Near Wellbore Characterization from Temperature Transient Analysis: Accounting for Non-Darcy Flow Effect

Abstract

Abstract Temperature transient analysis is evolving to implement the production induced thermal perturbations for reservoir and near wellbore characterization purposes. To observe strong temperature signals, temperature well testing often involve high drawdown, which may induce non-Darcy flow effect in the near wellbore region. The existing analytical solutions for temperature transient analysis generally assume Darcy’s law for pressure profiles, which can be invalid in both gas and oil productions. In this study, we derive an analytical solution for temperature transient analysis of slightly compressible fluid producing from a vertical well considering the non-Darcy flow effect. To validate the developed analytical solution, we model the sandface temperature signals analytically and verify the results with numerical simulation conducted under comparable conditions in non-damaged and damaged reservoirs. Good agreements are achieved between analytical and numerical modeling results under different production rates and non-Darcy flow coefficients. The non-Darcy flow effect significantly increases the sandface temperature variations during production, which approach to a constant increment for sufficient long production time. We develop a new permeability estimation method considering the non-Darcy flow effect, which is also applicable for damaged zone property and non-Darcy flow coefficient estimations. Two criteria to apply temperature transient analysis for non-Darcy flow effect evaluation are revealed as critical Forchheimer number and accuracy of the downhole temperature monitoring system. Sensitivity analyses reveal that the non-Darcy flow coefficient impacts the magnitude of the sandface temperature signals while the production rate affects the slope of temperature profiles in a semi-log plot. Based on the findings in this work, we build on the existing characterization procedures for temperature transient analysis and incorporate the non-Darcy flow effect to estimate the permeability and non-Darcy flow coefficient. For the cases presented in this study, the inversion process of temperature transient analysis can accurately estimate the reservoir and damaged zone permeabilities, as well as damaged zone radius (less than 10% errors). We also evaluate the non-Darcy flow coefficients with acceptable accuracies (less than 30% errors) in a field scale. With these improvements, the applicability of temperature transient analysis using analytical solutions can be extended from cases with limited sandface temperature signals of a few degC to stronger signals of 30-40 degC considering the non-Darcy flow effect.