A computational method for determining segmental and overall geothermal gradients and geothermal heat flow values

A new computational method is presented which calculates geothermal heat flow values and geothermal gradients with more precision than permitted by previously published techniques. The data required are: geothermal temperature at a known depth, mean surface temperature, the rock types in the stratigraphic column and the thermal resistivity values for the different types of rocks. This method is valuable in areas that have no measured gradient values. Basic equation used was the Fourier heat transfer equation where is heat flux in μcal/(cm² s), ρ_i is thermal resistivity (°C s cm/μcal) and ∂T/∂x is the x component of the temperature gradient (°C/cm). The thermal resistivity was allowed to vary linearly with temperature ρ_i = ρ_i^o 1 + K_i (T − 30)] where ρ_i is thermal resistivity of the lithographic segment «iå at a temperature T, ρ_i^o is thermal resistivity at 30°C and K_i is the temperature coefficient of thermal resistivity. The procedure consisted of integrating the combined equation for heat flux in terms of temperature dependent resistivity.Two iterative solutions were used to simplify the calculations: exact and approximate. The heat flux for each well was assumed to be 1.0 HFU and segmental temperatures were calculated from the bottom (arbitrarily) up, until a surface temperature was obtained. The calculated surface temperature could then be compared with the mean surface temperature (MST). Correction in the heat flux value was made until the calculated surface temperature and MST agreed. An analysis of three deep Appalachian test wells was made and the results showed the critical importance of lithographic ordering and the temperature dependence of thermal resistivity upon calculated geothermal quantities.