Modeling transient flow behavior with the high velocity non-Darcy effect in composite naturally fractured-homogeneous gas reservoirs

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A gas reservoir with composite properties contains two distinct regions, where one develops natural fractures and the other does not. To investigate the pressure transient behavior of the non-Darcy flow in composite naturally fractured-homogeneous gas reservoirs, a radial bi-zonal composite non-Darcy flow model was developed based on Izbash's equation. The inner region was considered as a dual-porosity medium to simulate the non-Darcy flow, whereas the outer region was considered as a homogeneous medium to simulate the Darcy flow. This model was solved using the Laplace transform, linearization and Stehfest numerical inversion. Then, the standard bi-logarithmic characteristic curves of the non-Darcy flow model were plotted. The flow stages were recognized and the influence of vital characteristic parameters on the transient behavior was analyzed and discussed in detail, such as the empirical constant, radius of the non-Darcy region, storage ratio, crossflow coefficient, etc. It is found that the values of the empirical constant n have a significant influence on the pressure transient behavior of the non-Darcy region. Moreover, three reduced models of the model proposed in this study were analyzed and discussed. Finally, it was found from the field application that this model had an excellent agreement between the measured and simulated pressure responses. The research results can be a helpful guide for researchers in the related fields when studying the transient behavior of high-velocity non-Darcy gas flow in composite naturally fractured-homogeneous gas reservoirs.