Thermal Adaptive Implicit Method: Temperature Stability Criteria

We present new linear-stability criteria for the Thermal Adaptive Implicit Method (TAIM) for thermal multiphasic compositional displacement. The analysis is applied to the mass and energy equations. Moncorgé and Tchelepi’s work (2009) is based on the assumption of divergence-free total velocity, and accounts for compressibility effects. Our analysis shows that the criteria proposed do not guarantee oscillation-free numerical solutions in case of displacement that involves steep temperature and saturation fronts. We derive new criteria that result from the analysis of a simplified coupled pressure-temperature linearized system, obtained by decoupling from saturations and compositions unknowns. The new criteria explains instabilities that were undetected by the previous analysis. Moreover, we demonstrate through scaling analysis and numerical examples that for most problems of practical interest, a simple temperature stability criterion obtained by assuming incompressible multiphase flow is quite robust. The relationship between the full and simplified stability criteria is analyzed in detail. The methodology is demonstrated using several thermal-compositional examples, including Steam Assisted Gravity Drainage.