  This paper develops a new 2D/3D stochastic closed-loop geothermal system with
a random hydraulic conductivity tensor. We use the finite element method (FEM)
and the Monte Carlo method (MCM) to discrete physical and probability spaces,
respectively. This FEM-MCM method is effective. The stability for velocity and
temperature is rigorously proved. Compared with the deterministic closed-loop
geothermal system, a same optimal error estimate for approximate velocity and
temperature is obtained. Furthermore, a series of numerical experiments were
carried out to show this method has better stability and accuracy results.
