Analytical Model for Rate-Transient Analysis of Shale Oil Wells Considering Multiphase Flow, Threshold Pressure Gradient, and Stress Sensitivity

Shale oil reservoirs exhibit ultralow permeability and complex pore structures, which result in non-Darcy low-velocity flow and cause permeability to be stress-sensitive. Moreover, two-phase flow of oil and gas frequently occurs during the depletion of shale oil reservoirs. Consequently, investigating the rate-transient behavior of shale oil wells necessitates comprehensive consideration of multiphase flow, threshold pressure gradients, and stress sensitivity. Although numerous analytical models exist for rate-transient analysis of multistage fractured horizontal wells, none of them simultaneously incorporate these critical factors. In this study, we extend the classical five-region model to incorporate multiphase flow, threshold pressure gradients, and stress sensitivity. The proposed model is solved using Pedrosa’s transformation, perturbation theory, the Laplace transform, and the Stehfest numerical inversion method. A systematic analysis of the influence of various parameters on the oil production rate and cumulative oil production is conducted, and a field case study is presented to validate the applicability and effectiveness of the model. It is found that the permeability modulus of the main fracture, the half-length of the main fracture, and the threshold pressure gradient of the unstimulated reservoir have a significant influence on cumulative oil production spanning 20 years. With a 100% relative input error, these parameters result in prediction errors of 23.77%, 16.65%, and 17.78%, respectively. In contrast, the threshold pressure gradient of the main fracture and the threshold pressure gradient of the stimulated reservoir have a negligible impact; under the same level of input error (100%), they cause only 0.36% and 0.48% prediction errors in the 20-year cumulative oil production period, respectively. This research provides an efficient and reliable framework for analyzing production data and forecasting shale oil well performance.