Implicit lattice Boltzmann flux solver: A novel mesoscopic numerical algorithm for geothermal reservoir simulation

Abstract

In this work, a novel implicit lattice Boltzmann flux solver (LBFS) for simulating geothermal reservoirs is developed. LBFS is a mesoscopic approach that uses the reconstructed lattice Boltzmann model to calculate fluxes on the cell interface, which has a more solid physics foundation. Compared with macroscopic methods that directly use mathematical approximations, the dynamic changes of pressure and temperature in a reservoir can be simulated more accurately with LBFS. Therefore, in the present work, LBFS is introduced into geothermal reservoir simulation for the first time, and a fully implicit temporal discretization was realized by using the proposed dummy scalar triplet method to assemble the sparse matrix. This means that the adopted time step can far exceed the limitation of the Courant-Friedrichs-Lewy condition. Several test cases are implemented to validate the present algorithm, including the Theis problem, one-dimensional fluid flow and heat transfer, and two-dimensional radial fluid flow and heat transfer in aquifers. Finally, a production-reinjection doublet system was simulated by using an unstructured mesh. All of the obtained results agree well with the corresponding analytical solutions.