Study on a POD reduced-order model for steady-state flows in fractured porous media

Traditional modeling methods of the reduced-order model can not be directly applied to fracture-dominated flow in porous media, violating the mass-conservation nature. In this paper, a global reduced-order model for the steady-state flow in fractured porous media based on the embedded discrete fracture model is established for the first time by using the proper orthogonal decomposition combined with Galerkin projection method. Differing from the typical modeling method of the reduced-order model commonly used in the literature, the discrete matrix equations instead of the primary governing equations are projected onto the low-dimensional space formed by the basis functions. The proposed reduced-order model can successfully handle the coupled terms between the matrix and fracture media. The accuracy and robustness of the proposed model are verified for three complex fracture cases with different boundary conditions. The results show that the maximum relative deviation in these three cases is 8.07 x 10(-6)%, which can be negligible in practical applications. Additionally, the constructed global reduced-order model is more effective than the finite volume method (at least speed-up 10 times) among these test cases.