Abstract
This study presents an advanced mathematical model that utilizes averaging methods to analyze the leaching process in hard porous soils.The model is predicated on the concept of a dimensionless pore diameter, a small parameter obtained by the ratio of the pore diameter to a characteristic length.This parameter serves as the foundation for a family of solutions within the model.The primary objective of this model is to investigate the limit of these solutions as the small parameter approaches zero.The mathematical framework employed involves a rigorous derivation of an averaged system of equations from the original set, accomplished by considering the limit as the parameter value diminishes.This method, while preferable for its precision, acknowledges the inherent challenges in justifying each step in complex nonlinear problems.Therefore, when stringent mathematical justification is unattainable, the solutions' postulated properties and the averaging rationale must be both physically and mathematically sound.This paper delineates the conditions under which such an averaging method is deemed physically reasonable for the mathematical model of the leaching process.The results underscore the efficacy of averaged models in simulating intricate chemical and physical phenomena within porous media.These models offer a balance between complexity and accuracy, proving crucial for informed decisionmaking in industrial contexts.The significance of this research lies in its contribution to refining mathematical models for the optimization of rare metal leaching processes.Such advancements are pivotal in enhancing both efficiency and precision in industrial production and related research endeavors.