Stability Criteria for the Thermal Adaptive Implicit Method

Advisor

Hamdi Tchelepi

Abstract

The stability criteria for thermal reservoir displacements are derived using Von Neumann analysis. It is shown that when reduced to the isothermal form, we recover the stability conditions presented by Coats [5], [6]. The derived stability criteria are tested by violating the time step size in a 1-D, oil-water thermal simulator coded using MATLAB. The stability criteria can be used to decide the time step size for an IMPEST (implicit in pressure, explicit in saturation and temperature) formulation. The criteria account for explicit treatment of capillary pressure, viscous forces, and heat convection and conduction terms. The criteria can be used as a switching rule in an adaptive implicit thermal model.