Stability Criteria for Thermal Adaptive Implicit Compositional Flows

Abstract

Summary Linear stability analysis is performed for thermal/compositional displacement processes, and a concise statement of the stability limits is given. The discrete formulation is based on standard (low-order) space- and time-discretization schemes of the mass- and energy-conservation equations, which are widely used in general-purpose reservoir simulators. The analysis is applicable for thermal multicomponent multiphase flows and accounts for mass and heat convection, heat conduction, fluid compressibility, gravity, and capillarity. The derived stability limits reduce to those presented by Coats (2003a, 2003b) for isothermal compositional systems. The thermal-adaptive-implicit method (TAIM) stability criteria are tested thoroughly using a flexible thermal/compositional reservoir simulator based on the natural variable-set formulation. These numerical tests indicate that the obtained stability limits are quite sharp for a wide range of the parameter space. Specifically, small violations of these limits lead to unstable solutions for temperature and saturations. Moreover, small violations of the stability limits lead to significant deviations from reference solutions, and large persistent violations lead to completely unstable numerical results. Detailed analysis and extensive numerical testing indicate that a TAIM-based formulation, which uses the stability limits derived here as adaptive local criteria to decide whether to treat a variable as implicit or explicit, is a very promising approach for efficient simulation of thermal/compositional problems.