Validation of Forchheimer's Law for Flow through Porous Media with Converging Boundaries

Venkataraman, P.; Rao, P. Rama Mohan

doi:10.1061/(asce)0733-9429(2000)126:1(63)

Cited by 31 publications

(8 citation statements)

References 8 publications

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“…Most of the laboratory‐scale experiments have involved gravelly type unconsolidated materials with the exception of Cornell and Katz [1953], who looked at a range of consolidated rocks, including sandstones, limestones, and dolomites. More recently, some two‐dimensional experiments have also been conducted using radially convergent permeameters [ Thiruvengadam and Kumar , 1997; Venkataraman and Rao , 2000; Reddy and Rao , 2006].…”

Section: Comparison Of Laboratory and Field‐scale Forchheimer Parametersmentioning

confidence: 99%

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Step‐drawdown tests and the Forchheimer equation

Mathias

Todman

2010

Water Resources Research

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[1] Step-drawdown tests (SDTs) typically involve pumping a well at a constant rate until a quasi-steady state (QSS) is observed in the drawdown response. The well is then pumped at a higher constant rate until a new QSS is achieved. The process is repeated for additional flow rates. Analysis involves plotting the QSS drawdowns against their corresponding abstraction rates and fitting a nonlinear empirical expression. A commonly used expression, the so-called Jacob method, contains a linear "formation loss" coefficient, A, and a nonlinear "well loss" coefficient, B. In this paper, an analytical formula is derived relating B to the Forchheimer parameter. The efficiency of the Forchheimer equation for simulating SDTs is demonstrated through four case studies. Quantitative guidance is given as to when the Jacob method can be used as an accurate alternative to numerical simulation of the Forchheimer equation. Finally, the four corresponding estimates of field-scale Forchheimer parameter are implicitly compared to those obtained from smaller scale laboratory experiments. Unfortunately, the comparison remains implicit due to uncertainty associated with quantifying effective well radius and aquifer formation thickness for the SDTs.

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Section: Comparison Of Laboratory and Field‐scale Forchheimer Parametersmentioning

confidence: 99%

“…Calculations are based on the Stage 3 parameter sets detailed in Table 1. MATHIAS AND TODMAN: STEP-DRAWDOWN TESTS W07514 W07514 vergent permeameters [Thiruvengadam and Kumar, 1997;Venkataraman and Rao, 2000;Reddy and Rao, 2006].…”

Section: Comparison Of Laboratory and Field-scale Forchheimer Parametersmentioning

confidence: 99%

Step‐drawdown tests and the Forchheimer equation

Mathias

Todman

2010

Water Resources Research

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“…(3) in a wide range of flow conditions. Thiruvengadam and Kumar (1997) and Venkataraman and Rama Mohan Rao (2000) modified the flow resistance law Eq. (3) so that it can be applied to flow through porous media with converging boundaries, where the hydraulic gradient varies in the streamwise direction.…”

Section: Previous Workmentioning

confidence: 99%

Discharge through a Permeable Rubble Mound Weir

et al. 2005

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The hydrodynamics of a rubble-mound weir are theoretically and experimentally examined. This type of weir is considered to be environmentally-friendly, since its permeability allows substances and aquatic life to pass through longitudinally. By performing a one-dimensional analysis on a steady non-uniform flow through the weir, discharge is described as a function of related parameters, such as flow depths on the up-and downstream sides of the weir, porosity and grain diameter of the rubble mound, weir length, etc. A laboratory experiment is carried out to determine the empirical coefficients included in the analytical model. The theoretical solution of the discharge is compared with the experimental data to verify the analysis. It is confirmed that agreement between theory and experiment is satisfactory for a wide range of flow conditions. The present study makes it possible to apply the rubble mound weir for practical use as a discharge control system. CE Database subject headings: Weirs; Open channel flow; Permeability; Rockfill structures; Porous media flow; Discharge coefficients.

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“…Applicability of this equation depends on the modelling accuracy of the Darcy and non-Darcy coefBcients. Extensive experimental studies have been reported in the literature on the behaviour of these coefBcients with different parameters such as media size (Huang et al 2013;Salahi et al 2015;van Lopik et al 2017), degree of packing (Boomsma and Poulikakos 2002;Dan et al 2016;Houben et al 2018), grain size distribution (van Lopik et al 2020), convergent angle (Thiruvengadam and Kumar 1997;Venkataraman and Rao 2000;Rao 2004, 2006;Pasupuleti et al 2014;, pore geometry (Macini et al 2011;Shao et al 2020) Reynolds number (Sidiropoulou et al 2007), maximum pore diameter (Huang et al 2020), etc.…”

Section: Introductionmentioning

confidence: 99%

Influence of fluid viscosity and flow transition over non-linear filtration through porous media

et al. 2021

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The present study investigates two important though relatively unexplored aspects of non-linear Bltration through porous media. The Brst aspect is the inCuence of viscosity variation over the coefBcients of the governing equations used for modelling non-linear Bltration through porous media. Velocity and hydraulic gradient data obtained for a wide range of Cuid viscosities (8.03E-07 to 3.72E-05 N/m 2 ) were studied. An increase in Cuid viscosity resulted in an increased pressure loss through packing which can be quantiBed using the coefBcients of the governing equations. CoefBcients of Forchheimer equation represent linearly increasing trend with the kinematic viscosity. On the other hand, coefBcient of Wilkins equation represents similar values for different Cuid viscosities and remained unaffected by the variation in packing properties. Obtained data were utilized to understand the nature of Cow transition in porous media. Behaviour of polynomial and Power-law coefBcient with variation in Cow velocity were also examined. Critical Reynolds number corresponding to the deviation of Cow from Darcy regime varies with the porous packing and was observed to be in the range of 0-100. CoefBcients of polynomial (Forchheimer) model were observed to be independent of the range of Cow velocity, whereas the Power law coefBcients are extremely sensitive to the data.

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Validation of Forchheimer's Law for Flow through Porous Media with Converging Boundaries

Cited by 31 publications

References 8 publications

Step‐drawdown tests and the Forchheimer equation

Step‐drawdown tests and the Forchheimer equation

Discharge through a Permeable Rubble Mound Weir

Influence of fluid viscosity and flow transition over non-linear filtration through porous media

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