| Gaia: | <p>Multiphase flow through porous media can be modelled as a complex system of partial differential equations. Such models can be used to optimize the recovery of oil and gas from subsurface reservoirs. In the case of highly viscous oils, thermal recovery techniques are typically used to enhance their extraction. To simulate this, models describing the flow of fluids (typically oil, water, and gas) are coupled with a model for heat flow. Thermal reservoir simulation entails solving these highly coupled systems. Their complexity and the computational effort needed to solve them motivate the need for highly efficient solvers.</p>
<p>In reservoir simulation, most of the computational time is spent on solving linearized systems with a preconditioned Krylov subspace iterative method. Industry-standard preconditioning techniques are based on the approach introduced by Wallis in 1983, the Constrained Pressure Residual method (CPR). This preconditioner is a two-stage process involving the solution of a restricted pressure system.</p>
<p>While initially designed for isothermal reservoir simulation, CPR is also the standard for thermal cases. However, its treatment of the conservation of energy equation does not incorporate heat diffusion, which is often dominant in thermal cases. We are interested in preconditioners specifically designed for thermal reservoir simulation. In this thesis, we present an extension of CPR: the Constrained Pressure-Temperature Residual (CPTR) method, where a restricted pressure-temperature system is solved in the first stage. To study the effects of both pressure and temperature on fluid and heat flow, we first consider a model of non-isothermal single-phase flow through porous media. For this model, we develop a block preconditioner with an efficient Schur complement approximation. Then, we extend this method for multiphase flow as a solver for the first stage of CPTR. We present a comparison of the algorithmic performance of the different preconditioning approaches under mesh refinement and parallelization.</p>
|
|---|