Comparison of a Fully Implicit and Sequential Formulation for Geothermal Reservoir Simulations

Abstract

This study compared a fully implicit formulation and a sequential formulation for geothermal reservoir simulation. In particular, it looked at how the difference between these two formulations of the reservoir simulation equations affects the nonlinear behavior in simulation. The main difference between the two formulations is that in the fully implicit formulation, the mass and energy equations are solved together at the nonlinear level. While for the sequential formulation, the mass and energy equations are solved separately and coupled together with a coupling term. These two formulations were implemented using the Automatic-Differentiation General Purpose Research Simulator (AD-GPRS). AD-GPRS is a computational framework that allows for fully compositional and thermal reservoir simulation. This framework also has the capability of a general sequential framework that allows coupling between other forms of physics such as geomechanics or chemical kinetics. This unified framework ensures that the differences in performances can be isolated due to the difference in formulation rather than implementation issues. To verify the results obtained from AD-GPRS, analytical, semianalytical and TOUGH2 solutions were used to compare the results. Once consistency was verified, a comparison of the nonlinear behavior for the two approaches was carried out. The results were quantified in terms of the time-step size and the number of Newton iterations that each formulation would take. The results from the numerical experiments showed that the performance of these two approaches was model-dependent and dependent on the dominant flow regime.