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

2006 ◽  
Author(s):  
Haiying Huang ◽  
Joseph Adib Ayoub
Keyword(s):  
Porous Media ◽  
Darcy Flow ◽  
Flow In Porous Media ◽  
Forchheimer Equation

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

SPE Journal ◽  
2008 ◽  
Vol 13 (01) ◽  
pp. 112-122 ◽  
Author(s):  
Haiying Huang ◽  
Joseph A. Ayoub
Keyword(s):  
Porous Media ◽  
Flow Velocity ◽  
Resistance Factor ◽  
Darcy Flow ◽  
High Rate ◽  
Flow In Porous Media ◽  
Nonlinear Flow ◽  
Quadratic Term ◽  
Forchheimer Equation ◽  
Flow Rates

Summary 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, ß, in the Forchheimer equation, and whether the beta factor ß 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. Introduction The effect of non-Darcy flow as one of the most critical factors in reducing the productivity of hydraulically fractured high-rate wells has been documented extensively with examples of field cases (Barree and Conway 2004; Holditch and Morse 1976; Olson et al. 2004; Smith et al. 2004; Vincent et al. 1999). The inertia resistance factor, or the so-called beta factor, a parameter in the Forchheimer equation for quantifying the non-Darcy flow effect, is now routinely measured for proppant packs. 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 ß of a proppant pack should be constant over the range of flow rates of practical interests. The so-called non-Darcy flow in porous media occurs if the flow velocity becomes large enough so that Darcy's law (Darcy 1856) for the pressure gradient and the flow velocity, i.e.,(Eq. 1) is no longer sufficient. In Eq. 1, permeability k is an intrinsic property of porous media. To describe the nonlinear flow situation, a quadratic term was included by Dupuit (1863) and Forchheimer (1901) to generalize the flow equation, i.e.,(Eq. 2) is commonly known as the Forchheimer equation.

A Predictive Pore-Scale Model for Non-Darcy Flow in Porous Media

SPE Journal ◽  
2009 ◽  
Vol 14 (04) ◽  
pp. 579-587 ◽  
Author(s):  
Matthew T. Balhoff ◽  
Mary F. Wheeler
Keyword(s):  
Porous Media ◽  
Darcy Flow ◽  
Flow In Porous Media ◽  
Scale Model ◽  
Pore Scale ◽  
Pore Scale Model

scholarly journals Assessing Porous Media Permeability in Non-Darcy Flow: A Re-Evaluation Based on the Forchheimer Equation

Materials ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 2535
Author(s):  
Simon Tupin ◽  
Makoto Ohta
Keyword(s):  
Porous Media ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Darcy Flow ◽  
Forchheimer Equation ◽  
Experimental Conditions ◽  
Minimum Surface ◽  
Surface Samples ◽  
Permeability Evaluation

In a recent paper published in Materials (Castro et al., 2019), the permeability evaluation of triple periodic minimum surface samples was carried out experimentally. Darcy’s law was used under unsuitable conditions, resulting in an underestimation of the results. In this comment, we highlight the problem and propose a new estimation of the permeability using the Forchheimer equation, which is better suited to the experimental conditions.

A Criterion for Non-Darcy Flow in Porous Media

2006 ◽  
Vol 63 (1) ◽  
pp. 57-69 ◽  
Author(s):  
Zhengwen Zeng ◽  
Reid Grigg
Keyword(s):  
Porous Media ◽  
Darcy Flow ◽  
Flow In Porous Media

scholarly journals The effect of pore structure on non-Darcy flow in porous media using the lattice Boltzmann method

2019 ◽  
Vol 172 ◽  
pp. 391-400 ◽  
Author(s):  
Zhilin Cheng ◽  
Zhengfu Ning ◽  
Qing Wang ◽  
Yan Zeng ◽  
Rongrong Qi ◽  
...  
Keyword(s):  
Porous Media ◽  
Pore Structure ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Darcy Flow ◽  
Flow In Porous Media ◽  
Boltzmann Method

scholarly journals On an Asymptotic Model for Free Boundary Darcy Flow in Porous Media

2020 ◽  
Vol 52 (5) ◽  
pp. 4937-4970
Author(s):  
Rafael Granero-Belinchón ◽  
Stefano Scrobogna
Keyword(s):  
Porous Media ◽  
Free Boundary ◽  
Darcy Flow ◽  
Flow In Porous Media ◽  
Asymptotic Model
Sign in / Sign up

Export Citation Format

Share Document