Numerical modeling of non-Darcy flow in near-well region of a geothermal reservoir

Non-Darcy flow behavior has been recognized as an important factor in fluid flow through porous and fractured rock, especially for the near-well region during high-flow-rate injection/production in a reservoir formation. The non-Darcy effect is mostly reported to exist in gas/oil fields due to the high flow rate of a gaseous fluid, but it has been increasingly suggested that liquid flow in a geothermal reservoir may also be influenced by the non-Darcy effect. In this study, non-Darcy well flow behavior is described using the Forchheimer equation, and a nonlinear finite element model is used to simulate the near-well performance in a geothermal reservoir with non-Darcy effects. Results show that by considering the Forchheimer flow in the near-well region, both the fluid velocity and the wellbore pressure are much different from the Darcy flow simulation and the production well pressure is sensitive to the non-Darcy flow coefficient. A series of pressure drawdown tests are simulated on a geothermal reservoir with liquid water, vapor and two phase mixture as working fluids. Thermodynamic properties of water are calculated by the latest industry steam table functions for determining the pressure/temperature-dependent fluid properties. The simulation results suggest that the ratio of fluid density to viscosity (ρ/μ) has significant impact on non-Darcy flow behavior in reservoir performance. The pressure drawdown increases 60% due to a 247% increase of ρ/μ in one of the well tests.