Analysis of solute transport in a divergent flow tracer test with scale‐dependent dispersion

It has been known for many years that dispersivities increase with solute displacement distance in a subsurface. The increase of dispersivities with solute travel distance results from significant variation in hydraulic properties of porous media and was identified in the literature as scale-dependent dispersion. In this study, Laplace-transformed analytical solutions to advection-dispersion equations in cylindrical coordinates are derived for interpreting a divergent flow tracer test with a constant dispersivity and with a linear scale-dependent dispersivity. Breakthrough curves obtained using the scale-dependent dispersivity model are compared to breakthrough curves obtained from the constant dispersivity model to illustrate the salient features of scale-dependent dispersion in a divergent flow tracer test. The analytical results reveal that the breakthrough curves at the specific location for the constant dispersivity model can produce the same shape as those from the scale-dependent dispersivity model. This correspondence in curve shape between these two models occurs when the local dispersivity at an observation well in the scale-dependent dispersivity model is 1·3 times greater than the constant dispersivity in the constant dispersivity model. To confirm this finding, a set of previously reported data is interpreted using both the scale-dependent dispersivity model and the constant dispersivity model to distinguish the differences in scale dependence of estimated dispersivity from these two models. The analytical result reveals that previously reported dispersivity/distance ratios from the constant dispersivity model should be revised by multiplying these values by a factor of 1·3 for the scale-dependent dispersion model if the dispersion process is more accurately characterized by scale-dependent dispersion. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  M. A. Collins,et al.  General Analysis of Longitudinal Dispersion in Nonuniform Flow , 1971 .

[2]  J. Sauty.  An analysis of hydrodispersive transfer in aquifers , 1980 .

[3]  B. Hunt,et al.  Solutions and verification of a scale-dependent dispersion model. , 2001, Journal of contaminant hydrology.

[4]  chia-shyun Chen.  Analytical and Approximate Solutions to Radial Dispersion From an Injection Well to a Geological Unit With Simultaneous Diffusion Into Adjacent Strata , 1985 .

[5]  J. Pickens,et al.  Scale‐dependent dispersion in a stratified granular aquifer , 1981 .

[6]  A. N. Stokes,et al.  An Improved Method for Numerical Inversion of Laplace Transforms , 1982 .

[7]  B. Hunt.  Scale-Dependent Dispersion from a Pit , 2002 .

[8]  Dirk Schulze-Makuch,et al.  Longitudinal dispersivity data and implications for scaling behavior , 2005, Ground water.

[9]  J. Pickens,et al.  Modeling of scale-dependent dispersion in hydrogeologic systems , 1981 .

[10]  Sean A. McKenna,et al.  Tracer tests in a fractured dolomite: 3. Double‐porosity, multiple‐rate mass transfer processes in convergent flow tracer tests , 2001 .

[11]  Georg Teutsch,et al.  Forced and natural gradient tracer tests in a highly heterogeneous porous aquifer: instrumentation and measurements , 1994 .

[12]  S. Yates.  An analytical solution for one‐dimensional transport in heterogeneous porous media , 1990 .

[13]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[14]  Ibrahim Kocabas,et al.  Concentration and temperature transients in heterogeneous porous media: Part II: Radial transport , 2000 .

[15]  chia-shyun Chen.  Analytical solutions for radial dispersion with cauchy boundary at injection well , 1987 .

[16]  Albert J. Valocchi,et al.  Effect of radial flow on deviations from local equilibrium during sorbing solute transport through homogeneous soils , 1986 .

[17]  C. Welty,et al.  A Critical Review of Data on Field-Scale Dispersion in Aquifers , 1992 .

[18]  Karen P. Smith,et al.  An Analytical Model for Simulating Step-Function Injection in a Radial Geometry , 2001 .

[19]  E. Hoehn,et al.  Advection‐Dispersion Interpretation of Tracer Observations in an Aquifer , 1982 .

[20]  Huaqing Wang,et al.  Method for interpreting tracer experiments in radial flow using modified analytical solutions , 1995 .

[21]  G. Moridis,et al.  The Laplace Transform Finite Difference Method for Simulation of Flow Through Porous Media , 1991 .

[22]  C. Welty,et al.  Evaluation of longitudinal dispersivity from nonuniform flow tracer tests , 1994 .

[23]  chia-shyun Chen.  Solutions for Radionuclide Transport From an Injection Well Into a Single Fracture in a Porous Formation , 1986 .

[24]  Vedat S. Arpaci,et al.  Conduction Heat Transfer , 2002 .

[25]  Bruce Hunt.  Contaminant Source Solutions with Scale-Dependent Dispersivities , 1998 .