POD Modeling for Gas Flow in Dual-Porosity Dual-Permeability Porous Media

Proper orthogonal decomposition (POD) method is introduced into numerical computations of shale gas flows in dual-porosity dual-permeability porous media. A POD projection model has been established. Although POD projection of the equations for matrix and fracture separately is correct in math while the mass conservation of matrix or fracture can be satisfied, artificial projection term caused by the mass transfer from matrix to fracture appears so that the mass conservation for the whole system cannot be guaranteed. Thus, the precision and robustness of the POD model are weak. To solve this problem, we propose a new projection manner that can guarantee the whole mass conservation of the matrix-fracture system. Numerical results show that the POD model can ensure high precision (mean relative deviation as low as 0. 8%) and fast computation (computational speed promoted 720 times) with strong robustness, after using the new projection manner.