where 𝑇 𝑖𝑛𝑗 is the temperature of the injection fluid and 𝑐 𝐹𝑙𝑢𝑖𝑑 is the working fluid's heat capacity. We assume that that heat extraction rate is constant (to be consistent with Equation ) and we substitute Equation 30 into Equation . While 𝑄 will actually decrease with time as the reservoir temperature decreases (assuming a constant mass flowrate), Equation will give approximate values of reservoir temperature at early time, before the temperature declines are substantial. We are most interested in temperature depletion at these early times. For later times, when the temperature depletion is large, the solution to Equation 29 will be conservative and over predict temperature depletion.