Linear Optimization Model with Nonlinear Constraints to Maximize Biogas Production from Organic Waste: A Practical Approach

The excessive use of fossil fuels and the increasing generation of solid waste, driven by population growth, industrialization, and economic development, have led to serious environmental, energy, and public health issues. In light of this problem, it is crucial to adopt sustainable solutions that promote the transition to renewable energy sources, such as biogas. Although progress has been made in optimizing biogas production, there is still no adaptable model for various environments that allows for the determination of optimal quantities of different organic wastes, simultaneously considering their composition, moisture content, and control of critical factors for biogas production, as well as the biodigester’s capacity and other relevant elements. In practice, the dosing of waste is conducted empirically, leading to inefficiencies that limit the potential for biogas production in real scenarios. The objective of this article is to propose a linear optimization model with nonlinear constraints that maximizes biogas production, considering fundamental parameters such as the moisture percentage, pH, carbon/nitrogen ratio (C/N), substrate volume, organic matter, volatile solids (VS), and biogas production potential from different wastes. The model estimates the optimal waste composition based on the biodigester capacity to ensure balanced substrates. The results for the proposed scenarios demonstrate its effectiveness: Scenario 1 achieved 3.42 m3 (3418.67 L) of biogas, while Scenario 2, with a greater diversity of waste, reached 8.06 m3 (8061.43 L). The model maintained pH (6.49–6.50), C/N ratio (20.00), and moisture (60.00%) within optimal ranges. Additionally, a Monte Carlo sensitivity analysis (1000 simulations) validated its robustness with a 95% confidence level. This model provides an efficient tool for optimizing biogas production and waste dosing in rural contexts, promoting clean and sustainable technologies for renewable energy generation.