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.

Automated summary

This paper introduces an approximation method for finite line source (FLS) solution in simulating geothermal systems, using a weighted sum of exponentials approximation of the Gaussian Q-function to obtain an approximate solution of FLS. The new approximation is proven to be sufficiently accurate for simulations and results in significant gains in computational speed. In one case, the computational time for 1000 evaluations of FLS solution was reduced from 3.52 seconds to 20 milliseconds.