scholarly journals Time‐Fractional Flow Equations (t‐FFEs) to Upscale Transient Groundwater Flow Characterized by Temporally Non‐Darcian Flow Due to Medium Heterogeneity

2021 ◽  
Author(s):  
Yuan Xia ◽  
Yong Zhang ◽  
Christopher T. Green ◽  
Graham E. Fogg
Keyword(s):  
Groundwater Flow ◽  
Fractional Flow ◽  
Flow Equations ◽  
Medium Heterogeneity

A coupled FE model for the joint resolution of the shallow water and the groundwater flow equations

2014 ◽  
Vol 24 (7) ◽  
pp. 1553-1569 ◽  
Author(s):  
H.G. Rábade ◽  
P. Vellando ◽  
F. Padilla ◽  
R. Juncosa
Keyword(s):  
Groundwater Flow ◽  
Shallow Water ◽  
Free Surface Flow ◽  
Element Model ◽  
Surface Flow ◽  
Fe Model ◽  
Content Type ◽  
Flow Equations ◽  
Natural Watersheds ◽  
Joint Resolution

Purpose – A new coupled finite element model has been developed for the joint resolution of both the shallow water equations, that governs the free surface flow, and the groundwater flow equation that governs the motion of water through a porous media. The paper aims to discuss these issues. Design/methodology/approach – The model is based upon two different modules (surface and ground water) previously developed by the authors, that have been validated separately. Findings – The newly developed software allows for the assessment of the fluid flow in natural watersheds taking into account both the surface and the underground flow in the way it really takes place in nature. Originality/value – The main achievement of this work has dealt with the coupling of both models, allowing for a proper moving interface treatment that simulates the actual interaction that takes place between surface and groundwater in natural watersheds.

Groundwater Flow Equations

2017 ◽  
pp. 15-27
Author(s):  
Florimond De Smedt ◽  
Wouter Zijl
Keyword(s):  
Groundwater Flow ◽  
Flow Equations

A Study of Gravity Counterflow Segregation

1962 ◽  
Vol 2 (02) ◽  
pp. 185-193 ◽  
Author(s):  
E.E. Templeton ◽  
R.F. Nielsen ◽  
C.D. Stahl
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Capillary Pressure ◽  
Closed System ◽  
Fractional Flow ◽  
Flow Rates ◽  
Flow Equations ◽  
Actual Flow ◽  
Capillary Pressures ◽  
Darcy Equations

Abstract It has been customary, in predicting saturation changes, to use the Leverett "fractional flow formula", obtained by eliminating the unknown pressure gradient from the generalized Darcy equations for the separate phases. The formula presents difficulties in the case of counterflow, since the "fractional" flow may be negative, greater than unity, or, in the case of a closed system, infinite. Recently, it has been shown by several authors that the corresponding equations (with capillary pressure and gravity terms) for actual flow of the phase may be used just as well. These equations are in agreement with Pirson's statement that, if the two mobilities differ considerably from each other in a closed system, the flow is largely governed by the lower value. The present study was undertaken because of an apparent lack of experimental data on gravity counterflow with which to test the theory. A 4-ft sandpacked tube in a vertical position was employed. Electrodes for determining saturations by resistivity were spaced along the tube, one phase being always an aqueous salt solution. Air, heptane, naphtha, or Bradford crude oil was used for the other phase. A reasonably uniform initial saturation was set up by pumping the phases through the system, after which the tube was shut in and saturation profiles obtained at definite intervals. Cumulative flows over certain horizontal levels were obtained by integration of the distributions; hence, differentiation of the cumulative flows with respect to time gave instantaneous flow rates. To compare experimental and theoretical flow values, capillary pressures were assumed given by the final saturation-distribution curve. The upper part corresponds to the "drainage" region and the lower part to the "imbibition" region, where trapping of the nonwetting phase occurred. While calculations indicated that the capillary pressure saturation function and, probably, the relative permeability saturation functions changed during the segregation, the relation of the measured rates to saturation distributions are in general accord with the frontal-advance equation. It appears that the Darcy equations, as modified for the separate phases, are generally valid for counterflow due to density differences. The usual method of predicting saturation changes, which involves a continuity equation and the elimination of the unknown pressure gradient from the flow equations, should therefore be applicable. However, the need for advance knowledge of drainage and imbibition "capillary pressures" and relative permeabilities during various stages presents difficulties. Introduction The present study was undertaken because of a seeming lack of experimental data relating to vertical counterflow of fluids of different densities in porous media. In particular, it was desired to determine whether data obtained from these laboratory tests were in accordance with certain mathematical treatments of counterflow which have been proposed. The gravity "correction" has been incorporated into the flow equations (and, hence, into displacement theory) nearly as long as both have been used. Field and laboratory data have generally borne out the validity of the theory as applied, for instance, to downward displacement by gas, with all fluids moving downward. However, the modifications for counterflow have only recently been pointed out. It has been customary to use fractional flow rates instead of actual flow rates in displacement calculations. In the case of counterflow, this results in negative values, values greater than unity and, when rates are equal and opposite, in infinite values. As pointed out by Sheldon, et al, and by Fayers and Sheldon, actual flow rates may be used just as well. The fact that these may be of opposite signs for the two fluids does not present any difficulty. SPEJ P. 185^

scholarly journals Non-monotonic Travelling Wave Fronts in a System of Fractional Flow Equations from Porous Media

2016 ◽  
Vol 114 (2) ◽  
pp. 309-340 ◽  
Author(s):  
O. Hönig ◽  
P. A. Zegeling ◽  
F. Doster ◽  
R. Hilfer
Keyword(s):  
Porous Media ◽  
Travelling Wave ◽  
Fractional Flow ◽  
Wave Fronts ◽  
Flow Equations

scholarly journals Groundwater flow equation, overview, derivation, and solution

2021 ◽  
Vol 314 ◽  
pp. 04007
Author(s):  
Lhoussaine El Mezouary ◽  
Bouabid El Mansouri
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Groundwater Flow ◽  
Numerical Solutions ◽  
Flow Equation ◽  
Heat Transfer Equation ◽  
Flow Equations ◽  
Basic Law ◽  
Flow Through ◽  
Groundwater Flow Equation

Darcy’s law is the basic law of flow, and it produces a partial differential equation is similar to the heat transfer equation when coupled with an equation of continuity that explains the conservation of fluid mass during flow through a porous media. This article, titled the groundwater flow equation, covers the derivation of the groundwater flow equations in both the steady and transient states. We look at some of the most common approaches and methods for developing analytical or numerical solutions. The flaws and limits of these solutions in reproducing the behavior of water flow on the aquifer are also discussed in the article.

The universal structure of the groundwater flow equations

1994 ◽  
Vol 30 (5) ◽  
pp. 1407-1419 ◽  
Author(s):  
Roger Beckie ◽  
Alvaro A. Aldama ◽  
Eric F. Wood
Keyword(s):  
Groundwater Flow ◽  
Flow Equations ◽  
Universal Structure

Transform approach to solution of groundwater flow equations

1977 ◽  
Vol 32 (3-4) ◽  
pp. 305-320 ◽  
Author(s):  
C.M. Case ◽  
M.K. Peck
Keyword(s):  
Groundwater Flow ◽  
Flow Equations
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