Rajesh Srivastava

Analytical solutions for one‐dimensional, transient infiltration toward the water table in homogeneous and layered soils

Analytical solutions describing the transient soil water pressure distributions during one-dimensional, vertical infiltration toward the water table through homogeneous and two-layer soils are derived. Exponential functional forms K = Kseαψ and θ = θr + (θs − θr)eαψ are used to represent the hydraulic conductivity and pressure relation and the soil water release curve. Steady state profiles are used as initial conditions. Hydraulic behavior of the soils during wetting and drainage processes is discussed in terms of the pressure head and moisture content profiles and temporal variation of the specific discharge. The solutions provide a reliable means of comparing the accuracy of various numerical methods, especially in very dry layered soils.

Using flow interruption to identify factors causing nonideal contaminant transport

The transport and fate of many contaminants in subsurface systems can be influenced by several rate-limited processes, such as rate-limited sorption, diffusional mass transfer, and transformation reactions. Identification of the controlling process in such systems is often difficult, and is confounded by the possible influence of additional factors such as nonlinear or hysteretic sorption. We present a relatively simple method, flow interruption, that can be used to discriminate between various sets of processes. The application of the method is illustrated with results obtained from experiments performed for selected systems. Specific process-pairs investigated include physical nonequilibrium vs. physical heterogeneity, rate-limited sorption vs. nonlinear sorption, and sorption vs. transformation reactions. The results show that, while both physical nonequilibrium and physical heterogeneity can cause enhanced spreading or dispersion, only the former causes a noticeable concentration perturbation upon imposition of flow interruption under typical conditions. In addition, while both rate-limited sorption and nonlinear sorption can cause breakthrough curves to exhibit tailing, only rate-limited sorption induces a concentration perturbation upon imposition of flow interruption. The information obtained from applying flow interruption can be used to assist in the planning of additional, process-specific experiments and to help identify appropriate mathematical models to be used for transport simulation.

A three-dimensional numerical model for water flow and transport of chemically reactive solute through porous media under variably saturated conditions

A three-dimensional numerical model is developed for the simulation of water flow and chemical transport through variably saturated porous media. The nonlinear flow equation is solved using the Galerkin finite element technique with the Picard iteration scheme and a continuous velocity field is obtained by separate application of the Galerkin technique to the flux equation. A two-site adsorption-desorption model with a first-order loss term is used to describe the chemical behavior of the reactive solute. The advective part of the transport equation is solved with one-step backward particle tracking while the dispersive part is solved by the regular Galerkin finite element technique. Preconditioned conjugate-gradient-like method is used for the iterative solution of the systems of linear simultaneous equations to save on computer memory and execution time. The model is applied to a few situations and the numerical results are compared with observed and analytic values. The model is found to work quite well, even near very sharp fronts.

Nonideal transport of reactive solutes in heterogeneous porous media 2. Quantitative analysis of the Borden natural-gradient field experiment

Abstract Field experiments constitute an integral component of research on transport and fate of contaminants in the subsurface. One of the most well known of the few field experiments performed with reactive solutes is the natural-gradient experiment conducted at the Borden site during 1982 to 1984. A major finding of the experiment was that the transport of the reactive, organic compounds was nonideal. First, the velocities of the centers of mass of the plumes decreased with time, which was reflected in a temporal increase in effective retardation. Second, the longitudinal spreading observed for the organic solutes was about three times larger than that of the nonreactive tracers for an equivalent travel distance. Third, the breakthrough curves measured at selected monitoring points exhibited greater asymmetry compared to the nonreactive tracers. The cause(s) of the nonideal transport observed for the organic solutes has remained unexplained, despite a number of attempts. We have used a multi-scale, multi-factor mathematical model to successfully predict the displacement and spreading behavior of the tetrachloroethene and tetrachloromethane plumes. Based on our analyses, we conclude that a near-field trend of increasing sorption capacity was a primary cause of the deceleration of the centers of mass of the organic-solute plumes. The coupled effects of nonlinear sorption and enhanced spreading caused by spatially variable hydraulic conductivity and spatially variable sorption also influenced plume displacement. In addition, it is possible that the combination of spatially variable hydraulic conductivity and sorption contributed directly to plume deceleration. However, a magnitude of sorption variability larger than has been measured to date is required for this contribution to be significant. The combined spatial variability of hydraulic conductivity and sorption, and a potential negative cross correlation between them, appears to have been the major cause of the enhanced longitudinal spreading observed for the organic-solute plumes in comparison to the nonreactive-solute plumes. However, nonlinear sorption, the spatial trend of increasing sorption capacity, and rate-limited sorption/mass transfer also influenced spreading behavior. In total, it is evident that the transport of the organic compounds during the Borden natural-gradient field experiment was influenced by several interacting factors and coupled processes, and that accurate prediction of the observed behavior requires the use of a mathematical model that accounts for this complexity.

Nonideal transport of reactive solutes in heterogeneous porous media: 1. Numerical model development and moments analysis

Abstract The transport of reactive solutes at the field scale is characteristically nonideal, and this nonideality is often caused by more than one factor. In these cases, mathematical models that explicitly account for multiple factors are necessary for proper simulation of transport and for accurate analysis of causative factors. The purpose of this paper is to present a mathematical model for simulating the transport of reactive solute in heterogeneous porous media. We have taken a multi-scale, multi-factor approach that explicitly accounts for such factors as hydraulic-conductivity variability, structured porous media, rate-limited diffusive mass transfer, and nonlinear, rate-limited, spatially variable sorption. The influence of these factors on the displacement and spreading of solute plumes and on mass flux is illustrated with a series of two-dimensional (vertical) simulations. It is shown that rate-limited sorption/mass transfer and nonlinear sorption can significantly influence the first, second, and third spatial moments, whereas hydraulic-conductivity variability significantly influences only the second spatial moment. Plume skewness is especially sensitive to the specific factor controlling nonideal transport. For example, both rate-limited sorption/mass transfer and nonlinear sorption can create negatively skewed plumes during early stages of transport. However, the plume influenced by rate-limited sorption/mass transfer tends toward symmetry as global residence time increases. Conversely, the plume influenced by nonlinear sorption tends toward a constant degree of asymmetry as the spreading forces balance the concentration-dependent retardation behavior associated with nonlinear sorption. Furthermore, the results illustrate that unique behavior can result from the coupling of multiple processes. For example, when influenced by coupled heterogeneity and nonlinear sorption, the shape of a plume may change from positive to negative skewness during the course of transport.

Reactive solute transport in macroscopically homogeneous porous media: analytical solutions for the temporal moments.

In this work, we investigate one-dimensional solute transport affected by rate-limited sorption, first-order mass transfer, and first-order transformation. Analytical expressions are obtained for the temporal moments of the solute in the solution phase. The effect of various rate coefficients on the temporal moments is examined. It was found that, in the presence of transformation reactions, the mean arrival time, and the spread and skewness of the breakthrough curves, are not monotonic functions of the rate coefficients. These solutions will be useful as a preliminary analysis tool for ascertaining the relative importance of various processes under given conditions. They may also be used to analyze the accuracy of various numerical techniques used for simulation of reactive transport.

NONIDEAL TRANSPORT OF REACTIVE SOLUTES IN HETEROGENEOUS POROUS MEDIA. 4. ANALYSIS OF THE CAPE COD NATURAL-GRADIENT FIELD EXPERIMENT

One of the largest field studies of reactive-solute transport is the natural-gradient experiment conducted at Cape Cod from 1985 to 1988. Major findings regarding the transport behavior of the reactive solute (lithium) were that the rate of plume displacement decreased with time (temporal increase in effective retardation), the degree of longitudinal spreading was much greater than that observed for bromide for an equivalent travel distance, and the plume was asymmetric, with maximum concentrations located near the leading edges. The objective of our work was to quantitatively analyze the transport of lithium and to attempt to identify the factor or factors that contributed significantly to its observed nonideal transport. We used a mathematical model that accounted for several transport factors, including spatially variable hydraulic conductivity and spatially variable, nonlinear, rate-limited sorption, with all parameter values obtained independently. The transport behavior observed during the first 250 days, corresponding to a transport distance of 60 m, was predicted reasonably well by the simulation that incorporated spatially variable hydraulic conductivity; nonlinear, rate-limited, spatially variable sorption; and uniform water chemistry. However, the larger degree of deceleration observed during the latter stage of the experiment (the filial 20 m) was not. The larger deceleration was successfully simulated by increasing 3-fold the mean sorption capacity of the latter portion of the transport domain. Such a change in sorption capacity is consistent with the potential impact on lithium sorption of measured changes in water chemistry (e.g.,pH increase, reduction in resident Zn)at occur in the zone through which the lithium plume traversed. The results of the analyses suggest that nonlinear sorption and variable water chemistry may have btors responsible for the nonuniform displacement of the lithium plume, with rate-limited sorption/desorption having minimal impact. In addition, the asymmetry of the plume appears to have been caused primarily by nonlinear sorption, whereas the enhanced longitudinal spreading appears to have been caused by the combined influences of spatially variable hydraulic conductivity and sorption, nonlinear sorption, and rate-limited sorption/desorption. A comparison of the results of this analysis to those we obtained from an analysis of the Borden natural-gradient study reveals several similarities regarding the transport of reactive contaminants at the field scale.

Simulation of saltwater intrusion in the Northern Guam Lens using a microcomputer

Abstract A two-dimensional (areal) finite element model of saltwater intrusion was modified so that it can run on a microcomputer. The model assumes a sharp interface between fresh water and salt water and simulates the movement of both fresh water and salt water. Linear triangular elements are used to discretize the domain. A preprocessor is used to renumber the nodes of a given network to reduce the bandwidth of the matrix. The model was applied to the Northern Guam aquifer. The hydraulic conductivity in three regions of the aquifer was calibrated using the water-level history for a few observation wells. Field measurements of the depth of the interface indicate that the sharp interface assumption is valid for most of the aquifer. Comparison of the depth of the measured 50% isochlor with the computed depth of the interface shows that the two are equal at most locations. In some cases, the computed depth is less than the measured depth which results in a conservative estimate of the interface depth.

Darcy velocity computations in the finite element method for multidimensional randomly heterogeneous porous media

For numerical modeling of transport of contaminants through porous media, an accurate determination of the velocity field is a prerequisite. Some previous schemes of obtaining the Darcian velocity field through numerical solution of the flow equation result in a physically inconsistent velocity distribution in a heterogeneous medium. A scheme that is consistent with the physics of velocity variation near material interfaces is examined and compared with previous schemes. Numerical simulations are used to demonstrate the capability and accuracy of the proposed scheme for randomly heterogeneous porous media.

Temporal Moments for Reactive Transport through Fractured Impermeable/Permeable Formations

AbstractThe transport of reactive solutes through fractured porous formations has been analyzed. The transport through the porous block is represented by a general multiprocess nonequilibrium equation (MPNE), which, for the fracture, is represented by an advection-dispersion equation with linear equilibrium sorption and first-order transformation. An implicit finite-difference technique has been used to solve the two coupled equations. The transport characteristics have been analyzed in terms of zeroth, first, and second temporal moments of the solute in the fracture. The solute behavior for fractured impermeable and fractured permeable formations are first compared and the effects of various fracture and matrix transport parameters are analyzed. Subsequently, the transport through a fractured permeable formation is analyzed to ascertain the effect of equilibrium sorption, rate-limited sorption, and the multiprocess nonequilibrium transport process. It was found that the temporal moments were nearly ident...