Diffusion source function identification in the process of gas seepage in a coal seam

Through piecewise linearization, the control equation of gas migration in coal is simplified to a parabolic differential equation with time-dependent source terms, and under the corresponding initial conditions, boundary and additional conditions are used to obtain a definite solution to the unknown source function identification of the parabolic differential equation. A triaxial gas migration experimental device to measure the axial gas pressure of a specimen is independently developed, and a gas migration test of coal samples is performed. With the use of the fundamental equation solution, by substituting the definite solution conditions obtained in the experiment, the above equation is discretized into a system of linear equations, the Tikhonov regularization method and generalized cross-validation (GCV) method are employed to solve the obtained ill-conditioned linear system of equations, and the diffusion source functions in the seepage equation are identified. The results suggest that the unknown function identification method for the differential equation, which avoids measurement and analysis of the pore and fissure structures of coal samples, accurately and directly obtains the change trend of desorption–diffusion sources in the process of gas seepage and provides a new idea for the study of the coal seam gas migration process.