An approximation of the finite line source solution to model thermal interactions between geothermal boreholes

This paper presents an approximation of the finite line source (FLS) solution for the simulation of geothermal systems. The FLS solution requires the evaluation of an integral involving a product of the error function which cannot be solved analytically. An approximate solution of the FLS solution can be obtained using an approximation of the Gaussian Q-function in the form of a weighted sum of exponentials. The new approximation of the FLS solution is shown to be adequately accurate for simulations. Substantial gains in computational speed are obtained, in one case decreasing the computational time for 1000 evaluations of the FLS solution from 3.52 s down to 20 milliseconds.