Analysis of the long-term behavior of solute transport with nonlinear equilibrium sorption using breakthrough curves and temporal moments

We analyzed the long-term behavior of breakthrough curves (BTCs) and temporal moments of a solute subjected to Freundlich equilibrium sorption (s = kc(n)). For one-dimensional transport in a homogeneous porous medium, we derived a power-law relation between travel time, tau, and solute displacement, chi, with the exponent being equal to the Freundlich n exponent. The mean solute velocity, derived from the first time moment, was found to change as tau(n-1). For n values larger than 0.66, the second time moment could be related to c chi(2/n), where c is a constant. An approach based on the use of a critical concentration was developed to estimate the presence of the asymptotic regime in the tail of the BTC. This approach was tested successfully using numerical case studies. One-dimensional numerical simulations with varying values of k, n and initial mass were run to verify the closed form analytical expressions for the large time behavior of temporal moments and the tailing part of breakthrough curves. Good agreement between the slope of the tailing part of log-log transformed BTCs and the predicted slope using asymptotic theory was found. Asymptotic theory in general underestimated the magnitude of the concentration in the tail. The quality of the estimated concentrations in the tail improved for small values of the dispersivity. Experimental BTCs of uranin and benazolin were analyzed in combination with sorption/desorption batch experiments using asymptotic theory. A good agreement between the value of n parameter derived from desorption experiment with benazolin and the value of the n parameter derived from the tail of the BTC was found.     

Evaluating equilibrium and non-equilibrium transport of bromide and isoproturon in disturbed and undisturbed soil columns

In this study, displacement experiments of isoproturon were conducted in disturbed and undisturbed columns of a silty clay loam soil under similar rainfall intensities. Solute transport occurred under saturated conditions in the undisturbed soil and under unsaturated conditions in the sieved soil because of a greater bulk density of the compacted undisturbed soil compared to the sieved soil. The objective of this work was to determine transport characteristics of isoproturon relative to bromide tracer. Triplicate column experiments were performed with sieved (structure partially destroyed to simulate conventional tillage) and undisturbed (structure preserved) soils. Bromide experimental breakthrough curves were analyzed using convective-dispersive and dual-permeability (DP) models (HYDRUS-1D). Isoproturon breakthrough curves (BTCs) were analyzed using the DP model that considered either chemical equilibrium or non-equilibrium transport. The DP model described the bromide elution curves of the sieved soil columns well, whereas it overestimated the tailing of the bromide BTCs of the undisturbed soil columns. A higher degree of physical non-equilibrium was found in the undisturbed soil, where 56% of total water was contained in the slow-flow matrix, compared to 26% in the sieved soil. Isoproturon BTCs were best described in both sieved and undisturbed soil columns using the DP model combined with the chemical non-equilibrium. Higher degradation rates were obtained in the transport experiments than in batch studies, for both soils. This was likely caused by hysteresis in sorption of isoproturon. However, it cannot be ruled out that higher degradation rates were due, at least in part, to the adopted first-order model. Results showed that for similar rainfall intensity, physical and chemical non-equilibrium were greater in the saturated undisturbed soil than in the unsaturated sieved soil. Results also suggested faster transport of isoproturon in the undisturbed soil due to higher preferential flow and lower fraction of equilibrium sorption sites.     

Modeling of non-reactive solute transport in fractured clayey till during variable flow rate and time

Fractures and biopores can act as preferential flow paths in clay aquitards and may rapidly transmit contaminants into underlying aquifers. Reliable numerical models for assessment of groundwater contamination from such aquitards are needed for planning, regulatory and remediation purposes. In this investigation, high resolution preferential water-saturated flow and bromide transport data were used to evaluate the suitability of equivalent porous medium (EPM), dual porosity (DP) and discrete fracture/matrix diffusion (DFMD) numerical modeling approaches for assessment of flow and non-reactive solute transport in clayey till. The experimental data were obtained from four large undisturbed soil columns (taken from 1.5 to 3.5 m depth) in which biopores and channels along fractures controlled 96-99% of water-saturated flow. Simulating the transport data with the EPM effective porosity model (FRACTRAN in EPM mode) was not successful because calibrated effective porosity for the same column had to be varied up to 1 order of magnitude in order to simulate solute breakthrough for the applied flow rates between 11 and 49 mm/day. Attempts to simulate the same data with the DP models CXTFIT and MODFLOW/MT3D were also unsuccessful because fitted values for dispersion, mobile zone porosity, and mass transfer coefficient between mobile and immobile zones varied several orders of magnitude for the different flow rates, and because dispersion values were furthermore not physically realistic. Only the DFMD modeling approach (FRACTRAN in DFMD mode) was capable to simulate the observed changes in solute transport behavior during alternating flow rate without changing values of calibrated fracture spacing and fracture aperture to represent the macropores.     

Water and solute movement in soil as influenced by macropore characteristics: 2. Macropore tortuosity

The paper describes the results of a laboratory study on the effects of macropore tortuosity on breakthrough curves BTCs and solute distribution in a Forman loam (fine loamy-mixed Udic Haploborolls) soil. BTC were obtained using 2-D columns (slab) containing artificial macropores of five different tortuosity levels. The BTCs were run under a constant hydraulic head of 0.08 m over an initially air dry soil. The input solutions contained 1190 mg l⁻¹ of potassium bromide, 10 mg l⁻¹ of Rhodamine WT, and 100 mg l⁻¹ of FD&C Blue #1. A soil column without macropores served as a control. The displacement of a non-adsorbed tracer was not affected by the tortuosity level. An increase in macropore tortuosity progressively increased the breakthrough time, increased the apparent retardation coefficient (R′), decreased the depth to the center of mass of a given adsorbed tracer, and increased the anisotropy in tracer distribution profile. The relative importance of macropore tortuosity increased with an increase in the adsorption coefficient of the tracer. Compared to macropore continuity, the macropore tortuosity had greater impact on solute distribution profile than in its leaching.     

Dual-domain solute transfer and transport processes: evaluation in batch and transport experiments

Soil macropore networks establish a dual-domain transport scenario in which water and solutes are preferentially channeled through soil macropores while slowly diffusing into and out of the bulk soil matrix. The influence of macropore networks on intra-ped solute diffusion and preferential transport in a soil typical of subsurface-drained croplands in the Midwestern United States was studied in batch- and column-scale experiments. In the batch diffusion studies with soil aggregates, the estimated diffusion radius (length) of the soil aggregates corresponded to the half-spacing of the aggregate fissures, suggesting that the intra-ped fissures reduced the diffusion impedance and preferentially allowed solutes to diffuse into the soil matrix. In the column-scale solute transport experiments, the average diffusion radius (estimated from HYDRUS-2D simulations and a first-order diffusive transfer term) was nearly double that of the batch-scale study. This increase may be attributed to a loss of pore continuity and a compounding of the small diffusion impedance through macropores at the larger scale. The column-scale solute transport experiments also suggest that two preferential networks exist in the soil. At and near soil saturation, a primary network of large macropores (possibly root channels and earthworm burrows) dominate advective transport, causing a high degree of physical and sorption nonequilibrium and simultaneous breakthrough of a nonreactive (bromide) and a reactive (alachlor) solute. As the saturation level decreases, the primary network drains, while transport through smaller macropores (possibly intra-ped features) continues, resulting in a reduced degree of nonequilibrium and separation in the breakthrough curves of bromide and alachlor.     

Experimental Zn(II) retention in a sandy loam soil by very small columns

The use of column experiments, usually performed to better approximate field conditions, may provide information that is not available from batch experiments. In such experiments heavy metals are often adsorbed until saturation followed by desorption experiments. When the affinity of the metal to soil is high, the retention factor (R) could be greater than thousands and the duration of experiments can become impractically long. In order to use reasonable laboratory time, the flow rate should be increased or the column size decreased. The increase in flow rate produces undesirable kinetic and dispersion effects, so we used very small soil columns (pore volume = 0.31–0.70 ml) and relatively high flow rates (0.03–0.12 ml min⁻¹) in studies of Zn(II) adsorption and retention in soils. Conservative tracer flow column experiments under saturation conditions were carried out to determine flow parameters for different flow rates. Column pore volume (V_p), Peclet numbers (Pe) and longitudinal dispersion coefficients (D_L) were determined from breakthrough curves. The effect of type of electrolyte and ionic strength on the Zn(II) retention onto soil was determined. The influence of flow rate and bed height on the retention coefficient and on the mass transfer zone was also studied. The effect of different influent Zn(II) concentrations on the R values obtained was analyzed. Freundlich parameters from column experiments were compared with batch ones. The leaching efficiency of different electrolytes, salts of weak organic acids and EDTA was also studied.     

Analytical model of solute transport by unsteady unsaturated gravitational infiltration

Penetration of reactive solute into a soil during a cycle of water infiltration and redistribution is investigated by deriving analytical closed form solutions for fluid flux, moisture content and contaminant concentration. The solution is developed for gravitational flow and advective transport and is applied to two scenarios of solute applications encountered in the applications: a finite pulse of solute dissolved in irrigation water and an instantaneous pulse broadcasted onto the soil surface. Through comparison to simulations of Richards' flow, capillary suction is shown to have contrasting effects on the upper and lower boundaries of the fluid pulse, speeding penetration of the wetting front and reducing the rate of drying. This leads to agreement between the analytical and numerical solutions for typical field and experimental conditions. The analytical solution is further incorporated into a stochastic column model of flow and transport to compute mean solute concentration in a heterogeneous field. An unusual phenomenon of plume contraction is observed at long times of solute propagation during the drying stage. The mean concentration profiles match those of the Monte-Carlo simulations for capillary length scales typical of sandy soils.     

Simple screening models of NAPL dissolution in the subsurface

Three simple screening models of nonaqueous phase liquid (NAPL) dissolution in the subsurface are proposed based on the NAPL mass conservation and the assumption of proportionality between the residual NAPL source zone concentration and the remaining residual NAPL mass. The purpose of the proposed models is to predict the solute concentration in the zone of the residual NAPL as a result of dissolution. The predicted source zone concentration decrease is used to simulate and account for the decrease of dissolution rate with time. The proposed simple NAPL dissolution models enable the pseudo-equilibrium formulation to be used and therefore the numerical simulations for field application problems can be simplified compared to the non-equilibrium counterpart. With proper choice of empirical parameters, the proposed simple screening models can work as well as more complex dissolution rate correlation models, such as that of Imhoff et al. [Water Resour. Res. 30 (1994) 307-320]. It is found that the proposed models are very good for quantifying non-equilibrium dissolution, which is characterized by tailing of breakthrough curves. The models are especially useful for situations of small residual NAPL saturation, which are typical for many field applications.     

Variable-density groundwater flow and solute transport in heterogeneous porous media: approaches, resolutions and future challenges

In certain hydrogeological situations, fluid density variations occur because of changes in the solute or colloidal concentration, temperature, and pressure of the groundwater. These include seawater intrusion, high-level radioactive waste disposal, groundwater contamination, and geothermal energy production. When the density of the invading fluid is greater than that of the ambient one, density-driven free convection can lead to transport of heat and solutes over larger spatial scales and significantly shorter time scales than compared with diffusion alone. Beginning with the work of Lord Rayleigh in 1916, thermal and solute instabilities in homogeneous media have been studied in detail for almost a century. Recently, these theoretical and experimental studies have been applied in the study of groundwater phenomena, where the assumptions of homogeneity and isotropy rarely, if ever, apply. The critical role that heterogeneity plays in the onset as well as the growth and/or decay of convective motion is discussed by way of a review of pertinent literature and numerical simulations performed using a variable-density flow and solute transport numerical code. Different styles of heterogeneity are considered and range from continuously "trending" heterogeneity (sinusoidal and stochastic permeability distributions) to discretely fractured geologic media. Results indicate that both the onset of instabilities and their subsequent growth and decay are intimately related to the structure and variance of the permeability field. While disordered heterogeneity tends to dissipate convection through dispersive mixing, an ordered heterogeneity (e.g., sets of vertical fractures) allows instabilities to propagate at modest combinations of fracture aperture and separation distances. Despite a clearer understanding of the processes that control the onset and propagation of instabilities, resultant plume patterns and their migration rates and pathways do not appear amenable to prediction at present. The classical Rayleigh number used to predict the occurrence of instabilities fails, in most cases, when heterogeneous conditions prevail. The incorporation of key characteristics of the heterogeneous permeability field into relevant stability criteria and numerical models remains a challenge for future research.     

A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport

Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability–possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.     

Modelling tritium and phosphorus transport by preferential flow in structured soil

Subsurface solute transport through structured soil is studied by model interpretation of experimental breakthrough curves from tritium and phosphorus tracer tests in three intact soil monoliths. Similar geochemical conditions, with nearly neutral pH, were maintained in all the experiments. Observed transport differences for the same tracer are thus mainly due to differences in the physical transport process between the different monoliths. The modelling is based on a probabilistic Lagrangian approach that decouples physical and chemical mass transfer and transformation processes from pure and stochastic advection. Thereby, it enables explicit quantification of the physical transport process through preferential flow paths, honouring all independently available experimental information. Modelling of the tritium breakthrough curves yields a probability density function of non-reactive solute travel time that is coupled with a reaction model for linear, non-equilibrium sorption–desorption to describe the phosphorus transport. The tritium model results indicate that significant preferential flow occurs in all the experimental soil monoliths, ranging from 60–100% of the total water flow moving through only 25–40% of the total water content. In agreement with the fact that geochemical conditions were similar in all experiments, phosphorus model results yield consistent first-order kinetic parameter values for the sorption–desorption process in two of the three soil monoliths; phosphorus transport through the third monolith cannot be modelled because the apparent mean transport rate of phosphorus is anomalously rapid relative to the non-adsorptive tritium transport. The occurrence of preferential flow alters the whole shape of the phosphorus breakthrough curve, not least the peak mass flux and concentration values, and increases the transported phosphorus mass by 2–3 times relative to the estimated mass transport without preferential flow in the two modelled monoliths.     

A field experiment with variable-suction multi-compartment samplers to measure the spatio-temporal distribution of solute leaching in an agricultural soil

Solutes spread out in time and space as they move downwards from the soil surface with infiltrating water. Solute monitoring in the field is often limited to observations of resident concentrations, while flux concentrations govern the movement of solutes in soils. A recently developed multi-compartment sampler is capable of measuring fluxes at a high spatial resolution with minimal disturbance of the local pressure head field. The objective of this paper is to use this sampler to quantify the spatial and temporal variation of solute leaching below the root zone in an agricultural field under natural rainfall in winter and spring. We placed two samplers at 31 and 25 cm depth in an agricultural field, leaving the soil above undisturbed. Each sampler contained 100 separate cells of 31 × 31 mm. Water fluxes were measured every 5 min for each cell. We monitored leaching of a chloride pulse under natural rainfall by frequently extracting the collected leachate while leaving the samplers buried in situ. This experiment was followed by a dye tracer experiment. This setting yielded information that widely surpassed the information that can be provided by separate anionic and dye tracer trials, and solute transport monitoring by coring or suction cups. The detailed information provided by the samplers showed that percolation at the sampling depth started much faster (approximately 3 h after the start of rainfall) in initially wet soil (pressure head above − 65 cm) than in drier soil (more than 14 h at pressure heads below − 80 cm). At any time, 25% of the drainage passed through 5–6% of the sampled area, reflecting the effect of heterogeneity on the flow paths. The amount of solute carried by individual cells varied over four orders of magnitude. The lateral concentration differences were limited though. This suggests a convective–dispersive regime despite the short vertical travel distance. On the other hand, the dilution index indicates a slight tendency towards stochastic–convective transport at this depth. There was no evidence in the observed drainage patterns and dye stained profiles of significant disturbance of the flow field by the samplers.     

Analytical solution of two-dimensional solute transport in an aquifer–aquitard system

This study deals with two-dimensional solute transport in an aquifer–aquitard system by maintaining rigorous mass conservation at the aquifer–aquitard interface. Advection, longitudinal dispersion, and transverse vertical dispersion are considered in the aquifer. Vertical advection and diffusion are considered in the aquitards. The first-type and the third-type boundary conditions are considered in the aquifer. This study differs from the commonly used averaged approximation (AA) method that treats the mass flux between the aquifer and aquitard as an averaged volumetric source/sink term in the governing equation of transport in the aquifer. Analytical solutions of concentrations in the aquitards and aquifer and mass transported between the aquifer and upper or lower aquitard are obtained in the Laplace domain, and are subsequently inverted numerically to yield results in the real time domain (the Zhan method). The breakthrough curves (BTCs) and distribution profiles in the aquifer obtained in this study are drastically different from those obtained using the AA method. Comparison of the numerical simulation using the model MT3DMS and the Zhan method indicates that the numerical result differs from that of the Zhan method for an asymmetric case when aquitard advections are at the same direction. The AA method overestimates the mass transported into the upper aquitard when an upward advection exists in the upper aquitard. The mass transported between the aquifer and the aquitard is sensitive to the aquitard Peclet number, but less sensitive to the aquitard diffusion coefficient.     

Numerical analysis of water and solute transport in variably-saturated fractured clayey till

This study numerically investigates the influence of initial water content and rain intensities on the preferential migration of two fluorescent tracers, Acid Yellow 7 (AY7) and Sulforhodamine B (SB), through variably-saturated fractured clayey till. The simulations are based on the numerical model HydroGeoSphere, which solves 3D variably-saturated flow and solute transport in discretely-fractured porous media. Using detailed knowledge of the matrix, fracture, and biopore properties, the numerical model is calibrated and validated against experimental high-resolution tracer images/data collected under dry and wet soil conditions and for three different rain events. The model could reproduce reasonably well the observed preferential migration of AY7 and SB through the fractured till, although it did not capture the exact depth of migration and the negligible impact of the dead-end biopores in a near-saturated matrix. A sensitivity analysis suggests fast flow mechanisms and dynamic surface coating in the biopores, and the presence of a plough pan in the till.     

Impact of varying soil structure on transport processes in different diagnostic horizons of three soil types

When soil structure varies in different soil types and the horizons of these soil types, it has a significant impact on water flow and contaminant transport in soils. This paper focuses on the effect of soil structure variations on the transport of pesticides in the soil above the water table. Transport of a pesticide (chlorotoluron) initially applied on soil columns taken from various horizons of three different soil types (Haplic Luvisol, Greyic Phaeozem and Haplic Cambisol) was studied using two scenarios of ponding infiltration. The highest infiltration rate and pesticide mobility were observed for the Bt₁ horizon of Haplic Luvisol that exhibited a well-developed prismatic structure. The lowest infiltration rate was measured for the Bw horizon of Haplic Cambisol, which had a poorly developed soil structure and a low fraction of large capillary pores and gravitational pores. Water infiltration rates were reduced during the experiments by a soil structure breakdown, swelling of clay and/or air entrapped in soil samples. The largest soil structure breakdown and infiltration decrease was observed for the Ap horizon of Haplic Luvisol due to the low aggregate stability of the initially well-aggregated soil. Single-porosity and dual-permeability (with matrix and macropore domains) flow models in HYDRUS-1D were used to estimate soil hydraulic parameters via numerical inversion using data from the first infiltration experiment. A fraction of the macropore domain in the dual-permeability model was estimated using the micro-morphological images. Final soil hydraulic parameters determined using the single-porosity and dual-permeability models were subsequently used to optimize solute transport parameters. To improve numerical inversion results, the two-site sorption model was also applied. Although structural changes observed during the experiment affected water flow and solute transport, the dual-permeability model together with the two-site sorption model proved to be able to approximate experimental data.     

A multi-flowpath model for the interpretation of immiscible displacement experiments in heterogeneous soil columns

This work focuses on the phenomenon of the immiscible two-phase flow of water and oil in saturated heterogeneous soil columns. The goal is to develop a fast and reliable method for quantifying soil heterogeneities for incorporation into the relevant capillary pressure and relative permeability functions. Such data are commonly used as input data in simulators of contaminant transport in the subsurface. Rate-controlled drainage experiments are performed on undisturbed soil columns and the transient response of the axial distribution of water saturation is determined from electrical measurements. The transient responses of the axial distribution of water saturation and total pressure drop are fitted with the multi-flowpath model (MFPM) where the pore space is regarded as a system of parallel paths of different permeability. The MFPM enables us to quantify soil heterogeneity at two scales: the micro-scale parameters describe on average the effects of pore network heterogeneities on the two-phase flow pattern; the macro-scale parameters indicate the variability of permeability at the scale of interconnected pore networks. The capillary pressure curve is consistent with that measured with mercury intrusion porosimetry over the low pressure range. The oil relative permeability increases sharply at a very low oil saturation (< 10^− 3) and tends to a high end value. The water relative permeability decreases abruptly at a low oil saturation (~ 0.1), whereas the irreducible wetting phase saturation is quite high. The foregoing characteristics of the two-phase flow properties are associated with critical (preferential) flowpaths that comprise a very small percentage of the total pore volume, control the overall hydraulic conductivity, and are consistent with the very broad range of pore-length scales usually probed in soil porous matrix.     

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. In particular it is shown that the Crank–Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection–dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution.     

Effects of degree of water saturation on dispersivity and immobile water in sandy soil columns

Three natural nonaggregated soil samples, with similar grain-size distributions, have been used to determine the dispersive behavior of porous media under steady, saturated and unsaturated flow conditions. Tritium was used as a tracer and was found to have no sorption on the solid matrix. Generated breakthrough curves (BTCs) for the unsaturated experiments were symmetrical with no evidence of tailing. The unsaturated experiments for two of the soils were adequately described by considering all the water in the pore volume as mobile. However, about 10% of the pore water, independent of the degree of saturation, was found to be immobile in the case of the third soil during unsaturated flow. For this soil, there was no mass transfer between the two water regions, indicating that the immobile water is essentially isolated from the flowing water fraction. For all three soils, dispersivity under unsaturated conditions was found to be higher, independent of the degree of water saturation, than the value determined for the saturated experiments. This is inconsistent with what would be expected from the simple bundle-of-capillary-tubes model and does not agree well with a more sophisticated conceptualization of the porous medium. The data, however, clearly indicate a wider range in pore-water velocities when these soils are desaturated.     

Application of continuous time random walk theory to nonequilibrium transport in soil

Continuous time random walk (CTRW) formulations have been demonstrated to provide a general and effective approach that quantifies the behavior of solute transport in heterogeneous media in field, laboratory, and numerical experiments. In this paper we first apply the CTRW approach to describe the sorbing solute transport in soils under chemical (or) and physical nonequilibrium conditions by curve-fitting. Results show that the theoretical solutions are in a good agreement with the experimental measurements. In case that CTRW parameters cannot be determined directly or easily, an alternative method is then proposed for estimating such parameters independently of the breakthrough curve data to be simulated. We conduct numerical experiments with artificial data sets generated by the HYDRUS-1D model for a wide range of pore water velocities (υ) and retardation factors (R) to investigate the relationship between CTRW parameters for a sorbing solute and these two quantities (υ, R) that can be directly measured in independent experiments. A series of best-fitting regression equations are then developed from the artificial data sets, which can be easily used as an estimation or prediction model to assess the transport of sorbing solutes under steady flow conditions through soil. Several literature data sets of pesticides are used to validate these relationships. The results show reasonable performance in most cases, thus indicating that our method could provide an alternative way to effectively predict sorbing solute transport in soils. While the regression relationships presented are obtained under certain flow and sorption conditions, the methodology of our study is general and may be extended to predict solute transport in soils under different flow and sorption conditions.