Effect of Convergence on Nonlinear Flow in Porous Media

Reddy, N. Bhanu Prakasham; Rao, P. Rama Mohan

doi:10.1061/(asce)0733-9429(2006)132:4(420)

Cited by 22 publications

(9 citation statements)

References 4 publications

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“…(5) corresponds to turbulent flow, and is identical to the empirical Izbah's equation for this flow regime (Reddy and Rao 2006). By inserting Eq.…”

Section: Mathematical Description Of the Recharging Aquifer Flowmentioning

confidence: 95%

“…(48) corresponds to the local timederivative inertial term (LTDI-term), the second term to the advective inertial term (AI-term), while the third term on the right hand side is the so-called "Brinkman viscous term." Several alternative forms are proposed in the literature, omitting the Brinkman term, the advective inertial term, or suggesting that the multiplying the LTDI-term should be multiplied by an adequate constant C (Burcharth and Anderson 1995;Thiruvengadam and Kumar 1997;Reddy and Rao 2006).…”

Section: Justification Of the Use Of The Forchheimer Equationmentioning

confidence: 99%

“…Sorek et al (2005) have demonstrated that Forchheimer's law can be obtained by integration of the Navier-Stokes equation. Although generalized expressions of the above-mentioned expression have been proposed (Burcharth and Anderson 1995;Thiruvengadam and Kumar 1997;Reddy and Rao 2006), the Forchheimer equation seems to be a reliable tool to simulate most real world problems (Nield 2002).…”

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confidence: 99%

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One-dimensional unsteady inertial flow in phreatic aquifers induced by a sudden change of the boundary head

Moutsopoulos

2007

Transp Porous Med

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We are examining the classical problem of unsteady flow in a phreatic semiinfinite aquifer, induced by sudden rise or drawdown of the boundary head, by taking into account the influence of the inertial effects. We demonstrate that for short times the inertial effects are dominant and the equation system describing the flow behavior can be reduced to a single ordinary differential equation. This equation is solved both numerically by the Runge-Kutta method and analytically by the Adomian's decomposition approach and an adequate polynomial-exponential approximation as well. The influence of the viscous term, occurring for longer times, is also taken into account by solving the full Forchheimer equation by a finite difference approach. It is also demonstrated that as for the Darcian flow, for the case of small fluctuations of the water table, the computation procedure can be simplified by using a linearized form of the mass balance equation. Compact analytical expressions for the computation of the water stored or extracted from an aquifer, including viscous corrections are also developed.

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“…(5) corresponds to turbulent flow, and is identical to the empirical Izbah's equation for this flow regime (Reddy and Rao 2006). By inserting Eq.…”

Section: Mathematical Description Of the Recharging Aquifer Flowmentioning

confidence: 95%

Section: Justification Of the Use Of The Forchheimer Equationmentioning

confidence: 99%

mentioning

confidence: 99%

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One-dimensional unsteady inertial flow in phreatic aquifers induced by a sudden change of the boundary head

Moutsopoulos

2007

Transp Porous Med

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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%

“…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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[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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Current awareness

2006

Hydrological Processes

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2006. Estimating hydraulic properties using a moving-model approach and multiple aquifer tests. Groundwater 44: 284-291. Hogue T, Gupta H, Sorooshian S. 2006. A 'User-Friendly' approach to parameter estimation in hydrologic models. Journal of Hydrology 320: 202-217. Khan M, Coulibaly P, Dibike Y. 2006. Uncertainty analysis of statistical downscaling methods. Journal of Hydrology 319: 357-382. Luo J, Wu W, Fienen M, Jardine P, Mehlhorn T. 2006. A nested-cell approach for in situ remediation. Groundwater 44: 266-274. Makinen E, Korhonen M, Viskari E, Haapamaki S, Jarvinen M, Lu L. 2006. Comparison of XRF and FAAS methods in analysing CCA contaminated soils. Water Air and Soil Pollution 171: 95-110.

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Effect of Convergence on Nonlinear Flow in Porous Media

Cited by 22 publications

References 4 publications

One-dimensional unsteady inertial flow in phreatic aquifers induced by a sudden change of the boundary head

One-dimensional unsteady inertial flow in phreatic aquifers induced by a sudden change of the boundary head

Step‐drawdown tests and the Forchheimer equation

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