Comparison of Nonlinear Formulations for Geothermal Reservoir Simulations

Abstract

This study compared two nonlinear formulations for geothermal reservoir simulation. In particular, it looked at how the nonlinear formulation of the reservoir simulation equations affects the nonlinear behavior in simulation. Two nonlinear formulations were investigated: the natural formulation based on a pressure, temperature and saturation (pTS) and the molar formulation based on a pressure and enthalpy (ph). The main difference between the two formulations is that the natural formulation requires variable switching and the molar formulation does not. The two different formulations were implemented using Automatic-Differentiation General Purpose Research Simulator (AD-GPRS). AD-GPRS is a computational framework that allows for fully compositional and thermal reservoir simulations. This framework was modified to incorporate these two nonlinear formulations. A unified framework ensures that the differences observed in the nonlinear convergence of simulation are related to the specifics of nonlinear formulation and not to implementation issues. To verify the results of AD-GPRS simulations, analytical, semianalytical and TOUGH2 solutions were used to compare the results. Once consistency was verified, a comparison of the nonlinear behavior between the two formulations was carried out. This was quantified in terms of the time-step size and the number of Newton iterations that each formulation performs. The results from the numerical experiments showed that the performance of the variable formulations depends on the dominant flow regime.