Enhanced Discretization for Improved Stability of Thermal Simulation

Abstract

Abstract Thermal simulation is notoriously more difficult than iso-thermal simulation due to the volatility of hydrocarbons and water in the reservoir. Moreover, thermal simulation typically involves injection of high temperature fluids relative to the reservoir and as such the simulator has to deal with sudden ‘shocks’ to the systems. The Finite Volume method with a two point flux approximation (TPFA), which is the industry standard discretization, is numerically robust for iso-thermal systems but ill-equipped to deal with shock waves of temperature and pressure propagating through the reservoir grid. Also, due to the nonlinearity of the governing partial differential equations (PDEs) and the instability of the phases introducing discontinuity in properties and their derivatives, nonlinear solvers such as Newton Raphson struggle to solve these systems. As a result thermal simulations are inherently more prone to time step reduction to reduce the nonlinearity of the problem. In turn this results in small time steps and long simulation times. In this paper we analyse the TPFA discretization for a Natural Variable Formulation and show it is failing to address rapid changes in phase states in reservoir grid cells. We present a set of modifications to the TPFA discretization based on the upstream direction that increase the robustness of the scheme without compromising physical results and may lead to dramatically improved performance.