Hydrodynamic Dispersion Coefficient Research Articles

Application of HYDRUS 1D model for assessment of phenol–soil adsorption dynamics

Laboratory-scale batch, vertical, and horizontal column experiments were conducted to investigate the attenuative capacity of a fine-grained clayey soil of local origin in the surrounding of a steel plant wastewater discharge site in West Bengal, India, for removal of phenol. Linear, Langmuir, and Freundlich isotherm plots from batch experimental data revealed that Freundlich isotherm model was reasonably fitted (R (2) = 0.94). The breakthrough column experiments were also carried out with different soil bed heights (5, 10, and 15 cm) under uniform flow to study the hydraulic movements of phenol by evaluating time concentration flow behavior using bromide as a tracer. The horizontal migration test was also conducted in the laboratory using adsorptive phenol and nonreactive bromide tracer to explore the movement of solute in a horizontal distance. The hydrodynamic dispersion coefficients (D) in the vertical and horizontal directions in the soil were estimated using nonlinear least-square parameter optimization method in CXTFIT model. In addition, the equilibrium convection dispersion model in HYDRUS 1D was also examined to simulate the fate and transport of phenol in vertical and horizontal directions using Freundlich isotherm constants and estimated hydrodynamic parameters as input in the model. The model efficacy and validation were examined through statistical parameters such as the coefficient of determination (R (2)), root mean square error and design of index (d).

Simulation and prediction of ion transport in the reclamation of sodic soils with gypsum based on the support vector machine.

The effect of gypsum on the physical and chemical characteristics of sodic soils is nonlinear and controlled by multiple factors. The support vector machine (SVM) is able to solve practical problems such as small samples, nonlinearity, high dimensions, and local minima points. This paper reports the use of the SVM regression method to predict changes in the chemical properties of sodic soils under different gypsum application rates in a soil column experiment and to evaluate the effect of gypsum reclamation on sodic soils. The research results show that (1) the SVM soil solute transport model using the Matlab toolbox represents the change in Ca2+ and Na+ in the soil solution and leachate well, with a high prediction accuracy. (2) Using the SVM model to predict the spatial and temporal variations in the soil solute content is feasible and does not require a specific mathematical model. The SVM model can take full advantage of the distribution characteristics of the training sample. (3) The workload of the soil solute transport prediction model based on the SVM is greatly reduced by not having to determine the hydrodynamic dispersion coefficient and retardation coefficient, and the model is thus highly practical.

Interaction of 3H+ (as HTO) and 36Cl- (as Na36Cl) with crushed granite and corresponding fracture infill material investigated in column experiments.

The transport of 3H+ (as HTO) and 36Cl− (as Na36Cl) was investigated in the dynamic system, i.e., in the columns filled with crushed pure granite and fracture infill of various grain sizes. The aim of column experiments was to determine important transport parameter, such as the retardation, respectively distribution coefficients, Peclet numbers and hydrodynamic dispersion coefficients. Furthermore, the research was focused to quantification of the effect of grain size on migration of studied radionuclides. The experimental breakthrough curves were fitted by a model based on the erfc-function, assuming a linear reversible equilibrium sorption/desorption isotherm, and the above mentioned transport parameters were determined. The results showed that influence of grain size on sorption of 3H+ and 36Cl− was negligible. Retardation and distribution coefficients of both tracers converged to one and zero, respectively, in case of all fractions of crushed granite and infill material. Generally, the presumed ion exclusion of 36Cl in anionic form was proved under given conditions, only very weak one seems to exist in a case of infill material. In principal, both radionuclides behaved as non-sorbing, conservative tracers. On the other hand, the influence of grain size on Peclet numbers value and on dispersion coefficient was observed for both crystalline materials, namely in agreement with theoretical suppositions that the values of Peclet numbers decrease with increasing grain size and values of dispersion coefficient increase.

Dispersion in Electro-Osmotic Flow Through a Slit Channel With Axial Step Changes of Zeta Potential

An analytical study is presented in this paper on hydrodynamic dispersion due to steady electro-osmotic flow (EOF) in a slit microchannel with longitudinal step changes of ζ potential. The channel wall is periodically patterned with alternating stripes of distinct ζ potentials. Existing studies in the literature have considered dispersion in EOF with axial nonuniformity of ζ potential only in the limiting case where the length scale for longitudinal variation is much longer than the cross-sectional dimension of the channel. Hence, the existing theories on EOF dispersion subject to nonuniform charge distributions are all based on the lubrication approximation, by which cross-sectional mixing is ignored. In the present study, the general case where the length of one periodic unit of wall pattern (which involves a step change of ζ potential) is comparable with the channel height, as well as the long-wave limiting case, are investigated. The problem for the hydrodynamic dispersion coefficient is solved numerically in the general case, and analytically in the long-wave lubrication limit. The dispersion coefficient and the plate height are found to have strong, or even nonmonotonic, dependence on the controlling parameters, including the period length of the wall pattern, the area fraction of the EOF-suppressing region, the Debye parameter, the Péclet number, and the ratio of the two ζ potentials.

Impact of thin aquitards on two-dimensional solute transport in an aquifer

The influence of aquitards on solute transport in an aquifer is an important and often overlooked process for subsurface contaminant transport. In particular, slow advection (leakage) into an aquitard is often neglected in previous analytical treatment of solute transport, making such analytical solutions unsuitable for benchmarking numerical simulations of transport when aquitard leakage exists. In this study, a semi-analytical solution to the two-dimensional conservative solute transport in an aquifer bounded by thin aquitards is derived in the Laplace domain. The governing equation in the aquifer (not aquitard) incorporates terms accounting for advection, longitudinal dispersion, and transverse vertical dispersion. Both one-dimensional vertical advection and molecular diffusion are considered for aquitard transport. The solutions are derived under conditions of steady-state flow and the first- and third-type transport boundary conditions in the aquifer along with assuming the continuity of concentration and vertical mass flux at aquifer and aquitard interfaces. The solutions in the real time domain are obtained by numerically inverting the solutions in the Laplace domain using the Stehfest (1970) algorithm. The semi-analytical solutions are compared with those from Zhan et al. (2009b), which considered aquitard leakage in infinitively thick aquitards. The concentration profiles, breakthrough curves and distribution profiles in the aquifer are different from those of Zhan et al. (2009b) at small ratios of the aquitard/aquifer thickness; whereas, the results of both are consistent for thick bounding aquitards. This study reveals that the residence time distribution (RTD) in the main aquifer is related to the aquitard/aquifer thickness ratios, Peclet numbers and porosities of adjacent aquitards. The results also suggest that MT3DMS (a commonly applied transport code) cannot successfully simulate solute transport at the aquifer-aquitard interfaces. The presented solutions improve available solutions for transport processes in an aquifer bounded by thin aquitards with leakage. The developed solutions can be directly extended to cases when the vertical hydrodynamic dispersion of the aquitards is considered by simply replacing the effective molecular diffusion coefficients of the aquitard by the vertical hydrodynamic dispersion coefficients of the aquitards.

Hybrid-Optimization Approach for Estimating Parameters of a Virus Transport Process in Aquifer

AbstractSimulation of a virus transport process in a groundwater aquifer is necessary for predicting the movement of viruses in an aquifer. It is also necessary in implementing remedial measures to inactivate viruses present in groundwater. For simulating the virus transport process in a groundwater aquifer, the parameters responsible for movement of viruses in an aquifer have to be estimated. In the case of saturated porous media, the transport parameters are linear distribution coefficient, hydrodynamic dispersion coefficient, and inactivation coefficient for aqueous and sorbed viruses. These parameters can be estimated using an inverse optimization procedure that minimizes an error function represented by the difference between the experimentally observed and simulated virus concentration. Gradient-based classical optimization methods can be applied to minimize the error function for estimating the parameters of the transport process. It is reported that the error function is nonlinear and nonconvex in...

Experimental Determination of Coefficient of Soil Hydrodynamic Dispersion

Hydrodynamic dispersion experiment was done with unsaturated silt loam. Depend on mass conservation law, the formulas to calculate coefficient of hydrodynamic dispersion was developed. According to the data of soil water and salt regime measured from the upright soil column, the coefficient of hydrodynamic dispersion was calculated, and the relation between hydrodynamic dispersion and average flow velocity in soil voids was built up. This approach has clear concept of physics, and the formulas are simple and applied.

Validation of Pore-Scale Simulations of Hydrodynamic Dispersion in Random Sphere Packings

AbstractWe employ the lattice Boltzmann method and random walk particle tracking to simulate the time evolution of hydrodynamic dispersion in bulk, random, monodisperse, hard-sphere packings with bed porosities (interparticle void volume fractions) between the random-close and the random-loose packing limit. Using Jodrey-Tory and Monte Carlo-based algorithms and a systematic variation of the packing protocols we generate a portfolio of packings, whose microstructures differ in their degree of heterogeneity (DoH). Because the DoH quantifies the heterogeneity of the void space distribution in a packing, the asymptotic longitudinal dispersion coefficient calculated for the packings increases with the packings’ DoH. We investigate the influence of packing length (up to 150 dp, where dp is the sphere diameter) and grid resolution (up to 90 nodes per dp) on the simulated hydrodynamic dispersion coefficient, and demonstrate that the chosen packing dimensions of 10 dpx 10 dpx 70 dp and the employed grid resolution of 60 nodes per dp are sufficient to observe asymptotic behavior of the dispersion coefficient and to minimize finite size effects. Asymptotic values of the dispersion coefficients calculated for the generated packings are compared with simulated as well as experimental data from the literature and yield good to excellent agreement.

Effect of grain size on the sorption and desorption of SeO4 2− and SeO3 2− in columns of crushed granite and fracture infill from granitic water under dynamic conditions

The sorption of 2 × 10−5 mol/dm3 Na2SeO4 and Na2SeO3 dissolved in synthetic granitic water (SGW) were investigated in columns of crushed granite and fracture infill (clay minerals) of various grain sizes. Desorption was studied using pure SGW. The goal of study was the quantification of the effect of grain size on the retardation and distribution coefficients of SeO42− and SeO32−, as well as on the other transport parameters (Peclet number and hydrodynamic dispersion coefficient). A model based on the erfc-function, assuming a non-linear reversible equilibrium sorption/desorption isotherm, was used for evaluation of sorption/desorption and transport parameters. The determination of selenium was performed using an ICP-MS technique. The experimental breakthrough curves were fitted using non-linear regression procedure, in the course of which the parameters mentioned were sought. Summing up, no sorption was recorded in the case of SeO42− under these conditions. The values of retardation coefficients were practically one for all studied grain sizes. On the other hand, significant sorption was found for SeO32−: depending on the grain size, the retardation coefficients varied between 1.6–8.7 in pure granite and 1.8–37.2 in infill materials. These values correspond to distribution coefficients of 0.2–2.5 and 0.2–12.7 cm3/g, respectively. The both parameters have similar values in a case of desorption which reflects the reversible character of sorption process. It was found that retardation and distribution coefficients and sorption capacity for SeO32− also increase with decreasing grain size.

Microscopic and Macroscopic Properties of Soils Used as Means for the Interpretation of the Efficiency of Soil Remediation Technologies

Reliable information for the multiphase transport coefficients of porous media (e.g. capillary pressure curve, relative permeability functions, hydrodynamic dispersion coefficients) is a prerequisite when investigating soil contamination and remediation processes. The majority of mineral soils are heterogeneous at multiple-scales but such characteristics are usually overlooked when measuring the effective transport coefficients. Transient immiscible and miscible displacement tests performed on long soil columns are coupled with inverse modeling algorithms to estimate the multiphase transport coefficients. Multipoint measurements of the electrical resistance are employed to determine the axial distribution of the fluid saturation as well as the solute concentration breakthrough curves. The transient responses of the solute concentration (breakthrough curve) over three cross-sections are inverted by using the one- region and two-region models so that the longitudinal dispersivity is estimated along with parameters quantifying the micro-heterogeneity at the pore network scale. The transient responses of the total pressure drop across the soil column, and fluid saturation averaged over five successive segments are inverted by using the single-permeability and multi-flow path model so that the dynamic capillary pressure and oil/water relative permeability curves are estimated along with parameters quantifying the macro-heterogeneity (e.g. permeability distribution) at the soil column scale. The measured multiphase transport properties are interpreted in terms of pore-scale parameters, and might be used for the interpretation of the efficiency of soil remediation technologies. The methodology is demonstrated with application to one homogeneous and one moderately heterogeneous soil used to test the non- thermal plasma discharge as a potential ex-situ remediation technology for mixtures of hydrocarbons.

Zeolite Effects on Immobile Water Content and Mass Exchange Coefficient at Different Soil Textures

The concern for groundwater pollution by agrichemicals through solute movement within the soil is widespread. Zeolite is a type of soil amendment that is utilized to improve physical properties of soil and ameliorate polluted soil. The high negative charge of the zeolite and its open space structure allows adsorption and access of heavy metals and other cations and anions. The objectives of this research were (i) to determine the effects of different application rates of zeolite (0, 2, 4, and 8 g kg−1) on the immobile water content and mass exchange coefficient in a loam soil and then (ii) to determine the effects of optimum application rate of zeolite on the immobile water content and mass exchange coefficient of sandy loam and clay loam soils in saturated conditions by a mobile and immobile (MIM) model. In a disturbed soil column, a method was proposed for determination of MIM model parameters, that is, immobile water content (θim), mass exchange coefficient (α), and hydrodynamic dispersion coefficient (Dh). Breakthrough curves were obtained for different soil textures with different zeolite applications in three replicates, by miscible displacement of chloride (Cl−1) in disturbed soil column. Cl−1 breakthrough curves were evaluated in terms of the MIM model. The results showed that the pore water velocity calculated based on the total soil volumetric water content (θim+ θm) and real pore water velocity calculated based on the mobile water content (θm) increased in the loam soil with an increase in zeolite application rate, so that, between these different rates of zeolite application, the maximum value of pore water velocity and real pore water velocity occurred at zeolite application rates of 8.6 and 11.5 g kg−1, which are indicated as the optimum application rates. However, the comparison between different soils showed that the zeolite application rate of 8 g kg−1 could increase pore water velocity of sandy loam and loam soils by 31% more than that of clay loam soil. The immobile water content and mass exchange coefficient of loam soil were correlated with the zeolite application rate and reduced with an increase in the rate of applied zeolite. In a comparison between different soils at zeolite application rate of 8 g kg−1, the immobile water contents of the zeolite-treated soil decreased by 57%, 60%, and 39% on sandy loam, loam, and clay loam soils, respectively, compared with the untreated soil. Furthermore, zeolite application could reduce mass exchange coefficient by 9%, 43%, and 21% on sandy loam, loam, and clay loam soils, respectively. A positive linear relationship was found between θim and α. Zeolite application increased real pore water velocity of sandy loam soil by 39% and 46% compared with loam and clay loam soils, respectively. In other studies there was a decrease in ammonium and nitrate leaching due to the zeolite application, and therefore, an increase in real pore water velocity due to zeolite application in sandy loam soil, as compared with the loam and clay loam soils, may not show more rapid movement of solute and agrichemicals to the groundwater.

Measuring hydrodynamic dispersion coefficients in unsaturated packed beds: Comparison of PEPT with conventional tracer tests

Hydrodynamic dispersion has a major impact on mass transport within packed bed and porous media systems. In this paper, dispersion coefficients of neutrally buoyant tracer particles located with positron emission particle tracking (PEPT) are compared to results obtained using a conventional salt tracer experiment. It is demonstrated that the axial dispersion coefficients obtained from PEPT are very similar to those obtained using the salt tracer. The PEPT method has the advantage that the details of the flow behaviour can be observed, thus allowing analysis of the mechanisms at work to be carried out. In addition, the radial dispersion coefficient was obtained with PEPT, which is hard to obtain using conventional salt tracer tests. The main drawback with the PEPT method is that very low flow rates could not be studied as these result in very low saturations, which causes the tracer particle to become stuck. In this work the tracer particles used are 400μm in diameter, though as the tracer fabrication technology improves, the size of tracer available will continue to decrease, allowing a wider range of conditions and particle beds to be studied.

Effect of grain size on the 85Sr2+ sorption and desorption in columns of crushed granite and infill materials from granitic water under dynamic conditions

The sorption of 85Sr2+ in the form of 10−6 M Sr(NO3)2 in synthetic granitic water (SGW), and its desorption using the same radiotracer-free solution, were investigated under dynamic conditions in columns loaded with crushed granitic materials. The goal of study was to evaluate the influence of grain size on the retardation (R) and distribution (Kd) coefficients of the soluble 85Sr2+, as well as on the other transport parameters type of Peclet number (Pe) and hydrodynamic dispersion coefficient (Dd). Pure granitic sample and granitic fissure infill samples were used, crushed and sieved into 4 different grain size from 0.063 to1.25 mm were used. In order to determine migration parameters, the model based on erfc-function was used, assuming reversible equilibrium linear or non-linear (Freundlich) sorption/desorption isotherms. By means of both model approaches, the experimental breakthrough curves were fitted using non-linear regression procedure according to Newton–Raphson method. The obtained results also validated the applicability of the linear equilibrium isotherms of the 85Sr2+ sorption/desorption in the studied systems. It was found that in the case of linear isotherm approach, both retardation and distribution coefficients increased with decreasing grain size. Moreover, their values for fracture infill samples are higher than comparing to granite. Depending on the grain size, the retardation coefficient R varied between 11 and 25 for pure granite and 33–58 between for fissure infill material. These values correspond to distribution coefficients Kd of 2–7 and 9–24 cm3/g, respectively. Consequently, the sorption capacity of crushed rocks also increases with decreasing grain size and are about 2.5-times higher for fracture infill than in pure granite. The values of Dd increase with increasing grain size. Due to inverse proportion, values of Pe number are decreasing.

Nuclear magnetic resonance measurement of hydrodynamic dispersion in porous media: preasymptotic dynamics, structure and nonequilibrium statistical mechanics

Measurement of displacement time and length scale dependent dynamics by pulsed gradient spin echo nuclear magnetic resonance in porous media directly provides the preasymptotic hydrodynamic dispersion coefficient. This allows for comparison with nonequilibrium statistical mechanics models of hydrodynamics dispersion in porous media. Preasymptotic dispersion data and models provide characterization of porous media structure length scales relevant to transport and are related to the permeability and sample heterogeneity.

Sorption of 125I−, 137Cs+, 85Sr2+ and 152,154Eu3+ during their transport in undisturbed vertical and horizontal soil cores under dynamic flow conditions

Transport and sorption of 125I−, 137Cs+, 85Sr2+ and 152,154Eu3+ in undisturbed soil cores have been studied under dynamic conditions. Radionuclides were dissolved in synthetic groundwater (SGW) of 0.015 mol/dm3 ionic strength, pH 8.4 and redox potential Eh = 145 mV. The soil samples were taken vertically and horizontally from the river bed at 5–100 cm depths, about 120 m southward of the Dukovany Low and Medium Level Radioactive Waste Repository. The respective water-soluble carriers in the 10−6 mol/dm3 concentration were added into the SGW prior to the experiments. The soil cores of 9 cm height and 3.8 cm in diameter were placed into columns made of 150 cm3 PE injection syringes of suitable dimensions. The SGW was introduced into columns from the Mariotte’s bottle through a glass manifolds to supply the soil columns by gravity flow at a constant flow-rate about 1.2 cm3/h. Into the water stream, radioactive nuclides were added individually in a form of a short pulse in 0.1 cm3 of demineralized water. In the case of 125I− transport, retardation and hydrodynamic dispersion coefficients were determined, using an integral form of a simple advection-dispersion equation. For each radionuclides, sorption and desorption data have been obtained, evaluated and the results were compared mutually. Residual distributions of the sorbed cationic radionuclides along the soil columns were also presented.

Modeling Cadmium Transport in Neutral and Alkaline Soil Columns at Various Depths

Human health has been potentially threatened by cadmium (Cd) contained in sewage irrigation water. Previous studies of Cd transport in soils were mainly conducted using small soil cores with pH values less than 6. The objectives of this study were to determine the parameters of the convection-dispersion equation (CDE) for Cd transport in relatively larger columns with neutral and alkaline soils, and to investigate the parameters' variability with depth. The soil columns were 50 cm in length and 12.5 cm in diameter. Ceramic suction lysimeters were buried at depths of 2.5, 7.5, 17.5, 27.5, and 37.5 cm to abstract soil solution. Cd concentration in the soil solution samples were subsequently analyzed to obtain breakthrough curves (BTCs). Equilibrium and nonequilibrium models in CXTFIT program were used to estimate parameters of the CDE. The results suggested that both equilibrium and non-equilibrium models performed well in modeling Cd transport. The hydrodynamic dispersion coefficient (D) ranged from 0.18 to 10.70 cm2 h−1, showing large differences among different depths. The retardation factor (Rd) ranged from 25.4 to 54.7 and the standard deviation of Rd value was lower than 30% of the mean value. Precipitation coefficient (Rp) decreased consistently with increasing depth, varying from 1.000 × 10−10 to 0.661 h−1. Sensitivity tests showed that D was less sensitive than Rd. These results would be helpful in understanding the transport and retention of Cd in non-acidic soils.

Preasymptotic hydrodynamic dispersion as a quantitative probe of permeability

We interpret a generalized short-time expansion of stochastic hydrodynamic dispersion dynamics in the case of small Reynolds number flow through macroscopically homogenous permeable porous media to directly determine hydrodynamic permeability. The approach allows determination of hydrodynamic permeability from pulsed field gradient spin-echo nuclear magnetic resonance measurement of the short-time effective hydrodynamic dispersion coefficient. The analytical expansion of asymptotic dynamics agrees with experimental NMR data and lattice Boltzmann simulation of hydrodynamic dispersion in consolidated random sphere pack media.

Influência do sistema de manejo na retenção e mobilidade da atrazina em amostras de solos

Atrazine is one of the most used pesticides in Brazil, however, its dynamic in soils is still unknown, specially regarding different management systems. Thus, the aim of this work was to evaluate the sorption and leaching of atrazine in a dystroferric Red Latosol cultivated under no-till or conventional till management system. Sorption was evaluated using the “batch” method and the miscible displacement method, using undisturbed soil columns from 0-20 cm layer. Results were expressed by Freundlich isotherm and the elution curves were to the dispersive-convective model in order to obtain the retardation factor (R) and the hydrodynamic dispersion coefficient (D). No significant difference of the the Freundlich coefficient (Kf) was found in the soil samples under no-till or conventional till management systems. The retardation factor was higher and the hydrodynamic dispersion coefficient was lower in the samples under conventional till system, showing evidences of a higher leaching potential in soils under no-till system.

Experimental Investigation and Pore-Scale Modeling Interpretation of Compound-Specific Transverse Dispersion in Porous Media

In this study, we performed multitracer laboratory bench-scale experiments and pore-scale simulations in different homogeneous saturated porous media (i.e., different grain sizes) with the objective of (i) obtaining a generalized parameterization of transverse hydrodynamic dispersion at the continuum Darcy scale; (ii) gaining an improved understanding of the role of basic transport processes (i.e., advection and molecular diffusion) at the subcontinuum scale and their effect on the macroscopic description of transverse mixing in porous media; (iii) quantifying the importance of compound-specific properties such as aqueous diffusivities for transport of different solutes. The results show that a non-linear compound-dependent parameterization of transverse hydrodynamic dispersion is required to capture the observed lateral displacement over a wide range of seepage velocities (0.1–35 m/day). With pore-scale simulations, we can prove the hypothesis that the interplay between advective and diffusive mass transfer results in vertical concentration gradients leading to incomplete mixing in the pore channels. We quantify mixing in the pore throats using the concept of flux-related dilution index and show that different solutes undergoing transport in a flow-through system with a given average velocity can show different degrees of incomplete mixing. Furthermore, it is this compound-specific incomplete mixing within pores that causes different local transverse (mechanical) dispersion to result at the Darcy scale for high flow velocities. We conclude that physical processes at the microscopic level significantly determine the observed macroscopic behavior and, therefore, should be properly reflected in up-scaled parameterizations of transport processes such as local hydrodynamic dispersion coefficients.

Preliminary investigation of zinc transport through zeolite-X barrier: Linear isotherm assumption

Hydrated sodium zeolite-X was synthesized and tested to evaluate its technical feasibility as a permeable reactive barrier (PRB) for remediating contaminated groundwater. Laboratory tests have been performed to characterize the synthesized material and determine some of its important physical and chemical properties. Batch and column techniques were used to give insight into the optimum conditions at which this material can efficiently retain zinc, as a model for bivalent cations, from contaminated aqueous solution. The batch investigations were directed to study the effect of initial zinc concentration and the plume pH on the retention characteristics. It was found that zeolite-X will efficiently remove Zn2+ ions from slightly contaminated groundwater under slightly acidic or alkali conditions. For highly contaminated groundwater and under acidic conditions, the zeolite efficiency for remediating the groundwater is reduced. Then zinc transport under saturated conditions was studied using column technique. Two methods were used to estimate the hydrodynamic dispersion coefficient; namely Brigham and nonlinear fitting. Simple analytical pulse model was used to preliminary investigate zinc transport through the barrier and a comparison between the two methods was performed. It was found that nonlinear regression method produces more realistic prediction for zinc transport.