http://www2.geo.uni-bonn.de/doc/Kemna_etal_Hydrol_2002.pdf

Imaging and characterisation of subsurface solute transport using electrical resistivity tomography (ERT) and equivalent transport models

Longitudinal dispersivity (alpha) data were compiled from 109 different authors for different types of geological media. The data were subdivided into different subsets. Dispersivity values for consolidated media were subdivided as basalts, granites, sandstones, and carbonate rocks, while unconsolidated sediments were subdivided into three reliability classes. The data sets provided here may provide ground water practitioners a preliminary guide to estimate dispersivity values at various scales and to guide and verify theories on scaling behavior. Based on the data set presented here, the relationship that empirically best described the dispersivity data in regard to scale of measurement was in the form of a power law. The scaling exponent for consolidated and unconsolidated geological media varied between 0.40 and 0.92, and 0.44 and 0.94, respectively. Higher reliability subsets of data for the unconsolidated sediments and more frequently tested rock formations indicate that the scaling exponent is at the lower end of the observed range, close to 0.5. No significant difference in scaling exponent was found among different media, and no clear evidence exists for the presence of an upper bound or asymptotic behavior on the relationship for any of the analyzed media.

Longitudinal dispersivity data and implications for scaling behavior.

http://www.geol.lsu.edu/blanford/NATORBF/2%20Stream%20Hydraulic%20Tracer%20Tests/Ptak_04_Tracer%20tests%20for%20the%20investigation%20of%20heterogeneous%20.pdf

Tracer tests for the investigation of heterogeneous porous media and stochastic modelling of flow and transport—a review of some recent developments

[1] The conventional analysis of pumping tests by type-curve methods is based on the assumption of a homogeneous aquifer. Applying these techniques to pumping test data from real heterogeneous aquifers leads to estimates of the hydraulic parameters that depend on the choice of the pumping and observation well positions. In this paper, we test whether these values may be viewed as pseudo-local values of transmissivity and storativity, which can be interpolated by kriging. We compare such estimates to those obtained by geostatistical inverse modeling, where heterogeneity is assumed in all stages of estimation. We use drawdown data from multiple pumping tests conducted at the test site in Krauthausen, Germany. The geometric mean values of transmissivity and storativity determined by type-curve analysis are very close to those obtained by geostatistical inversion, but the conventional approach failed to resolve the spatial variability of transmissivity. In contrast, the estimate from geostatistical inversion reveals more structure. This indicates that the estimates of the type-curve approaches can not be treated as pseudo-local values. Concerning storativity, both analysis methods show strong fluctuations. Because the variability of all terms making up the storativity is small, we believe that the estimated variability of storativity is biased. We examine the influence of measurement error on estimating structural parameters of covariance functions in the inversion. We obtain larger correlation lengths and smaller prior variances if we trust the measured data less.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2006WR005333

Two-dimensional characterization of hydraulic heterogeneity by multiple pumping tests

[1] The relevance of aquifer heterogeneity for flow and transport is recognized broadly; however, its characterization is hampered by the inaccessibility of the subsurface. Time-lapse electrical resistivity tomography (ERT) offers the possibility of imaging noninvasively subsurface transport. We present results of two tracer tests that were carried out successively in a shallow aquifer at the Krauthausen test site (Germany). The breakthroughs of an electrically conductive and a resistive tracer were monitored with ERT and local multilevel groundwater samplers (MLS) along two cross sections perpendicular to the mean flow direction. Sinking of the conductive salt tracer due to density effects was observed with ERT. We applied a stream tube model to characterize the spatially variable transport. ERT-derived stream tube parameters showed similar patterns for the two tracer experiments, reflecting the effect of aquifer heterogeneity on transport. MLS data did not show similar spatial patterns, which indicates that these measurements may be prone to subtle changes of the flow field in the small sampling volume and mixing within screened wells. Between 50% and 10% of the tracer was recovered in the ERT-derived breakthrough curves. Compared with transport simulations in a homogeneous aquifer, ERT-derived time-integrated changes in electrical conductivity were locally larger but focused in a smaller area. MLS data indicated that in this area, ERT did not underestimate the tracer recovery. The relatively low tracer recovery was attributed to undetected tracer breakthrough in regions with low ERT sensitivity and in regions where the length of the tracer plume and the electrical conductivity contrast were small.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2008WR007595

Imaging and characterization of solute transport during two tracer tests in a shallow aquifer using electrical resistivity tomography and multilevel groundwater samplers

Analysis of solute transport in a heterogeneous aquifer: the Krauthausen field experiment

We present two- and three-dimensional calculations for the longitudinal and transverse macrodispersion coefficient for conservative solutes derived by particle tracking in a velocity field which is based on the linearized flow equation. The simulations were performed upto 5000 correlation lengths in order to reach the asymptotic regime. We used a simulation method which does not need any grid and therefore allows simulations of very large transport times and distances. Our findings are compared with results obtained from linearized transport, from Corrsin's Conjecture and from renormalization group methods. All calculations are performed with and without local dispersion. The variance of the logarithm of the hydraulic conductivity field was chosen to be one to investigate realistic model cases. While in two dimensions the linear transport approximation seems to be very good even for this high variance of the logarithmic hydraulic conductivity, in three dimensions renormalization group results are closer to the numerical calculations. Here Dagan's theory and the theory of Gelhar and Axness underestimate the transverse macrodispersion by far. Corrsin's Conjecture always overestimates the transverse dispersion. Local dispersion does not significantly influence the asymptotic behavior of the various approximations examined for two-dimensional and three-dimensional calculations.

Estimation of Macrodispersion by Different Approximation Methods for Flow and Transport in Randomly Heterogeneous Media

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

In dem heterogenen Grundwasserleiter des Testfeldes Krauthausen wurden zur Untersuchung des Transports von gelosten Stoffen drei Tracerversuche (Bromid, Lithium, Uranin) durchgefuhrt Um den Einfluss der naturlichen Heterogenitat auf den Stofftransport zu untersuchen, wurden die transportrelevanten Parameter des Grundwasserleiters hoch aufgelost untersucht In den Tracerversuchen wurde bei den Stoffen Uranin und Lithium im Vergleich zu Bromid eine deutliche Retardierung festgestellt, die mit abnehmender Stoffkonzentration zunahm Dieses Verhalten kann fur Uranin und Lithium mit einer Freundlich-Sorptions-Isotherme beschrieben werden Die longitudinale Aufweitung der Wolke von Lithium war deutlich groser als die von Uranin Dies lasst sich durch eine hohere Einleitkonzentration von Lithium, abweichende Freundlich-Parameter und die unterschiedliche Sorptionskinetik erklaren Die Sorption von Uranin und Lithium war mit dem Tongehalt und der Kationenaustauschkapazitat korrelierbar Fur die spezifische Oberflache wurde eine Korrelation mit der Sorption von Uranin festgestellt Die vertikalen Autokorrelationslangen der physiko-chemischen Parameter und der hydraulischen Durchlassigkeit sind von gleicher Grosenordnung

Transport von gelösten Stoffen im Grundwasser – Untersuchungen am Testfeld Krauthausen

The quality of solute transport calculations in heterogeneous aquifers depends greatly on the model of the groundwater velocity field. The normal procedure is to measure the hydraulic conductivity at various points and to calculate the Darcy velocities using a numerical model. In this work we compare the statistics of this approach with measured velocities from a natural test field and the stochastic generation of groundwater velocities based on the first-order perturbation theory. Measured conductivities and velocity vectors showed good statistical correspondence, especially with regard to correlation lengths and the occurrence of a lognormal distribution. The simulated velocity field gave a good representation of the measured data, whereas the statistically generated velocity field differed considerably. This is due to the fact that the method is conceived to produce Gaussian distribution properties, which is not appropriate for real-field conditions.

Holger Schwarze

Papers

Analysis of solute transport in a heterogeneous aquifer: the Krauthausen field experiment

Estimation of Macrodispersion by Different Approximation Methods for Flow and Transport in Randomly Heterogeneous Media

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

Transport von gelösten Stoffen im Grundwasser – Untersuchungen am Testfeld Krauthausen

A physically and chemically heterogeneous aquifer : field study and reactive transport modelling