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Journal of Porous Media
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ISSN Imprimir: 1091-028X
ISSN En Línea: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v19.i8.30
pages 687-700

DETERMINATION OF NON-DARCY FLOW BEHAVIOR IN A TIGHT FORMATION

Yu Shi
Petroleum Systems Engineering, Faculty of Engineering and Applied Science, University of Regina, Regina, Canada, S4S 0A2
Zhengming Yang
Institute of Porous Flow and Fluid Mechanics, UCAS, Hebei, 065007, China; PetroChina Research Institute of Petroleum Exploration and Development, Langfang, 065007, China
Daoyong Yang
Petroleum Systems Engineering, Faculty of Engineering and Applied Science, University of Regina, Regina, Saskatchewan, Canada, S4S 0A2

SINOPSIS

A novel technique has been experimentally and theoretically developed and applied to quantify the non-Darcy behavior caused by boundary flow that adheres to the grain of the rock in tight oil formations. Experimentally, constant-rate mercury injection experiments are conducted to determine the distribution of the pore throat as a function of its radius for three core samples. The threshold pressure gradient is then obtained through a permeability test with water for an additional three core samples collected from the same formation. Theoretically, the total flow rate model is derived by integrating the flow rate of an individual throat with respect to its distribution function, while the modified Hagen−Poiseuille equation, which considers the effect of boundary flow in the microscale, is employed to characterize single-phase flow in low-permeability sandstone formations. Once the permeability and pressure gradient with non-Darcy effect have been obtained for the single-phase flow, the relative permeability equation of two-phase flow is correspondingly developed based on the modified capillary tube model. It is found from experimental results and theoretical models that both permeability and threshold pressure gradient are nonlinear functions of the pressure gradient in single-phase flow when the pressure gradient ranges from 0.0086 to 0.4323 MPa/m. Meanwhile, a larger pressure gradient is required to overcome the negative resistance due to the non-Darcy flow on the relative permeability curve. At water saturation of 60.2%, the oil relative permeability can be increased by 13.4%, while water cut is decreased by 17.2% with an increase of pressure gradient from 0.0200 MPa/m to its maximum threshold pressure gradient (i.e., 0.4323 MPa/m).


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