S.E.A.T.M. van der Zee

Plume development of a nonlinearly adsorbing solute in heterogeneous porous formations

Transport of nonlinearly adsorbing solutes in homogeneous and heterogeneous porous formations is considered. Initially, a fixed amount of solute is assumed to be present in the domain. Transport is characterized in terms of the first and second spatial moments. Nonlinear equilibrium adsorption is described by the Freundlich isotherm, with the Freundlich exponent n, 0 < n < 1. By asymptotic balancing we derive first-order approximations of the limiting behavior of the plume position and plume growth as a function of time for the homogeneous case. In the heterogeneous case we consider random variation of a physical (log conductivity) and a chemical (log adsorption coefficient) parameter, both with an isotropic exponential covariance function. Expected behavior of the relevant spatial moments is obtained by applying a Monte Carlo approach. Individual realizations are solved numerically with a particle-tracking scheme in which nonlinear adsorption is accounted for by a time-dependent retarded velocity. We assess the effects of varying certain transport parameters, such as the degree of physical and chemical heterogeneity, degree of nonlinearity, the adsorption coefficient, and the degree of correlation between hydraulic conductivity and adsorption coefficient. Results of the homogeneous case for a strong degree of nonlinearity show good agreement between the numerical calculations and the limiting analytical expressions. Nonlinear adsorption is shown to have a strong effect on the shape of the plume, especially in longitudinal direction. For the heterogeneous case the analytical expressions predict well the time dependence of the growth rate of the spatial moments. Variation of the transport parameters demonstrates a dominating effect of the degree of nonlinearity on the plume dimensions, which is hardly affected by the degree of heterogeneity, correlation, and the adsorption coefficient. The variance of the mean plume position is affected by all parameters. Although the degree of heterogeneity has a strong impact, the longitudinal and transverse variances are reduced with respect to the linear adsorption case, due to the large size of the plumes.

Multi-phase flow modeling of air sparging

Air injection into groundwater (air sparging) in a homogeneous axially symmetric porous medium is modeled using a two-phase flow approach. A numerical method based on the mixed form of the Richards equation for both phases is presented. Furthermore two analytical approximations are discussed to explain the numerical results. One is a one-dimensional description explaining the occurrence of small air saturations. The other is a closed form approximation for the distribution of the air saturation in the resulting steady state. From the latter we can estimate the maximum radius of influence of air sparging, as a function of the physical parameters. The analytical approximation at steady state and the numerical results are in good agreement.

Modeling of air sparging in a layered soil: Numerical and analytical approximations

Air sparging in an aquifer below a less permeable horizontal layer is modeled using a two-phase flow approach. Supported by numerical simulations, we show that a steady state situation is reached. For an analysis of the steady state, we distinguish three different flow regimes, which occur between the well screen and the unsaturated zone. Just below the interface that separates the high and the low permeable layers a regime with almost hydrostatic capillary pressures develops. We use this observation to derive an ordinary differential equation for the pressure at the interface, which leads to an approximation of the air flow pattern just below and within the low permeable layer. The approximation provides an estimate for the radius of influence as a function of the physical parameters. The agreement between the analytical approximation and the numerical steady state results is almost perfect when heterogeneity is increased. With a few modifications the analysis applies also to a dense non-aqueous phase liquid (DNAPL) spill above a less permeable layer. Comparison with an illustrative numerical simulation shows that the analytical approximation provides a good estimate of the radial spreading of the DNAPL flow on top of and within the low permeable layer.

Analytical approximation to characterize the performance of in situ aquifer bioremediation

The performance of in situ bioremediation to remove organic contaminants from contaminated aquifers depends on the physical and biochemical parameters. We characterize the performance by the contaminant removal rate and the region where biodegradation occurs, the biologically active zone (BAZ). The numerical fronts obtained by one-dimensional in situ bioremediation modeling reveal a traveling wave behavior: fronts of microbial mass, organic contaminant and electron acceptor move with a constant velocity and constant front shape through the domain. Hence, only one front shape and a linear relation between the front position and time is found for each of the three compounds. We derive analytical approximations for the traveling wave front shape and front position that agree perfectly with the traveling wave behavior resulting from the bioremediation model. Using these analytical approximations, we determine the contaminant removal rate and the BAZ. Furthermore, we assess the influence of the physical and biochemical parameters on the performance of the in situ bioremediation technique.

A Similarity Solution for Oil Lens Redistribution Including Capillary Forces and Oil Entrapment

Redistribution of a LNAPL lens (oil) at the phreatic surface is described using a multi-phase flow model, with emphasis on the effect of oil entrapment by water. The flow process is analyzed under the assumption that the vertical capillary and gravitational forces balance. Vertical integration leads to explicit functions which approximate the relations between the free oil volume per unit lateral area and the vertically averaged oil relative permeability on the one hand and the vertical position of the interface between zones with either two or three phases on the other hand. A linear relation between the trapped and free oil volume per unit lateral area approximates the vertically integrated nonlinear expression for the trapped oil saturation. The resulting differential equation admits a similarity solution describing the lateral spreading of free oil and the amount and location of trapped oil. Comparison with illustrative numerical computations, which are based on the nonreduced flow model in a two-dimensional planar or axisymmetric domain, shows that the analytical solution provides a good approximation of the free oil distribution at all later times.

Root zone salinity and sodicity under seasonal rainfall due to feedback of decreasing hydraulic conductivity

Soil sodicity, where the soil cation exchange complex is occupied for a significant fraction by Na+, may lead to vulnerability to soil structure deterioration. With a root zone flow and salt transport model, we modeled the feedback effects of salt concentration (C) and exchangeable sodium percentage (ESP) on saturated hydraulic conductivity Ks(C, ESP) for different groundwater depths and climates, using the functional approach of McNeal (1968). We assume that a decrease of Ks is practically irreversible at a time scale of decades. Representing climate with a Poisson rainfall process, the feedback hardly affects salt and sodium accumulation compared with the case that feedback is ignored. However, if salinity decreases, the much more buffered ESP stays at elevated values, while Ks decreases. This situation may develop if rainfall has a seasonal pattern where drought periods with accumulation of salts in the root zone alternate with wet rainfall periods in which salts are leached. Feedback that affects both drainage/leaching and capillary upward flow from groundwater, or only drainage, leads to opposing effects. If both fluxes are affected by sodicity-induced degradation, this leads to reduced salinity (C) and sodicity (ESP), which suggests that the system dynamics and feedback oppose further degradation. Experiences in the field point in the same direction.

Front spreading with nonlinear sorption for oscillating flow

In this paper, we consider dispersive and chromatographic mixing at an interface, under alternating flow conditions. In case of a nonreactive or linearly sorbing solute, mixing is in complete analogy with classical dispersion theory. For nonlinear exchange, however, oscillating convective flow leads to an alternation of sharpening (Traveling Wave TW) and spreading (Rarefaction Wave RW). As the limiting TW form is not necessarily accomplished at the end of the TW half cycle, the oscillating fronts show gradual continuous spreading that converges to a zero-convection nonlinear pure diffusion spreading, which is mathematically of quite different nature. This behavior is maintained in case the total (background) concentration differs at both sides of the initial exchange front.

Upscaling of tracer transport including convection and Brownian motion using a 3D network model

We present a rigorous Lagrangian-Eulerian numerical approach for up-scaling transport in porous media from the Brownian motion of tracer particles to the core scale. The porous medium is assumed to be a surrogate of variously sized non-deformable Taylors cylindrical tubes in 3D Euclidian space (i.e., a 3D pore network), where flow of incompressible fluid is assumed to obey the Hagen-Poiseuille law. In the Lagrangian-Eulerian framework, Brownian tracer particles are allowed to describe three-dimensional random leaps in a velocity field described by the parabolic law. This algorithm was verified by reproducing Taylors classical experiments. The most intriguing problem in such a network is that the dispersion function at the intersection of tubes is discontinuous. This poses the problem in tracking the particles from the exit of one tube to the entrance of another. This problem has been tackled with the help of transition probabilities that are based on the Sorbie-Clifford conjecture [8]. Simulations have been carried out with two different intratube velocity profiles (parabolic and non-parabolic) and two different nodal jump conditions, i.e., with and without taking diffusion into account. The relation between the longitudinal dispersion ( D L ) and the characteristic Peclet Number (Pe l ) obtained in this work is very close to theoretical and experimental evidence. The results show that the velocity profile changes the relation qualitatively, whereas incorporation of diffusion in the nodal jump algorithm only leads to some quantitative differences.

Analysis of oil lens removal by extraction through a seepage face.

Removal of LNAPL (oil) from an aquifer is described using a multi‐phase flow model. At the well boundary seepage face conditions are imposed. These conditions are implemented in a numerical model and withdrawal in a two‐dimensional domain is simulated for two different geometries of the oil lens and for varied values of the physical parameters. Assuming vertical equilibrium, the oil flow equation is reduced by vertical integration. The well boundary condition is approximated by imposing zero oil lens thickness. Similarity solutions of the reduced equations for the two geometries show good agreement with the numerical results in most cases.Removal of LNAPL (oil) from an aquifer is described using a multi‐phase flow model. At the well boundary seepage face conditions are imposed. These conditions are implemented in a numerical model and withdrawal in a two‐dimensional domain is simulated for two different geometries of the oil lens and for varied values of the physical parameters. Assuming vertical equilibrium, the oil flow equation is reduced by vertical integration. The well boundary condition is approximated by imposing zero oil lens thickness. Similarity solutions of the reduced equations for the two geometries show good agreement with the numerical results in most cases.

Three-phase flow analysis of dense nonaqueous phase liquid infiltration in horizontally layered porous media

We considered dense nonaqueous phase liquid (DNAPL) infiltration into a water-unsaturated porous medium that consists of two horizontal layers, of which the top layer has a lower intrinsic permeability than the bottom layer. DNAPL is the intermediate-wetting fluid with respect to the wetting water and the nonwetting air. The layer interface forms a barrier to DNAPL flow, which causes the DNAPL to spread out horizontally just above the interface. An analytical approximation has been developed to estimate the DNAPL pressure and saturation and the horizontal extension of the DNAPL above the layer interface at steady state for low water saturations. The analytical approximation shows that the DNAPL infiltration is determined by five dimensionless numbers: the heterogeneity factor γ, the capillary pressure parameter λ, the gravity number Ng, the ratio of the capillary and gravity numbers Nc/Ng, and the critical DNAPL pressure Poc. Its predictions were compared with the results of a numerical three-phase flow simulator for a number of parameter combinations. For most of these combinations the analytical approximation predicts the DNAPL pressure and saturation profiles at the interface adequately. Using the analytical approximation, we carried out a sensitivity study with respect to the maximum horizontal extension of the plume. The extension of the plumes appears to be highly sensitive to variation of the dimensionless numbers Poc, λ and γ.