Improved Method for Estimating Reaction Rates During Push-Pull Tests

The breakthrough curve obtained from a single-well push-pull test can be adjusted to account for dilution of the injection fluid in the aquifer fluid. The dilution-adjusted breakthrough curve can be analyzed to estimate the reaction rate of a solute. The conventional dilution-adjusted method assumes that the ratios of the concentrations of the nonreactive and reactive solutes in the injection fluid vs. the aquifer fluid are equal. If this assumption is invalid, the conventional method will generate inaccurate breakthrough curves and may lead to erroneous conclusions regarding the reactivity of a solute. In this study, a new method that generates a dilution-adjusted breakthrough curve was theoretically developed to account for any possible combination of nonreactive and reactive solute concentrations in the injection and aquifer fluids. The newly developed method was applied to a field-based data set and was shown to generate more accurate dilution-adjusted breakthrough curves. The improved dilution-adjusted method presented here is simple, makes no assumptions regarding the concentrations of the nonreactive and reactive solutes in the injection and aquifer fluids, and easily allows for estimating reaction rates during push-pull tests.     

Heat Tracing in a Fractured Aquifer with Injection of Hot and Cold Water

Heat as a tracer in fractured porous aquifers is more sensitive to fracture-matrix processes than a solute tracer. Temperature evolution as a function of time can be used to differentiate fracture and matrix characteristics. Experimental hot (50 °C) and cold (10 °C) water injections were performed in a weathered and fractured granite aquifer where the natural background temperature is 30 °C. The tailing of the hot and cold breakthrough curves, observed under different hydraulic conditions, was characterized in a log–log plot of time vs. normalized temperature difference, also converted to a residence time distribution (normalized). Dimensionless tail slopes close to 1.5 were observed for hot and cold breakthrough curves, compared to solute tracer tests showing slopes between 2 and 3. This stronger thermal diffusive behavior is explained by heat conduction. Using a process-based numerical model, the impact of heat conduction toward and from the porous rock matrix on groundwater heat transport was explored. Fracture aperture was adjusted depending on the actual hydraulic conditions. Water density and viscosity were considered temperature dependent. The model simulated the increase or reduction of the energy level in the fracture-matrix system and satisfactorily reproduced breakthrough curves tail slopes. This study shows the feasibility and utility of cold water tracer tests in hot fractured aquifers to boost and characterize the thermal matrix diffusion from the matrix toward the flowing groundwater in the fractures. This can be used as complementary information to solute tracer tests that are largely influenced by strong advection in the fractures.     

Influence of injection conditions on field tracer experiments

Calibration of ground water transport models is often performed using results of field tracer experiments. However, little attention is usually paid to the influence, on resulting breakthrough curves, of injection conditions and well-aquifer interactions, more particularly of the influence of the possible trapping of the tracer in the injection wellbore. Recently, a new mathematical and numerical approach has been developed to model injection conditions and well-aquifer interactions in a very accurate way. Using an analytical solution derived from this model, a detailed analysis is made of the evolution of the tracer input function in the aquifer. By varying injection conditions from one simulation to another, synthetic breakthrough curves are generated with the SUFT3D ground water flow and transport finite-element simulator. These tests show clearly that the shape of the breakthrough curves can be dramatically affected by injection conditions. Using generated breakthrough curves as "actual" field results, a calibration of hydrodispersive parameters is performed, neglecting the influence of injection conditions. This shows that neglecting the influence of actual injection conditions can lead to (1) errors on fitted parameters and (2) misleading identification of the active transport processes. Conclusions and guidelines are drawn in terms of proposed methodologies for better controlling the tracer injection in the field, in order to minimize risk of misinterpretation of results.     

Field Demonstration of Permeable Wall Flushing for Biostimulation of a Shallow Sandy Aquifer

A pilot-scale nutrient injection will (NIW) (4 m by 4 m by 1 m) was installed in the Borden Aquifer lo serve as a pulsed injection source of a potassium acetate solution for the stimulation of anaerobic microbial activity. The success of the flushing procedure was evaluated by monitoring the breakthrough of the acetate solution at several multilevel piezometers installed in the wall. Although some variation in the ground water velocity was observed with depth, the wall was flushed with reasonable uniformity after about six hours of injection and withdrawal, representing about one pore volume, Calculations bused on head level data collected during the flush, and on the solute breakthrough curves, indicated that about 90% of the flow induced by the pumping and injecting was confined to the permeable wall. These results show that a permeable wall injection system is a viable method of introducing solutes uniformly to a cross section of aquifer, with minimal perturbation of the natural flow system. In addition lo its importance for the biostimulation system tested in this project the flushing of permeable walls may have applications in other semi-passive remedial systems, such as the rejuvenation of reactive barriers.     

A spreadsheet program for two-well tracer test data analysis

Two-well tracer tests are often conducted to investigate subsurface solute transport in the field. Analyzing breakthrough curves in extraction and monitoring wells using numerical methods is nontrivial due to highly nonuniform flow conditions. We extended approximate analytical solutions for the advection-dispersion equation for an injection-extraction well doublet in a homogeneous confined aquifer under steady-state flow conditions for equal injection and extraction rates with no transverse dispersion and negligible ambient flow, and implemented the solutions in Microsoft Excel using Visual Basic for Application (VBA). Functions were implemented to calculate concentrations in extraction and monitoring wells at any location due to a step or pulse injection. Type curves for a step injection were compared with those calculated by numerically integrating the solution for a pulse injection. The results from the two approaches are similar when the dispersivity is small. As the dispersivity increases, the latter was found to be more accurate but requires more computing time. The code was verified by comparing the results with published-type curves and applied to analyze data from the literature. The method can be used as a first approximation for two-well tracer test design and data analysis, and to check accuracy of numerical solutions. The code and example files are publicly available.     

Can Contaminant Transport Models Predict Breakthrough?

A solute breakthrough curve measured during a two-well tracer test was successfully predicted in 1986 using specialized contaminant transport models. Water was injected into a confined, unconsolidated sand aquifer and pumped out 125 feet (38.3 m) away at the same steady rate. The injected water was spiked with bromide for over three days; the outflow concentration was monitored for a month. Based on previous tests, the horizontal hydraulic conductivity of the thick aquifer varied by a factor of seven among 12 layers. Assuming stratified flow with small dispersivities, two research groups accurately predicted breakthrough with three-dimensional (12-layer) models using curvilinear elements following the arc-shaped flowlines in this test.
Can contaminant transport models commonly used in industry, that use rectangular blocks, also reproduce this breakthrough curve? The two-well test was simulated with four MODFLOW-based models, MT3D (FD and HMOC options), MODFLOWT, MOC3D, and MODFLOW-SURFACT.
Using the same 12 layers and small dispersivity used in the successful 1986 simulations, these models fit almost as accurately as the models using curvilinear blocks. Subtle variations in the curves illustrate differences among the codes. Sensitivities of the results to number and size of grid blocks, number of layers, boundary conditions, and values of dispersivity and porosity are briefly presented. The fit between calculated and measured breakthrough curves degenerated as the number of layers and/or grid blocks decreased, reflecting a loss of model predictive power as the level of characterization lessened. Therefore, the breakthrough curve for most field sites can be predicted only qualitatively due to limited characterization of the hydrogeology and contaminant source strength.     

Solute Migration from the Aquifer Matrix into a Solution Conduit and the Reverse

A solution conduit has a permeable wall allowing for water exchange and solute transfer between the conduit and its surrounding aquifer matrix. In this paper, we use Laplace Transform to solve a one‐dimensional equation constructed using the Euler approach to describe advective transport of solute in a conduit, a production‐value problem. Both nonuniform cross‐section of the conduit and nonuniform seepage at the conduit wall are considered in the solution. Physical analysis using the Lagrangian approach and a lumping method is performed to verify the solution. Two‐way transfer between conduit water and matrix water is also investigated by using the solution for the production‐value problem as a first‐order approximation. The approximate solution agrees well with the exact solution if dimensionless travel time in the conduit is an order of magnitude smaller than unity. Our analytical solution is based on the assumption that the spatial and/or temporal heterogeneity in the wall solute flux is the dominant factor in the spreading of spring‐breakthrough curves, and conduit dispersion is only a secondary mechanism. Such an approach can lead to the better understanding of water exchange and solute transfer between conduits and aquifer matrix. Highlights:

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Evaluation of longitudinal and transverse dispersivities/distance ratios for tracer test in a radially convergent flow field with scale-dependent dispersion

This study presents a novel mathematical model for analysis of non-axisymmetrical solute transport in a radially convergent flow field with scale-dependent dispersion. A two-dimensional, scale-dependent advection–dispersion equation in cylindrical coordinates is derived based on assuming that the longitudinal and transverse dispersivities increase linearly with the distance of the solute transported from its injected source. The Laplace transform finite difference technique is applied to solve the two-dimensional, scale-dependent advection–dispersion equation with variable-dependent coefficients. Concentration contours for different times, breakthrough curves of average concentration over concentric circles with a fixed radial distance, and breakthrough curves of concentration at a fixed observation point obtained using the scale-dependent dispersivity model are compared with those from the constant dispersivity model. The salient features of scale-dependent dispersion are illustrated during the non-axisymmetrical transport from the injection well into extraction well in a convergent flow field. Numerical tests show that the scale-dependent dispersivity model predicts smaller spreading than the constant-dispersivity model near the source. The results also show that the constant dispersivity model can produce breakthrough curves of averaged concentration over concentric circles with the same shape as those from the proposed scale-dependent dispersivity model at observation point near the extraction well. Far from the extracting well, the two models predict concentration contours with significantly different shapes. The breakthrough curves at observation point near the injection well from constant dispersivity model always produce lesser overall transverse dispersion than those from scale-dependent dispersivity model. Erroneous dimensionless transverse/longitudinal dispersivity ratio may result from parametric techniques which assume a constant dispersivity if the dispersion process is characterized by a distance-dependent dispersivity relationship. A curve-fitting method with an example is proposed to evaluate longitudinal and transverse scale-proportional factors of a field with scale-dependent dispersion.     

Comparison of Stainless Steel vs. PTFE Miniwells for Monitoring Halogenated Organic Solute Transport

Field tests of organic solute transport behavior have often been monitored using small-diameter wells (miniwells). To determine if experimental results could be significantly biased by sorption to, desorption from, or diffusion through sampling lines, dissolved concentrations of tetrachloroethene and carbon tetrachloride were measured in ground water samples collected simultaneously from the same spatial location during a forced-gradient test in the Borden aquifer using polytetrafluoroethene (PTFE) and stainless steel miniwells (1/8-inch O.D.).
A semiautomated organic analytical system was used on-site to obtain real-time results, which avoided sample holding problems and permitted optimizing sampling times. The breakthrough curves (plots of concentration vs. time) for both organic compounds indicate that under the conditions of this experiment (low organic solute concentrations, short exposure time of sampling lines to the plume, adequate flushing of sampling lines) there is no significant difference between concentration histories (breakthrough curves) collected using a polytetrafluoroethene sampling line and those collected using a stainless steel sampling line. This suggests that organic solute tailing seen in this and also in a similar transport experiment previously conducted at the site is the result of transport processes in the aquifer rather than an artifact introduced by the PTFE miniwells.     

Field Tracer Test for the Design of LNAPL Source Zone Surfactant Flushing

A field tracer test was carried out in a light nonaqueous phase liquid (LNAPL) source zone using a well pattern consisting of one injection well surrounded by four extraction wells (5‐spot well pattern). Multilevel sampling was carried out in two observation wells located inside the test cell characterized by heterogeneous lithology. Tracer breakthrough curves showed relatively uniform flow within soil layers. A numerical flow and solute transport model was calibrated on hydraulic heads and tracer breakthrough curves. The model was used to estimate an average accessible porosity of 0.115 for the swept zone and an average longitudinal dispersivity of 0.55 m. The model was further used to optimize the relative effects of viscous forces versus capillary forces under realistic imposed hydraulic gradients and to establish optimal surfactant solution properties. Maximum capillary number (N_Ca) values between injection and extraction wells were obtained for an injection flow rate of 16 L/min, a total extraction flow rate of 20 L/min, and a surfactant solution with a viscosity of 0.005 Pa?s. The unconfined nature of the aquifer limited further flow rate or viscosity increases that would have led to unrealistic hydraulic gradients. An N_Ca range of 3.8 × 10^?4 to 7.6 × 10^?3 was obtained depending on the magnitude of the simulated LNAPL‐water interfacial tension reduction. Finally, surfactant and chase water slug sizing was optimized with a radial form of the simplified Ogata‐Banks analytical solution (Ogata and Banks 1961) so that injected concentrations could be maintained in the entire 5‐spot cell.     

Lattice Boltzmann Models for Flow and Transport in Saturated Karst

Flow and transport simulation in karst aquifers remains a significant challenge for the ground water modeling community. Darcy's law–based models cannot simulate the inertial flows characteristic of many karst aquifers. Eddies in these flows can strongly affect solute transport. The simple two-region conduit/matrix paradigm is inadequate for many purposes because it considers only a capacitance rather than a physical domain. Relatively new lattice Boltzmann methods (LBMs) are capable of solving inertial flows and associated solute transport in geometrically complex domains involving karst conduits and heterogeneous matrix rock. LBMs for flow and transport in heterogeneous porous media, which are needed to make the models applicable to large-scale problems, are still under development. Here we explore aspects of these future LBMs, present simple examples illustrating some of the processes that can be simulated, and compare the results with available analytical solutions. Simulations are contrived to mimic simple capacitance-based two-region models involving conduit (mobile) and matrix (immobile) regions and are compared against the analytical solution. There is a high correlation between LBM simulations and the analytical solution for two different mobile region fractions. In more realistic conduit/matrix simulation, the breakthrough curve showed classic features and the two-region model fit slightly better than the advection-dispersion equation (ADE). An LBM-based anisotropic dispersion solver is applied to simulate breakthrough curves from a heterogeneous porous medium, which fit the ADE solution. Finally, breakthrough from a karst-like system consisting of a conduit with inertial regime flow in a heterogeneous aquifer is compared with the advection-dispersion and two-region analytical solutions.     

Modelling of the groundwater flow and of tracer movement in the porous and fissured media: Chalk Aquifer (Northern part of Paris Basin,France)

A groundwater flow model has been developed in order to study the chalk aquifer of Paris Basin, based on most of the geological and hydrological available data. The numerical processes are intended to modelling the groundwater flow in the Senonian (Late Cretaceous) formations and to visualize the tracer movement in groundwater resources in the experimental site of LaSalle Beauvais (northern part Paris Basin). Both objectives were achieved as follows: (i) the comprehension of the spatial distribution of the hydraulic conductivity in the chalk aquifer taking into account the characteristics of the hydrogeological system and (ii) the use of the analytical solution for describing one‐dimensional to two‐dimensional solute transport in a unidirectional steady‐state flow tracer with scale‐dependent dispersion. Advection and diffusion mechanisms are taken into account. Comparison between the breakthrough curves of the analytical and the numerical solutions provided an excellent agreement for various ranges of scale‐related transport parameters of interest. The developed power series solution facilitates fast prediction of the breakthrough curves at each observation point. Thus, the derived new solutions are widely applicable and are very useful for the validation of numerical transport. The numerical approach is carried out by MT3DMS, a Modular 3‐D Multi‐Species Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems, and based on total variation‐diminishing method using the ULTIMATE algorithm. The estimation of the infected surface could constitute an approach in water management and allows to prevent the risks of pollution and to manage the groundwater resource from a durable development perspective. Copyright © 2016 John Wiley & Sons, Ltd.     

New combined log and tracer test interpretation method for identifying transfers in fissured aquifers

Tracer tests represent the most appropriate approach for assessing hydrodispersive parameters such as transversal and longitudinal dispersivities or kinematic porosity on an aquifer scale. They are generally carried out by injecting a tracer in a borehole and measuring its concentration over time in neighboring boreholes by extracted volume sampling or downhole measurements. Logging is one of the most suitable methods for evaluating fissured reservoirs. But short circuits between fractures with different hydraulic potential through boreholes induce mixing phenomena that cannot be avoided without packers. This mixing can shift the breakthrough curves deduced from the logs for each producing fracture and distort determination of their location.
The method proposed in this paper aims at measuring the flow rate and the solute breakthrough for hydraulically active fractures, in open boreholes. It involves estimating a velocity profile along the borehole column by the analysis of two successive logs: a shift function according to depth is thus determined by comparison between log portions on each successive one. The velocity gradients reflect the inward or outward flow rates produced by each fracture. On the basis of these flow rates, it is possible to determine the mixing effects inside the borehole and then to plot unbiased breakthrough curves for each producing fracture.
This method was applied at a granitic site in the eastern Pyrenees. In spite of some questionable limitations, the results showed that the method seems adapted to situations with many fractures. The precise hydraulic pattern which is obtained at the borehole scale is discussed in terms of a dual porosity model. Furthermore, interpretation of the breakthrough curves for fractures corrected for mixing effects revealed that Peclet numbers are strongly underestimated if this phenomenon is not considered.     

Two-dimensional power series solution for non-axisymmetrical transport in a radially convergent tracer test with scale-dependent dispersion

It has been known for many years that dispersivity increases with solute travel distance in a subsurface environment. The increase of dispersivity with solute travel distance results from the significant variation of hydraulic properties of heterogeneous media and was identified in the literature as scale-dependent dispersion. This study presents an analytical solution for describing two-dimensional non-axisymmetrical solute transport in a radially convergent flow tracer test with scale-dependent dispersion. The power series technique coupling with the Laplace and finite Fourier cosine transform has been applied to yield the analytical solution to the two-dimensional, scale-dependent advection–dispersion equation in cylindrical coordinates with variable-dependent coefficients. Comparison between the breakthrough curves of the power series solution and the numerical solutions shows excellent agreement at different observation points and for various ranges of scale-related transport parameters of interest. The developed power series solution facilitates fast prediction of the breakthrough curves at any observation point.     

Comparison of approaches for predicting solute transport: sandbox experiments

The main purpose of this paper was to compare three approaches for predicting solute transport. The approaches include: (1) an effective parameter/macrodispersion approach (Gelhar and Axness 1983); (2) a heterogeneous approach using ordinary kriging based on core samples; and (3) a heterogeneous approach based on hydraulic tomography. We conducted our comparison in a heterogeneous sandbox aquifer. The aquifer was first characterized by taking 48 core samples to obtain local-scale hydraulic conductivity (K). The spatial statistics of these K values were then used to calculate the effective parameters. These K values and their statistics were also used for kriging to obtain a heterogeneous K field. In parallel, we performed a hydraulic tomography survey using hydraulic tests conducted in a dipole fashion with the drawdown data analyzed using the sequential successive linear estimator code (Yeh and Liu 2000) to obtain a K distribution (or K tomogram). The effective parameters and the heterogeneous K fields from kriging and hydraulic tomography were used in forward simulations of a dipole conservative tracer test. The simulated and observed breakthrough curves and their temporal moments were compared. Results show an improvement in predictions of drawdown behavior and tracer transport when the K tomogram from hydraulic tomography was used. This suggests that the high-resolution prediction of solute transport is possible without collecting a large number of small-scale samples to estimate flow and transport properties that are costly to obtain at the field scale.     

A field study of the coupled effects of aquifer stratification,fluid density,and groundwater fluctuations on dispersivity assessments

A number of experimental studies have tackled the issue of solute transport parameter assessments either in the laboratory or in the field. But yet, the behavior of a plume in the field under density driven forces, is not well known due to possible development of instabilities. Some field tracer tests on the fate of plumes denser than native groundwater such as those encountered under waste disposal facilities, have pointed out the processes of sinking and splitting at the early stage of migration. The process of dispersion was widely investigated, but the range of dispersivity values obtained from either experimental tests, or numerical and theoretical calculations is still very large, even for the same type of aquifers. These discrepancies were considered to be essentially caused by soil heterogeneities and scale effects. In the meantime, studies on the influence of sinking and fingering have remained more scarce. The objective of the work is to analyze how transport parameters such as dispersivities can be affected by unstable conditions, which lead to plume sinking and fingering. A series of tracer tests were carried out to study under natural conditions, the transport of a dense chloride solution injected in a shallow two-layered aquifer. Two types of experiments were performed: in the first type, source injection was such that the plume could travel downward from one layer to the other of higher pore velocity, and in the second one, the migration took place only in the faster layer. The results suggest some new insights in the processes occurring at the early stages of a dense plume migration moving in a stratified aquifer under groundwater fluctuations, which can be summarized through the following points: (i) Above a stability criterion threshold, a fingering process and a multi modal plume transport take place, but local dispersivities can be cautiously derived, using breakthrough curves matching. (ii) When water table is subject to some cycling or rising, the plume can be significantly distorted in the transverse direction, leading to unusual values of the ratio between longitudinal and transverse dispersivities. (iii) Under stable conditions, for example in the case of straightforward injection in the faster aquifer layer, longitudinal dispersivity is greater than the transverse component as usually encountered, and the obtained transport parameters are closed to macro dispersivity values, which reach their asymptotic limit at very short distances. (iv) The classical scale effect about the varying dispersivity at short distances could be a process mainly due to the distance required for a plume stabilization.     

Combining 3D Hydraulic Tomography with Tracer Tests for Improved Transport Characterization

Hydraulic tomography (HT) is a method for resolving the spatial distribution of hydraulic parameters to some extent, but many details important for solute transport usually remain unresolved. We present a methodology to improve solute transport predictions by combining data from HT with the breakthrough curve (BTC) of a single forced‐gradient tracer test. We estimated the three dimensional (3D) hydraulic‐conductivity field in an alluvial aquifer by inverting tomographic pumping tests performed at the Hydrogeological Research Site Lauswiesen close to Tübingen, Germany, using a regularized pilot‐point method. We compared the estimated parameter field to available profiles of hydraulic‐conductivity variations from direct‐push injection logging (DPIL), and validated the hydraulic‐conductivity field with hydraulic‐head measurements of tests not used in the inversion. After validation, spatially uniform parameters for dual‐domain transport were estimated by fitting tracer data collected during a forced‐gradient tracer test. The dual‐domain assumption was used to parameterize effects of the unresolved heterogeneity of the aquifer and deemed necessary to fit the shape of the BTC using reasonable parameter values. The estimated hydraulic‐conductivity field and transport parameters were subsequently used to successfully predict a second independent tracer test. Our work provides an efficient and practical approach to predict solute transport in heterogeneous aquifers without performing elaborate field tracer tests with a tomographic layout.     

Irreversible sorption of benzene in sandy aquifer materials

Hydrocarbon compounds in aquifers are generally known to show a retardation effect due to sorption onto the surfaces of solid particles. In this study, we investigated the effect of sorption on the transport of benzene in sandy aquifer materials by conducting batch and column tests for both sandy aquifer materials and sandy materials to which had been added 0·5% powdered activated carbon. The batch test was conducted by equilibrating dry materials with benzene solutions of various initial concentrations, and by analysing the concentrations of benzene in the initial and equilibrated solutions using high‐performance liquid chromatography (HPLC). The column test was performed to monitor the concentrations of effluent versus time, known as a breakthrough curve (BTC). We injected KCl and benzene solutions as tracers into the inlet boundary as two different types of square pulse and step, and monitored the effluent concentrations at the exit boundary under a steady‐state condition using an electrical conductivity meter and HPLC. Simulation of benzene transport was performed using the convective–dispersive equation model with the distribution coefficients obtained from the batch test and the transport parameters of the conservative solute KCl from the column test. The observed BTCs of KCl and benzene for pulse injection showed that the arrival times of the peaks of both tracers coincided well, but the relative peak concentration of benzene was much lower than that of KCl. Comparison of the simulated and observed BTCs showed a great discrepancy for all cases of injection mode and material texture, indicating the absence of retardation effect. These results reveal that the predominant process affecting the benzene transport in the sandy aquifer materials is an irreversible sorption rather than retardation. This tentative conclusion was verified by simulation of benzene transport using an irreversible sorption parameter that led to a good agreement between the simulated and observed BTCs. Copyright © 2002 John Wiley & Sons, Ltd.     

Temporal variability of solute transport under vadose zone conditions

The heterogeneity of the solute flux field in the horizontal plane at the field scale has been documented in several field studies. On the other hand, little information is available on the persistence of certain solute transport scenarios over consecutive infiltration cycles. This study was initiated to analyse the recurrence of solute leaching behaviour as estimated in two soil column tests emphasizing the preferential flow phenomenon. Twenty-four small-sized soil samples were subjected to two consecutive unsaturated steady-state flow leaching experiments with bromide as tracer. Observed breakthrough curves (BTCs) were analysed by the method of moments and by the advection–dispersion equation (ADE) to classify solute behaviour. Frequency distributions of the parameters indicating the solute velocity were heavily skewed or bimodal, reflecting the broad variability of the leaching scenarios, including some with pronounced preferential solute breakthrough. Exclusion of the preferential flow columns from our calculations revealed an average amount of 37% of immobile water. The large-scale BTCs derived from assembling the individual concentration courses of each run showed similar features, such as an early bromide breakthrough. However, two distinct apices, viz. one preferential and one matrix, were observed only in the first run, whereas the concentration decrease between the peaks was missing from the second run. A change in soil structure with continuous leaching was presumed to modify the interplay of the various flow domains, thereby altering the spreading of the BTCs. Correlation analysis between parameters of both tests suggests that preferential transport conditions are likely to occur at the same locations in the field over several infiltration cycles, whereas the ‘classical’ or expected matrix flow is time variant and therefore seems to be hardly predictable. © 1998 John Wiley & Sons, Ltd.     

Analytical power series solutions to the two-dimensional advection–dispersion equation with distance-dependent dispersivities

As is frequently cited, dispersivity increases with solute travel distance in the subsurface. This behaviour has been attributed to the inherent spatial variation of the pore water velocity in geological porous media. Analytically solving the advection–dispersion equation with distance-dependent dispersivity is extremely difficult because the governing equation coefficients are dependent upon the distance variable. This study presents an analytical technique to solve a two-dimensional (2D) advection–dispersion equation with linear distance-dependent longitudinal and transverse dispersivities for describing solute transport in a uniform flow field. The analytical approach is developed by applying the extended power series method coupled with the Laplace and finite Fourier cosine transforms. The developed solution is then compared to the corresponding numerical solution to assess its accuracy and robustness. The results demonstrate that the breakthrough curves at different spatial locations obtained from the power series solution show good agreement with those obtained from the numerical solution. However, owing to the limited numerical operation for large values of the power series functions, the developed analytical solution can only be numerically evaluated when the values of longitudinal dispersivity/distance ratio e_L exceed 0·075. Moreover, breakthrough curves obtained from the distance-dependent solution are compared with those from the constant dispersivity solution to investigate the relationship between the transport parameters. Our numerical experiments demonstrate that a previously derived relationship is invalid for large e_L values. The analytical power series solution derived in this study is efficient and can be a useful tool for future studies in the field of 2D and distance-dependent dispersive transport. Copyright © 2008 John Wiley & Sons, Ltd.