Our methodology uses analytical solutions to calculate electric power generation and offer insights into a geothermal reservoir's useful lifetime. These analytical solutions are also compared to a numerical solution, similar to the one in . The electric power generation is related to the produced fluid's flow rate and temperature. Therefore, in Secs. 2.1 and 2.2, we provide analytical solutions for the reservoir impedance and wellbore heat loss. The reservoir lifetime is related to reservoir heat depletion because power generation decreases with reservoir temperature. Therefore, in Sec. 2.3 we provide an analytical solution for reservoir heat depletion. Since comparison to the numerical solution is a key aspect of this study, we recap the numerical solution that we have previously used , which remains mostly unchanged in this work. Sec. 2.5 details how electric power generation is calculated. These electric power calculations use the same methodology as , except that the reservoir impedance comes from the analytical solutions (Sec. 2.1), and wellbore heat loss is included (Sec. 2.2).