[1] Multiphase flow and contaminant transport in porous media are strongly influenced by the presence of fluid-fluid interfaces. Recent theoretical work based on conservation laws and the second law of thermodynamics has demonstrated the need for quantitative interfacial area information to be incorporated into multiphase flow models. We have used synchrotron based X-ray microtomography to investigate unsaturated flow through a glass bead column. Fully three-dimensional images were collected at points on the primary drainage curve and on the secondary imbibition and drainage loops. Analysis of the high-resolution images (17 micron voxels) allows for computation of interfacial areas and saturation. Corresponding pressure measurements are made during the course of the experiments. Results show the fluid-fluid interfacial area increasing as saturation decreases, reaching a maximum at saturations ranging from 20 to 35% and then decreasing as the saturation continues to zero. The findings support results of numerical studies reported in the literature.

A three‐dimensional solute transport model has been developed to study detailed contaminant movements through large heterogeneous flow systems in porous media. The model is based upon a random walk particle method (RWPM) which can readily treat multidimensional advection and dispersion processes in saturated or unsaturated media in a computationally efficient manner. The transport simulations are used to examine the large time and spatial effects of the variable flow field on developing solute plumes, and, in particular, to investigate the nature of the large‐scale dispersive behavior. Numerical transport experiments were conducted using single realizations of random hydraulic conductivity fields with three different degrees of heterogeneity. Experiments with different source locations were used to investigate preasymptotic and nonergodic effects that would appear as differences in plume evolution among the experiments. Analyses of the simulations indicate the spatial moments of the particle distributions in statistically isotropic saturated media compare favorably with stochastic theory predictions in terms of longitudinal advection and mixing, but differ markedly from predictions of transverse mixing. The simulations also demonstrate that significant nonergodic effects occur, as reflected in strong differences in the second moment evolution curves among the individual experiments and as predicted from the ensemble stochastic theory.

The random-walk method for simulating solute transport in porous media is typically based on the assumption that the velocity and velocity-dependent dispersion tensor vary smoothly in space. However, in cases where sharp interfaces separate materials with contrasting hydraulic properties, these quantities may be discontinuous. Normally, velocities are interpolated to arbitrary particle locations when finite difference or finite element methods are used to solve the flow equation. The use of interpolation schemes that preserve discontinuities in velocity at material contacts can result in a random-walk model that does not locally conserve mass unless a correction is applied at these contacts. Test simulations of random-walk particle tracking with and without special treatment of material contacts demonstrate the problem. Techniques for resolving the problem, including interpolation schemes and a reflection principle, are reviewed and tested. Results from simulations of transport in porous media with discontinuities in the dispersion tensor show which methods satisfy continuity. Simulations of transport in twodimensional heterogeneous porous media demonstrate the potentially significant effect of using a nonconservative model to compute spatial moments and breakthrough of a solute plume. Introduction The random-walk particle method (RWPM) has been used successfully for years to simulate conservative and reactive transport in porous media [Ahlstrom et al., 1977; Prickerr et al., 1981; Uffink, 1985; Tompson e! al., 1987; Tompson, 1993]. This method is computationally appealing because it is grid independent and therefore, given the proper conditions, will require little computer storage relative to finite element, finite difference, and method of characteristic models. In addition, this method does not Suffer from numerical dispersion in problems dominated by advection. Traditional finite element and finite difference models generally perform poorly under such conditions unless the computational grid is highly resolved. As a result, a random walk is often the method of choice for simulating transport in large, heterogeneous flow systems [Tompson and Gelhat, 1990; Tompson, 1993; Tompson et al., 1994]. Global mass conservation is compulsory with the RWPM because particles cannot disappear. This distinct advantage of the RWPM, however, is often overstated; accurate solutions require local as well as global mass conservation.In practice, the flow Problem is often solved numerically, and velocities are interpolated to arbitrary particle locations.Advective particle tracking models can be made mass conservative by using a divergence-free velocity interpolation scheme [Schafer-Perini and Wilson, 199i]. However, additional criteria are necessary to formulate a mass conservative random-walk model. For example, discontinuities in the velocity or effective porosity may yield a dispersion tensor that is discontinuous in space. Local mass conservation conditions for the RWPM require that the dispersion tensor be continuous in spa...

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