Monitoring of drawdown pattern during pumping in an unconfined physical aquifer model

In this study, we attempted to analyse a drawdown pattern around a pumping well in an unconfined sandy gravelly aquifer constructed in a laboratory tank by means of both experimental and numerical modelling of groundwater flow. The physical model consisted of recharge, aquifer and discharge zones. Permeability and specific yield of the aquifer material were determined by Dupuit approximation under steady‐state flow and stepwise gravitational drainage of groundwater, respectively. The drawdown of water table in pumping and neighbouring observation wells was monitored to investigate the effect of no‐flow boundary on the drawdown pattern during pumping for three different boundary conditions: (i) no recharge and no discharge with four no‐flow boundaries (Case 1); (ii) no recharge and reservoir with three no‐flow boundaries (Case 2); (iii) recharge and discharge with two no‐flow boundaries (Case 3). Based on the aquifer parameters, numerical modelling was also performed to compare the simulated drawdown with that observed. Results showed that a large difference existed between the simulated drawdown and that observed in wells for all cases. The reason for the difference could be explained by the formation of a curvilinear type water table between wells rather than a linear one due to a delayed response of water table in the capillary fringe. This phenomenon was also investigated from a mass balance study on the pumping volume. The curvilinear type of water table was further evidenced by measurement of water contents at several positions in the aquifer between wells using time domain reflectometry (TDR). This indicates that the existing groundwater flow model applicable to an unconfined aquifer lacks the capacity to describe a slow response of water table in the aquifer and care should be taken in the interpretation of water table formation in the aquifer during pumping. Copyright © 2001 John Wiley & Sons, Ltd.     

Determination of the conduit structure in a karst aquifer based on tracer data—Lurbach system,Austria

A structure model was used to analyse solute‐transport parameter estimates based on tracer breakthrough curves. In the model system, groundwater flow is envisioned to be organised in a complex conduit network providing a variety of short circuits with relative small carrying capacities along different erosion levels. The discharge through the fully filled conduits is limited owing to void geometries and turbulent flow; thus, a hierarchic overflow system evolves where conduits are (re‐)activated or dried up depending on the flow condition. Exemplified on the Lurbach–Tanneben karst aquifer, the applicability of the model approach was tested. Information derived from multi‐tracer experiments performed at different volumetric flow rates enabled to develop a structural model of the karst network, under constraint of the geomorphological and hydrological evolution of the site. Depending on the flow rate, groundwater is divided into up to eight flow paths. The spatial hierarchy of flow paths controls the sequence of flow path activation. Conduits of the topmost level are strongly influenced by reversible alteration processes. Sedimentation or blocking causes an overflow of water to the next higher conduit. Flow path specific dissolutional denudation rates were estimated using the temporal development of the partial discharge. Copyright © 2012 John Wiley & Sons, Ltd.     

Determination of two‐dimensional laboratory‐scale dispersivities

A tracer test was conducted in a laboratory chamber representing a two‐dimensional aquifer to investigate the longitudinal dispersivity (α_L) and the ratio (α_T/α_L) of transverse to longitudinal dispersivity of sandy aquifer materials. Dispersive parameters were obtained by matching the observed chloride plumes at 9 hours and 16 hours after tracer injection with those simulated by a flow and transport model. The best match was found for α_L = 0·2 ? 0·25 cm and α_T/α_L = 0·2. The ratio of α_T/α_L = 0·2 was within the range of laboratory values reported in the literature. Sensitivity analysis revealed that the tracer plume concentration and shape were more sensitive to variations in longitudinal dispersivity than to the ratio of transverse to longitudinal dispersivity. This result contrasted with findings of others, showing that the dispersivity ratio greatly affects contaminant plume shape. However, our experimental boundary conditions restricted expansion of the plume normal to the direction of flow and thus affected the parameter estimation. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Estimation of the effective precipitation recharge coefficient in an unconfined aquifer using stochastic analysis

Effectively managing groundwater relies heavily on estimating the amount of precipitation that may infiltrate the subsurface and supply groundwater. In this study, we present a novel estimation method based on a stochastic approach to evaluate the quantity of precipitation that may recharge groundwater. The precipitation recharge coefficient is also investigated based on an unconfined aquifer with an unbound, infinitely extended boundary condition. Moreover, a spectrum's relationship to the precipitation and groundwater level variation is also derived. The precipitation recharge coefficient can be obtained from the solution of the spectrum equation. Furthermore, sensitivity analysis is performed in order to determine the key variable on the precipitation recharge coefficient. Analysis results indicate that the location of an observation well affects the estimated precipitation recharge coefficient. If the precipitation recharge area is large enough, the precipitation recharge coefficient becomes insensitive to the location of the observation well. The spectrum's relationship between the precipitation recharge and groundwater level variation is also applied when estimating the precipitation recharge coefficient upstream of the Cho‐Shui River alluvial fan. According to those results, the precipitation recharge coefficient is 0·03 and the amount of groundwater recharge from precipitation is 35 million tons of water annually upstream of the Cho‐Shui River alluvial fan. Copyright © 2000 John Wiley & Sons, Ltd.     

Estimation of unconfined aquifer parameters by genetic algorithms

Abstract

Unconfined aquifer parameters, viz. transmissivity, storage coefficient, specific yield and delay index from a pumping test are estimated using the genetic algorithm optimization (GA) technique. The parameter estimation problem is formulated as a least-squares optimization, in which the parameters are optimized by minimizing the deviations between the field-observed and the model-predicted time–drawdown data. Boulton's convolution integral for the determination of drawdown is coupled with the GA optimization technique. The bias induced by three different objective functions: (a) the sum of squares of absolute deviations between the observed and computed drawdown; (b) the sum of squares of normalized deviations with respect to the observed drawdown; and (c) the sum of squares of normalized deviations with respect to the computed drawdown, is statistically analysed. It is observed that, when the time–drawdown data contain no errors, the objective functions do not induce any bias in the parameter estimates and the true parameters are uniquely identified. However, in the presence of noise, these objective functions induce bias in the parameter estimates. For the case considered, defining the objective function as the sum of the squares of absolute deviations between the observed and simulated drawdowns resulted in the best possible estimates. A comparison of the GA technique with the curve-matching procedure and a conventional optimization technique, such as the sequential unconstrained minimization technique (SUMT), is made in estimating the aquifer parameters from a reported field pumping test in an unconfined aquifer. For the case considered, the GA technique performed better than the other two techniques in parameter estimation, with the sum-of-squares errors obtained from the GA about one fourth of those obtained by the curve matching procedure, and about half of those obtained by SUMT.

Citation Rajesh, M., Kashyap, D. & Hari Prasad, K. S. (2010) Estimation of unconfined aquifer parameters by genetic algorithms. Hydrol. Sci. J. 55(3), 403–413.     

A general solution for tide‐induced groundwater fluctuation in an estuarine‐coastal confined and unconfined aquifer system

This paper presents an analytical solution to tide‐induced head fluctuations in a two‐dimensional estuarine‐coastal aquifer system that consists of an unconfined aquifer and a heterogeneous confined aquifer extending under a tidal river with a semipermeable layer between them. This study considers the joint effects of tidal‐river leakage, inland leakage, dimensionless transmissivity between the tidal‐river and inland confined aquifer, and transmissivity anisotropic ratios. The analytical solution for this model is obtained via the separation of variables method. Three existing solutions related to head fluctuation in one‐ or two‐dimensional leaky confined aquifers are considered as special cases in the present solution. This study shows that there is a threshold of tidal‐river confined aquifer length. When the tidal‐river length is greater than the threshold length, the inland head fluctuations remain sensitive to the leakage effect but become insensitive to the tidal‐river width and dimensionless transmissivity. Considering leakage and transmissivity anisotropy, this study also demonstrates that at a location farther from the river–inland boundary, head fluctuations increase with increasing leakage and transmissivity anisotropy; the maximum head fluctuation occurs when leakage and transmissivity anisotropy are both at their maximum values. The combined action of the 3 effects of loading, tidal‐river aquifer leakage, and inland aquifer leakage differs significantly according to various aquifer parameters. The analytical solution in this paper can be applied to demonstrate the behaviours of the head fluctuations of an estuarine‐coastal aquifer system, and the head fluctuations can be clearly described when the tidal and hydrogeological parameters are derived from field measurement data or hypothetical cases.     

Study of the feasibility of an aquifer storage and recovery system in a deep aquifer in Belgium

Abstract

The feasibility of aquifer storage and recovery (ASR) was tested in a deep aquifer near Koksijde, Belgium. To achieve this, oxic drinking water was injected into a deep aquifer (the Tienen Formation) that contains anoxic brackish water. The hydraulic properties of the aquifer were determined using a step-drawdown test. Chemical processes caused by the injection of the water were studied by two push—pull tests. The step-drawdown test was interpreted by means of an inverse numerical model, resulting in a transmissivity of 3.38 m²/d and a well loss coefficient of 0.00038 d²/m⁵. The push—pull tests identified mixing between the injection and pristine waters, and cation exchange, as the major processes determining the quality of the recovered water. Mobilization of DOC, aerobic respiration, denitrification and mobilization of phosphate were also observed.     

Analysis of the water content in an unconfined aquifer with a partially penetrated pumping well

Most methods developed to represent water flow phenomena in an unconfined aquifer with a fully penetrated pumping well are either numerical, such as the well‐known FEMWTER model, or experimental; analytical models of a partially penetrated pumping well are rare. This study employs the linearized Richards equation as the governing equation, with the aid of Fourier Integral Transformation, to obtain an analytical solution of the water content distribution in an unconfined aquifer with a partially penetrated pumping well. The results from this study could serve to substantiate in some sense results from numerical models. In addition, the theory developed herein can be modified to simulate a vacuum‐pressured pumping well since it is derived by considering, among others, the location and length of a well screen with fluxes. Copyright © 2008 John Wiley & Sons, Ltd.     

Spatio‐temporal analysis of groundwater recharge and mound dynamics in an unconfined aquifer: a GIS‐based approach

Groundwater recharge and mounding of water‐table is a complex phenomenon involving time‐ and space‐dependent hydrologic processes. The effect of long‐term groundwater mounding in the aquifer depends on soil, aquifer geometry and the area contributing to recharge. In this paper, a GIS‐based spatio‐temporal algorithm has been developed for the groundwater mound dynamics to estimate the potential rise in the water‐table and groundwater volume balance residual in an unconfined aquifer. The recharge and mound dynamics as predicted using the methodology recommended here were compared with those using the Hantush equation, and the differences were quite significant. The significance of the study is to assess the effectiveness of the basin in terms of its hydrologic and hydraulic properties for sustainable management of groundwater recharge. Copyright © 2007 John Wiley & Sons, Ltd.     

Regression method for estimating rainfall recharge at unconfined sandy aquifers with an equatorial climate

A reliable estimate of rainfall recharge is essential for groundwater system managements. This study develops a method based on regression equations for estimating rainfall recharge at unconfined sandy aquifers with an equatorial climate. The developed method (GR-I method) is generally efficient for estimating long-term regional recharge, as the computational procedures could be formulated and executed easily using Microsoft's Excel spreadsheet. More importantly, its application could be extended to sand textures different from the sand texture used in developing the regression equations. To evaluate its reliability, the method was applied to estimate monthly gross recharge percentages at the Changi reclaimed land. When ignoring the effect of rainfall clusters, the GR-I method was found to underestimate the monthly gross recharge percentages for those months with high monthly rainfall depths. By integrating the effect of rainfall clusters, the GR-I method yields reliable estimates of monthly gross recharge percentages. By including daily potential evaporation as an additional input variable, the Extended GR-I method was found to be not superior to the GR-I method, implying that soil moisture availability is the major governing factor for actual soil evaporation in the highly porous sand medium, instead of atmospheric demand represented by the potential evaporation rate. Using the GR-I method, the mean annual net recharge percentage of the study site was found to fall between 56·9 and 69·9%, which corresponds to a net recharge depth of 1073·8–1745·8 mm. Although the developed method provides a good alternative to other widely used methods, its recharge estimates still needs to be collaborated with estimates from other methods, as multiple techniques are highly recommended in any groundwater recharge estimations. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Groundwater response to tidal fluctuations in a leaky confined coastal aquifer with a finite length

The study on the hydraulic properties of coastal aquifers has significant implications both in hydrological sciences and environmental engineering. Although many analytical solutions are available, most of them are based on the same basic assumption that assumes aquifers extend landward semi‐infinitely, which does not necessarily reflect the reality. In this study, the general solutions for a leaky confined coastal aquifer have been developed that consider both finitely landward constant‐head and no‐flow boundaries. The newly developed solutions were then used to examine theoretically the joint effects of leakage and aquifer length on hydraulic head fluctuations within the leaky confined aquifer, and the validity of using the simplified solution, which assumes the aquifer is semi‐infinite. The results illustrated that the use of the simplified solution may cause significant errors, depending on joint effects of leakage and aquifer length. A dimensionless characteristic parameter was then proposed as an index for judging the applicability of the simplified solution. In addition, practical application of the general solution for the constant‐head inland boundary was used to characterize the hydraulic properties of a leaky confined aquifer using the data collected from a field site at the Seine River estuary, France, and the versatility of the general solution was further justified.     

Impact of debris dams on hyporheic interaction along a semi‐arid stream

Hyporheic exchange increases the potential for solute retention in streams by slowing downstream transport and increasing solute contact with the substrate. Hyporheic exchange may be a major mechanism to remove nutrients in semi‐arid watersheds, where livestock have damaged stream riparian zones and contributed nutrients to stream channels. Debris dams, such as beaver dams and anthropogenic log dams, may increase hyporheic interactions by slowing stream water velocity, increasing flow complexity and diverting water to the subsurface. Here, we report the results of chloride tracer injection experiments done to evaluate hyporheic interaction along a 320 m reach of Red Canyon Creek, a second order stream in the semi‐arid Wind River Range of Wyoming. The study site is part of a rangeland watershed managed by The Nature Conservancy of Wyoming, and used as a hydrologic field site by the University of Missouri Branson Geologic Field Station. The creek reach we investigated has debris dams and tight meanders that hypothetically should enhance hyporheic interaction. Breakthrough curves of chloride measured during the field experiment were modelled with OTIS‐P, a one‐dimensional, surface‐water, solute‐transport model from which we extracted the storage exchange rate α and cross‐sectional area of the storage zone A_s for hyporheic exchange. Along gaining reaches of the stream reach, short‐term hyporheic interactions associated with debris dams were comparable to those associated with severe meanders. In contrast, along the non‐gaining reach, stream water was diverted to the subsurface by debris dams and captured by large‐scale near‐stream flow paths. Overall, hyporheic exchange rates along Red Canyon Creek during snowmelt recession equal or exceed exchange rates observed during baseflow at other streams. Copyright © 2005 John Wiley & Sons, Ltd.     

Determination of aquifer parameters based on measurements of tidal effects on a coastal aquifer near Beihai,China

Measurements of the tide and groundwater levels in coastal zones are of importance in determining the properties of coastal aquifers. The solution to a one‐dimensional unsteady groundwater flow model in a coastal confined aquifer with sinusoidal fluctuation of the tide shows that the tidal efficiency decreases exponentially with distance and the time lag increases linearly with distance from the coast. The aquifer property described by the ratio of storage coefficient to transmissivity is determined if the damping constant of the tidal efficiency or the slope of the time lag with distance are obtained on the basis of tidal measurements. Hourly observations of the tide and groundwater levels at 10 wells on the northern coast near Beihai, China show that with distance from the coast, tidal efficiency decreases roughly exponentially and the time lag increases roughly linearly. The estimated ratio of storage coefficient to transmissivity of the confined aquifer ranges from 1·169 × 10^?6 d m^?2 to 1·83 × 10^?7 d m^?2. For a given transmissivity of 750 m² d^?1, the storage coefficient of the aquifer is 8·7675 × 10^?4 with the tidal efficiency method and 1·3725 × 10^?4 with the time lag method. The damping constant of the tidal efficiency with distance can be defined as the tidal propagation coefficient. The value of the confined aquifer is determined as 0·0018892 m^?1. Copyright © 2007 John Wiley & Sons, Ltd.     

Identification of aquifer parameters from residual drawdowns: an optimization approach

Abstract

An optimization method based on nonlinear least squares is proposed for the identification of aquifer transmissivity and two storage coefficients, one for the pumping phase and the other for the recovery phase, using only residual drawdowns at an observation well. The method is applicable irrespective of whether pumping and recovery storage coefficients are the same or are different and the argument of well function during recovery is less than or greater than 0.01. The method can check for the changed value of storage coefficient during the recovery phase and can quantify this change. Use of the method is illustrated through examples, which show that the parameters are estimated reliably.     

Effects of meteorological and hydrogeological factors on gross recharge percentage at unconfined sandy aquifers with an equatorial climate

A thorough understanding of rainfall recharge processes and their controlling factors is essential for management of groundwater systems. This study investigates the effects of various meteorological and hydrogeological factors on the gross recharge percentages, the rainfall–recharge relationships and the recharge threshold values for unconfined sandy aquifers under an equatorial climate. Among the meteorological factors investigated, rainfall intensity was found to have the most significant impact on the gross recharge rate. The effects of potential evaporation rate, relative humidity and air temperature on the gross recharge percentage were significant when the vadose zone thickness is larger than 2·5 m. The recharge threshold values were found to depend strongly on the vadose zone thickness. The rainfall–recharge relationships could generally be well defined by a normal–log relationship. The rainfall–recharge relationships derived here are applicable to yield estimates of gross recharge percentages for unconfined sandy aquifers under an equatorial climate, using rainfall intensity and vadose zone thickness as input variables. In this study, a theory was developed and validated to provide physical explanations for the observations, based on the residence time of the percolated rainwater within the vadose zone. Among the soil hydraulic parameters tested, porosity and saturated hydraulic conductivity were found to have the most pronounced effects on the gross recharge percentage. Utilizing the sensitivity results and the theory derived, an approach was developed for extending the application of the derived rainfall–recharge relationships to other sand textures. The approach was found to be capable of producing rough and fast estimations of gross recharge percentage for other sand textures. Copyright © 2007 John Wiley & Sons, Ltd.     

A stochastic optimization framework for the restoration of an over-exploited aquifer

ABSTRACT

This study investigates the impact of hydraulic conductivity uncertainty on the sustainable management of the aquifer of Lake Karla, Greece, using the stochastic optimization approach. The lack of surface water resources in combination with the sharp increase in irrigation needs in the basin over the last 30 years have led to an unprecedented degradation of the aquifer. In addition, the lack of data regarding hydraulic conductivity in a heterogeneous aquifer leads to hydrogeologic uncertainty. This uncertainty has to be taken into consideration when developing the optimization procedure in order to achieve the aquifer’s sustainable management. Multiple Monte Carlo realizations of this spatially-distributed parameter are generated and groundwater flow is simulated for each one of them. The main goal of the sustainable management of the ‘depleted’ aquifer of Lake Karla is two-fold: to determine the optimum volume of renewable groundwater that can be extracted, while, at the same time, restoring its water table to a historic high level. A stochastic optimization problem is therefore formulated, based on the application of the optimization method for each of the aquifer’s multiple stochastic realizations in a future period. In order to carry out this stochastic optimization procedure, a modelling system consisting of a series of interlinked models was developed. The results show that the proposed stochastic optimization framework can be a very useful tool for estimating the impact of hydraulic conductivity uncertainty on the management strategies of a depleted aquifer restoration. They also prove that the optimization process is affected more by hydraulic conductivity uncertainty than the simulation process.

Editor Z.W. Kundzewicz; Guest editor S. Weijs     

A general solution for groundwater flow in an estuarine's leaky aquifer system after considering aquifer anisotropy

This paper presents an analytical model for describing the tidal effects in a two‐dimensional leaky confined aquifer system in an estuarine delta where ocean and river meet. This system has an unconfined aquifer on top and a confined aquifer on the bottom with an aquitard in between the two. The unconfined and confined aquifers interact with each other through leakage. It was assumed that the aquitard storage was negligible and that the leakage was linearly proportional to the head difference between the unconfined and confined aquifers. This model's solution was based on the separation of variables method. Two existing solutions that deal with the head fluctuation in one‐dimensional or two‐dimensional leaky confined aquifers are shown as special cases in the present solution. Based on this new solution, the dynamic effect of the water table's fluctuations can be clearly explored, as well as the influence of leakage on the behaviour of fluctuations in groundwater levels in the leaky aquifer system. Copyright © 2015 John Wiley & Sons, Ltd.     

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.