A Fast Embedded Discrete Fracture Model Based on Proper Orthogonal Decomposition POD Method

Abstract

This paper presents a fast embedded discrete fracture model (EDFM) based on POD method to improve the computational efficiency. Firstly, this paper gives a brief review of EDFM and derive the form of functional equations of pressure vector or saturation vector for global equations, and this form indicates the dimension of the discrete dynamic system is about the number of cells. Then, the time costs of EDFM are analyzed in detail, and the analysis shows that reducing the order of global equations is critical to decrease the time cost. Finally, this paper derives the POD basis function expansion of the pressure or saturation vector and gives the new global equations with a low order. The accuracy and efficiency of the fast model is compared in case of different sample numbers and mode numbers, and the results show that the POD-based EDFM can significantly improve the computational efficiency while ensuring enough accuracy.