Abstract
Darcy’s law is not suit for describing high velocity flow in the near wellbore region of gas reservoirs. The non-Darcy coefficient β 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 β 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 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.
Highlights
The Darcy law describes the flow of the subsurface fluid and shows the linear relationship between the pressure gradient and the volume flow (Darcy’s velocity)
The goal of our work is to obtain an inner relationship of the non-Darcy flow in porous media by a random fractal pore-scale network model
This study is limited to single-phase flow in isotropic porous media
Summary
The Darcy law describes the flow of the subsurface fluid and shows the linear relationship between the pressure gradient and the volume flow (Darcy’s velocity). Geertsma [1] conducted an experiment to establish the quantitative relationship between non-Darcy coefficient and porosity and permeability as well as influence of the immobile fluids on non-Darcy coefficients. Just from the short overview of the previous literature mentioned above, one can see that a lot of theoretical and experimental work was conducted to obtain different forms of non-Darcy coefficient expression, of which the main form is the quantitative relationship between permeability, porosity, and the non-Darcy coefficient. Due to the different methods applied as well as various porous media and fluids, the non-Darcy coefficient expressions are quite different [13,14,15]. The goal of our work is to obtain an inner relationship of the non-Darcy flow in porous media by a random fractal pore-scale network model. This study is limited to single-phase flow in isotropic porous media
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