The advection-dispersion equation that is used to model the solute transport in a porous medium is based on the premise that the fluctuating components of the flow velocity, hence the fluxes, due to a porous matrix can be assumed to obey a relationship similar to Fick’s law. This introduces phenomenological coefficients which are dependent on the scale of the experiments. This book presents an approach, based on sound theories of stochastic calculus and differential equations, which removes this basic premise. This leads to a multiscale theory with scale independent coefficients. This book illustrates this outcome with available data at different scales, from experimental laboratory scales to regional scales.

This research-based book provides a mathematical approach based on stochastic calculus which describes state-of-the-art information regarding porous media science and engineering - prediction of dispersivity from covariance of hydraulic conductivity (velocity). The complication is of great significance for tracer examination, for improved recovery by injection of miscible gases, etc. The book elucidates a generalized mathematical model and efficient numerical methodologies that may greatly affect the stochastic porous media hydrodynamics. It begins with a descriptive basic analysis of the complication of scale dependence of the dispersion coefficient in porous media. Furthermore, relevant topics of stochastic calculus which would be helpful in modeling are discussed subsequently. An in-depth elaborative discussion regarding the development of a generalized stochastic solute transport model for any provided velocity covariance without conferring to fickian expectations from laboratory scale to field scale is also illustrated in this book. The mathematical approaches described in this book will serve as useful solutions for several other complications associated with chemical dispersion in porous media.

This book provides a unified and comprehensive overview of physical explanations of the stochastic concepts of solute transport processes, important scaling issues, and practical tools for the analysis of solute transport.

In recent decades, the study of groundwater flow and solute transport has advanced into new territories that are beyond conventional theories, such as Darcy’s law and Fick’s law. The studied media have changed from permeable porous and fractured ones to much less permeable ones, such as clay and shale. The studied pore sizes have also changed from millimetres to micro-meters or even nano-meters. The objective of this Special Issue is to report recent advances in groundwater flow and solute transport that push the knowledge boundary into new territories which include, but are not limited to, flow and transport in sloping aquifer/hillslopes, coupled unsaturated and saturated flow, coupled aquifer-vertical/horizontal/slant well flow, interaction of aquifer with connected and disconnected rivers, non-Darcian flow, anomalous transport beyond the Fickian scheme, and flow and transport in extremely small pore spaces such as shale and tight sandstones. Contributions focusing on innovative experimental, numerical, and analytical methods for understanding unconventional problems, such as the above-listed ones, are encouraged, and contributions addressing flow and transport at interfaces of different media and crossing multiple temporal and spatial scales are of great value

Groundwater flow and solute transport are affected by the connectivity of high hydraulic conductivity (K) sediments. This research used numerical modeling and field experiments to assess and quantify connectivity and to compare alternative transport models and approaches for representing connected heterogeneity. Field work was conducted at the well-known Macrodispersion Experiment (MADE) site to investigate transport hypothesized to be controlled by a network of highly connected preferential flow paths (PFP). The research results in three self-contained, closely related, papers. The first paper evaluates the ability of different transport models to reproduce the transport behavior in a synthetic 2-D aquifer system with a high-K network embedded in a low-K matrix. Results confirm that the classical Fickian advection-dispersion model (ADM) is unable to effectively reproduce solute transport unless heterogeneity is explicitly considered. Conversely, two non-Fickian models (dual-domain mass transfer and continuous-time random walk) are able to accurately match the transport behavior using only effective parameters. However, the continuous time random walk model requires a calibrated transport velocity that is physically unrealistic. The second paper investigates flow and transport connectivity in a small block of the MADE site aquifer. K values estimated from grain size analysis of 19 cores are used to generate 3-D conditional realizations of the K field. Anomalous transport in the generated K fields is revealed by particle tracking simulations and significant connectivity is quantified by a variety of connectivity indicators. Particle paths geometry shows that flow and transport connectivity do not require fully percolating high-K clusters. The third paper presents the results of new tracer test. Breakthrough curves measured at the extraction well and at 14 multilevel sampling ports along the vertical extension of the MADE site aquifer clearly reveal the presence of a complex network of PFPs. Numerical modeling based on experimental data shows that the dual-domain mass transfer model successfully captures the characteristics of the integrated breakthrough curve at the extraction well, but it is ineffective in reproducing the concentrations observed at the multilevel sampling locations, indicating that a high-resolution characterization of the aquifer heterogeneity would be needed to fully capture 3D transport details.