Temperature distribution around a well during thermal injection and a graphical technique for evaluating aquifer thermal properties

Analytical solutions of temperature distribution are developed for the problem of thermal injection into a confined aquifer with a caprock of finite thickness. Heat transfer by horizontal conduction and convection within the aquifer and by vertical conduction in the caprock and bedrock is considered. Steady state and two asymptotic unsteady state solutions of temperature distribution around a thermal injection well are determined. One unsteady state solution is for short time periods and the other is for long time periods. The caprock thickness is only important in the long time period solution. A graphical technique is presented using hypothetical data for evaluationg four pertinent aquifer thermal properties: (1) the horizontal thermal conductivity of the aquifer, (2) the thermal capacity of the aquifer, (3) the vertical thermal conductivity of the caprock, and (4) the thermal capacity of the caprock. Field measurements of aquifer temperatures near the steady state condition are theoretically needed to utilize the graphical technique. In many practical situations a long time period is required to achieve a steady state condition. Therefore, a modified graphical technique employing an unsteady temperature distribution is illustrated and can be used to estimate the horizontal thermal conductivity and aquifer thermal capacity.