A robust optimization technique for analysis of multi-tracer experiments.

Fate and transport of solutes in heterogeneous porous media is largely affected by diffusive mass exchange between mobile and immobile water zones. Since it is difficult to directly measure and determine the effect in the aquifers, multi-tracer experiments in combination with mathematical modeling are used to obtain quantitative information about unknown system parameters such as the effective mobile and immobile porosity, and the diffusive mass exchange between mobile and immobile water zones. The Single Fissure Dispersion Model (SFDM) describing nonreactive transport of solutes in saturated dual-porosity media, has been employed as a modeling approach to explain dual-porosity experiments in the field and laboratory (column experiments). SFDM optimization with conventional methods of minimization was immensely difficult due to its complex analytical form. Thus, previous studies used a trial and error procedure to fit it to the experimental observations. In this study, a rigorous optimization technique based on the newly developed scatter search method is presented that automatically minimizes the SFDM to find the optimal values of the hydrogeologically related parameters. The new program (OptSFDM) is accompanied with an easy-to-use graphical user interface (GUI) that is flexible and fully integrated. The program usability is showcased by a few, previously presented experimental case studies, and compared against the currently available, trial-and-error based, command-line executable, SFDM code.

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

[2]  P. Maloszewski,et al.  Quantifying the impact of immobile water regions on the fate of nitroaromatic compounds in dual-porosity media. , 2016, Journal of contaminant hydrology.

[3]  M. Haeckel,et al.  Simulating the chemical kinetics of CO2-methane exchange in hydrate , 2019, Journal of Natural Gas Science and Engineering.

[4]  Feike J. Leij,et al.  Analytical solutions for non-equilibrium solute transport in three-dimensional porous media , 1993 .

[5]  B. Kueper,et al.  Matrix Diffusion‐Derived Plume Attenuation in Fractured Bedrock , 2005, Ground water.

[6]  J. Klafter,et al.  The dynamical foundation of fractal stream chemistry: The origin of extremely long retention times , 2001, cond-mat/0202326.

[7]  P. Maloszewski,et al.  Analytical transport modelling of metabolites formed in dual-porosity media , 2017, Environmental Science and Pollution Research.

[8]  P. J. Wierenga,et al.  Immobile water during solute transport in unsaturated sand columns , 1990 .

[9]  M. Dentz,et al.  Modeling non‐Fickian transport in geological formations as a continuous time random walk , 2006 .

[10]  M. Elsner,et al.  Isotope Fractionation Pinpoints Membrane Permeability as a Barrier to Atrazine Biodegradation in Gram-negative Polaromonas sp. Nea-C , 2018, Environmental science & technology.

[11]  X. Sanchez‐Vila,et al.  On matrix diffusion: formulations, solution methods and qualitative effects , 1998 .

[12]  M. T. van Genuchten,et al.  Some Exact Solutions for Solute Transport Through Soils Containing Large Cylindrical Macropores , 1984 .

[13]  B. Kueper,et al.  Plume Detachment and Recession Times in Fractured Rock , 2010, Ground water.

[14]  B. Reichert,et al.  Contaminant Transport in Fractured Chalk: Laboratory and Field Experiments , 2003, Ground water.

[15]  Pierre Régnier,et al.  A reactive transport modeling approach to simulate biogeochemical processes in pore structures with pore-scale heterogeneities , 2012, Environ. Model. Softw..

[16]  C. Newell,et al.  Relative contribution of DNAPL dissolution and matrix diffusion to the long-term persistence of chlorinated solvent source zones. , 2012, Journal of contaminant hydrology.

[17]  P. Kitanidis,et al.  Characterization of mixing and dilution in heterogeneous aquifers by means of local temporal moments , 2000 .

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

[19]  D. Grebenkov,et al.  Diffusion-limited reactions in dynamic heterogeneous media , 2018, Nature Communications.

[20]  Mehdi Gharasoo,et al.  Introduction of a new platform for parameter estimation of kinetically complex environmental systems , 2017, Environ. Model. Softw..

[21]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..

[22]  Tobias Licha,et al.  Multitracer Test Approach to Characterize Reactive Transport in Karst Aquifers , 2007, Ground water.

[23]  Daniel M. Tartakovsky,et al.  Perspective on theories of non-Fickian transport in heterogeneous media , 2009 .

[24]  Paul W. Reimus,et al.  Testing and parameterizing a conceptual model for solute transport in a fractured granite using multiple tracers in a forced‐gradient test , 2003 .

[25]  Paul W. Reimus,et al.  Matrix diffusion rates in fractured volcanic rocks at the Nevada Test Site : Evidence for a dominant influence of effective fracture apertures , 2007 .

[26]  E. A. Sudicky,et al.  Contaminant transport in fractured porous media: Analytical solution for a single fracture , 1981 .

[27]  B. Parker,et al.  Plume persistence caused by back diffusion from thin clay layers in a sand aquifer following TCE source-zone hydraulic isolation. , 2008, Journal of contaminant hydrology.

[28]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[29]  G. Vachaud,et al.  Solute Transfer, with Exchange between Mobile and Stagnant Water, through Unsaturated Sand1 , 1977 .

[30]  P. Maloszewski,et al.  Measurements and interpretations of36Cl in groundwater, Milk River aquifer, Alberta, Canada , 1991 .

[31]  M. V. Genuchten,et al.  Mass transfer studies in sorbing porous media. I. Analytical solutions , 1976 .

[32]  P. Maloszewski,et al.  Diffusive mass exchange of non‐reactive substances in dual‐porosity porous systems – column experiments under saturated conditions , 2016 .

[33]  Emil O. Frind,et al.  Contaminant transport in fractured porous media: Analytical solutions for a system of parallel fractures , 1982 .

[34]  Charles J. Newell,et al.  Performance of DNAPL Source Depletion Technologies at 59 Chlorinated Solvent‐Impacted Sites , 2006 .

[35]  Fred W. Glover,et al.  A Template for Scatter Search and Path Relinking , 1997, Artificial Evolution.

[36]  Estimating Diffusion Coefficients in Low-Permeability Porous Media Using a Macropore Column , 1998 .

[37]  F. Centler,et al.  Kinetics of Substrate Biodegradation under the Cumulative Effects of Bioavailability and Self-Inhibition. , 2015, Environmental science & technology.

[38]  I. M. Sokolov,et al.  Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities , 2016, 1611.06202.

[39]  M. Th. van Genuchten,et al.  Convective-dispersive transport of solutes involved in sequential first-order decay reactions , 1985 .

[40]  Piotr Maloszewski,et al.  On the theory of tracer experiments in fissured rocks with a porous matrix , 1985 .

[41]  P. Maloszewski,et al.  Tracer tests in fractured rocks with a new fluorescent dye—pyrene-1,3,6,8-tetra sulphonic acid (PTS) / Tests de traçage en roches fracturées avec un nouveau produit fluorescent—l'acide pyrène 1.3.6.8 tétra sulfonique (PTS) , 2005 .

[42]  Rainer Helmig,et al.  Numerical methods for reactive transport on rectangular and streamline-oriented grids , 1999 .

[43]  Fred W. Glover,et al.  Scatter Search and Local Nlp Solvers: A Multistart Framework for Global Optimization , 2006, INFORMS J. Comput..

[44]  Beth L. Parker,et al.  Plume persistence due to aquitard back diffusion following dense nonaqueous phase liquid source removal or isolation , 2005 .

[45]  Nu Nu Wai,et al.  Dyes as tracers for vadose zone hydrology , 2003 .

[46]  Piotr Maloszewski,et al.  Tracer experiments in fractured rocks: Matrix diffusion and the validity of models , 1993 .

[47]  T. Sale,et al.  Testing high resolution numerical models for analysis of contaminant storage and release from low permeability zones. , 2012, Journal of contaminant hydrology.

[48]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[49]  Piotr Maloszewski,et al.  Mathematical modeling of tracer behavior in short‐term experiments in fissured rocks , 1990 .

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