The heat loss is solved using Equation from , where 𝑘 𝑒𝑓𝑓 is the effective thermal conductivity of rock/water porous media mixture, 𝛽 is a non-dimensional, time-dependent factor for heat transfer, 𝑇 𝑤 is the well casing temperature and 𝑇 𝑒 is the background, far-field temperature at depth equal to the product of geologic temperature gradient and depth plus the average surface temperature. It is assumed that the well casing and fluid heat transfer resistances are small compared to conduction through the rock and are thus neglected.