Simplified Analytical Model for Performance Prediction of Multistage Fractured Horizontal Well in Unconventional Tight Gas Reservoirs Considering Non-Darcy Flow in Unstimulated Regions

A common way to develop and exploit unconventional tight reservoirs is to use horizontal wells with multiple fractures. It has been postulated that in unconventional tight reservoirs as a result of hydraulic fracturing the stimulated region can be created near the hydraulic fracture. Recently, as practical alternatives to computationally intensive numerical models, analytical multi-linear flow models for unconventional tight reservoirs have been developed. In these models, fluid flow is assumed to obey Darcy's law. However, as unconventional tight gas reservoirs are characterized by widespread micro/nanoscale pores, non-Darcy flow typically occurs in the unstimulated region. In many unconventional tight reservoirs, despite their low permeability and the existence of the stimulated region, unstimulated regions can also affect the production significantly and thus it is necessary to consider the non-Darcy flow in unstimulated regions for modeling the reservoir production. In this paper, an analytical multi-linear flow model considering non-Darcy flow effect for unstimulated regions is proposed. Pseudo-time including pressure-dependent apparent permeability is introduced to derive the model. The pseudo-time is evaluated at the average pressure within the region of influence. The applicability of the model has been discussed. The model was validated by comparison with numerical simulation. It was found that the model's results are in reasonable agreement with the numerical simulation results and the average relative error is less than 15%. The model can be used to simulate the multistage fractured horizontal well production in unconventional tight gas reservoirs where the non-Darcy flow effect is significant for practical purposes.