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

Huang, Haiying; Ayoub, Joseph A.

doi:10.2118/102715-pa

Cited by 125 publications

(66 citation statements)

References 61 publications

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“…3 does not apply at all flow velocities. In many studies (Fand et al 1987;Huang and Ayoub 2008;Seguin et al 1998a;Seguin et al 1998b), departures from Eq. 3 were observed at very high flow velocities.…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann Simulation of Non-Darcy Flow In Stochastically Generated 2D Porous Media Geometries

Newman

Yin

2013

SPE Journal

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It is important to consider the additional pressure drops associated with non-Darcy flows in the near-wellbore region of conventional gas reservoirs and in propped hydraulic fractures. These pressure drops are usually described by the Forchheimer equation, in which the deviation from the Darcy's law is proportional to the inertial resistance factor (b-factor). While the b-factor is regarded as a property of porous media, detailed study on the effect of pore geometry has not been performed. This study characterized the effect of geometry on the flow transition and the b-factor using lattice Boltzmann simulations and stochastically constructed 2D porous media models. The effect of geometry was identified from a large set of data within a porosity range of 8-35%. It was observed that the contrast between pore throat and pore body triggers an early transition to non-Darcy flows. Following a quick transition where the correction to the Darcy's law was cubic in velocity, the flows entered the Forchheimer regime. The b-factor increased with decreasing porosity or an increasing level of heterogeneity. Inspection of flow patterns revealed both steady vortices and onset of unsteady motions in the Forchheimer regime. The latter correlated well with published points-of-transition. In developing a dimensionally consistent correlation for the b-factor, we show that it is necessary to include two distinctive characteristic lengths to account for the effect of pore-scale heterogeneity. This finding reflects the fact that it is the contrast between pore bodies and throats that dictates the flow properties of many porous media. In this study, we used the square root of the permeability and the fluid-solid contact length as the two characteristic lengths.

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Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann Simulation of Non-Darcy Flow In Stochastically Generated 2D Porous Media Geometries

Newman

Yin

2013

SPE Journal

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“…If the reservoir is damaged, the damage mechanism should be taken into account when relating the non-Darcy skin to a b factor. For example, if the completion is damaged by an invading fluid, the derived b factor represents the altered rock rather than the uninvaded reservoir that is used to extrapolate back to the sandface, as assumed in the definition of skin (Van Everdingen 1953;Hawkins 1956;Hurst et al 1969).…”

Section: Resultsmentioning

confidence: 99%

“…Typically, the Forchheimer equation that considers both viscous and inertial impact is used to describe this phenomenon (Bear 1972). Recently, Barree and Conway (2004) and Huang and Ayoub (2008) showed that the b coefficient and Forchheimer equation have limitations, and proposed a new model with a plateau regime (Lai et al 2012).…”

Section: Introductionmentioning

confidence: 99%

A Different Perspective on the Forchheimer and Ergun Equations

et al. 2016

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The need to better estimate the performance of hydraulically fractured wells in shale-gas formations has focused attention on the description of the non-Darcy flow in the region of the hydraulic fracture near the borehole where the converging flow may be increasingly dominated by the inertia effect. The analogy between high-rate flow in proppant-filled hydraulic fractures-best described by the Forchheimer equation-and the flow of reactants in fixed beds or granular beds in catalysis-widely described by the Ergun equation-may offer insights on how to estimate the value of the coefficient b across the complete range of velocities (or, equivalently, Reynolds numbers). In this paper, we show that, although the value of b varies over a wide range depending on the porosity (/) and permeability (K) of the porous medium, the value of the product bK is confined in the range of 10 À5 to 10 À4 m, and a correlation is obtained with narrower uncertainty compared with published ones.

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“…The viscous porous resistance tensor is determined by the horizontal and vertical permeability of the sediment. The equations of the CFD model are included in the supporting information section S1 of the paper (CD- ADAPCO, 2015;Huang & Ayoub, 2008;Jongen, 1992;Liu et al, 2012;Reynolds, 1894;Schmitt, 2007;Shih et al, 1995;Versteeg & Malaasekera, 1995;Wolfshtein, 1969).…”

Section: High-resolution Cfd Modelmentioning

confidence: 99%

Riverbed Hydrologic Exchange Dynamics in a Large Regulated River Reach

Zhou

Bao

Huang

et al. 2018

Water Resources Research

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Hydrologic exchange flux (HEF) is an important hydrologic component in river corridors that includes both bidirectional (hyporheic) and unidirectional (gaining/losing) surface water‐groundwater exchanges. Quantifying HEF rates in a large regulated river is difficult due to the large spatial domains, complexity of geomorphologic features and subsurface properties, and the great stage variations created by dam operations at multiple time scales. In this study, we developed a method that combined numerical modeling and field measurements for estimating HEF rates across the riverbed in a 7 km long reach of the highly regulated Columbia River. A high‐resolution computational fluid dynamics (CFD) modeling framework was developed and validated by field measurements and other modeling results to characterize the HEF dynamics across the riverbed. We found that about 85% of the time from 2008 to 2014 the river was losing water with an annual average net HEF rates across the riverbed (Qz) of −2.3 m3 s−1 (negative indicating downwelling). June was the only month that the river gained water, with monthly averaged Qz of 0.8 m3 s−1. We also found that the daily dam operations increased the hourly gross gaining and losing rate over an average year of 8% and 2%, respectively. By investigating the HEF feedbacks at various time scales, we suggest that the dam operations could reduce the HEF at seasonal time scale by decreasing the seasonal flow variations, while also enhance the HEF at subdaily time scale by generating high‐frequency discharge variations. These changes could generate significant impacts on biogeochemical processes in the hyporheic zone.

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

Cited by 125 publications

References 61 publications

Lattice Boltzmann Simulation of Non-Darcy Flow In Stochastically Generated 2D Porous Media Geometries

Lattice Boltzmann Simulation of Non-Darcy Flow In Stochastically Generated 2D Porous Media Geometries

A Different Perspective on the Forchheimer and Ergun Equations

Riverbed Hydrologic Exchange Dynamics in a Large Regulated River Reach

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