H11B-0293 0800h
Transport Processes in the Fault Zones of the Crystalline Crust - A Conceptual Model for the Natural Flow, Discussed for the KTB Area -
To prove the geochemical and isotopic results of the scientific drilling test site KTB Oberpfalz a conceptual numerical model for the natural flow and transport process was build with the program FEFLOW. With the calculation we answered the question how it is possible that the isotopic components of the fluid recovered from the deep crystalline rock indicate a west - east fluid flow from a topographic lower sedimentary area to the higher hilly area of the KTB site. In particular CH$_4$ isotopic signature of the gas indicates the CH$_4$ is migrated from the western sedimentary formation into the crystalline formation. Large transport paths of sedimentary components in the crystalline rock with a high topography are investigated and postulated by different scientist world wide. To explain this phenomenon, the existence of a permanent, density driven flow with simultaneous dilution is suggested. Such a system explains fluid flow in the deep crust against the higher level of the groundwater surface. By means of a simple convection model it can be shown that the density driven dilution motor can create a more effective hydraulic potential than a motor driven by precipitation and the related hydraulic head of the groundwater surface. Furthermore, with common geothermal gradients, the geothermal convection motor is weak compared to the fluid density effects discussed here. The numerical calculation shows, that the density driven flow model escribed above is realistic and can produce in great depth hydraulic flow against the direction of the shallow groundwater flow. A coupled hydraulic - geothermal FE calculation was also done. The downward directed water flow in the fault zones produce here a cooling of $0.5\, ^\circ $C after a simulation time of 2000 a. This results agrees well with the observed temperatures. \textbf{References:} KESSELS W., W. GR\"ASLE (2002): Mineral Dilution and Shallow Groundwater Dynamics as Motor to Drive Fluid Migration in the Deep Crystalline Crust - Interpretation of Hydraulic Investigations From the 9101 m Super Deep German Continental Drillhole. - Fall Meeting of the AGU, 6.\,-\,10. Dec. 2002, San Francisco/California/USA, paper T21A 1081. GR\"ASLE W., W. KESSELS (2003): Three dimensional modelling of fluid movement and transport of fluid components in the SE1 and SE2 fault zones driven by processes on a regional scale - Hydraulic and tracer test interpretation regarding the stress coupling and the probability of the hydraulic induced shear failures and as technical support. - ICDP Kolloquium, 26.\,-\,28. March 2003, Mainz, 4 S.
http://www.gga-hannover.de
H11B-0294 0800h
Power averaging and inverse smoothing: implications for porous media flow
An extremely large data set of Venus elevation is used to study the behavior of spatial statistics (eg. variance) under power averaging (eg. geometric averaging over blocks). It is shown that a model of univariate and bivariate Gaussianity can be adopted for this data set. Multivariate Gaussianity, however, is clearly disproved by comparing the multiple point statistics of high and low indicator values with those from the multivariate Gaussian distribution. Power averaging is performed on the data set over increasing block sizes using a wide power parameter range going from -40 to +40. The spatial variance of each of these power averages is plotted against increasing averaging volume. Geostatistical theory predicts a decreasing trend for the variance of linear averages. This is the classical smoothing effect. However, for this elevation data set, the variance of power averages shows a significant non-decreasing trend for a range of power values from -4 to -0.5. The cause behind such ``inverse smoothing" is linked to the spatial clustering of extreme values. Note that the block-effective permeability of porous media lies, in general (but, not necessarily), within the two limiting power averages -1 (harmonic average) and +1 (linear average). Since the observed power range for inverse smoothing overlaps this interval, the consequences of inverse smoothing for permeability averaging are discussed. This inverse smoothing arises because of spatial clustering of extreme values in non-Gaussian and finite sized fields. Therefore, this bodes caution for techniques resorting to such assumptions which simplify the analytical and numerical computation of effective permeability, but, possibly, at some unexpected risk.
H11B-0295 0800h
Characterization of Unsaturated Soil Properties Using A Markov Chain Monte Carlo Approach
We consider transient flow and solute transport in an unsaturated heterogeneous soil column under infiltration and assume that the constitutive relationships between unsaturated hydraulic conductivity vs. pressure head and the water content vs. pressure head follow the van Genuchten-Mualem model. The parameters that characterize the van Genuchten-Mualem model are measured at some spatial locations. In addition to these direct measurements, time-dependent observations on state variables (pressure head, moisture content, and solute concentration or tracer travel time) are also available at some locations. The aim is to develop a general technique to estimate the infiltration rate and the spatial distributions of soil parameters, as well as the uncertainties associated with these estimates, given an arbitrary sampling of different kinds of measured data D. We do so using a Markov Chain Monte Carlo approach (MCMC). Each soil parameter is represented (parameterized) by the combination of some basis kernels centered at fixed spatial locations. The prior distribution for the vector of coefficients $\theta$ in this combination is specified and some hyperparameters $\lambda_\theta$ in this distribution are updated. The samples for the vector $\theta$ are then taken from a posterior distribution $\pi(\theta, \lambda_\theta|D)$. Starting from any initial setting, realizations of a Markov chain are generated by updating only one component of q at a time according to Metropolis rules. The posterior mean of the parameter $\theta$ (and thus the infiltration and the soil properties conditional to all observations) can be estimated from the Markov chain realizations (ignoring some early realizations). The uncertainties associated with the mean quantities can also be assessed from these realizations. In addition, the MCMC approach provides an alternative for estimating conditional predictions of state variables and their associated uncertainties. Numerical tests for flow in a hypothetic random porous medium show that estimated soil properties from the MCMC approach are close to the original hypothetical random fields. These tests also reveal the relative worth of various types of data in constraining the estimates of infiltration rate and transport velocity. This information can be used to optimize data collection activities in a field setting.
H11B-0296 0800h
Numerical study about the natural and induced heat convection on far-field groundwater flow.
In the safety assessment of nuclear waste disposal, the influences of heat convection on far-field groundwater flows cannot be neglected. These influences should be estimated by conducting detailed thermal-hydrological (TH) numerical analysis at the site characterization stage. However, as a first step, it is worthwhile to estimate the influence of heat convection using only the thermodynamic parameters and the geological model obtained in the early stage of site characterization. In this study, the thermal-hydrological coupled simulation code TOUGH2 was applied to a homogenous and heterogeneous models with vertical highly permeable zone. The homogeneous model was used to estimate the influence of permeability on the natural groundwater flow caused by the surface topography, and the heterogeneous models were used to estimate the influence of permeability, heat flow from the bottom, and the thickness of the highly permeable zone on the local onset of natural convection. From the results of numerical simulations, we extracted path lengths and travel times along stream traces representing regional groundwater flow and compare them to uncoupled models that assume the temperature distribution is fixed. Two dimensionless numbers (Peclet number and Reyleigh number) were derived to analyze the results of sensitivity studies. The following are the main results of this study. 1. In the homogeneous case, comparing the results of the TH coupled model to the uncoupled model, when the Peclet number is less than 0.2, the error of the average velocity along the stream traces in the uncoupled model is less than 10%. 2. The ratio of the average velocity along the stream traces between the coupled model and the uncoupled model increases with an increase of the Peclet number until the Peclet number is 2.0. When the Peclet number exceeds 2.0, the ratio of the average velocity becomes smaller and close to 1.0. 3. In the inhomogeneous model with a vertical highly permeable zone, the critical Rayleigh number and the critical temperature gradient for the onset of natural convection were estimated from the analytical solution of heat convection considering the aspect ratio of a convection cell. In this case, as the cell height increases, the critical temperature gradient decreases, and a small convection cell is generated in the highly permeable zone. As the result, the influence on the stream trace in the natural groundwater flow system is small. 4. In the inhomogeneous model with a vertical highly permeable zone with a low permeabily core, the critical Rayleigh number and the critical temperature gradient can be estimated by approximating the local heterogeneity as a permeability anisotropy. In this case, the existence of a low permeability core prevents the formation of a small convection cell, and the height of the convection cell becomes larger than in the vertical highly permeable zone case. As the result, the stream traces can be discharged in the highly permeable zone in the middle of the model with thermodynamic parameters that do not cause the discharge in highly permeable zone in other cases.
H11B-0297 0800h
Dynamic Micro-CT Study of Fracture-Matrix Flow During Capillary Imbibition in Layered Berea Sandstone
Studies concerning flow in fractured rocks have important applications in hydrocarbon recovery, hydrogeology, and environmental remediation of subsurface spills, such as DNAPLs. To properly design immiscible flow processes in those systems, it is crucial to understand fracture-matrix transfer mechanisms. The goal of this work is to provide a mechanistic description of capillary-driven imbibition in fractured media and the effects of fluid occupancy in the fracture and of matrix heterogeneity on saturation distribution. Capillary imbibition experiments where performed in a layered Berea sample, 4.75 cm long and 2.54 cm in diameter, with a single longitudinal fracture. The artificially created fracture was oriented perpendicular to the natural bedding of the rock. The sample was initially vacuum saturated with non-wetting phase. Small amounts of a wetting phase were introduced into the bottom of the fracture, allowing it to imbibe and exchange places with the resident non-wetting phase through the fracture-matrix interface. Progress of the imbibition process was monitored after each injection using high-resolution Micro Computed Tomography (CT). Micro-CT also provided non-destructive means to characterize the fracture structure and rock properties. A series of simulation scenarios were also tested using a commercially available package developed by the Computer Modeling Group (CMG). Experimental observations combined with simulation results indicate that the fracture itself exhibits a strong capillary behavior. Its rough-walled nature, leads to a two-phase flow similar to that in porous media. Experimental observations also show a strong correspondence between fluid invasion in the matrix and variations in porosity in the rock's bedding planes. Our results suggest that different porosities correspond to different permeabilities and capillary pressure curves. Fluid accessibility in the fracture space is also an important factor governing imbibition in fractured media. Fluid discontinuity and occupancy are key parameters affecting fluid accessibility between matrix and fracture space. Other factors affecting imbibition are interfacial tension, fracture roughness, and presence of micro-fractures.
H11B-0298 0800h
Uncertainty Analysis of Flow and Transport Through Heterogeneous, Variably-Saturated Field at INTEC, INEEL
The main purpose of this study is to examine the uncertainty associated with water flow and solute transport through the variably-saturated, heterogeneous field at the Idaho Nuclear Technology and Engineering Center (INTEC), Idaho National Engineering and Environmental Laboratory (INEEL). Specifically, we will (i) analyze the uncertainty in water and solute travel time as a function of spatial distribution of sediment interbedding through geostatistical analysis of existing borehole data and applying Monte Carlo techniques to a deterministic model for flow and solute transport under variably-saturated flow; and (ii) evaluate the compound effect of major physical settings (source location and boundary conditions) and subsurface spatial heterogeneity on the model predictions. Empirical probabilistic density functions (pdf) are used to describe the uncertainty in subsurface flow rates and travel time. Both one-dimensional and two-dimensional results are presented to illustrate the effects of subsurface spatial heterogeneity and hydrological settings on water flow and contaminant transport
H11B-0299 0800h
On The Tailing Behavior Of The Backward Travel Time Probability Density (BTTPD) Of Contaminants In Alluvial Aquifer Systems
The shape of the backward travel time probability density (BTTPD) of groundwater contaminant is important to water-quality related problems, such as contaminant remediation and aquifer vulnerability assessment. The BTTPD in alluvial aquifer systems may have significant weight in one or both tails because of the anomalous transport of plumes, which is due to the preferential flow in networks of ancient stream channels and the sequestration of plumes in surrounding fine-grained aquitard materials. The behavior of BTTPD tails and the controlling factors were explored systematically using thousands of km-scale numerical models based on geologically constrained realizations of alluvial systems, generated with exponential transition probability (TP) geostatistics. The numerical models were discretized on a very fine scale (5*10*0.5m) to capture the interactions of numerous depositional facies. The numerical results show that although the BTTPD contains an early arrival peak, the early tail is Gaussian-like with a slope on a log-log plot larger than $\sim$6. The simulated backward location probability (BLP) indicates that the distribution of vertical displacements of solute particles only has a weak power-law exponent that varies with time, and the longitudinal movement of particles inside of channel is negatively skewed upstream. The sediment layering and the short correlation scale of channels on the vertical direction may limit the large jumps of particles vertically. In contrast, the simulated BTTPDs contain late-time tails varying from exponential to power-law, depending on the proportion of low-K materials, the distribution of the size of low-K materials, and the value of the local dispersion coefficient. A heavy late-time tail with a slope on a log-log plot of -2 to -3 was found for systems dominated by aquitards, while a weaker tail with a slope $<$-3 or an exponential tail was found for systems with abundant coarse-grained materials. The exponential density function of the 'sizes' of the low-K units simulated by the exponential-form TP gives rise to a late-time BTTPD that is a predictable function of the advection time, geostatistics of the low-K material, and the molecular diffusion coefficient.
H11B-0300 0800h
Effects of Bedding Plane Orientations on Two-Phase Flow in Shear Fractures
Multi-phase transport in fractured rocks has a significant impact on hydrocarbon recovery processes in hydrology and petroleum engineering. This study examines the transport mechanisms in two types of cylindrical layered sandstones that were fractured in shear mode: a. samples were cut perpendicular to bedding and sheared perpendicular to bedding, and b. samples cut parallel to bedding and sheared parallel to bedding. The cylindrical samples (length=70mm, diameter=25mm) were fractured in shear mode under a constant strain rate and a fixed radial confining stress. The axial fracture displacements were about 0.5 mm. The samples were saturated with water, then, sequentially flooded with tagged water (miscible), oil (immiscible), and tagged water. The topology of the fractures and the distribution of fluids in the samples were determined by x-ray Computed Tomography (CT) at a voxel resolution of about 0.03 mm. The fracture perpendicular to bedding (case a) has few large porosity voids, exhibits a significant process zone, and has a high frequency of ridges driven by the bedding planes. The combination of the layers and the perpendicular fracture caused the displacements to sweep the entire volume of the sample. Only some of the few large fracture pores were not displaced by the last water injection stage. The fracture did not form a significant flow channel. About half of the oil was recovered during the last water injection stage. The fracture parallel to bedding (case b) has large porosity voids, has a small process zone, and has a low frequency of ridges. The presence of the parallel to bedding fracture created a flow channel in the sample, causing very low displacement sweep in the matrix. Some of the large pores in the fracture plane were not displaced during the first miscible injection stage. The immiscible injection stage invaded a portion of the fracture pores that were previously displaced by the tagged water. Finally, the last tagged water injection stage displaced most of the oil from the fracture. Only a portion of the large pores in the fracture form the flow channel, but some of the oil remains trapped in the largest pores of the channel. The relative orientation of the fracture plane with respect to the bedding planes has a significant impact on multi-phase fluid transport in fractured rocks. Fractures parallel to bedding tend to form large connected pores that channel fluid flow and reduce mass transport from the fracture to the matrix. Strong channel flow has not been observed when the fractures were perpendicular to bedding.
H11B-0301 0800h
Fluid Flow Modeling Through Bed-Confined Fracture Networks in Heterogeneous Layered Rocks
Fractures are discrete features that often serve as preferential pathways for fluid flow, especially in rocks with low matrix permeability. One common fracture network observed in sedimentary rocks consists of an earlier set of systematic joints and a later set of cross joints, that together form a well-connected, ladder-like pattern. The goal of our study is to investigate effects of cross joint attributes such as geometry, orientation, aperture and density on flow through bed-confined fracture networks. The 2-D models calculate volumetric flow under steady state conditions through a fracture network consisting of up to 2600 internal nodes. A large system of equations determines hydraulic head values at fracture intersections and calculates volumetric flow through each fracture segment according to the cubic law. For all scenarios the systematic joints are assigned hydraulic apertures of 0.3 mm, whereas cross joint apertures are varied from 0.001 mm to 0.3 mm. A rotation of 0° corresponds to a hydraulic gradient parallel to the systematic joints. We first investigate cross joints with a uniform fracture spacing ratio (FSR) of 1:1 and an angle between the two fracture sets of 90°. Upon rotating the fracture network at 5° increments, the volumetric flow rate (Q) remains approximately constant (~2.3 ml/s) for cross joint apertures of 0.3 mm, implying isotropic behavior for the fracture network. However, using a cross joint aperture of 0.15 mm reduces Q to 1.9 ml/s for 0° rotation, and a more dramatic reduction to 0.4 ml/s at 90° rotation where the gradient is parallel to the cross joint trend. Thus, flow is highly anisotropic in the likely event of smaller cross joint apertures. We next investigate effects of cross joint density by varying the spacing of cross joints for rotations of 0° and 90°. When flow is parallel to the systematic joints, the cross joint spacing has only a minor effect on flow rate. However, when the flow direction is perpendicular to the systematic joints, high cross joint densities (FSR>3) can result in a five-fold increase in Q. Fracture connectivity in the shallow subsurface is greatly enhanced by the presence of cross joints. Our sensitivity analysis provides constraints on how cross joints influence flow in fractured rocks, which may prove useful in the characterization of heterogeneous formations.
H11B-0302 0800h
A new Method to Estimate the Representative Elementary Volume (REV) for Porosity in Heterogeneous Karst Aquifers Using Geographic Information Systems
Karst limestones are characterized by solution-enhanced macropores and conduits that lead to exceptional heterogeneity at the aquifer scale. The interconnected network of solution cavities often results in a conduit flow regime that bypasses the less permeable rock matrix. Efforts to manage and protect karst aquifers, which are vital water resources in many parts of the world, will benefit from meaningful characterizations of the heterogeneity inherent in these formations. To this end, we propose a new method to estimate the representative elementary volume (REV) for macroporosity within karst aquifers using techniques borrowed from remote sensing and geospatial analysis. The REV represents a sampling window in which numerous measurements of a highly-variable property (e.g., porosity, hydraulic conductivity) can be averaged into a single representative value of statistical and physical significance. High-resolution borehole images are classified into binary images consisting of pixels designated as either rock matrix or pore space. A two-dimensional porosity is calculated by summing the total area occupied by pores within a rectangular sampling window placed over the binary image. Small sampling windows quantify the heterogeneous nature of porosity distribution in the aquifer, whereas large windows provide an estimate of overall porosity. Applying this procedure to imagery taken from the Biscayne aquifer of south Florida yields a macroporosity of ~40%, considerably higher than the ~28% porosity measured from recovered core samples. Geospatial analysis may provide the more reliable estimate because it incorporates large solution cavities and conduits captured by the borehole image. The REV is estimated by varying the size of sampling windows around prominent conduits and evaluating the change in porosity as a function of window size. Average porosities decrease systematically with increasing sampling size, eventually converging to a constant value and thus validating the REV concept for porosity in the Biscayne aquifer.
H11B-0303 0800h
Defining the Spatial Structure of Sedimentary Interbeds within Basalt at the Idaho National Laboratory Vadose Zone Research Park
The Vadose Zone Research Park (VZRP) is a multidisciplinary field research center located at the Idaho National Laboratory. The VZRP vadose zone consists of variably fractured interfingering basalt flows intercalated with sedimentary interbeds. Recent field studies at the VZRP have shown that sedimentary interbeds intercept, attenuate, and laterally redistribute preferential flow in the basalts. Although geologic data on the spatial location of sedimentary interbeds is sparse at the VZRP (33 boreholes), a nearby site, Idaho Nuclear Technology and Engineering Center (INTEC), has sufficient geologic data (95 boreholes) for geostatistical characterization of sedimentary interbeds. Our objective is to determine if INTEC can be used as a geostatistical analog for the VZRP. Indicator variograms of INTEC interbeds show clear anisotropic spatial structure in the horizontal plane, while variograms at the VZRP show a nugget effect. Vertical variograms from both locations compare well. Using subsets of the INTEC data, we evaluate the uncertainty in the VZRP variograms due to a limited number of sampling locations. Our results suggest that indicator geostatistics for sedimentary interbeds at INTEC are an analog for the VZRP
H11B-0304 0800h
Effective Conductivity of Periodic Media with Cuboid Inclusions
We present a numerical solution for the effective conductivity of a periodic binary medium with cuboid inclusions located on an octahedral lattice. The problem is defined by five dimensionless geometric parameters and one dimensionless conductivity contrast parameter. The effective conductivity is determined by considering the flow through the "elementary flow domain" (EFD), which is an octant of the unitary domain of the periodic media. We derive practical bounds of interest for the six-dimensional parameter space of the EFD and numerically compute solutions at regular intervals throughout the entire bounded parameter space. A continuous solution of the effective conductivity within the limits of the simulated parameter space is then obtained via interpolation of the numerical results. Comparison to effective conductivities derived for random heterogeneous media demonstrate similarities and differences in the behavior of the effective conductivity in regular periodic (low entropy) versus random (high entropy) media. The results define the low entropy bounds of effective conductivity in natural media, which is neither completely random nor completely periodic, over a large range of structural geometries. For aniso-probable inclusion spacing, the absolute bounds of Keff for isotropic inclusions are the Wiener bounds, not the Hashin-Shtrikman bounds. For isotropic inclusion and isoprobable conditions well below the percolation threshold, the results are in agreement with the self-consistent approach. For anisotropic cuboid inclusions, or at relatively close spacing in at least one direction (aniso-probable conditions), the effective conductivity of the periodic media is significantly different from that found in anisotropic random binary or Gaussian media.
H11B-0305 0800h
Effect of Embedded Sand Lenses on Transport in Till
Till deposits were previously considered to provide an effective protection against contamination of underlying aquifers from surface spills or application of nutrients and pesticides. However, several investigations have now documented that fractures in the till constitute preferential pathways for contaminants thus undermining the protective nature of till. Furthermore, till often contains embedded sand lenses of varying thickness and lateral extent which also may facilitate a rapid transport of contaminants towards deeper aquifer systems. In this research we have investigated the spatial distribution of the embedded sand lenses in a till block and examined their impact on solute transport by numerical modeling. In a till block of dimensions 100m x 50 m x 8m a total 32 cone penetration tests were carried to map the presence of embedded sand lenses. The data were analyzed in a geostatistical framework using the Transition Probability Geostatistical Software (TPROGS) and on this basis a number of realizations were generated of the spatial distribution of the sand lenses in the till. These realizations were subsequently imported into the GMS modeling system for simulations of flow, particle tracking and solute transport. In the simulations a vertical head gradient was enforced over the block and no-flow conditions were specified along the vertical planes hereby focusing on the vertical transport characteristics. Flux-averaged breakthrough curves across the lower boundary were simulated following a release of tracer across the upper boundary. The simulations documented that the presence of embedded sand lenses in the till block has a significant impact on the transport pattern by causing a more rapid breakthrough and a longer tailing. The study suggests that the presence of the sand lenses leads to a further reduction in the protective capability of till deposits.
H11B-0306 0800h
Analysis Of Field-Scale Contaminant Transport Behavior Using Continuous Time Random Walk Theory
Conservative solute transport across a spectrum of alluvial aquifer systems was evaluated using high-resolution numerical simulation and non-Fickian transport theory based on a continuous time random walk (CTRW) method. Numerical experiments with hydrofacies patterns that varied with respect to connectivity and geometry associated with various high-K (channel) fractions were conducted to simulate a variety of non-Fickian transport phenomena. In addition, effects of facies mean lengths and of conductivity contrast between high- and low-K (floodplain) materials on the transport behavior were examined in a separate experiment. Each simulated cumulative breakthrough curve was optimally fitted with the solution of cumulative first passage time distribution (CFPTD) formulation. The fitting parameter $\beta$ controlling dispersive transport in the CFPTD solution was used to characterize the simulated transport behavior. Our results showed that growth of $\beta$ values, indicating diminishing non-Fickian transport behavior, tends to occur as volumetric fractions of high-K material increases and the K contrast between low- and high- K materials decreases. However, no overall systematic change in the $\beta$ values according to the change only in channel mean length was observed. Importantly, significant variation of $\beta$ values among the equally probable realizations demonstrates that complex channel geometries and connectivity lead to transport behaviors that cannot necessarily be captured solely from $\beta$ values derived from statistics on K or velocity field. This suggests indirect estimation of $\beta$ from K or velocity distribution should be viewed with caution when there exists complex network of high-K materials. Fitting error between the numerically simulated breakthrough curve and best-fitted CFPTD curve increased with increasing non-Fickian behavior, although clearly smaller than with macroscopic advection-dispersion model. Overall, analyses of simulated transport behavior based on CTRW solutions were compatible with the ones based on other measures such as breakthrough curves, plume spatial moments, and dilution indices.
H11B-0307 0800h
Apparent Macrodispersion at the Forced Gradient Tracer Test
A forced gradient tracer test is carried out by artificially generating a forced flow field, often through a single or multiple pumping or injecting wells, then subsequently observing the tracer concentration at a fixed point. Three different forced gradient tracer tests that are commonly employed by hydrogeologists are diverging, converging, and two-well tests. The forced gradient tracer tests have the advantage of accelerating the process of transport, thus can obtain the result timely. In addition, they are often less expensive because they use only a few wells or boreholes. Their disadvantage is that the non-uniform flow pathways have been introduced because of the usage of pumping or injecting wells, which make breakthrough curves much more difficult to interpret. As far as we know, there is no exact theory and closed-form analytical solutions that can describe the breakthrough curve in a forced gradient test because of the difficulty of incorporating the non-uniform flow into the transport equation. Theories based on small perturbations have been developed and broadly employed to interpret the forced gradient tests. This article will provide exact closed-form analytical solutions for two different kinds of forced gradient flow by neglecting the local-scale dispersion. The first is the two-well test with equal pumping and injecting rates, the second is the converging test with regional flow. The purpose is to assess the apparent macrodispersion caused exclusively by the non-uniformity of the flow. The breakthrough curves due to the apparent macrodispersion will be obtained. These solutions can be used as the first cut calculations of concentrations in non-uniform flow fields. Because the solutions are exact, they can be used to test previous approximation theories such as the small perturbation method by neglecting the local-scale dispersion.
http://geoweb.tamu.edu/Faculty/Zhan/Zhan.html