Combinatorial model of solute transport in porous media

Modeling of solute transport is a key issue in the area of soil physics and hydrogeology. The most common approach (the convection-dispersion equation) considers an average convection flow rate and Fickian-like dispersion. Here,we propose a solute transport model in porous media of continuously expanding scale, according to the combinatorics principle. The model supposed actual porous media as a combinative body of many basic segments. First, we studied the solute transport process in each basic segment body, and then deduced the distribution of pore velocity in each basic segment body by difference approximation, finally assembled the solute transport process of each basic segment body into one of the combinative body. The simulation result coincided with the solute transport process observed in test. The model provides useful insight into the solute transport process of the non-Fickian dispersion in continuously expanding scale.

Experimental study on moving boundaries of fluid flow in porous media

Researches on the boundary shape of fluid flow in porous media play an important role in engineering practices, such as petroleum exploitation, nuclear waste disposal and groundwater contamination. In this paper, six types of artificial porous samples (emery jade) with different porosities are manufactured. With the background of slow flow in porous media, laboratory experiments are carried out by observing the movement of five types of fluids with different dynamic viscosities in various types of porous media. A digital video recorder is employed to record the complete process of the fluid flow in the porous media. Based on the digital photos of the moving boundaries of fluid flow in porous media, the average displacement and fractal dimension of the moving boundary are estimated for different combinations of porosity and dynamic viscosity. Moreover, the evolution behavior of the average velocity and fractal dimension of the moving boundary with time is known. The statistical relations of the average velocity, the fractal dimension of the moving boundary and the porosity of porous media and the dynamic vis- cosity of fluids are proposed in this paper. It is shown that the front shape of the moving boundary of fluid flow in porous media is an integrated result of the porosity of porous media and the dynamic viscosity of fluids.

EXISTENCE AND UNIQUENESS OF BV SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH DIRAC MEASURE AS SOURCES

The aim of this paper is to discuss the existence and uniqueness ofsolutions for the porous medium equation ut-(u^m)xx=μ（x） in （x，t）∈R×（0，+∞） with initial condition u(x,0)=u0(x) x∈（-∞，+∞），where μ(x) is a nonnegative finite Radon measure, u0∈L^1 (R)∩L^∞ (R) is a nonnegative function, and m>1, and R≡(-∞, +∞).

Simulation procedure of unconfined seepage with an inner seepage face in a heterogeneous field

An inner seepage face phenomenon is given and a numerical simulation procedure has been developed.It may appear at the interface of two materials when an unconfined seepage flows from a porous media to a coarser porous media with a higher permeability.Inaccuracy and divergent problems may arise both in a saturated-only and in a variably saturated analysis while an inner seepage face is not simulated with a special procedure.The position of the seepage face is determined during the nonlinear iteration process and the flux of the inner seepage face nodes is transferred to the downstream side nodes.Validity and efficiency of the procedure are illustrated by the simulation of two dimensional steady state seepage examples of heterogeneous zoned dams which is usually used to validate algorithms.An analysis of a three-dimensional earth core rockfill dam is also presented here.The procedure can also be applied to general transient seepage problems.

THE UPWIND FINITE DIFFERENCE FRACTIONAL STEPS METHOD FOR NONLINEAR COUPLED SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA

For nonlinear coupled system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward, trod two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources.