ANALYTICAL MODEL OF NON-ISOTHERMAL TWO-PHASE FILTRATION OF OIL AND GAS

Abstract

Thermohydrodynamic well testing is widely used to evaluate the filtration properties of hydrocarbon reservoirs. However, the application of this method to characterize the near-wellbore zone under two-phase oil–gas flow remains a challenging task. Most existing analytical interpretation models have been developed for single-phase flow and therefore do not account for the competing thermodynamic effects associated with oil heating and gas cooling during throttling. As a result, the accuracy of estimating near-wellbore zone parameters is significantly reduced.The objective of this study is to develop an analytical model and an interpretation methodology that enable independent determination of the radius and permeability of the altered near-wellbore zone during two-phase oil–gas filtration.The proposed approach is based on a new analytical solution describing the transient temperature field. The solution is derived for a model with a steady-state pressure distribution and convection-dominated heat transport. Thermal conduction within the reservoir is assumed to be negligible compared with convective heat transfer, while heat exchange between the reservoir and the surrounding rock is neglected. The mathematical formulation additionally incorporates the Joule–Thomson effect and the adiabatic expansion effect.The proposed interpretation methodology employs a bilinear approximation of the temperature versus logarithmic time curve. The radius of the altered zone is determined from the time corresponding to the intersection of the two linear segments using the mass flow rates and volumetric heat capacities of the flowing phases. Subsequently, the permeabilities of the inner and outer zones are estimated from the slopes of the linear segments, taking into account the effective Joule–Thomson and adiabatic expansion coefficients of the oil–gas mixture.The analysis demonstrates that the combined thermal effects associated with oil and gas throttling produce a non-monotonic relationship between temperature and gas saturation. Validation of the proposed methodology using synthetic data generated by numerical simulations showed high predictive accuracy. The relative errors in estimating both the radius and the permeability of the altered zone did not exceed 5–6 %.The developed analytical model provides a physically based framework for the interpretation of thermohydrodynamic well testing data and can be used to determine the characteristics of the altered near-wellbore zone in oil and gas reservoirs.