Numerical modeling of flow processes inside geothermal wells: An approach for predicting production characteristics with uncertainties

One dimensional steady and transient numerical modeling for describing the heat and fluid dynamic transport inside geothermal wells has been conducted. The mass, momentum and energy governing equations were solved using a segregated numerical scheme. Discretized governing equations for the fluid flow were coupled and solved with a fully implicit step by step method. The mathematical formulation used suitable empirical correlations for estimating the convective heat transfer coefficients as well as the shear stress and the void fraction parameters. Heat conduction across the wellbore materials was solved by an implicit central difference numerical scheme using the tri-diagonal matrix algorithm (TDMA). The flow characteristics of producer geothermal wells (pressure, temperature, enthalpy, heat fluxes, etc.) at each depth node were computed. Analytical data reported in the literature were used to validate the numerical capability of the wellbore simulator developed for this study (GEOWELLS). This simulator, together with another computer code (ORKISZEWSKI), was applied for modeling the heat and fluid flow processes inside some wells drilled in Mexican geothermal fields. The simulated pressure and temperature profiles were statistically compared against stable measured field data (through the computation of the residual sum of squares and Chi-square). A good agreement between the simulated and measured profiles of pressure and temperature was consistently obtained, having the best matching results for the GEOWELLS predictions. An analysis of the sensitivity and uncertainty was finally conducted to estimate the confidence to be accorded the simulation results predicted by GEOWELLS. Matching the sensitivity to variations in some input parameters (e.g., pressure, temperature, enthalpy and void fraction) was examined. The void fraction was identified as one of the most important parameters that affect the GEOWELLS simulations for matching measured field data correctly.