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Summary

The velocity-pressure drop relationship in the near-wellbore region of high capacity gas and condensate reservoirs often deviates from Darcy's law. Furthermore, many naturally occurring porous media are anisotropic and often layered. This study is directed at combining these facts in developing a mechanistic understanding of non-Darcy gas flow in anisotropic porous media. Non-Darcy flow coefficients, permeabilities, and electrical tortuosities are measured in cores with layers both in the parallel and perpendicular directions to flow and in nonlayered, anisotropic cores. The presence of a connate water saturation decreases permeability in all cores but increases the non-Darcy coefficient significantly only in the perpendicular core. Both a macroscopic and a pore-scale network (microscopic) model of anisotropy are proposed. The product of permeability and non-Darcy coefficient is shown to be less anisotropic than either the permeability or the non-Darcy coefficient tensors in both experiments and simulations. In the microscopic model, the non-Darcy term has been found to be tensorial and proportional to the square of the superficial velocity at the macroscopic scale. As the pore-scale anisotropic parameter increases, the non-Darcy coefficient and tortuosity increase, but permeability decreases. Models show order of magnitude agreement with experimental data.

Introduction

Gas deliverability is one of the key issues in gas and gas-condensate reservoirs. The pressure drop in the near-wellbore region controls gas deliverability. Near-wellbore flow of gas or condensates in these reservoirs involve high Reynolds numbers (up to 100) and high capillary numbers (up to 0.01) in the presence of small amounts of water. The lowering of the pressure in this region can lead to condensate dropout which impedes the flow of gas. Understanding high Reynolds number and high capillary number flow is important to simulation and optimization of these reservoirs.

At low flow rates (e.g., Re<0.01), the flow in each pore is in the Stokes flow regime. The pressure drop across the porous medium is linearly proportional to the flow rate, i.e., Darcy's law is followed. At high flow rates, the pressure drop exceeds that predicted by Darcy's law. This phenomenon is known as non-Darcy flow, although sometimes referred to as high-velocity flow to imply the lack of a different flow regime.