A connection element method: Both a new computational method and a physical data-driven framework—-Take subsurface two-phase flow as an example

Abstract

In traditional reservoir simulation methods, the computational domain is often discretized into a grid system (FDM, FVM, FEM, etc.) or a mesh reduction system (point source solution, BEM, meshless methods, etc.). This paper develops a connection-based method, which uses connection elements to discretize the computational domain from the flow perspective (named as connection element method, CEM). Based on a generalized finite difference approximation of the pressure diffusion term, each connection element can be characterized by two parameters, namely connection transmissibility and connection volume. The connection transmissibility measures the diffusion capacity of the connection element, and the connection volume measures the volume of the connection element as a geometric entity. Then, the flow equation can be solved directly on the connection elements, by either a fully implicit scheme or a sequential coupled scheme. The fully implicit scheme solves pressures and saturations simultaneously with high accuracy, but the computational cost is very high when the number of connections is large. The sequential coupled scheme calculates the pressure at the nodes of connection elements at the coarse-scale, then solves the fine-scale saturation along the connection elements. In this way, high computational efficiency can be achieved with accuracy. Furthermore, CEM can efficiently and intuitively obtain the possible flow paths between connection elements and reveal the interaction between the nodes by the path-tracking algorithm in graph theory. In addition, CEM with a sequential coupled scheme can be regarded as a physical network framework with small degrees of freedom, as well as a good data-driven framework. In the end, two numerical examples and one field case are presented to demonstrate the superiority of the developed CEM.