization efforts to encompass the entire energy system. Ensuring optimally sized components—such as solar panels, wind turbines, biogas reactors, and storage facilities—can enhance overall efficiency and reliability. Adaptive models leveraging real-time data could further enable dynamic adjustments to biogas production and storage based on live fluctuations in biomass supply, demand, and renewable availability. Such advancements would streamline logistics, reduce biogas release, and improve energy availability, paving the way for a robust and flexible hybrid energy system that meets diverse operational requirements. Planning supply chains around these optimized parameters further strengthens energy security and system performance.

This study’s findings also have implications for making and future research. From a policy perspective, the results highlight the importance of coupling logistical optimization with renewable energy production—particularly in rural hybrid systems with abundant biomass resources. Policymakers could leverage these insights to design frameworks and incentives (e.g., subsidies for advanced logistical technologies) that encourage the co-development of biogas infrastructure alongside local agricultural operations, ensuring more sustainable energy access and rural development. In terms of future research, there is significant potential to explore adaptive control systems that harness real-time data to optimize biogas production and storage and investigate the model’s scalability in larger or more dynamic energy networks. Additionally, emerging technologies such as blockchain offer new avenues for improving supply chain transparency and traceability in biomass sourcing and distribution. By pursuing these directions, subsequent work can extend the applicability of the approach, fostering more resilient and sustainable renewable energy systems.