Analytical solutions of one-dimensional macrodispersion in stratified porous media by the quadrupole method: convergence to an equivalent homogeneous porous medium

2004 ◽  
Vol 27 (6) ◽  
pp. 657-667 ◽  
Author(s):  
S. Didierjean ◽  
D. Maillet ◽  
C. Moyne
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Analytical Solutions ◽  
One Dimensional ◽  
Homogeneous Porous Medium ◽  
Quadrupole Method

Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Laplace Transformation ◽  
Seepage Velocity ◽  
Transformation Technique ◽  
Numerical Examples ◽  
One Dimensional ◽  
Porous Domain ◽  
Conservative Solute Transport ◽  
Source Concentration

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

Capillary Impregnation of Viscous Fluids in a Multi-Layered Porous Medium

2019 ◽  
Author(s):  
Shabina Ashraf ◽  
Jyoti Phirani
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Oil Recovery ◽  
Viscous Fluids ◽  
Spontaneous Imbibition ◽  
Lab On Chip ◽  
Capillary Impregnation ◽  
Relative Placement ◽  
Homogeneous Porous Medium ◽  
Wetting Fluid

Abstract Capillary impregnation of viscous fluids in porous media is useful in diagnostics, design of lab-on-chip devices and enhanced oil recovery. The impregnation of a wetting fluid in a homogeneous porous medium follows Washburn’s diffusive law. The diffusive dynamics predicts that, with the increase in permeability, the rate of spontaneous imbibition of a wetting fluid also increases. As most of the naturally occurring porous media are composed of hydrodynamically interacting layers having different properties, the impregnation in a heterogeneous porous medium is significantly different from a homogeneous porous medium. A Washburn like model has been developed in the past to predict the imbibition behavior in the layers for a hydrodynamically interacting three layered porous medium filled with a non-viscous resident phase. It was observed that the relative placement of the layers impacts the imbibition phenomena significantly. In this work, we develop a quasi one-dimensional lubrication approximation to predict the imbibition dynamics in a hydrodynamically interacting multi-layered porous medium. The generalized model shows that the arrangement of layers strongly affects the saturation of wetting phase in the porous medium, which is crucial for oil recovery and in microfluidic applications.

Solidification With a Throughflow in a Porous Medium

1992 ◽  
Vol 114 (3) ◽  
pp. 675-680
Author(s):  
T. Banerjee ◽  
C. Chang ◽  
W. Wu ◽  
U. Narusawa
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Analytical Solutions ◽  
Peclet Number ◽  
Flow In Porous Media ◽  
Circular Pipe ◽  
Parallel Plates ◽  
Péclet Number ◽  
Solid Interface

A steady throughflow in a porous medium is studied in the presence of a solidified layer due to cooling of the walls. Under the assumption of a moderately sloped melt-solid interface, analytical solutions are obtained for both a flow between parallel plates and a circular pipe. Differences and similarities are examined between the Darcian and the Brinkman porous media, as well as the effects of various parameters, such as the Peclet number, the ratio of diffusivities in the longitudinal and the lateral directions, and a parameter indicating the degree of wall cooling and flow heating, on thermofluid structure of a flow in porous media accompanied by solidification.

SHOCK PROPAGATION IN A FLOW THROUGH DEFORMABLE POROUS MEDIA: ASYMPTOTIC BEHAVIOUR AS THE POROSITY APPROXIMATES A CONSTANT

2007 ◽  
Vol 17 (08) ◽  
pp. 1261-1278
Author(s):  
ELENA COMPARINI ◽  
MAURA UGHI
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Hydraulic Conductivity ◽  
Asymptotic Behaviour ◽  
Incompressible Flow ◽  
Shock Propagation ◽  
One Dimensional ◽  
Deformable Porous Media ◽  
Flux Intensity ◽  
Flow Through

We consider a one-dimensional incompressible flow through a porous medium undergoing deformations such that the porosity and the hydraulic conductivity can be considered as functions of the flux intensity. We prove that if one approximates the porosity with a constant then the solution of the hyperbolic problem converges to the classical continuous Green–Ampt solution, also in the presence of shocks. In general, however, the shocks remain present in any approximating solution.

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