SPE Annual Technical Conference and Exhibition 2004
DOI: 10.2118/89325-ms
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Beyond Beta Factors: A Complete Model for Darcy, Forchheimer, and Trans-Forchheimer Flow in Porous Media

Abstract: The limitations of Darcy's Law to a relatively small velocity region have long been recognized. A commonly accepted approach has been to use Forchheimer's equation, and its inertial flow parameter (ß), as an extension of Darcy's Law beyond the linear flow region. This "trans-Darcy" flow is especially important in hydraulic fracture conductivity calculations, where flow velocities in the proppant pack are much higher than in the surrounding reservoir. The computation and presentation of ß values as functions of… Show more

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Cited by 116 publications
(59 citation statements)
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“…Therefore, it is legitimated to consider respective flow rate as the onset of turbulent regime. At higher increments of flow rate, the permeability decreases which follows the trend introduced by Forchheimer in 1901 (Barree and Conway [2]). Finally, the last experiment at the basis flow rate showed that the porous media had not been changed during the tests and the permeability values in turbulent regimes can be used for characteristics of this regime.…”
Section: Test Profilesupporting
confidence: 69%
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“…Therefore, it is legitimated to consider respective flow rate as the onset of turbulent regime. At higher increments of flow rate, the permeability decreases which follows the trend introduced by Forchheimer in 1901 (Barree and Conway [2]). Finally, the last experiment at the basis flow rate showed that the porous media had not been changed during the tests and the permeability values in turbulent regimes can be used for characteristics of this regime.…”
Section: Test Profilesupporting
confidence: 69%
“…, (1) where q is the flow rate in cc/min and A is the cross section area of flow in cm 2 . In this equation, μ and dp/dL are fluid viscosity in cp and gradient of pressure loss in atm/cm, respectively.…”
Section: Introductionmentioning
confidence: 99%
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“…Forchheimer's equation fits some experimental data very well by Forchheimer (1901;1930) and others (Blake, 1922 Barree and Conway (2004;2005) for a minimum-permeability plateau has validity and are supported theoretically and numerically.…”
Section: Introductionsupporting
confidence: 63%
“…Even the Forchheimer equation remains subject to numerous criticisms as several authors 30 have doubted the ability of the quadratic term in this relationship to capture all flow regimes beyond the Darcy flow (viscosity dominated). It is not the aim of this article to further put the numerous empirical relations to test, but to use the Darcy and Forchheimer equations as functional relationships for analysis of the LBM simulation results to calculate the permeability and the nonDarcy coefficient.…”
Section: Empirical Relationships For Inertial Flow In Porous Mediamentioning
confidence: 99%