A combined method using Lattice Boltzmann Method (LBM) and Finite Volume Method (FVM) to simulate geothermal reservoirs in Enhanced Geothermal System (EGS)

With the development of industrial activities, global warming has accelerated due to excessive emission of CO2. Enhanced Geothermal System (EGS) utilizes deep geothermal heat for power generation. Although porous medium theory is commonly employed to model geothermal reservoirs in EGS, Hot Dry Rock (HDR) presents a challenge as it consists of impermeable granite with zero porosity, potentially distorting the physical interpretation. To address this, the Lattice Boltzmann Method (LBM) is employed to simulate CO2 flow within geothermal reservoirs and the Finite Volume Method (FVM) to solve the energy conservation equation for temperature distribution. This combined method of LBM and FVM is implemented using MATLAB. The results showed that the Reynolds numbers (Re) of 3,000 and 8,000 lead to higher heat extraction rates from geothermal reservoirs. However, higher Re values may accelerate thermal breakthrough, posing challenges to EGS operation. Meanwhile, non-equilibrium of density in fractures becomes more pronounced during the system's life cycle, with non-Darcy's law becoming significant at Re values of 3,000 and 8,000. Density stratification due to buoyancy effects significantly impacts temperature distribution within geothermal reservoirs, with buoyancy effects at Re=100 under gravitational influence being noteworthy. Larger Re values (3,000 and 8,000) induce stronger forced convection, leading to more uniform density distribution. The addition of proppant negatively affects heat transfer performance in geothermal reservoirs, especially in single fractures. Practical engineering considerations should determine the quantity of proppant through detailed numerical simulations.