Validity of Linearized Colmation Models for Methane Migration and Smart Ventilation Design in Underground Mines

Colmation phenomena play a critical role in long-term gas flow through porous media, significantly influencing methane migration, mine ventilation efficiency, and emission control in both active and abandoned coal mines. In colmation modeling, three fundamental kinetic types are commonly distinguished, with the third kinetic providing a generalized nonlinear formulation capable of describing state-dependent and spatially variable permeability degradation. However, the strong nonlinearity of the coupled transport–colmation equations prevents the derivation of closed-form solutions, which necessitates the application of linearization techniques. In this study, gas flow with colmation governed by third-kinetics is analyzed with particular emphasis on methane migration in underground mining environments. Linearization of nonlinear kinetic terms is applied at the level of the coupled mass balance and colmation equations, resulting in an approximate form of Darcy’s law and an explicit analytical solution describing the evolution of the porous medium state. The primary objective of the study is to quantify the error introduced by the adopted linearization and to analyze its spatial and temporal propagation with respect to the nonlinear reference solution. A rigorous error estimation based on Taylor series truncation is developed, yielding an explicit criterion that defines the validity range of the linearized solution. The results demonstrate that the approximation remains reliable within the regime of weak colmation, while the associated error is locally generated and propagates through transport mechanisms without exhibiting uncontrolled growth.