Numerical Simulation of the Non-Darcy Flow Based on Random Fractal Micronetwork Model for Low Permeability Sandstone Gas Reservoirs

Abstract

Darcy’s law is not suit for describing high velocity flow in the near wellbore region of gas reservoirs. The non-Darcy coefficient $\beta$ of the Forchheimer’s equation is a main parameter for the evaluation of seepage capacity in gas reservoirs. The paper presented a new method to calculate $\beta$ by performing gas and con-water flow simulations with random 3D micropore network model. Firstly, a network model is established by random fractal method. Secondly, based on the network simulation method of non-Darcy flow in the literature of Thauvin and Mohanty, a modified model is developed to describe gas non-Darcy flow with irreducible water in the porous medium. The model was verified by our experimental measurements. Then, we investigated the influence of different factors on the non-Darcy coefficient, including micropore structure (pore radius and fractal dimension), irreducible water saturation ( $S_{\text{wi}}$ ), tortuosity, and other reservoir characteristics. The simulation results showed that the value of the non-Darcy coefficient decreases with the increase in all: the average pore radius, fractal dimension, irreducible water saturation, and tortuosity. The non-Darcy coefficients obtained by the fractal method of microparameters are estimated more precisely than the conventional methods. The method provides theoretical support for the productivity prediction of non-Darcy flow in gas reservoirs.