Another difference comes in the way that heat is removed from the reservoir. In the analytical solution, heat is removed at a constant rate. In the numerical solution, a flow rate and injection Increasing flow rate (kg/s) 10 100 500 temperature are specified such that the initial heat removal rate matches the rate in the analytical solution. However, as the reservoir cools, the heat removal rate decreases. The numerical solution may be more realistic for sedimentary basin geothermal systems in this aspect, but the analytical solution represents a worst-case (i.e., cold) bound for heat depletion, especially at later times. Other differences between the numerical and analytical solutions may be due to differences in problem geometry. The numerical solution uses a 3D geometry with 1D, cartesian heat conduction from above and below the reservoir. In contrast, the analytical solution follows a 1D radial geometry, and the equivalent radius is adjusted to match the volume and surface area of the numerical solution (see Sec.