Klaus Rathfelder

Mass conservative numerical solutions of the head‐based Richards equation

Numerical procedures for efficient mass conservative solutions of the head-based form of the Richards equation are presented. Mass conservative solutions are shown to result when the capacity coefficient, C, is formulated by equating the storage term and its chain rule expansion in their discretized forms. Equivalence in the storage term expansion is maintained in finite difference models when C is evaluated with a standard chord slope approximation. This scheme is shown to produce excellent global mass balance accuracy in simulations of vertical moisture infiltration. An analogous approach to the expansion of the storage term using finite elements results in element dependent expressions of C. Application of this approach produces mass balance accuracy with errors less than 1%, but also exhibits slow convergence in the consistent form. A nontraditional finite element procedure is presented which maintains equivalence in the storage term expansion when C is evaluated with the standard chord slope approximation. This scheme exhibits excellent mass balance accuracy, in either the consistent or lumped forms, without significant loss in computational efficiency.

Mathematical simulation of soil vapor extraction systems: Model development and numerical examples

This paper describes the development of a numerical model for prediction of soil vapor extraction processes. The major emphasis is placed on field-scale predictions with the objective to advance development of planning tools for design and operation of venting systems. The numerical model solves two-dimensional flow and transport equations for general n-component contaminant mixtures. Flow is limited to the gas phase and local equilibrium partitioning is assumed in tracking contaminants in the immiscible fluid, water, gas, and solid phase. Model predictions compared favorably with analytical solutions and multicomponent column venting experiments. Sensitivity analysis indicates equilibrium phase partitioning is a good assumption in modeling organic liquid volatilization occurring in field venting operations. Mass transfer rates in volatilization from the water phase and contaminant desorption are potentially rate limiting. Simulations of hypothetical field-scale problems show efficiency of venting operations is most sensitive to vapor pressure and the magnitude and distribution of soil permeability.

A numerical model (MISER) for the simulation of coupled physical, chemical and biological processes in soil vapor extraction and bioventing systems

The efficiency and effectiveness of soil vapor extraction (SVE) and bioventing (BV) systems for remediation of unsaturated zone soils is controlled by a complex combination of physical, chemical and biological factors. The Michigan soil vapor extraction remediation (MISER) model, a two-dimensional numerical simulator, is developed to advance our ability to investigate the performance of field scale SVE and BV systems by integrating processes of multiphase flow, multicomponent compositional transport with nonequilibrium interphase mass transfer, and aerobic biodegradation. Subsequent to the model presentation, example simulations of single well SVE and BV systems are used to illustrate the interplay between physical, chemical and biological processes and their potential influence on remediation efficiency and the pathways of contaminant removal. Simulations of SVE reveal that removal efficiency is controlled primarily by the ability to engineer gas flow through regions of organic liquid contaminated soil and by interphase mass transfer limitations. Biodegradation is found to play a minor role in mass removal for the examined SVE scenarios. Simulations of BV systems suggest that the effective supply of oxygen may not be the sole criterion for efficient BV performance. The efficiency and contaminant removal pathways in these systems can be significantly influenced by interdependent dynamics involving biological growth factors, interphase mass transfer rates, and air injection rates. Simulation results emphasize the need for the continued refinement and validation of predictive interphase mass transfer models applicable under a variety of conditions and for the continued elucidation and quantification of microbial processes under unsaturated field conditions.

Flow and entrapment of dense nonaqueous phase liquids in physically and chemically heterogeneous aquifer formations

The migration and entrapment of dense nonaqueous phase liquids (DNAPLs) in aquifer formations is typically believed to be controlled by physical heterogeneities. This belief is based upon the assumption that permeability and capillary properties are determined by the soil texture. Capillarity and relative permeability, however, will also depend on porous medium wettability characteristics. This wettability may vary spatially in a formation due to variations in aqueous phase chemistry, contaminant aging, and/or variations in mineralogy and organic matter distributions. In this work, a two-dimensional multiphase flow simulator is modified to simulate coupled physical and chemical formation heterogeneity. To model physical heterogeneity, a spatially correlated permeability field is generated, and then related to the capillary pressure-saturation function according to Leverett scaling. Spatial variability of porous medium wettability is assumed to be correlated with the natural logarithm of the intrinsic permeability. The influence of wettability on the hysteretic hydraulic property relations is also modeled. The simulator is then employed to investigate the potential influence of coupled physical and chemical heterogeneity on DNAPL flow and entrapment. For reasonable ranges of wettability characteristics, simulations demonstrate that spatial variations in wettability can have a dramatic impact on DNAPL distributions. Higher organic saturations, increased lateral spreading, and decreased depth of infiltration were predicted when the contact angle was varied spatially. When chemical heterogeneity was defined by spatial variation of organic-wet solid fractions (fractional wettability porous media), however, the resultant organic saturation distributions were more similar to those for perfectly water-wet media, due to saturation dependent wettability effects on the hydraulic property relations.

The influence of capillarity in numerical modeling of organic liquid redistribution in two-phase systems

Numerical experiments are performed to explore the influence of model assumptions and parameters on the prediction of two-phase flow during long-term NAPL redistribution. Sensitivity of numerical solutions to grid resolution and the use of alternative fitting functions for capillary retention data are examined. Due to the inclusion of capillary entrapment, numerical solutions in one- and two-dimensions are strongly dependent on grid resolution. Solution convergence tests based upon spreading behavior reveal that nodal spacings as small as one-fifth to one-tenth of the displacement pressure head may be required to obtain reasonable convergence in some simulations. Solutions employing the Brooks and Corey and van Genuchten functional forms are found to yield different solution behavior. These differences are attributed to the representation of capillary pressure below the entry pressure. Brooks and Corey solutions exhibited greater spreading, less inclination to penetrate semi-permeable layers, and poorer spatial convergence behavior.

Surfactant enhanced recovery of tetrachloroethylene from a porous medium containing low permeability lenses. 2. Numerical simulation.

A numerical model of surfactant enhanced solubilization was developed and applied to the simulation of nonaqueous phase liquid recovery in two-dimensional heterogeneous laboratory sand tank systems. Model parameters were derived from independent, small-scale, batch and column experiments. These parameters included viscosity, density, solubilization capacity, surfactant sorption, interfacial tension, permeability, capillary retention functions, and interphase mass transfer correlations. Model predictive capability was assessed for the evaluation of the micellar solubilization of tetrachloroethylene (PCE) in the two-dimensional systems. Predicted effluent concentrations and mass recovery agreed reasonably well with measured values. Accurate prediction of enhanced solubilization behavior in the sand tanks was found to require the incorporation of pore-scale, system-dependent, interphase mass transfer limitations, including an explicit representation of specific interfacial contact area. Predicted effluent concentrations and mass recovery were also found to depend strongly upon the initial NAPL entrapment configuration. Numerical results collectively indicate that enhanced solubilization processes in heterogeneous, laboratory sand tank systems can be successfully simulated using independently measured soil parameters and column-measured mass transfer coefficients, provided that permeability and NAPL distributions are accurately known. This implies that the accuracy of model predictions at the field scale will be constrained by our ability to quantify soil heterogeneity and NAPL distribution.

Entrapment and dissolution of DNAPLs in heterogeneous porous media

Two-dimensional multiphase flow and transport simulators were refined and used to numerically investigate the entrapment and dissolution behavior of tetrachloroethylene (PCE) in heterogeneous porous media containing spatial variations in wettability. Measured hydraulic properties, residual saturations, and dissolution parameters were employed in these simulations. Entrapment was quantified using experimentally verified hydraulic property and residual saturation models that account for hysteresis and wettability variations. The nonequilibrium dissolution of PCE was modeled using independent estimates of the film mass transfer coefficient and interfacial area for entrapped and continuous (PCE pools or films) saturations. Flow simulations demonstrate that the spatial distribution of PCE is highly dependent on subsurface wettability characteristics that create differences in PCE retention mechanisms and the presence of subsurface capillary barriers. For a given soil texture, the maximum and minimum PCE infiltration depth was obtained when the sand had intermediate (an organic-wet mass fraction of 25%) and strong (water- or organic-wet) wettability conditions, respectively. In heterogeneous systems, subsurface wettability variations were also found to enhance or diminish the performance of soil texture-induced capillary barriers. The dissolution behavior of PCE was found to depend on the soil wettability and the spatial PCE distribution. Shorter dissolution times tended to occur when PCE was distributed over large regions due to an increased access of flowing water to the PCE. In heterogeneous systems, capillary barriers that produced high PCE saturations tended to exhibit longer dissolution times.

Simulation of organic liquid flow in porous media using estimated and measured transport properties

Many numerical models which describe the movement of a separate organic liquid phase in the subsurface require information about the relationships between capillary pressure and saturation, and between relative permeability and saturation. An evaluation of the information available for these relationships suggests that substantial discrepancies may be introduced into simulations if estimated, rather than measured, data are employed. The purpose of this study was to quantify these deviations. Two-phase displacement simulations were performed in one and two dimensions for several organic liquid-water systems. Both constant-head and constant-flux boundary conditions were employed at a variety of flow rates and time scales, using both measurements and estimates of capillary pressure and relative permeability for a sandy aquifer material. The results demonstrate that the use of estimated transport relationships produces significantly different predictions of organic liquid migration. The magnitude of the deviations between predictions may be as high as 25% or more after relatively short displacement periods, depending on the boundary conditions of the simulated scenario, as well as on the physical characteristics of the two-phase system. For the systems examined, most of the deviations resulted from the estimates for relative permeability to the organic liquid. Thus, improved methods for the estimation of the relative permeability to the organic liquid are needed to reduce the uncertainty in displacement simulations.

Effects of ethanol addition on micellar solubilization and plume migration during surfactant enhanced recovery of tetrachloroethene

Alcohol addition has been suggested for use in combination with surfactant flushing to enhance solubilization kinetics and permit density control of dense non-aqueous phase liquid (DNAPL)-laden surfactant plumes. This study examined the effects of adding ethanol (EtOH) to a 4% Tween 80 (polyoxyethylene (20) sorbitan monooleate) solution used to flush tetrachloroethene (PCE)-contaminated porous media. The influence of EtOH concentration, subsurface layering and scale on flushing solution delivery and PCE recovery was investigated through a combination of experimental and mathematical modeling studies. Results of batch experiments demonstrated that the addition of 2.5%, 5% and 10% (wt.) EtOH incrementally increased the PCE solubilization capacity and viscosity of the surfactant solution, while reducing solution density from 1.002 to 0.986 g/cm3. Effluent concentration data obtained from one-dimensional (1-D) column experiments were used to characterize rate-limited micellar solubilization of residual PCE, which was strongly dependent upon flow velocity and weakly dependent upon EtOH concentration. Two-dimensional (2-D) box studies illustrated that minor differences (0.008 g/cm3) between flushing and resident solution density can strongly influence surfactant front propagation. A two-dimensional multiphase simulator, MISER, was used to model the influence of EtOH composition on the aqueous flow field and PCE mass recovery. The ability of the numerical simulator to predict effluent concentrations and front propagation was demonstrated for both 1-D columns and 2-D boxes flushed with EtOH-amended Tween 80 solutions. Results of this study quantify the potential influence of alcohol addition on surfactant solution properties and solubilization capacity, and demonstrate the importance of considering small density variations in remedial design.

Influence of surfactant-facilitated interfacial tension reduction on chlorinated solvent migration in porous media: observations and numerical simulation.

The ability of a multiphase flow model to capture the migration behavior of chlorinated solvents under conditions of surfactant-facilitated interfacial tension (IFT) reduction is assessed through comparison of model predictions with observations from controlled laboratory experiments. Tetrachloroethene (PCE) was released in two-dimensional saturated systems, packed with sandy media that incorporated rectangular lenses of capillary contrast. Spatially uniform interfacial tension conditions were created in the tanks by pre-flushing the porous medium with either Milli Q water or an aqueous surfactant solution. Experimental observations showed that surfactant-facilitated IFT reductions substantially lowered capillary resistance to the vertical downward migration of PCE and enabled PCE to enter finer grained, less permeable lenses that were not penetrated in the absence of surfactant. An immiscible flow model was used to simulate the conditions of the laboratory experiments. Under higher IFT conditions (47.5 and 5 dyn/cm), the model could successfully predict the general migration behavior of the organic liquid. Model predictions, however, exhibited poorer agreement with observed migration pathways under low IFT conditions (0.5 dyn/cm). In all cases, the predicted PCE distributions were influenced by selection of the parametric model for capillary retention and relative permeability. Simulated migration rates were more consistent with observed behavior when the Brooks-Corey/Burdine model was employed. For low interfacial tensions, improved predictions of migration pathways were obtained through grid refinement and incorporation of small-scale packing variability. Simulations highlight the substantial sensitivity of model predictions to the capillary pressure-scaling factor, grid resolution, and small-scale porosity variations at interfaces of permeability contrast under reduced IFT conditions.