Discussion of SPE 89325, "Beyond Beta Factors: A Complete Model for Darcy, Forchheimer, and Trans-Forchheimer Flow in Porous Media"

Batenburg, Diederik van; Milton-Tayler, David

doi:10.2118/0805-0072-jpt

Cited by 18 publications

(14 citation statements)

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“…Their data are concave downward, which they explain is caused by streamlining and partitioning in porous media at higher velocities. Batenburg and Milton-Taylor (2005) produced the data that disagreed with Barree and Conway and appeared to validate the Forchheimer model. However, Huang and Ayoub (2006) argue that the study of Barree and Conway (2004) was partially in a turbulent flow regime, whereas Batenburg and Milton-Taylor's (2005) data entirely in the turbulent regime.…”

Section: Introductionmentioning

confidence: 81%

“…Batenburg and Milton-Taylor (2005) produced the data that disagreed with Barree and Conway and appeared to validate the Forchheimer model. However, Huang and Ayoub (2006) argue that the study of Barree and Conway (2004) was partially in a turbulent flow regime, whereas Batenburg and Milton-Taylor's (2005) data entirely in the turbulent regime. Nonlinearities associated with the Forchheimer equation occur at velocities well before, and not related to, turbulence.…”

Section: Introductionmentioning

confidence: 81%

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Polynomial Filtration Laws for Low Reynolds Number Flows Through Porous Media

2009

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In this study, we use the method of homogenization to develop a filtration law in porous media that includes the effects of inertia at finite Reynolds numbers. The result is much different than the empirically observed quadratic Forchheimer equation. First, the correction to Darcy's law is initially cubic (not quadratic) for isotropic media. This is consistent with several other authors (Mei and Auriault, J Fluid Mech 222:647-663, 1991; Wodié and Levy, CR Acad Sci Paris t.312: 157-161, 1991; Couland et al. J Fluid Mech 190:393-407, 1988; Rojas and Koplik, Phys Rev 58:4776-4782, 1988) who have solved the Navier-Stokes equations analytically and numerically. Second, the resulting filtration model is an infinite series polynomial in velocity, instead of a single corrective term to Darcy's law. Although the model is only valid up to the local Reynolds number, at the most, of order 1, the findings are important from a fundamental perspective because it shows that the often-used quadratic Forchheimer equation is not a universal law for laminar flow, but rather an empirical one that is useful in a limited range of velocities. Moreover, as stated by Mei and Auriault (J Fluid 123 36 M. Balhoff et al.be the intrinsic Darcy permeability. A major contribution of this study is that the coefficients of the polynomial law can be derived a priori, by solving sequential Stokes problems. In each case, the solution to the Stokes problem is used to calculate a coefficient in the polynomial, and the velocity field is an input of the forcing function, F, to subsequent problems. While numerical solutions must be utilized to compute each coefficient in the polynomial, these problems are much simpler and robust than solving the full Navier-Stokes equations.

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Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 81%

Polynomial Filtration Laws for Low Reynolds Number Flows Through Porous Media

2009

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“…Nevertheless, how to derive the beta factor ␤ from experimental data is still controversial. In the August 2005 issue of JPT, there was a discussion by van Batenburg and Milton-Tayler (2005) and a reply by Barree and Conway (2005) regarding paper SPE 89325 (Barree and Conway 2004) on whether the beta factor ␤ of a proppant pack should be constant over the range of flow rates of practical interests.…”

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

“…One aspect of the discussion concerns the inertia resistance factor, or the so-called beta factor, ␤, in the Forchheimer equation, and whether the beta factor ␤ of a proppant pack should be constant over the range of flow rates of practical interests. The problem was highlighted in a recent discussion by van Batenburg and Milton-Tayler (2005) and the reply by Barree and Conway (2005) regarding paper SPE 89325 (Barree and Conway 2004) in the August 2005 JPT.This discussion in essence revolves around the applicability of the Forchheimer equation and whether the Forchheimer equation is adequate to describe the experimental results of high rate flow in proppant packs. In order to properly assess the arguments in this debate, and to get a better understanding of the state-of-the-art on non-Darcy flow in porous media in general, literature concerning the theoretical basis of the Forchheimer equation and experimental work on the identification of flow regimes is reviewed.…”

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confidence: 99%

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Applicability of the Forchheimer Equation for Non-Darcy Flow in Porous Media

2008

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The subject of non-Darcy flow in hydraulically fractured wells has generated intense debates recently. One aspect of the discussion concerns the inertia resistance factor, or the so-called beta factor, ␤, in the Forchheimer equation, and whether the beta factor ␤ of a proppant pack should be constant over the range of flow rates of practical interests. The problem was highlighted in a recent discussion by van Batenburg and Milton-Tayler (2005) and the reply by Barree and Conway (2005) regarding paper SPE 89325 (Barree and Conway 2004) in the August 2005 JPT.This discussion in essence revolves around the applicability of the Forchheimer equation and whether the Forchheimer equation is adequate to describe the experimental results of high rate flow in proppant packs. In order to properly assess the arguments in this debate, and to get a better understanding of the state-of-the-art on non-Darcy flow in porous media in general, literature concerning the theoretical basis of the Forchheimer equation and experimental work on the identification of flow regimes is reviewed. These areas of work provide insights into the applicability of the Forchheimer equation to conventional oilfield flow tests for proppant packs. Models for flow beyond the Forchheimer regime are also suggested.

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