A Picard-Newton approach for simulating two-phase flow in petroleum reservoirs

Abstract

In this work, we perform a comparative study of some of the most well-known approaches for solving the system of algebraic equations, obtained by discretizing the governing equations using the Finite Volume Method, for a three-dimensional two-phase (water-oil and water-gas) flow in an oil reservoir. We consider that the flow is isothermal, the fluids immiscible, and we take into account the compressibility of the fluid and the porous matrix. We also use a model of well-reservoir coupling for specified flow rates of injection and production. The solution strategies considered are the Fully Implicit Method, the IMPES Method, the Sequential Method, and a Picard-Newton Method, which represents the main contribution of this work. To illustrate the accuracy of the methods, we considered a two-phase flow in slab geometry, two-phase flow in a five-spot arrangement well, and gas production in a reservoir. For the cases simulated here, the Picard-Newton Method was able to correctly reproduce the flow physics with accuracy comparable to the other three methods.

Machine learning acceleration for nonlinear solvers applied to multiphase porous media flow

“…However, sequential methods have been gaining ground in recent years (Salinas et al, 2017a;Jiang and Tchelepi, 2019;Freitas et al, 2020). These type of methods are attractive because the multiphysics problem can be subdivided and each subproblem solved separately, which gives wide flexibility and extensibility.…”