Delineation of connectivity structures in 2‐D heterogeneous hydraulic conductivity fields

Connectivity is a critical aquifer property controlling anomalous transport behavior at large scales. But connectivity cannot be easily defined in a continuous field based on information of the hydraulic conductivity alone. We conceptualize it as a connecting structure—a connected subset of a continuous hydraulic conductivity field that consists of paths of least hydraulic resistance. We develop a simple and robust numerical method to delineate the connectivity structure using information of the hydraulic conductivity field only. First, the topology of the connectivity structure is determined by finding the path(s) of least resistance between two opposite boundaries. And second, a series of connectivity structures are created by inflating and shrinking the individual channels. Finally, we apply this methodology to different heterogeneous fields. We show that our method captures the main flow channels as well as the pathways of early time solute arrivals. We find our method informative to study connectivity in 2-D heterogeneous hydraulic conductivity fields.

[1]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[2]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[3]  Philippe Davy,et al.  Statistical characteristics of flow as indicators of channeling in heterogeneous porous and fractured media , 2010 .

[4]  T. Harter.  Finite-size scaling analysis of percolation in three-dimensional correlated binary Markov chain random fields. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[6]  David H. Douglas,et al.  ALGORITHMS FOR THE REDUCTION OF THE NUMBER OF POINTS REQUIRED TO REPRESENT A DIGITIZED LINE OR ITS CARICATURE , 1973 .

[7]  Alberto Guadagnini,et al.  Origins of anomalous transport in heterogeneous media: Structural and dynamic controls , 2014 .

[8]  D. W. Pollock.  Semianalytical Computation of Path Lines for Finite‐Difference Models , 1988 .

[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]  Gaisheng Liu,et al.  Spatial connectivity in a highly heterogeneous aquifer: From cores to preferential flow paths , 2011 .

[11]  Allen G. Hunt,et al.  Upscaling in Subsurface Transport Using Cluster Statistics of Percolation , 1998 .

[12]  Philippe Renard,et al.  Connectivity metrics for subsurface flow and transport , 2013 .

[13]  S. P. Neuman.  Universal scaling of hydraulic conductivities and dispersivities in geologic media , 1990 .

[14]  X. Sanchez‐Vila,et al.  On the formation of breakthrough curves tailing during convergent flow tracer tests in three‐dimensional heterogeneous aquifers , 2013 .

[15]  X. Sanchez‐Vila,et al.  Conditional stochastic mapping of transport connectivity , 2010 .

[16]  Steven M Gorelick,et al.  Effective permeability of porous media containing branching channel networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Jesús Carrera,et al.  On the use of apparent hydraulic diffusivity as an indicator of connectivity , 2006 .

[18]  Jesús Carrera,et al.  Transport upscaling in heterogeneous aquifers: What physical parameters control memory functions? , 2008 .

[19]  Graham E. Fogg,et al.  The impact of medium architecture of alluvial settings on non-Fickian transport , 2013 .

[20]  David A. Benson,et al.  Apparent directional mass‐transfer capacity coefficients in three‐dimensional anisotropic heterogeneous aquifers under radial convergent transport , 2014 .

[21]  Percolation Cluster Statistics and Conductivity Semi-Variograms , 2000 .