Finite-Element Method Solution of Non-Fickian Transport in Porous Media: The CTRW-FEM Package.

An exposition is given of a finite-element method (FEM) software package to calculate solutions for the continuous time random walk (CTRW) integro-differential equation for non-Fickian (and Fickian) conservative or reactive transport in disordered media. The solutions encompass one-dimensional/two-dimensional (1D/2D) breakthrough curves and spatial concentration profiles for general geometry and grid. The velocity field, used as input to the 2D solutions, may also be calculated by applying a compatible Darcy flow 2D solver.

Anomalous reactive transport in porous media: Experiments and modeling.

We analyze dynamic behavior of chemically reactive species in a porous medium, subject to anomalous transport. In this context, we present transport experiments in a refraction-index-matched, three-dimensional, water-saturated porous medium. A pH indicator (Congo red) was used as either a conservative or a reactive tracer, depending on the tracer solution pH relative to that of the background solution.

Non-Fickian transport in porous media with bimodal structural heterogeneity.

Tracer tailing in breakthrough curves in porous media with two distinct porosities is analyzed in terms of the dynamic responses of experimental fixed bed columns filled either with solid or porous beads. The flow is fast in the column interstitial space between beads (for both solid and porous beads) but slow within the porous beads that act as controlled 'traps' constituting an immobile zone. The transport is quantified using a Continuous Time Random Walk (CTRW) framework, which accounts for domains with controlled structural and flow heterogeneity associated with two distinct spatial and time spectra.

Transport in disordered media with spatially nonuniform fields.

The theoretical treatment of transport in a disordered system in the presence of a system-wide force field F(x) or spatially varying macroscopic velocity field v(x) is developed in the framework of continuous time random walk (CTRW). The physical basis of CTRW and related fractional derivative equations relies on a mapping of the aggregate of transition rates w(s,s'), between sites s and s', in the Master equation describing the system kinetics, onto a joint probability distribution function psi(s,t). This distribution is calculated from the ensemble average of a position-dependent functional of w(s,s'); the procedure is effective when the scale of heterogeneities is much smaller than the system size.

Anomalous transport in correlated velocity fields.

We examine different types of heterogeneous hydraulic conductivity fields to ascertain the basic structural features that dominate the transport behavior. We contrast two approaches to the analysis, within the framework of the continuous time random walk (CTRW), considering recent simulations of particle transport in two correlated flow fields to discern these key features. These flow fields are the steady-state solutions of Darcy flow in systems with correlated distributions, P(K(x)), of hydraulic conductivity values K(x).

Transport behavior of coupled continuous-time random walks.

The origin of anomalous or non-Fickian transport in disordered media is the broad spectrum of transition rates intrinsic to these systems. A system that contains within it heterogeneities over multiple length scales is geological formations. The continuous time random walk (CTRW) framework, which has been demonstrated to be an effective means to model non-Fickian transport features in these systems and to have predictive capacities, has at its core this full spectrum represented as a joint probability density psi(s,t) of random space time displacements (s,t) .

Numerical study of diffusion on a random-mixed-bond lattice.

Diffusion on lattices with random mixed bonds in two and three dimensions is reconsidered using a random walk (RW) algorithm, which is equivalent to the master equation. In this numerical study the main focus is on the simple case of two different transition rates W(1),W(2) along bonds between sites. Although analysis of diffusion and transport on this type of disordered medium, especially for the case of one-bond pure percolation (i.

Quantitative characterization of pore-scale disorder effects on transport in "homogeneous" granular media.

Breakthrough curves (BTC) of a passive tracer in macroscopically homogeneous granular materials (well-sorted, unconsolidated sands or glass beads) were measured in a series of column experiments. The early and late arrival times are observed to differ systematically from theoretical predictions based on solution of the advective-dispersion equation for uniform porous media. We propose that subtle and residual pore-scale disorder effects in the porous media can account for these observations.