On the use of apparent hydraulic diffusivity as an indicator of connectivity

Summary Connectivity of high permeability paths is recognized as important but has not been properly quantified in the groundwater literature. In fact, it has been shown that the concept is process dependent and difficult to define so that it applies both to water flow and solute transport phenomena. Field and numerical evidence from hydraulic tests suggest that the apparent hydraulic diffusivity, D a , could potentially inform about the phenomena. In order to test this conjecture, we present a Monte Carlo analysis based on series of fields that display varying degrees of connectivity. Our results confirm that D a does indeed indicate the presence of connectivity. D a is found to correlate well with early tracer arrival time, and also with the product of a flow connectivity indicator, CF, and a transport connectivity indicator, CT. This indicates that D a accounts both for connectivity effects controlling the average plume movement (through CF) and for connectivity effects not linked to the effective medium properties that control the progression of the solute front (through CT). Analysis of seven binary fields suggests that flow connectivity hinges more on the continuity of fast paths, whereas transport connectivity seems to be more dependent on the width of connected features forming, possibly discontinuous, fast paths. In conjunction with previous studies, our results suggest that hydraulic response arrival times and early arrival times of tracer can be expected to correlate well in most types of hydrogeologic systems.

[1]  Thomas Ptak,et al.  Tracer tests for the investigation of heterogeneous porous media and stochastic modelling of flow and transport—a review of some recent developments , 2004 .

[2]  James J. Butler,et al.  Pumping tests in networks of multilevel sampling wells: Motivation and methodology , 1999 .

[3]  Peter Dietrich,et al.  A travel time based hydraulic tomographic approach , 2003 .

[4]  Emil O. Frind,et al.  The Dual Formulation of Flow for Contaminant Transport Modeling: 1. Review of Theory and Accuracy Aspects , 1985 .

[5]  L. Lebbe,et al.  Combined interpretation of pumping and tracer tests: theoretical considerations and illustration with a field test , 2003 .

[6]  J. Gómez-Hernández,et al.  Upscaling hydraulic conductivities in heterogeneous media: An overview , 1996 .

[7]  T. Yeh,et al.  Hydraulic tomography: Development of a new aquifer test method , 2000 .

[8]  Günter Blöschl,et al.  Advances in the use of observed spatial patterns of catchment hydrological response , 2002 .

[9]  Charles F. Harvey,et al.  When good statistical models of aquifer heterogeneity go bad: A comparison of flow, dispersion, and mass transfer in connected and multivariate Gaussian hydraulic conductivity fields , 2003 .

[10]  A. Journel,et al.  Entropy and spatial disorder , 1993 .

[11]  W. Illman,et al.  Asymptotic analysis of cross-hole pneumatic injection tests in unsaturated fractured tuff , 2005 .

[12]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[13]  Arlen W. Harbaugh,et al.  MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model - User Guide to Modularization Concepts and the Ground-Water Flow Process , 2000 .

[14]  Andrew V. Goldberg,et al.  Shortest paths algorithms: Theory and experimental evaluation , 1994, SODA '94.

[15]  Jesús Carrera,et al.  Geostatistical Inversion of Cross‐Hole Pumping Tests for Identifying Preferential Flow Channels Within a Shear Zone , 2001 .

[16]  J. Gómez-Hernández,et al.  To be or not to be multi-Gaussian? A reflection on stochastic hydrogeology , 1998 .

[17]  Graham E. Fogg,et al.  Groundwater Flow and Sand Body Interconnectedness in a Thick, Multiple-Aquifer System , 1986 .

[18]  Xian-Huan Wen,et al.  Numerical modeling of macrodispersion in heterogeneous media: a comparison of multi-Gaussian and non-multi-Gaussian models , 1998 .

[19]  Jesús Carrera,et al.  A Numerical Study on the Relationship Between Transmissivity and Specific Capacity in Heterogeneous Aquifers , 1999 .

[20]  R. Yates,et al.  Integrodifferential equations for systems of leaky aquifers and applications 3. A numerical method of unlimited applicability , 1977 .

[21]  H. S. Price,et al.  Flow in Heterogeneous Porous Media , 1961 .

[22]  G. Matheron.  Éléments pour une théorie des milieux poreux , 1967 .

[23]  Chunmiao Zheng,et al.  Analysis of Solute Transport in Flow Fields Influenced by Preferential Flowpaths at the Decimeter Scale , 2003, Ground water.

[24]  C. E. Jacob,et al.  A generalized graphical method for evaluating formation constants and summarizing well‐field history , 1946 .

[25]  Jesús Carrera,et al.  An analysis of hydraulic conductivity scale effects in granite (Full‐scale Engineered Barrier Experiment (FEBEX), Grimsel, Switzerland) , 2005 .

[26]  X. Sanchez‐Vila,et al.  Convergent-flow tracer tests in heterogeneous media: combined experimental-numerical analysis for determination of equivalent transport parameters. , 2002, Journal of contaminant hydrology.

[27]  X. Sanchez‐Vila,et al.  Pumping tests in heterogeneous aquifers: An analytical study of what can be obtained from their interpretation using Jacob's Method , 1999 .

[28]  K. Karasaki,et al.  Estimation of reservoir properties using transient pressure data: An asymptotic approach , 2000 .

[29]  Jesús Carrera,et al.  A comparison of hydraulic and transport parameters measured in low-permeability fractured media , 2000 .

[30]  S. P. Neuman,et al.  Three‐dimensional numerical inversion of pneumatic cross‐hole tests in unsaturated fractured tuff: 2. Equivalent parameters, high‐resolution stochastic imaging and scale effects , 2001 .

[31]  Steven F. Carle,et al.  Connected-network paradigm for the alluvial aquifer system , 2000 .

[32]  Jesús Carrera,et al.  Scale effects in transmissivity , 1996 .

[33]  Charles F. Harvey,et al.  What does a slug test measure: An investigation of instrument response and the effects of heterogeneity , 2002 .

[34]  S. Silliman.  The importance of the third dimension on transport through saturated porous media: case study based on transport of particles , 1996 .

[35]  H. S. Carslow,et al.  Conduction of Heat in Solids, Second Edition , 1986 .

[36]  J. Herweijer.  Constraining uncertainty of groundwater flow and transport models using pumping tests , 1996 .

[37]  James J. Butler,et al.  Steady shape analysis of tomographic pumping tests for characterization of aquifer heterogeneities , 2002 .

[38]  Graham E. Fogg,et al.  Automatic Generation of Flow Nets with Conventional Ground-Water Modeling Algorithmsa , 1985 .

[39]  F. G. Alabert,et al.  Stochastic Models of Reservoir Heterogeneity: Impact on Connectivity and Average Permeabilities , 1992 .

[40]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[41]  R. Grayson,et al.  Toward capturing hydrologically significant connectivity in spatial patterns , 2001 .

[42]  W. Illman,et al.  Asymptotic analysis of three-dimensional pressure interference tests: A line-injection line-monitoring solution , 2004 .

[43]  D. Freyberg,et al.  On using the equivalent conductivity to characterize solute spreading in environments with low‐permeability lenses , 2002 .

[44]  Ian G. Main,et al.  Relating flow channelling to tracer dispersion in heterogeneous networks , 2004 .

[45]  G. Teutsch,et al.  Effects of the investigation scale on pumping test results in heterogeneous porous aquifers , 1994 .

[46]  Olaf A. Cirpka,et al.  Homogenization of Richards equation in permeability fields with different connectivities , 2005 .

[47]  A. Sahuquillo,et al.  Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data—I. Theory , 1997 .

[48]  X. Sanchez‐Vila,et al.  An evaluation of Jacob's Method for the interpretation of pumping tests in heterogeneous formations , 1998 .

[49]  Jesús Carrera,et al.  Binary upscaling—the role of connectivity and a new formula , 2006 .

[50]  Jesús Carrera,et al.  On the relationship between indicators of geostatistical, flow and transport connectivity , 2005 .

[51]  C. Tsang,et al.  Determination of fracture storativity in hard rocks using high‐pressure injection testing , 1998 .

[52]  Allen G. Hunt,et al.  Applications of percolation theory to porous media with distributed local conductances , 2001 .

[53]  Timothy D. Scheibe,et al.  Scaling of flow and transport behavior in heterogeneous groundwater systems , 1998 .

[54]  Jesús Carrera,et al.  Upscaling transmissivity under radially convergent flow in heterogeneous media , 1999 .

[55]  Vinay Ambegaokar,et al.  Hopping Conductivity in Disordered Systems , 1971 .

[56]  X. Sanchez‐Vila,et al.  On the striking similarity between the moments of breakthrough curves for a heterogeneous medium and a homogeneous medium with a matrix diffusion term , 2004 .