Numerical Study on Conditions for Generation of Periodic Wellbore Flows

Abstract

Periodic changes in wellhead pressure and production rates of production wells are observed occasionally and result in difficulties in connecting such wells into geothermal power plants. Revealing mechanisms of these periodic changes is useful for improving plant efficiency. Yamamura et al. (2017, Proceedings of the 42nd Stanford Geothermal Workshop) developed mathematical and numerical models of two-phase transient wellbore flow and successfully simulated generation of the periodic changes in production rates as a result of interference between shallower and deeper feed zones. This study demonstrates numerical solutions of the mathematical model using a redeveloped numerical code adopting an enhanced numerical technique. This code has improved numerical stability by adopting a fully implicit scheme that includes solving a large nonlinear system for advancing each time step, while Yamamura et al. (2017) adopted a semi-implicit scheme. Improving numerical stability, we have found that the periodic production can continue stably as seen in real geothermal wells in a wide range of model conditions that totally resulted in ceasing of production within several hours in the past study. A parametric study using the redeveloped code has revealed relationship between dimensionless parameters and wellbore flow pattern: stable constant flow, stable periodic flow, and unstable flow ceasing within several hours. The result of this study implies that generation of the periodic production is only controlled by contrast of specific enthalpy between two reservoirs supplying fluid to shallower and deeper feed zones, respectively.