M. Th. van Genuchten

Modeling the Nonequilibrium Transport of Linearly Interacting Solutes in Porous Media: A Review

The transport of linearly interacting solutes in porous media is investigated with the help of residence time distributions, transfer functions, methods of system dynamics, and time-moment analyses. The classical one-dimensional convection-dispersion equation is extended to two-region (mobile-immobile water) transport by including diffusional mass transfer limitations characteristic of aggregated soils. The two-region model is further revised by incorporating the effects of multiple retention sites (in parallel or in series), multiple porosity levels, and arbitrary but steady flow fields. It is shown that different physical situations can be represented by a relatively small number of transfer functions containing only two types of parameters: distribution coefficients to account for equilibrium properties and characteristic times reflecting kinetic processes. Relevant kinetic processes include convective transport, hydrodynamic dispersion, adsorption-desorption, and physical or chemical mass transfer limitations. In most situations, theoretical breakthrough curves are found to be relatively insensitive to the mathematical structure of the transfer function, irrespective of the physical interpretation of the distribution coefficients and the characteristic times in the model. This means that alternative physical and chemical interpretations of model parameters can lead to nearly identical breakthrough curves. Certain transfer time distributions can lead to quite unusual shapes in the breakthrough curves; these curves strongly depend on the characteristic times and a few operational variables. Results of this study show that the transfer time distribution is an extremely useful tool for explaining some unexpected experimental results in the solute transport literature.

Experimental Investigation of Solute Transport in Large, Homogeneous and Heterogeneous, Saturated Soil Columns

Laboratory tracer experiments were conducted to investigate solute transport in 12.5-m long, horizontally placed soil columns during steady saturated water flow. Two columns having cross-sectional areas of 10×10cm2 were used: a uniformly packed homogeneous sandy column and a heterogeneous column containing layered, mixed, and lenticular formations of various shapes and sizes. The heterogeneous soil column gradually changed, on average, from coarse-textured at one end to fine-textured at the other end. NaCl breakthrough curves (BTCs) in the columns were measured with electrical conductivity probes inserted at 50- or 100-cm intervals. Observed BTCs in the homogeneous sandy column were relatively smooth and sigmoidal (S-shaped), while those in the heterogeneous column were very irregular, nonsigmoidal, and exhibited extensive tailing. Effective average pore-water velocities (veff) and dispersion coefficients (Deff) were estimated simultaneously by fitting an analytical solution of the convection-dispersion equation to the observed BTCs. Velocity variations in the heterogeneous medium were found to be much larger than those in the homogeneous sand. Values of the dispersivity,α=Deff/veff, for the homogeneous sandy column ranged from 0.1 to 5.0 cm, while those for the heterogeneous column were as high as 200cm. The dispersivity for transport in both columns increased with travel distance or travel time, thus exhibiting scale-dependency. The heterogeneous soil column also showed the effects of preferential flow, i.e., some locations in the column showed earlier solute breakthrough than several locations closer to the inlet boundary. Spatial fluctuations in the dispersivity could be explained qualitatively by the particular makeup of the heterogeneities in the column.

Numerical simulation of transport and sequential biodegradation of chlorinated aliphatic hydrocarbons using CHAIN_2D

Microbiological degradation of perchloroethylene (PCE) under anaerobic conditions follows a series of chain reactions, in which, sequentially, trichloroethylene (TCE), cis-dichloroethylene (c-DCE), vinylchloride (VC) and ethene are generated. First-order degradation rate constants, partitioning coeAcients and mass exchange rates for PCE, TCE, c-DCE and VC were compiled from the literature. The parameters were used in a case study of pump-and-treat remediation of a PCE-contaminated site near Tilburg, The Netherlands. Transport, non-equilibrium sorption and biodegradation chain processes at the site were simulated using the CHAIN_2D code without further calibration. The modelled PCE compared reasonably well with observed PCE concentrations in the pumped water. We also performed a scenario analysis by applying several increased reductive dechlorination rates, reflecting diAerent degradation conditions (e.g. addition of yeast extract and citrate). The scenario analysis predicted considerably higher concentrations of the degradation products as a result of enhanced reductive dechlorination of PCE. The predicted levels of the very toxic compound VC were now an order of magnitude above the maximum permissible concentration levels. Copyright # 1999 John Wiley & Sons, Ltd.

Field measurement of the saturated hydraulic conductivity of a macroporous soil with unstable subsoil structure

A field method for measuring saturated hydraulic conductivity, K s , was developed to characterize water flow in highly-weathered soils of Sitiung, Indonesia. Soils in this area are known to absorb large volumes of rainwater rapidly. However, K s data obtained on soil cores do not corroborate field-observed rapid infiltration rates. In the field method, a constant rate irrigation was applied to a field plot, delineated to a depth of 120 cm, and bordered on the surface to contain a depth of ponded water. The rate of irrigation was sufficient to maintain the ponding depth at a constant level as well as cause water to overflow from the ponded surface. The difference between the steady-state irrigation and overflow rates was considered to be the instantaneous flux and was assumed applicable to all depths. Simultaneous tensiometric measurements of pressure head as a function of depth provided the hydraulic gradients needed for calculation of K s using Darcys law. Hydraulic gradients deviated considerably from unity, and soil saturation did not exceed 92% of porosity. Laboratory-measured K s values for the stable-structured topsoil agreed well with the field data. However, those for the subsoil were 2 to 3 orders of magnitude lower than the field-measured values. The susceptibility of the subsoil to compaction during core extraction and slaking when in contact with free water appeared to be responsible for the highly reduced rates of flow in the laboratory samples. The subsoil pore structure was preserved only as long as it was overlain by the stable structured topsoil. Results suggest that measurements of water flow on small soil cores may, in some cases, be of questionable value. The field method provided accurate in situ data on plot-size areas. The field plot method used in this study causes minimal disturbance of the soil while the effects of sample confinement and overburden are represented fully in the measurements.

A Semidiscrete Model for Water and Solute Movement in Tile-Drained Soils: 1. Governing Equations and Solution

A finite element model has been developed to simulate solute transport in tile-drained soil-aquifer systems. Water flow in the unsaturated zone and to drains in the saturated zone was assumed to be at steady state. The model considers the transport of nonreactive solutes, as well as of reactive solutes whose behavior can be described by a distribution coefficient. The exact-in-time numerical solution yields explicit expressions for the concentration field at any future point in time without having to compute concentrations at intermediate times. The semidiscrete method involves the determination of an eigensystem of eigenvalues and eigenvectors of the coefficient matrix. The eigensystem may be complex (i.e., it may have imaginary components) due to asymmetry created by the convection term in the governing convection-dispersion equation. The proposed approach facilitates long-term predictions of concentrations in drainage effluents and of salt distributions in soil and groundwater. The accuracy of the model was verified by comparing model results with those based on an analytical solution for two-dimensional solute transport in groundwater.

An Hermitian finite element solution of the two-dimensional saturated-unsaturated flow equation☆

Abstract This paper describes a Galerkin-type finite element solution of the two-dimensional saturated-unsaturated flow equation. The numerical solution uses an incomplete (reduced) set of Hermitian cubic basis functions and is formulated in terms of normal and tangential coordinates. The formulation leads to continuous pressure gradients across interelement boundaries for a number of well-defined element configurations, such as for rectangular and circular elements. Other elements generally lead to discontinuous gradients; however, the gradients remain uniquely defined at the nodes. The method avoids calculation of second-order derivatives, yet retains many of the advantages associated with Hermitian elements. A nine-point Lobatto-type integration scheme is used to evaluate all local element integrals. This alternative scheme produces about the same accuracy as the usual 9- or 16-point Gaussian quadrature schemes, but is computationally more efficient.

Solution of the nonlinear transport equation using modified Picard iteration

Abstract The transport and fate of reactive chemicals in groundwater is governed by equations which are often difficult to solve due to the nonlinear relationship between the solute concentrations for the liquid and solid phases. The nonlinearity may cause mass balance errors during the numerical simulation in addition to numerical errors for linear transport system. We have generalized the modified Picard iteration algorithm of Celia et al.5 for unsaturated flow to solve the nonlinear transport equation. Written in a ‘mixed-form’ formulation, the total solute concentration is expanded in a Taylor series with respect to the solution concentration to linearize the transport equation, which is then solved with a conventional finite element method. Numerical results of this mixed-form algorithm are compared with those obtained with the concentration-based scheme using conventional Picard iteration. In general, the new solver resulted in negligible mass balance errors (

A Semidiscrete Model for Water and Solute Movement in Tile‐Drained Soils: 2. Field Validation and Applications

An exact-in-time two-dimensional finite element model for simulating convective-dispersive solute transport in a tile-drained field is validated against observed data from a subsurface drainage experiment. The model is capable of predicting the long-term effects of different irrigation and drainage practices on the salt distribution in an artificially drained soil-aquifer system. The model was used to predict transient changes in the salinity of the soil, the shallow ground water table, and the drain effluent. Results are also presented on the effects of imposing alternative drain spacing-depth combinations, initial groundwater salinities, solute distribution coefficients, and different types of layering of the aquifer, on the computed salinity distributions in the unsaturated zone, the groundwater, and the drain effluent.

Economic, Environmental, and Natural Resource Benefits of Plastic Shelters in Vegetable Production in a Humid Tropical Environment

ABSTRACT This paper reports the effectiveness of plastic shelters in overcoming soil-related and biotic constraints to vegetable production in Belize, Central America, where rainy-season tomatoes and sweet peppers are almost totally destroyed by geminiviruses. Use of pesticides is rampant, while rapid decline in soil productivity induces farmers to abandon previously used lands and clear new lands from virgin forests. We postulated that plants growing in the open-field environment are infected early by the soil-borne pathogens deposited on the plants from clouds of fine soil particles arising from the soil splash during high-intensity rainfall. The products of fungal and bacterial decay attract white flies (the vector for geminiviruses) and plants already weakened by the infection succumb easily to the viruses. A production system in which plant and soil surfaces are protected from direct rainfall using plastic shelters, was designed and field tested with tomatoes and sweet peppers. On average, plastic shelters increased tomato and sweet pepper yields by 169% and 96%, respectively, without any use of pesticides. Weed growth under the shelter was negligible, and plants maintained greenness and production well into the fourth month after transplanting. In contrast, open-field plots were infested with weeds, and plants were completely destroyed by the middle of the third month. The number of white flies visiting the plastic-shelter plants was only about 28% of that in the open-field. We conclude that total protection of soil and plant surfaces from rainfall is the most effective plant protection measure. The proposed system uses small land area on a continuous basis, provides stable production, requires little or no plant protection chemicals, and raises farmer income.

Revisiting the horizontal redistribution of water in soils : Experiments and numerical modeling

Abstract A series of experiments and related numerical simulations were carried out to study one‐dimensional water redistribution processes in an unsaturated soil. A long horizontal Plexiglas box was packed as homogenously as possible with sand. The sandbox was divided into two sections using a very thin metal plate, with one section initially fully saturated and the other section only partially saturated. Initial saturation in the dry section was set to 0.2, 0.4, or 0.6 in three different experiments. Redistribution between the wet and dry sections started as soon as the metal plate was removed. Changes in water saturation at various locations along the sandbox were measured as a function of time using a dual‐energy gamma system. Also, air and water pressures were measured using two different kinds of tensiometers at various locations as a function of time. The saturation discontinuity was found to persist during the entire experiments, while observed water pressures were found to become continuous immediately after the experiments started. Two models, the standard Richards equation and an interfacial area model, were used to simulate the experiments. Both models showed some deviations between the simulated water pressures and the measured data at early times during redistribution. The standard model could only simulate the observed saturation distributions reasonably well for the experiment with the lowest initial water saturation in the dry section. The interfacial area model could reproduce observed saturation distributions of all three experiments, albeit by fitting one of the parameters in the surface area production term.