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Special issue on fundamental advances in modeling dispersion in porous media
Advances in Water Resources 32 (2009) 633–634
Contents lists available at ScienceDirect
Advances in Water Resources journal homepage: www.elsevier.com/locate/advwatres
Preface
Special issue on fundamental advances in modeling dispersion in porous media
1. Introduction This issue of Advances in Water Resources evolved from a special session at the Fall 2006 American Geophysical Union Meeting dealing with roughly a century of quantitative research on dispersive fluxes in natural porous media. One of the earliest studies of dispersion in porous media is the work of the applied mathematician (and sometimes field hydrologist) Charles S. Slichter [6]. Slichter was developing methods to measure the electrical conductivity of salt solutions (ammonium chloride) transported in groundwater as a means for inferring the velocity. During this work, he was intrigued by the spreading of the injected solutes, which appeared to him to be many times greater than could be described by diffusion alone. Slichter and co-workers conducted a sequence of laboratory experiments in a 1.2 m 1.2 m flow cell (sampled on a 15 cm grid) to generate a high-resolution data set illustrating the spreading that he had observed. Although Slichter did not propose a formal mathematical model of the spreading, he did identify the variations in velocity created by the particles composing the porous medium as the spreading mechanism. Aside from some remarkable work done by Kitagawa in 1934 (who recognized that the dispersive spreading was described by a normal distribution [4], and that the spreading was a function of velocity [5]), virtually no research was done on dispersion for the 50 years following the work of Slichter. Then, in the 1950s, chemical engineers and hydrologists independently recognized the importance of dispersion to transport processes in porous media. It was at this time that the ‘‘classical” theories of dispersion in porous media were developed. Many notable works were developed during this time, including the seminal work of Taylor [7] and Aris [1]; a recent review of the literature on pore-scale dispersion in porous media has been compiled by Delgado [3]. Research on dispersion continues to evolve, and over the last 20 years or so, the research has been focused primarily on developing descriptions of spreading in highly heterogeneous media where the assumptions of asymptotic dispersion or even linear (so-called ‘Fickian’) flux law behavior have been examined (for a recent survey of the literature, see [2]). This issue includes current topical contributions that go beyond primarily phenomenological depictions of dispersion and seek basic descriptions of how fluxes are propagated in porous media exhibiting realistic and often multiscale spatial variability. The papers fall into four categories: (1) theory of solute transports, (2) upscaling of flow and transport laws, (3) laboratory experiments and analyses for testing dispersion representations, and (4) dispersion in reactive solute transport. The articles addressing theoretical investigations of solute transport include Zavala-Sanchez et al., who revisit the idealized stratified aquifer 0309-1708/$ - see front matter Ó 2009 Published by Elsevier Ltd. doi:10.1016/j.advwatres.2009.02.002
model but with vertical boundaries that impart asymptotic conditions; Frampton and Cvetkovic, who evaluate the impacts of different (high- vs. low-Péclet) sources on solute transport in fracture networks; Jankovic et al., who continue their exploration of stochastic potential fields associated with media comprised of matrix-supported spherical inclusions to evaluate the role of local diffusion on the overall transport; and Neuman and Tartakovsky, who provide a comprehensive compare/contrast study of four interrelated non-local theories of dispersion in porous media. Papers addressing the upscaling of flow and transport laws include: Gray and Miller, who continue their investigations of how thermodynamic constraints can be exercised in derivation of macroscopic balance equations for flow and transport while honoring a constrained entropy inequality; Lin and Tartakovsky’s explicit stochastic approach that uses a Karhunen-Loeve expansion of the loghydraulic conductivity field in which balance laws are solved using an extension of generalized polynomial chaos that includes a probabilistic collocation on sparse grids; and a paper by Wood, who finds that selection of scaling law with inherent particular assumptions drives the results of upscaling more than the particular mathematical methodology employed. Analyses of particular laboratory data is primary in two papers. Moroni et al. use particle-tracking velocimetry to provide detailed graphics of streamlines and particle traces in a convoluted channel with strongly nonuniform flow and further analyze the data to quantify dispersive fluxes in terms of the Lyapunov mixing exponent and the intermediate scattering function. In Berkowitz and Scher, previous analysis of breakthrough curve data from sandbox experiments using a single-parameter powerlaw residence time distribution that resulted in an excellent fit to the data is revisited with a three-parameter truncated powerlaw residence-time distribution that results in an excellent fit to the data without velocitydependence of the parameters. Reactive transport is studied in Guadagnini et al., who apply a mixing ratio approach to quantify multicomponent reactive transport in terms of spatiotemporally distributed reaction rates with favorable comparison to results from explicit deterministic modeling; and in Attinger et al., who use homogenization techniques to analyze the propagation of solute chemical species that undergo sorption in heterogeneous subsurface porous media. References [1] Aris R. On the dispersion of a solute in a fluid flowing through a tube. Proc Roy Soc (London, A) 1956;235:67–77. [2] Cushman JH, Bennethum LS, Hu BX. A primer on upscaling tools for porous media. Adv Water Resour 2002;25:1043–67. [3] Delgado J. A critical review of dispersion in packed beds. Heat Mass Transfer 2006;42:279–310.
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Preface / Advances in Water Resources 32 (2009) 633–634
[4] Kitagawa K. Sur le dispersement et l’écart moyen de l’écoulement des eaux souterraines, I, Experinces avec un modèle de laboratoir. Memoirs, Serie A, Kyoto University, College of Science 1934;17:37–42. [5] Kitagawa K. Sur le dispersement et l’écart moyen de l’écoulement des eaux souterraines, II, Proportionalité du dispersement et de l’éspace parcouru et variation de celui-ci avec la vitesse de l’écoulement. Memoirs, Serie A, Kyoto University, College of Science 1934;17:431–41. [6] Slichter CS. Field measurement of the rate of movement of underground waters, US Geological Survey, 1905. [7] Taylor SG. Dispersion of soluble matter in solvent flowing slowly through a tube. Proc Roy Soc London 1953;219:186–203.
T.R. Ginn E-mail address: [email protected] D.M. Tartakovsky E-mail address: [email protected] B.D. Wood E-mail address: [email protected]
Contents lists available at ScienceDirect
Advances in Water Resources journal homepage: www.elsevier.com/locate/advwatres
Preface
Special issue on fundamental advances in modeling dispersion in porous media
1. Introduction This issue of Advances in Water Resources evolved from a special session at the Fall 2006 American Geophysical Union Meeting dealing with roughly a century of quantitative research on dispersive fluxes in natural porous media. One of the earliest studies of dispersion in porous media is the work of the applied mathematician (and sometimes field hydrologist) Charles S. Slichter [6]. Slichter was developing methods to measure the electrical conductivity of salt solutions (ammonium chloride) transported in groundwater as a means for inferring the velocity. During this work, he was intrigued by the spreading of the injected solutes, which appeared to him to be many times greater than could be described by diffusion alone. Slichter and co-workers conducted a sequence of laboratory experiments in a 1.2 m 1.2 m flow cell (sampled on a 15 cm grid) to generate a high-resolution data set illustrating the spreading that he had observed. Although Slichter did not propose a formal mathematical model of the spreading, he did identify the variations in velocity created by the particles composing the porous medium as the spreading mechanism. Aside from some remarkable work done by Kitagawa in 1934 (who recognized that the dispersive spreading was described by a normal distribution [4], and that the spreading was a function of velocity [5]), virtually no research was done on dispersion for the 50 years following the work of Slichter. Then, in the 1950s, chemical engineers and hydrologists independently recognized the importance of dispersion to transport processes in porous media. It was at this time that the ‘‘classical” theories of dispersion in porous media were developed. Many notable works were developed during this time, including the seminal work of Taylor [7] and Aris [1]; a recent review of the literature on pore-scale dispersion in porous media has been compiled by Delgado [3]. Research on dispersion continues to evolve, and over the last 20 years or so, the research has been focused primarily on developing descriptions of spreading in highly heterogeneous media where the assumptions of asymptotic dispersion or even linear (so-called ‘Fickian’) flux law behavior have been examined (for a recent survey of the literature, see [2]). This issue includes current topical contributions that go beyond primarily phenomenological depictions of dispersion and seek basic descriptions of how fluxes are propagated in porous media exhibiting realistic and often multiscale spatial variability. The papers fall into four categories: (1) theory of solute transports, (2) upscaling of flow and transport laws, (3) laboratory experiments and analyses for testing dispersion representations, and (4) dispersion in reactive solute transport. The articles addressing theoretical investigations of solute transport include Zavala-Sanchez et al., who revisit the idealized stratified aquifer 0309-1708/$ - see front matter Ó 2009 Published by Elsevier Ltd. doi:10.1016/j.advwatres.2009.02.002
model but with vertical boundaries that impart asymptotic conditions; Frampton and Cvetkovic, who evaluate the impacts of different (high- vs. low-Péclet) sources on solute transport in fracture networks; Jankovic et al., who continue their exploration of stochastic potential fields associated with media comprised of matrix-supported spherical inclusions to evaluate the role of local diffusion on the overall transport; and Neuman and Tartakovsky, who provide a comprehensive compare/contrast study of four interrelated non-local theories of dispersion in porous media. Papers addressing the upscaling of flow and transport laws include: Gray and Miller, who continue their investigations of how thermodynamic constraints can be exercised in derivation of macroscopic balance equations for flow and transport while honoring a constrained entropy inequality; Lin and Tartakovsky’s explicit stochastic approach that uses a Karhunen-Loeve expansion of the loghydraulic conductivity field in which balance laws are solved using an extension of generalized polynomial chaos that includes a probabilistic collocation on sparse grids; and a paper by Wood, who finds that selection of scaling law with inherent particular assumptions drives the results of upscaling more than the particular mathematical methodology employed. Analyses of particular laboratory data is primary in two papers. Moroni et al. use particle-tracking velocimetry to provide detailed graphics of streamlines and particle traces in a convoluted channel with strongly nonuniform flow and further analyze the data to quantify dispersive fluxes in terms of the Lyapunov mixing exponent and the intermediate scattering function. In Berkowitz and Scher, previous analysis of breakthrough curve data from sandbox experiments using a single-parameter powerlaw residence time distribution that resulted in an excellent fit to the data is revisited with a three-parameter truncated powerlaw residence-time distribution that results in an excellent fit to the data without velocitydependence of the parameters. Reactive transport is studied in Guadagnini et al., who apply a mixing ratio approach to quantify multicomponent reactive transport in terms of spatiotemporally distributed reaction rates with favorable comparison to results from explicit deterministic modeling; and in Attinger et al., who use homogenization techniques to analyze the propagation of solute chemical species that undergo sorption in heterogeneous subsurface porous media. References [1] Aris R. On the dispersion of a solute in a fluid flowing through a tube. Proc Roy Soc (London, A) 1956;235:67–77. [2] Cushman JH, Bennethum LS, Hu BX. A primer on upscaling tools for porous media. Adv Water Resour 2002;25:1043–67. [3] Delgado J. A critical review of dispersion in packed beds. Heat Mass Transfer 2006;42:279–310.
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Preface / Advances in Water Resources 32 (2009) 633–634
[4] Kitagawa K. Sur le dispersement et l’écart moyen de l’écoulement des eaux souterraines, I, Experinces avec un modèle de laboratoir. Memoirs, Serie A, Kyoto University, College of Science 1934;17:37–42. [5] Kitagawa K. Sur le dispersement et l’écart moyen de l’écoulement des eaux souterraines, II, Proportionalité du dispersement et de l’éspace parcouru et variation de celui-ci avec la vitesse de l’écoulement. Memoirs, Serie A, Kyoto University, College of Science 1934;17:431–41. [6] Slichter CS. Field measurement of the rate of movement of underground waters, US Geological Survey, 1905. [7] Taylor SG. Dispersion of soluble matter in solvent flowing slowly through a tube. Proc Roy Soc London 1953;219:186–203.
T.R. Ginn E-mail address: [email protected] D.M. Tartakovsky E-mail address: [email protected] B.D. Wood E-mail address: [email protected]