Semianalytical stream-function solutions on unstructured grids for flow in heterogeneous media

This paper outlines a Boundary Element Method (BEM) for a piece-wise analytic solution of the Laplace (Poisson) equation for pseudo-steady state, single phase flow on unstructured, rectangular grids. The method models flow through a reservoir that has been segmented into interacting homogeneous rectangular regions; no further discretization of the solution space analogous to grid refinement in numerical schemes is required for improved accuracy. Previous work on pressure distribution modeling is extended to analytically capture the stream-function. Stream-function solutions can then form the basis for other performance measures, such as improved oil recovery efficiency estimation or tracer flow analysis. Moving beyond structured grids into unstructured grid geometry allows for advanced flexibility in problem development and improved efficiency in solution construction. The analytic approach avoids the need for numerical differentiation of the pressure field and particle tracking methods to recover streamlines. Capturing flow around thin impermeable barriers, without local grid refinement, is demonstrated to showcase the robustness of the technique in handling complex reservoir architecture.