A Similarity-Based Semi-analytical Solution for Recovery Performance Assessment of Unconventional Oil and Gas Reservoirs With Interfacial-Tension-Dependent Capillary Pressure Effects

Nanometer-pore characteristic of unconventional reservoirs significantly enlarges the impact of the role that capillary pressure (p_c) plays on the recovery mechanism. A growing number of research has been focused on understanding the high p_c effect in tight and ultra-tight reservoir systems, but mainly numerical simulation models and experimental studies are investigated. This work proposes an alternate, semi-analytical solution that readily applies to the analysis of production performance of multi-fractured horizontal wells in unconventional formations, capturing the phase behavior and fluid property-alteration effects under significant p_c influence found in these systems. Capillary pressure is considered as interfacial-tension (IFT)-dependent function that impacts fluid flow in the sense of phase behavior and fluid properties. To arrive at the solutions, the similarity method is applied to the governing system of multiphase partial differential equations, and the resulting system of ordinary differential equations is solved simultaneously for pressure and saturation via shooting method coupled with Runge–Kutta solver. The proposed solution is validated by matching against numerically simulated data generated by an in-house simulator. Both oil-dominate and gas-dominate examples are presented. We also apply the proposed method to examine the sensitivity of production performance to degree of undersaturation and critical saturations. Results show that the altered fluid property and phase behavior due to IFT-dependent p_c have ineligible effects on recovery performance of multi-fractured horizontal wells, and specific effects on production rates and producing gas–oil ratio also tie closely to the mobility of each phase.