Abstract:This study focuses on the determination of the Forchheimer equation coefficients a and b for non-Darcian flow in porous media. Original theoretical equations are evaluated and empirical relations are proposed based on an investigation of available data in the literature. The validity of these equations is checked using existing experimental data, and their accuracy versus existing approaches is studied. On the basis of this analysis, some insight into the physical background of the phenomenon is also provided. The dependence of the coefficients a and b on the Reynolds number is also detected, and potential future research areas, e.g. investigation of inertial effects for consolidated porous media, are pointed out.
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.
The small grains in a bidisperse porous medium have the greater influence on
the permeability, while the large grains are more effective in dispersing chemical
tracers. We compute the dispersion induced by a dilute array of large spheres in
a Brinkman medium whose permeability is determined by the radii and volume
fraction of the small spheres. The effective diffusivity contains a purely hydrodynamic
contribution proportional to Ua1ϕ1 and an
O(Ua1ϕ1 ln
(Ua1/D)) contribution from
the mass transfer boundary layers near the spheres. Here, U is the mean velocity in
the medium, a1 and ϕ1 are the radii and volume
fraction of the large spheres and D is
the molecular diffusivity. The boundary-layer dispersion is small when the Brinkman
screening length κ (or square root of permeability) is much smaller than a1, but is
important for κ[ges ]O(a1). Experimental results for the dispersion due to flow through
a bidisperse packed bed are reported and compared with the theoretical predictions.
In addition to its application to bidisperse porous media, the present calculation
allows an extension of Koch & Brady's (1985) analysis of monodisperse fixed beds to
include higher-order terms in the expansion for small particle volume fraction.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.