Abstract
The objectives of this study are to develop a new approximate analytical solution for predicting drawdown temperature transient behavior of a fully penetrating vertical well in a radial composite reservoir system and to use it as a forward model for estimating the fluid flow and thermal parameters of the system by nonlinear regression. The analytical solution considers a radial composite reservoir model, where the inner zone may represent a skin zone and the outer zone represents an infinitely extended reservoir. The analytical solution for predicting sandface temperatures is obtained by solving the decoupled isothermal diffusivity (pressure) and temperature equations for the inner and outer zones by using the Boltzmann transformation. The convection, transient adiabatic expansion and Joule-Thomson heating effects are all considered in solving the temperature equation. The developed analytical solution is validated by using both a commercial non-isothermal numerical simulator and a semianalytical solution available in the literature for different synthetic cases. For estimating the system parameters by history matching of observed temperature and/or pressure data with the model, we use the Levenberg-Marquardt method. We investigate the impact of noise in temperature and/or pressure data on the estimated parameters by inspecting statistical measures such as confidence intervals and correlation coefficients between parameter pairs. It is observed that selecting proper initial guesses of parameter is critical for estimating reliable values of the parameters through nonlinear regression of temperature data because the parameters are more correlated in the temperature equation than in pressure equation. Hence, we provide an effective methodology based on semi-log analysis and log-log diagnostic plots of pressure and temperature data to obtain good initial guesses of parameters that will derive the nonlinear regression method to have refined optimized estimates. The results show that the rock, fluid and thermal properties of the skin zone and non-skin zone can be reliably estimated from sandface temperature transient data jointly with pressure transient data in presence of noise, recorded during constant-rate drawdown tests with our approximate solutions and effective methodology proposed for obtaining initial guesses of the parameters.
