Local Thermal Non-Equilibrium Interfacial Interactions in Heterogeneous Reservoirs - Divergence of Numerical Methods to Simulate the Fluid and Heat Flow

摘要

This paper focuses on the impact that underground fluid velocity has in numerical algorithms used to model and solve fluid and energy flow problems in heterogeneous geothermal reservoirs. The discussion is based on the energy flow conservation equations for local thermal non-equilibrium conditions. The Integrated Finite Volume method is used here to illustrate this problem. The heat transfer from the solid matrix to the moving fluid at different temperature is modeled for several velocities and global different heat transfers. Especial attention is paid to the dynamic process of cold fluids injected into a reservoir at higher temperature: Water at 50°C is injected into a reservoir at 350°C; if the fluid migrates with constant speed through a permeable corridor from the injection point to a production zone, what is the fluid temperature profile? During the numerical simulation of coupled heat and mass flows in multiple porosity-permeability systems it is necessary to average highly variable physical parameters at the boundaries between different rock domains represented geometrically in a computational mesh. This can be effectively achieved using appropriate average techniques at the contact interfaces of the domains. The averaging process should represent also the correct behavior of the fluid velocity crossing different geologic areas of the reservoir. Therefore, the averages have a decisive influence on the numeric results of the reservoir simulation and in pressure test analysis. Many, if not all, numerical divergence problems arise from the fluid velocity value and the interfacial interactions at the boundaries of different continua. To understand the convergence behavior of the simulated temperature in the injection problem, a new analytical diffusion-convection model was created and its results compared to the finite volume method. A very stable, convergent differencing scheme emerges from this comparison. Two main objectives are achieved herein: the physical reason for the divergence of a numerical model, and the exploration of the range of validity of the local thermal equilibrium hypothesis during the injection of cold water into a hot reservoir.