Temperature distribution around a well during thermal injection and a graphical determination of thermal properties of the aquifer

Abstract

Analytical models of hot water injection into groundwater aquifers were developed in this study. Available analytical models of this problem assume that the caprock overlying the aquifer is of infinite thickness. However, many groundwater aquifers have caprock thicknesses of only a few meters. This paper shows two mathematical models which were developed to examine the influence of a caprock with finite thickness on the thermal response of an aquifer. In both models, the horizontal heat conduction in the caprock are considered. The first model (Model 1) assumed that the vertical temperature gradient in the caprock is linear, which can be approached in a caprock with a relatively small thickness. The second model (Model II) removed this restriction and allowed the vertical temperature gradient in the caprock to be nonlinear. For Model 1, a steady state and an unsteady state solution for the water temperature distribution surrounding an injection well were obtained. For Model II, a steady state and two unsteady state solutions for the water temperature distribution surrounding an injection well were obtained. One of the two unsteady state solution is for a short-time period and the other one is for a long-time period. ...