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Many groundwater contamination incidents begin with the release of an essentially immiscible fluid into the subsurface environment. Once in the subsurface, an immiscible fluid participates in a complex pattern of transport processes. For immiscible fluids that are commonly found in contaminated groundwater environments the interphase mass transfer between the nonaqueous phase liquids (NAPLs) phase and the aqueous phase is an important process. An experimental apparatus and procedure were used to isolate and measure mass transfer between toluene and water in glass bead media systems. The rate of interphase mass transfer was investigated in two-fluid systems as a function of aqueous phase velocity, aqueous-and nonaqueous-phase fluid saturations, and porous media characteristics. The rate of interphase mass transfer is found to be directly related to aqueous phase velocity and nonaqueous phase fluid saturation level, but no significant relation to mean particle size is found. Correlation expressions for the rate of interphase mass transfer are developed using relevant dimensionless parameters and are compared to literature values. Equilibrium between the two fluid phases investigated is shown to be achieved rapidly, over wide ranges of nonaqueous phase fluid saturations and aqueous phase velocities. The derived correlations provide a means for estimating the appropriateness of the local equilibrium assumption for a nonaqueous phase liquid-aqueous phase couple in multiphase groundwater systems. A. S. Mayer and C. T. Miller

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[1] We simulate two-fluid-phase flow at the pore scale using a lattice Boltzmann (LB) approach. Using a parallel processing version of the Shan-Chen model that we developed, we simulate a set of ideal two-fluid systems and a model two-fluid-phase porous medium system comprised of a synthetic packing with a relatively uniform distribution of spheres. We use the set of ideal two-phase systems to validate the approach and provide parameter information, which we then use to simulate a sphere-pack system. The spherepack system is designed to mimic laboratory experiments conducted to evaluate the hysteretic capillary pressure saturation relation for a system consisting of water, tetrachloroethylene, and a glass bead porous medium. Good agreement is achieved between the measured hysteretic capillary pressure saturation relations and the LB simulations when comparing entry pressure, displacement slopes, irreducible saturation, and residual entrapment. Our results further show that while qualitatively similar results are obtained when comparing systems consisting of 1200 spheres and 150 spheres, there is a significant difference between these two levels, suggesting a lower bound on the size of a representative elementary volume.

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Abstract. Capillary pressure-saturation-relative permeability relations described using the van Genuchten [1980] and Mualem [1976] models for nonuniform porous media lead to numerical convergence difficulties when used with Richards' equation for certain auxiliary conditions. These difficulties arise because of discontinuities in the derivative of specific moisture capacity and relative permeability as a function of capillary pressure. Convergence difficulties are illustrated using standard numerical approaches to simulate such problems. We investigate constitutive relations, interblock permeability, nonlinear algebraic system approximation methods, and two time integration approaches. An integral permeability approach approximated by Hermite polynomials is recommended and shown to be robust and economical for a set of test problems, which correspond to sand, loam, and clay loam media. An example of such a case was for infiltration from a ponded surface boundary condition into a system originally drained to static equilibrium.These experiences motivated this work, which had several objectives: (1) to document a common class of variably saturated flow problems that lack robustness when solved using standard solution approaches, (2) to determine the reason why traditional approaches lack robustness for this class of problems, (3) to investigate a variety of alternative approaches, and (4) to compare a set of alternative approaches for a range of porous media conditions to test robustness and efficiency. BackgroundFour aspects of the literature on unsaturated flow warrant at least a brief consideration: (1) constitutive relations used to describe pressure-saturation-conductivity relations and typical parameter values for natural, unconsolidated media, (2) approaches typically used to approximate RE, (3) methods for approximating relative permeabilities for a discrete approximation of RE, and (4) strategies used to estimate the relatively complex constitutive relations that are a part of the formulations of concern. Pressure-Saturation-Conductivity RelationsA well-posed formulation of RE requires that constitutive relations be specified to describe the interdependence among fluid pressures, saturations, and relative permeabilities, which will be referred to as p-s-k relations.

Several mathematical formulations have analyzed the time-dependent behaviour of a tumor mass. However, most of these propose simplifications that compromise the physical soundness of the model. Here, multiphase porous media mechanics is extended to model tumor evolution, using governing equations obtained via the Thermodynamically Constrained Averaging Theory (TCAT). A tumor mass is treated as a multiphase medium composed of an extracellular matrix (ECM); tumor cells (TC), which may become necrotic depending on the nutrient concentration and tumor phase pressure; healthy cells (HC); and an interstitial fluid (IF) for the transport of nutrients. The equations are solved by a Finite Element method to predict the growth rate of the tumor mass as a function of the initial tumor-to-healthy cell density ratio, nutrient concentration, mechanical strain, cell adhesion and geometry. Results are shown for three cases of practical biological interest such as multicellular tumor spheroids (MTS) and tumor cords. First, the model is validated by experimental data for time-dependent growth of an MTS in a culture medium. The tumor growth pattern follows a biphasic behaviour: initially, the rapidly growing tumor cells tend to saturate the volume available without any significant increase in overall tumor size; then, a classical Gompertzian pattern is observed for the MTS radius variation with time. A core with necrotic cells appears for tumor sizes larger than 150 μm, surrounded by a shell of viable tumor cells whose thickness stays almost constant with time. A formula to estimate the size of the necrotic core is proposed. In the second case, the MTS is confined within a healthy tissue. The growth rate is reduced, as compared to the first case – mostly due to the relative adhesion of the tumor and healthy cells to the ECM, and the less favourable transport of nutrients. In particular, for tumor cells adhering less avidly to the ECM, the healthy tissue is progressively displaced as the malignant mass grows, whereas tumor cell infiltration is predicted for the opposite condition. Interestingly, the infiltration potential of the tumor mass is mostly driven by the relative cell adhesion to the ECM. In the third case, a tumor cord model is analyzed where the malignant cells grow around microvessels in a 3D geometry. It is shown that tumor cells tend to migrate among adjacent vessels seeking new oxygen and nutrient. This model can predict and optimize the efficacy of anticancer therapeutic strategies. It can be further developed to answer questions on tumor biophysics, related to the effects of ECM stiffness and cell adhesion on tumor cell proliferation.