A study for estimating reservoir transmissivity based on the recovery process of a wellbore water level after water injection: Numerical modeling of the temperature recovery component

The author reports a numerical modeling study considering the recovery process of a wellbore water level due to temperature recovery after water injection into a geothermal well. This study intends to estimate the transmissivity of a geothermal reservoir based on this recovery process. We assume that the real recovery process of a wellbore water level after water injection consists of two components: the component of pressure recovery in the geothermal reservoir and that of temperature recovery at each depth in the well. The former component can be estimated by modeling the latter component and eliminating it from the recovery process of a wellbore water level. The numerical model takes into account heat transfer due to advection in a well and conduction in rocks. Heat exchange between the well and rocks is estimated based on an empirical equation. The numerical techniques and code developed originally for this study are validated by referring to the analytic solutions of simplified problems and heat balance. The numerical solution of the recovering water level is characterized by the slope of the linear trend line defined in the Horner plot. Numerical experiments are demonstrated for revealing the sensitivities of this slope to both the dimensional and dimensionless parameters. An empirical equation is derived based on these numerical experiments.