Algebraic Dynamic Multilevel Method for Single-phase Flow in Heterogeneous Geothermal Reservoirs

Abstract

Accurate numerical simulation of coupled fluid flow and heat transfer in heterogeneous geothermal reservoirs demand for high resolution computational grids. The resulting fine-scale discrete systems--though crucial for accurate predictions--are typically upscaled to lower resolution systems due to computational efficiency concerns. Therefore, advanced scalable methods which are efficient and accurate for real-field applications are more than ever on demand. To address this need, we present an algebraic dynamic multilevel method for flow and heat transfer in heterogeneous formations, which allows for different temperature values for fluid and rock. The fine-scale fully-implicit discrete system is mapped to a dynamic multilevel grid, the solution at which are connected through local basis functions. These dynamic grid cells are imposed such that the sub-domain of sharp gradients are resolved at fine-scale, while the rest of the domain remains at lower (coarser) resolutions. In order to guarantee the quality of the local (heat front) components, advanced multiscale basis functions are employed for global (fluid pressure and rock temperature) unknowns at coarser grids. Numerical test cases are presented for homogeneous and heterogeneous domains, where ADM employs only a small fraction of the finescale grids to find accurate complex nonlinear thermal flow solutions. As such, it develops a promising scalable
framework for field-scale geothermal simulations.