Coupled Surface–Subsurface Solute Transport Model for Irrigation Borders and Basins. II. Model Evaluation

The development of a coupled surface–subsurface solute transport model for surface fertigation management is presented in a companion paper (Part I). This paper discusses an evaluation of the coupled model. The numerical solution for pure advection of solute in the surface stream was evaluated using test problems with steep concentration gradients. The result shows that the model can simulate advection without numerical diffusion and oscillations, an important problem in the solution of the advection–dispersion equation in advection dominated solute transport. In addition, a close match was obtained between the numerical solution of the one-dimensional advection–dispersion equation and a simplified analytical solution. A comparison of field data and model output show that the overall mean relative residual between field observed and model predicted solute breakthrough curves in the surface stream is 16.0%. Excluding only two outlier (in the graded basin data) reduces the over all mean relative residual between field observed and model predicted breakthrough curves to 5.2%. Finally, potential applications of the model in surface fertigation and salinity management are highlighted.     

Coupled Consolidation and Contaminant Transport in Compressible Porous Media

This paper presents an experimental and numerical investigation of coupled consolidation and contaminant transport in compressible porous media. Numerical simulations were performed using the CST2 computational model, in which a dual-Lagrangian framework is used to separately follow the motions of fluid and solid phases during consolidation. Diffusion and large strain consolidation-induced transport tests were conducted on composite specimens of kaolinite slurry consisting of an upper uncontaminated layer and a lower layer contaminated with potassium bromide. Assessment of the importance of the consolidation process on solute transport is based on measured and simulated solute breakthrough curves and final contaminant concentration profiles. CST2 simulations closely match the experimental data for three different loading conditions. Diffusion and consolidation-induced advection made important contributions to solute transport and mass outflow in this study. Additional simulations indicate that consolidation-induced contaminant transport may also be affected by specimen boundary drainage and initial concentration conditions.     

Sorption Behavior and Long-Term Retention of Reactive Solutes in the Hyporheic Zone of Streams

This paper analyzes the transport of sorbing solutes by extending the advective storage path model developed for longitudinal transport of inert solutes in streams coupled with flow-induced uptake in the hyporheic zone. Independent observations of a conservative (3H) and a reactive (51Cr) tracer in both the stream water and the hyporheic zone were used to differentiate between hydraulic and sorption processes. The method of temporal moments was found to be inadequate for parameter determination, whereas fitting versus the entire tracer breakthrough curves with special emphasis on the tail indicates that the proposed model could be used to represent both conservative and reactive transport. Information on the tracer inventory of the conservative tracer in the hyporheic zone was found to be of vital importance to the evaluation of the hydraulic exchange. A model evaluation based on stream water data alone can yield predictions of a wash-out in the hyporheic zone that deviates markedly from the observed wash-out. This prohibits long-term predictions of the wash-out from the hyporheic zone as well as the evaluation of sorption properties. The sorption in the hyporheic zone was found to follow a two-step model, where the first step is instantaneous and the second kinetic. A model with a single-step sorption process could not reproduce the observed breakthrough curves. An evaluation of the relative importance of including sorption kinetics in solute stream transport models is elucidated by means of the analytical expressions for the temporal moments. The omission of the kinetics in the second sorption step in the hyporheic zone will result in relative errors in the moments of second order or higher. The error will increase with decreasing residence time in the hyporheic zone. Especially, long-term predictions of the wash-out from the hyporheic zone require consideration of the rate-limited sorption.     

Parametric Study of One-Dimensional Solute Transport in Deformable Porous Media

Formulation for the effect of dissipation of excess pore water pressure on one-dimensional advective-diffusive transport of solutes in clays is presented. The formulation is based on the effect of the rate of consolidation or swelling and excess pore pressure or suction dissipation on transient, nonlinear advective component of transport through clay. One partial differential equation is presented for advective diffusive transport that is dependent upon soil/solute properties and transient hydraulic head gradient, which is calculated from the Terzaghi consolidation equation. Finite difference method is used to solve the system of partial differential equations for consolidation and solute transport. Four hypothetical cases are evaluated to demonstrate the effect of consolidation under loading and swelling under hydraulic gradient on advective-diffusive transport and breakthrough in single and double drainage clay layer. The results show that consolidation in doubly drained clay impacts concentration profiles, but does not significantly impact breakthrough of the diffusive flux. Consolidation under single drainage conditions, significantly impacts the diffusional flux. When drainage path is the same as the diffusional flux, consolidation accelerates transport and breakthrough time can be less than 5% of the diffusional breakthrough time under no consolidation. Swelling under hydraulic gradient application can either accelerate or retard the advective diffusive flux, depending upon the ratio of the effective diffusion coefficient relative to the coefficient of consolidation. Higher the effective diffusion coefficient and lower the coefficient of consolidation result in an increase in the effect of pressure dissipation on transport.     

Predicting Solute Flux through a Clay Membrane Barrier

Measured solute flux breakthrough curves (FBCs) from column tests performed on a semipermeable clay membrane subjected to KCl solutions are compared with predicted FBCs using independently measured flow and transport properties. The predicted FBCs are based on three scenarios: (1) Advective–dispersive transport that neglects membrane behavior; (2) advective–dispersive transport that accounts for the concentration dependency of the effective salt-diffusion coefficient (Ds?) resulting from membrane behavior, referred to as partially coupled transport; and (3) fully coupled transport that includes both the explicit coupling terms (e.g., hyperfiltration, chemico-osmosis) associated with clay membrane behavior and the concentration dependency of Ds?. The FBCs predicted by fully coupled transport agree best with the measured FBCs. However, for the diffusion-controlled conditions of the column tests, the steady-state solute fluxes predicted by partially coupled transport are only 23–69% higher than the measured steady-state fluxes. The results imply that the advective–dispersive transport theory can be used to provide reasonably accurate, albeit somewhat conservative, estimates of steady-state solute flux through clays that behave as semipermeable membranes, provided diffusion is a significant, if not dominant, solute transport process and the concentration dependency of Ds? are taken into account.     

Coupled Surface–Subsurface Solute Transport Model for Irrigation Borders and Basins. I. Model Development

Surface fertigation is widely practiced in irrigated crop production systems. Lack of design and management tools limits the effectiveness of surface fertigation practices. The availability of a process-based coupled surface–subsurface hydraulic and solute transport model can lead to improved surface fertigation management. This paper presents the development of a coupled surface–subsurface solute transport model. A hydraulic model described in a previous paper by the writers provided the hydrodynamic basis for the solute transport model presented here. A numerical solution of the area averaged advection–dispersion equation, based on the split-operator approach, forms the surface solute transport component of the coupled model. The subsurface transport process is simulated using HYDRUS-1D, which also solves the one-dimensional advection–dispersion equation. A driver program is used for the internal coupling of the surface and subsurface transport models. Solute fluxes calculated using the surface transport model are used as upper boundary conditions for the subsurface model. Evaluation of the model is presented in a companion paper.     

Predictive Modeling of Transient Storage and Nutrient Uptake: Implications for Stream Restoration

This study examined two key aspects of reactive transport modeling for stream restoration purposes: the accuracy of the nutrient spiraling and transient storage models for quantifying reach-scale nutrient uptake, and the ability to quantify transport parameters using measurements and scaling techniques in order to improve upon traditional conservative tracer fitting methods. Nitrate (NO3?) uptake rates inferred using the nutrient spiraling model underestimated the total NO3? mass loss by 82%, which was attributed to the exclusion of dispersion and transient storage. The transient storage model was more accurate with respect to the NO3? mass loss (±20%) and also demonstrated that uptake in the main channel was more significant than in storage zones. Conservative tracer fitting was unable to produce transport parameter estimates for a riffle-pool transition of the study reach, while forward modeling of solute transport using measured/scaled transport parameters matched conservative tracer breakthrough curves for all reaches. Additionally, solute exchange between the main channel and embayment surface storage zones was quantified using first-order theory. These results demonstrate that it is vital to account for transient storage in quantifying nutrient uptake, and the continued development of measurement/scaling techniques is needed for reactive transport modeling of streams with complex hydraulic and geomorphic conditions.     

Nonuniform and Unsteady Solute Transport in Furrow Irrigation. II: Description of Field Experiments and Calibration of Infiltration and Roughness Coefficients

Field tests were conducted to obtain irrigation evaluation and solute transport data. The data were used to calibrate and validate an advection-dispersion model for furrow irrigation. The empirical infiltration equation and roughness parameters were estimated from the evaluation data. The inflow rate was measured with a volumetric meter and a flume and resulted in different average inflow rates. Hydraulic simulation results proved nearly as accurate with infiltration function estimates derived from the meter or flume data despite the difference in measured flow rate. Hence, the calibrated infiltration functions provide limited clues about possible problems with the inflow data. The choice of the infiltration equation used to fit the data (Branch versus modified Kostiakov) produced greater differences in the hydraulic modeling results. The timing and spread of the solute concentration pulses were well predicted independently of the inflow data and infiltration equation used to fit the data. However, differences between the meter and flume inflow rate were clearly manifested in the predicted peak solute concentrations. Results highlight the importance of accurate inflow measurements for parameter estimation.     

Effect of Adsorbent Particle Layering on Performance of Conventional and Tapered Fixed-Bed Adsorbers

Experimental and modeling studies were conducted for the adsorption of phenol from aqueous solutions onto activated carbon in fixed beds with the adsorbent particles layered according to particle size. In the conventional stratified cylindrical adsorber (SCA), the particles were layered according to natural stratification, and increased in size with column depth. In the reverse stratified tapered adsorber (RSTA), the particle size decreased with column depth, and the fluid velocity decreased in the direction of flow. Experimental data indicate that for a uniform particle size distribution, the breakthrough time for the RSTA was about 60% higher than for the SCA under identical carbon loading and flow conditions. The homogeneous solid phase diffusion model with Linear-Freundlich isotherm was used to model the layered adsorbers. It provides excellent predictions for breakthrough curves at various column depths. Bed capacity utilization can be increased with the RSTA due to the sharpening of the solute front, and this will translate into lower capital and operating costs for the carbon adsorption system due to the smaller unit required, lower carbon inventory, and lower pumping costs.     

Overland Water Flow and Solute Transport: Model Development and Field-Data Analysis

The application of plant nutrients with irrigation water is an efficient and cost-effective method for fertilizer application to enhance crop production and reduce or eliminate potential environmental problems related to conventional application methods. In this study, a combined overland water flow and solute transport model for analysis and management of surface fertigation/chemigation is presented. Water flow is predicted with the well-known Saint-Venant’s equations using a control volume of moving cells, while solute transport is modeled with the advection-dispersion equation. The 1D transport equation was solved using a Crank-Nicholson finite-difference scheme. Four, large-scale, field experiments were conducted on blocked-end and free draining furrows to calibrate and verify the proposed model. The results showed that application of solute during the entire irrigation event, or during the second half of the irrigation for blocked end conditions with appropriate inflow rates, produced higher solute uniformity than application of solute during the first half of the irrigation event. Measured fertilizer distribution uniformity of the low quarter ranged from 21 to 76% while fertilizer distribution uniformity of the low half values varied between 62 to 87%. The model was subsequently applied to the experimental data; results showed good agreement with all field data. Water balance errors for the different experiments varied from 0.004 to 1.8%, whereas fertilizer mass balance errors ranged from 1.2 to 3.6%. A sensitivity analysis was also performed to assess the effects of longitudinal dispersivity parameter on overland solute concentrations. A value of 10 cm for dispersivity provided a reasonable fit to the experimental data.     

Electrical Conductivity Breakthrough Curves

The factors affecting the applicability of electrical conductivity (EC) breakthrough curves as an indicator of chemical equilibrium between effluent and influent solutions in compatibility tests are illustrated. The shapes of EC breakthrough curves are shown to be a function of the flow rate, the solute retardation factor, the species of cation and anion in the permeant liquid, and the cation initially occupying the exchange complex of the clay. Measured data show that the magnitude of the EC in the soil due to the existence of soluble salts relative to the EC of the influent solution (permeant liquid) affects significantly the observed shapes of the EC breakthrough curves. Comparison between theoretically predicted and measured EC breakthrough curves varies from good to excellent, depending on the initial conditions for the test. The results indicate that chemical equilibrium can not be attained before complete EC breakthrough is attained, regardless of the shape of the EC breakthrough curve. Thus, EC breakthrough curves offer a potentially simple, practical, and inexpensive method for determining chemical equilibrium in laboratory compatibility tests involving permeation with electrolyte solutions.     

Epidermal iontophoresis: I. Development of the ionic mobility-pore model

PURPOSE: An integrated ionic mobility-pore model for epidermal iontophoresis is developed from theoretical considerations using both the free volume and pore restriction forms of the model for a range of solute radii (rj) approaching the pore radii (rp) as well as approximation of the pore restriction form for rj/rp < 0.4. In this model, we defined the determinants for iontophoresis as solute size (defined by MV, MW or radius), solute mobility, solute shape, solute charge, the Debye layer thickness, total current applied solute concentration, fraction ionized, presence of extraneous ions (defined by solvent conductivity), epidermal permselectivity, partitioning rates to account for interaction of unionized and ionized lipophilic solutes with the wall of the pore and electroosmosis. METHODS: The ionic mobility-pore model was developed from theoretical considerations to include each of the determinants of iontophoretic transport. The model was then used to reexamine iontophoretic flux conductivity and iontophoretic flux-fraction ionized literature data on the determinants of iontophoretic flux. RESULTS: The ionic mobility-pore model was found to be consistent with existing experimental data and determinants defining iontophoretic transport. However, the predicted effects of solute size on iontophoresis are more consistent with the pore-restriction than free volume form of the model. A reanalysis of iontophoretic flux-conductivity data confirmed the model's prediction that, in the absence of significant electroosmosis, the reciprocal of flux is linearly related to either donor or receptor solution conductivity. Significant interaction with the pore walls, as described by the model, accounted for the reported pH dependence of the iontophoretic transport for a range of ionizable solutes. CONCLUSIONS: The ionic mobility-pore iontophoretic model developed enables a range of determinants of iontophoresis to be described in a single unifying equation which recognises a range of determinants of iontophoretic flux.     

Investigation of Consolidation-Induced Solute Transport. II: Experimental and Numerical Results

This paper presents an experimental and numerical investigation of consolidation-induced solute transport. Diffusion and large strain consolidation tests were performed on composite specimens of kaolinite clay consisting of an upper uncontaminated layer and a lower layer contaminated with potassium bromide. Experimental measurements of effluent concentration, solute mass outflow, and final concentration profiles were obtained for a variety of initial, boundary, and loading conditions, including unload/reload. Numerical simulations were conducted using a computational model in which solute transport occurs by advection, dispersion, and sorption and is consistent with temporal and spatial variations of porosity and seepage velocity in the consolidating layer. Large strains were taken into account as well as variation of effective diffusion coefficient with porosity and nonlinear nonequilibrium sorption effects. The numerical simulations are in good to excellent agreement with the experimental measurements. Results indicate that, depending on conditions, diffusion and consolidation-induced advection can make important contributions to solute transport and mass outflow. Thus, both mechanisms should be considered for transport analyses involving soft contaminated clays undergoing large volume change. Results also indicate that nonequilibrium sorption effects were not significant for the materials and test conditions used in this study.     

Retardation of Nonlinearly Sorbed Solutes in Porous Media

The impact of the assumption of linear sorption on retardation of nonlinearly sorbed solutes in porous media is numerically explored in this paper. Breakthrough data of nonlinearly sorbed solutes are generated using the BIO1D simulation code along with the Freundlich-type nonlinear sorption model. Retardation coefficients (R) from generated breakthrough curves are estimated using first-moment analysis. Variations of R with experimental conditions revealed that R of a nonlinearly sorbed solute is a function of the input concentration, the injection period and the pore-water velocity but is independent of the length scale. This study also showed that it is appropriate to estimate R of a nonlinearly sorbed solute using a linearized isotherm if all soil particles experience sorption with liquid concentration equal to the induced concentration. Otherwise, the estimated linearized R will be either under- or overestimated depending on the applied experimental conditions and Freundlich parameters. The study further revealed that inability to account for sorption nonlinearity may in some cases erroneously be interpreted as evidence of the presence of transport nonequilibrium. A method is suggested to determine nonlinear sorption parameters from miscible displacement experiments.     

Goodness-of-Fit Test for Modeling Tracer Breakthrough Curves in Wetlands

Wetland transport models generally either assume plug flow (with or without dispersion) or conceptualize the wetland as a series of continuously stirred tank reactors (CSTRs). To evaluate the CSTR approach, we present a goodness-of-fit test suitable for evaluating breakthrough curves from tracer experiments. The test, which makes use of confidence intervals associated with the multivariate normal distribution, can be used to test the fit of the breakthrough curve model, but requires sampling across a transect rather than from a single point. To test the CSTR assumption, we conducted a pair of two-dimensional tracer experiments within a 9.9?ha wetland constructed to receive effluent from a wastewater treatment plant in San Jacinto, Calif. The wetland operates with five parabolic inlets and a single large parabolic outlet to encourage lateral uniformity. In both experiments tritium oxide (HTO) was used as the tracer. Rhodamine WT dye was also included in the second experiment. Tracer samples were collected along transects installed perpendicular to the direction of flow. Analysis of the results indicates satisfactory lateral mixing and no significant short-circuiting. Rhodamine WT dye performed similarly to HTO when detectable but was too dilute to be observed at the outlet. When tracer movement was modeled as a series of continuously stirred reaction vessels, the parameter associated with the integer number of vessels increased from 2 at the first transect to 8 at the outlet. At each transect, the model was checked with a new goodness-of-fit test. At the α = 0.05 confidence level, all fitted models were rejected, suggesting that while the CSTR assumption may usefully approximate transport processes, it is not statistically valid for this wetland.     

Long-Term Tritium Transport through Field-Scale Compacted Soil Liner

A 13-year study of tritium transport through a field-scale earthen liner was conducted by the Illinois State Geological Survey to determine the long-term performance of compacted soil liners in limiting chemical transport. Two field-sampling procedures (pressure-vacuum lysimeter and core sampling) were used to determine the vertical tritium concentration profiles at different times and locations within the liner. Profiles determined by the two methods were similar and consistent. Analyses of the concentration profiles showed that the tritium concentration was relatively uniformly distributed horizontally at each sampling depth within the liner and thus there was no apparent preferential transport. A simple one-dimensional analytical solution to the advective–dispersive solute transport equation was used to model tritium transport through the liner. Modeling results showed that diffusion was the dominant contaminant transport mechanism. The measured tritium concentration profiles were accurately modeled with an effective diffusion coefficient of 6×10?4?mm2/s, which is in the middle of the range of values reported in the literature.     

Retardation of Nonlinearly Sorbed Solutes in Porous Media

The impact of the assumption of linear sorption on retardation of nonlinearly sorbed solutes in porous media is numerically explored in this paper. Breakthrough data of nonlinearly sorbed solutes are generated using the BIO1D simulation code along with the Freundlich-type nonlinear sorption model. Retardation coefficients (R) from generated breakthrough curves are estimated using first-moment analysis. Variations of R with experimental conditions revealed that R of a nonlinearly sorbed solute is a function of the input concentration, the injection period, and the pore–water velocity but is independent of the length scale. This study also showed that it is appropriate to estimate R of a nonlinearly sorbed solute using a linearized isotherm if all soil particles experience sorption with liquid concentration equal to the induced concentration. Otherwise, the estimated linearized R will be either under- or overestimated depending on the applied experimental conditions and Freundlich parameters. The study further revealed that inability to account for sorption nonlinearity may in some cases erroneously be interpreted as evidence of the presence of transport nonequilibrium. A method is suggested to determine nonlinear sorption parameters from miscible displacement experiments.     

Solute washout experiments for characterizing mass transport in hollow fiber immunoisolation membranes

The transport characteristics of immunoisolation membranes can have a critical effect on the design of hybrid artificial organs and cell therapies. However, it has been difficult to quantitatively evaluate the desired transport properties of different hollow fiber membranes due to bulk mass transfer limitations in the fiber lumen and annular space. An attractive alternative to existing methodologies is to use the rate of solute removal or "washout" from the annular space during constant flow perfusion through the fiber lumen. Experimental washout curves were obtained for glucose and a 10 kD dextran in two different hollow fiber devices. Data were analyzed using a theoretical model which accounts for convective and diffusive transport in the lumen, membrane, and annular space. The model was in good agreement with the experimental results and provided an accurate measure of the effective membrane diffusion coefficient for both small and large solutes. This approach should prove useful in theoretical analyses of solute transport and performance of hollow fiber artificial organs.     

Analysis of Point-Source and Boundary-Source Solutions of One-Dimensional Groundwater Transport Equation

The solute transport equation is commonly used to describe the migration and fate of solutes in a groundwater flow system. Depending on the problem nature, the source of the solute may be represented as a point source term in the equation or specified as the first-type or third-type boundary condition. The solutions derived under the condition that the solute introduced into the flow system is from the boundary is herein considered as the boundary-source solutions. The solution obtained when solving the transport equation with a point-source term is considered as the point-source solution. The Laplace transform technique is employed to derive the formulas for those solutions expressed in terms of the normalized mass release rate. The underlying nature of different source release modes and the differences among those boundary-source solutions and the constant point-source solution can be easily and clearly differentiated based on the derived formulas for one-dimensional transport. The methodology could, however, be easily extended to two- and three-dimensional problems.     

Model for Consolidation-Induced Solute Transport with Nonlinear and Nonequilibrium Sorption

A numerical model, called CST2, is presented for coupled large strain consolidation and solute transport in saturated porous media. The consolidation and solute transport algorithms include the capabilities of a previous model, CST1, with the addition of a variable effective diffusion coefficient during consolidation and nonlinear nonequilibrium sorption. The model is based on a dual-Lagrangian framework that tracks separately the motions of fluid and solid phases. Verification checks of CST2 show excellent agreement with analytical and numerical solutions for solute transport in rigid porous media. A parametric study illustrates that, for the test cases considered, variation of effective diffusion coefficient during consolidation has an important effect on solute transport, whereas nonlinearity of the sorption isotherm has a less important effect. Additional simulations show that nonequilibrium sorption can have a strong effect on consolidation-induced solute transport and that this effect becomes more important as the rate of consolidation increases. The simulations also corroborate previous findings that consolidation can have a lasting effect on solute migration because transient advective flows change the distribution of solute mass which then becomes the initial condition for subsequent transport processes.