Tracer tests in a fractured dolomite: 2. Analysis of mass transfer in single‐well injection‐withdrawal tests

We investigated multiple-rate diffusion as a possible explanation for observed behavior in a suite of single-well injection-withdrawal (SWIW) tests conducted in a fractured dolomite. We first investigated the ability of a conventional double-porosity model and a multirate diffusion model to explain the data. This revealed that the multirate diffusion hypothesis/model is consistent with available data and is capable of matching all of the recovery curves. Second, we studied the sensitivity of the SWIW recovery curves to the distribution of diffusion rate coefficients and other parameters. We concluded that the SWIW test is very sensitive to the distribution of rate coefficients but is relatively insensitive to other flow and transport parameters such as advective porosity and dispersivity. Third, we examined the significance of the constant double-log late time slopes (−2.1 to −2.8), which are present in several data sets. The observed late time slopes are significantly different than would be predicted by either conventional double-porosity or single-porosity models and are believed to be a distinctive feature of multirate diffusion. Fourth, we found that the estimated distributions of diffusion rate coefficients are very broad, with the distributions spanning a range of up to 3.6 orders of magnitude. Fifth, when both heterogeneity and solute drift are present, late time behavior similar to multirate mass transfer can occur. Although it is clear that multirate diffusion occurs in the Culebra, the number of orders of magnitude of variability may be overestimated because of the combined effects of drift and heterogeneity.

[1]  J. Hadermann,et al.  The Grimsel (Switzerland) migration experiment : integrating field experiments, laboratory investigations and modelling , 1996 .

[2]  R. E. Jessup,et al.  EXPERIMENTAL AND THEORETICAL ASPECTS OF SOLUTE DIFFUSION IN SPHERICAL AND NONSPHERICAL AGGREGATES , 1982 .

[3]  Philip M. Gschwend,et al.  Numerical modeling of sorption kinetics of organic compounds to soil and sediment particles , 1988 .

[4]  D. Ruthven,et al.  The effect of crystallite shape and size distribution on diffusion measurements in molecular sieves , 1971 .

[5]  Joseph J. Pignatello,et al.  Mechanisms of Slow Sorption of Organic Chemicals to Natural Particles , 1996 .

[6]  Jeffrey A Cunningham,et al.  Effects of grain‐scale mass transfer on the transport of volatile organics through sediments: 2. Column results , 1997 .

[7]  J. Bahr,et al.  Direct comparison of kinetic and local equilibrium formulations for solute transport affected by surface reactions , 1987 .

[8]  Jeffrey A Cunningham,et al.  Effects of grain‐scale mass transfer on the transport of volatile organics through sediments: 1. Model development , 1997 .

[9]  F. Lafolie,et al.  One-dimensional solute transport modelling in aggregated porous media Part 1. Model description and numerical solution , 1993 .

[10]  L. Konikow,et al.  Ambiguity in Measuring Matrix Diffusion with Single‐Well Injection/Recovery Tracer Tests , 1997 .

[11]  S. Gorelick,et al.  Modeling Mass Transfer Processes in Soil Columns with Pore-Scale Heterogeneity , 1998 .

[12]  Brian J. Wagner,et al.  Evaluating the Reliability of the Stream Tracer Approach to Characterize Stream‐Subsurface Water Exchange , 1996 .

[13]  Cass T. Miller,et al.  Heterogeneous sorption processes in subsurface systems. 1. Model formulations and applications. , 1994, Environmental science & technology.

[14]  Teresa B. Culver,et al.  Modeling the Desorption of Organic Contaminants from Long-Term Contaminated Soil Using Distributed Mass Transfer Rates , 1997 .

[15]  R. Haggerty,et al.  A method for estimating distributions of mass transfer rate coefficients with application to purging and batch experiments , 1999 .

[16]  R. Wagenet,et al.  Description of Atrazine Transport in Soil with Heterogeneous Nonequilibrium Sorption , 1997 .

[17]  Brian J. Wagner,et al.  Experimental design for estimating parameters of rate‐limited mass transfer: Analysis of stream tracer studies , 1997 .

[18]  Richard L. Beauheim,et al.  Interpretations of Tracer Tests Performed in the Culebra Dolomite at the Waste Isolation Pilot Plant Site , 2000 .

[19]  Y. Tsang,et al.  Study of alternative tracer tests in characterizing transport in fractured rocks , 1995 .

[20]  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 .

[21]  Solute transport in aggregated media: Aggregate size distribution and mean radii , 1990 .

[22]  A. Valocchi,et al.  Stochastic analysis of the transport of kinetically sorbing solutes in aquifers with randomly heterogeneous hydraulic conductivity , 1993 .

[23]  Roy Haggerty,et al.  Solute Transport and Multirate Mass Transfer in Radial Coordinates , 2000 .

[24]  Michael L. Shuler,et al.  Description of time-varying desorption kinetics : release of naphthalene from contaminated soils , 1993 .

[25]  David Andrew Barry,et al.  Mass transfer in soils with local stratification of hydraulic conductivity , 1994 .

[26]  A. Valocchi.  Use of temporal moment analysis to study reactive solute transport in aggregated porous media , 1990 .

[27]  Vincent C. Tidwell,et al.  Effects of spatially heterogeneous porosity on matrix diffusion as investigated by X-ray absorption imaging , 1998 .

[28]  Norman R. Draper,et al.  Applied regression analysis (2. ed.) , 1981, Wiley series in probability and mathematical statistics.

[29]  R. Wagenet,et al.  Solute transport in porous media with sorption-site heterogeneity. , 1995, Environmental science & technology.

[30]  J. Villermaux.  Theory of Linear Chromatography , 1981 .

[31]  Ivars Neretnieks,et al.  Diffusion in the rock matrix: An important factor in radionuclide retardation? , 1980 .

[32]  T. Brubaker,et al.  Nonlinear Parameter Estimation , 1979 .

[33]  Ivars Neretnieks,et al.  2 – Solute Transport in Fractured Rock — Applications to Radionuclide Waste Repositories , 1993 .

[34]  Mark N. Goltz,et al.  Using the method of moments to analyze three-dimensional diffusion-limited solute transport from tem , 1987 .

[35]  Sean Andrew McKenna,et al.  On the late‐time behavior of tracer test breakthrough curves , 2000 .

[36]  S. Gorelick,et al.  Multiple‐Rate Mass Transfer for Modeling Diffusion and Surface Reactions in Media with Pore‐Scale Heterogeneity , 1995 .

[37]  C T Miller,et al.  Heterogeneous sorption processes in subsurface systems. 2. Diffusion modeling approaches. , 1995, Environmental science & technology.

[38]  A. Rasmuson.  The effect of particles of variable size, shape and properties on the dynamics of fixed beds , 1985 .

[39]  Mark L. Brusseau,et al.  Reply [to Comment on Modeling the transport of solutes influenced by multiprocess nonequilibrium , 1989 .

[40]  Charles F. Harvey,et al.  Aquifer remediation: A method for estimating mass transfer rate coefficients and an evaluation of pulsed pumping , 1994 .

[41]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

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

[43]  R. Holt.  Conceptual model for transport processes in the Culebra Dolomite Member, Rustler Formation , 1997 .

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

[45]  William P. Ball,et al.  Long-term sorption of halogenated organic chemicals by aquifer material. 2. Intraparticle diffusion , 1991 .

[46]  Richard L. Beauheim,et al.  Tracer tests in a fractured dolomite: 1. Experimental design and observed tracer recoveries , 2001 .

[47]  R. L. Beauheim,et al.  Analysis of hydraulic tests of the Culebra and Magenta Dolomites and Dewey Lake Redbeds conducted at the Waste Isolation Pilot Plant Site , 1998 .

[48]  R. E. Jessup,et al.  Solute transport in aggregated porous media: Theoretical and experimental evaluation. , 1980 .

[49]  M. Reeves,et al.  Theory and implementation for SWIFT II. The Sandia waste-isolation flow and transport model for fractured media. Release 4. 84 , 1986 .

[50]  A. Zuber,et al.  Comments on "Flux-Averaged and Volume-Averaged Concentrations in Continuum Approaches to Solute Transport" by J. C. Parker , 1986 .