Download or read book Scale Effect of Contaminant Transport in Saturated Porous Media Identified by the Time Fractional Advection dispersion Equation written by Rhiannon Maire Garrard and published by . This book was released on 2017 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time nonlocal transport models such as the time fractional advection-dispersion equation (t-fADE) were proposed to capture well-documented non-Fickian dynamics for conservative solutes transport in heterogeneous media, with the underlying assumption that the time nonlocality (which means that the current concentration change is affected by previous concentration load) embedded in the physical models can release the effective dispersion coefficient from scale dependency. This assumption however has never been systematically examined using real data. This study fills this historical knowledge gap by capturing non-Fickian transport (likely due to solute retention) documented in literature (Huang et al. 1995) and observed in our laboratory from small to intermediate spatial scale using the promising, tempered t-fADE model. Fitting exercises show that the effective dispersion coefficient in the t-fADE, although differing subtly from the dispersion coefficient in the standard advection-dispersion equation, increases nonlinearly with the travel distance (varying from 0.5 to 12 m) for both heterogeneous and macroscopically homogeneous sand columns. Further analysis reveals that, while solute retention in relatively immobile zones can be efficiently captured by the time nonlocal parameters in the t-fADE, the retention-independent solute movement in the mobile zone is affected by the spatial evolution of local velocities in the host medium, resulting in a scale-dependent dispersion coefficient. The same result may be found for the other standard time nonlocal transport models, such as the well-known multi-rate mass transfer (MRMT) model and the hydrologic version of continuous time random walk (CTRW), that separate solute retention and jumps (i.e., displacement). Therefore, the t-fADE with a constant dispersion coefficient cannot capture scale-dependent dispersion in saturated porous media, challenging the application for stochastic hydrogeology methods in quantifying real-world, pre-asymptotic transport. Hence, improvements on time nonlocal models using, for example the novel subordination approach, are necessary to incorporate the spatial evolution of local velocities without adding cumbersome parameters. Future improvements are also explored, given knowledge obtained in this study.

Download or read book Role Of Intra Pore Geometry And Flow Rate On Length Scales For The Transition Of Non Fickian To Fickian Contaminant Transport written by Jacob Michael Bradley and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hydraulic heterogeneity in aquifers contributes to non-Fickian transport characteristics, i.e., which cannot be defined by the continuum-scale advection-dispersion equation (ADE). We investigate the role of first-order heterogeneity, i.e., pore geometry's effect on the dispersion phenomenon of porous media. The research questions addressed are; how can we determine dispersion coefficient and dispersivity as a function of pore-scale geometry and various flow rate? Does dispersivity scale with length-scale even at the pore-scale? In this computational study, a series of intra-pore geometries are designed and quantified by a dimensionless pore geometry factor ([beta]), which captures a broad range of pores that likely exists due to diagenetic processes. Navier-Stokes and Advection-Diffusion equations are solved to examine the transport phenomenon via breakthrough curve (BTC) and residence time distribution (RTD). We determine a length-scale when non-Fickian features transition to the Fickian transport regime by sequentially extending the number of pores. Our results indicate that not only is the velocity distribution and its variance ([sigma]2) are dependent on the pore geometry, but its impact is amplified with flow rate. Consequently, the magnitude of non-Fickian becomes significant for complex pore shapes and require a longer length-scale for the Fickian transport. Thus, a larger velocity variance due to the effect of pore geometry and flow rate contributes to a larger dispersion and Dispersity where variations are found to be a function of [beta] and flow rate. We determine various constitutive equations to predict the length-scale needed for Fickian dispersion, the magnitude of non-Fickian features, the Fickian dispersion and dispersivity coefficients as a function of pore geometry factor (Îø) and velocity variance ([sigma]2) for various flow regimes, bridging the gap between the pore-scale and the continuum-sale.

Download or read book Diffusion in Natural Porous Media written by Peter Grathwohl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusion in Natural Porous Media: Contaminant Transport, Sorption/Desorption and Dissolution Kinetics introduces the general principles of diffusion in the subsurface environment and discusses the implications for the fate and transport of contaminants in soils and groundwater. Emphasis is placed on sorption/desorption and the dissolution kinetics of organic contaminants, both of which are limited by the slow speed of molecular diffusion. Diffusion in Natural Porous Media: Contaminant Transport, Sorption/Desorption and Dissolution Kinetics compiles methods for calculating the diffusion coefficients of organic compounds (in aqueous solution or vapor phase) in natural porous media. The author uses analytical solutions of Fick's 2nd law and some simple numerical models to model diffusive transport under various initial and boundary conditions. A number of these models may be solved using spreadsheets. The book examines sorption/desorption rates of organic compounds in various soils and aquifer materials, and also examines the dissolution kinetics of nonaqueous phase liquids in aquifers, in both the trapped residual phase and in pools. Diffusion in Natural Porous Media: Contaminant Transport, Sorption/Desorption and Dissolution Kinetics concludes with a discussion of the impact of slow diffusion processes on soil and groundwater decontamination and the implications of these processes for groundwater risk assessment.

Download or read book Stochastic Subsurface Hydrology written by L. W. Gelhar and published by Prentice Hall. This book was released on 1993 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume describes new stochastic subsurface hydrology techniques and results and examines the basic stochastic methods used to treat flow and contaminant transport in naturally heterogeneous permeable earth materials.

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1995 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fractional Calculus Theory and Applications written by Francesco Mainardi and published by MDPI. This book was released on 2018-09-20 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Fractional Calculus: Theory and Applications" that was published in Mathematics

Download or read book Approaches to Modeling Contaminant Transport in Porous Media written by Pascual Horacio Benito and published by . This book was released on 2008 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Advection diffusion Theory of Contaminant Transport for Stratified Porous Media microform written by Edward Allan Sudicky and published by National Library of Canada. This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Non fickian Solute Transport in Porous Media written by Don Kulasiri and published by Springer. This book was released on 2015-05-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Modeling Groundwater Flow and Contaminant Transport written by Jacob Bear and published by Springer Science & Business Media. This book was released on 2010-01-18 with total page 851 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many parts of the world, groundwater resources are under increasing threat from growing demands, wasteful use, and contamination. To face the challenge, good planning and management practices are needed. A key to the management of groundwater is the ability to model the movement of fluids and contaminants in the subsurface. The purpose of this book is to construct conceptual and mathematical models that can provide the information required for making decisions associated with the management of groundwater resources, and the remediation of contaminated aquifers. The basic approach of this book is to accurately describe the underlying physics of groundwater flow and solute transport in heterogeneous porous media, starting at the microscopic level, and to rigorously derive their mathematical representation at the macroscopic levels. The well-posed, macroscopic mathematical models are formulated for saturated, single phase flow, as well as for unsaturated and multiphase flow, and for the transport of single and multiple chemical species. Numerical models are presented and computer codes are reviewed, as tools for solving the models. The problem of seawater intrusion into coastal aquifers is examined and modeled. The issues of uncertainty in model input data and output are addressed. The book concludes with a chapter on the management of groundwater resources. Although one of the main objectives of this book is to construct mathematical models, the amount of mathematics required is kept minimal.

Download or read book Advances in Agronomy written by Donald L. Sparks and published by Gulf Professional Publishing. This book was released on 2003-08-19 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Agronomy continues to be recognized as a leading reference and a first-rate source of the latest research in agronomy. Major reviews deal with the current topics of interest to agronomists, as well as crop and soil scientists. As always, the subjects covered are varied and exemplary of the myriad subject matter dealt with by this long-running serial. Editor Donald Sparks, former president of the Soil Science Society of America and current president of the International Union of Soil Science, is the S. Hallock du Pont Chair of Plant and Soil Sciences at The University of Delaware. Maintains the highest impact factor among serial publications in Agriculture Presents timely reviews on important agronomy issues Enjoys a long-standing reputation for excellence in the field

Download or read book Instruks f Udf relsen af de praktiske Eksamensarbejder i Ladmaalin og Nivvelering ved Skovbrugseksamen written by and published by . This book was released on 1911 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Flow And Transport In Porous Media Proceedings Of The Summer School written by Brian Howard Gilding and published by World Scientific. This book was released on 1992-09-16 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents:Mathematical Modelling of Saturated and Unsaturated Groundwater Flow (B H Gilding)Applications of the Homogenization Method to Flow and Transport in Porous Media (U Hornung)Finite-Element-Approximation of Solute Transport in Porous Media with General Adsorption Processes (P Knabner)Free Boundary Problems in Fresh-Salt Goundwater Flow (C J van Duijn) Readership: Applied mathematicians and engineers. Keywords:Porous Media Equation;Diffusion Equation;Transport Equation;Infiltration Equation;Partial Differential Equation(PDE);Degenerate Parabolic Equation;Nonlinear PDE;Multiphase Flow in Porous Media;Nonlinear Diffusion;Reactive Solutes;Adsorption;Fresh and Salt Groundwater Flow;Homogenisation;Nonlinear Partial Differential Equations

Download or read book An advection diffusion theory of contaminant transport for stratified porous media thesis written by Edward Allan Sudicky and published by . This book was released on 1983 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mass Transport of Solutes in Saturated Porous Media written by Miguel A. Mariño and published by . This book was released on 1975 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Laboratory Evidence of the Scale Effect in Solute Transport Through Saturated Porous Media written by Stephen Edward Joseph Silliman and published by . This book was released on 1981 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mechanism and Stochastic Dynamics of Transport in Darcy scale Heterogeneous Porous Media written by Alessandro Comolli and published by . This book was released on 2018 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solute transport in heterogeneous porous media in general exhibits anomalous behaviors, in the sense that it is characterized by features that cannot be explained in terms of traditional models based on the advection-dispersion equation with constant effective coefficients. Signatures of anomalous transport are the non-linear temporal growth of the variance of solute concentration, non- Gaussian density profiles and heavy-tailed breakthrough curves. Understanding and predicting transport behavior in groundwater systems is crucial for several environmental and industrial applications, including groundwater management and risk assessment for nuclear waste repositories. The complexity of this task lies in the intrinsic multi-scale heterogeneity of geological formations and in the large amount of degrees of freedom. Hence, the predictive description of transport requires a process of upscaling that is based on measurable medium and flow attributes. The time domain random walk (TDRW) and continuous time random walk (CTRW) approaches provide suitable frameworks for transport upscaling. In this thesis, we identify different mechanisms that induce anomalous transport and we quantify their impact on transport attributes. We propose average transport models that can be parameterized in terms of flow and medium properties. Among the mechanisms that induce non-Fickian behaviors, a pivotal role is played by the heterogeneity of the flow field, which is directly linked to medium disorder. Due to its importance, the impact of advective heterogeneity is studied throughout the thesis, alongside with other mechanisms. First, we consider solute trapping due to physical or chemical heterogeneity, which we parameterize in terms of a constant trapping rate and a distribution of return times. We observe three distinct transport regimes that are linked to characteristic trapping time scales. At early times, transport is advection- controlled until particles start to get trapped. Then, the increasing distance between mobile and immobile particles gives rise to a superdiffusive regime which finally evolves towards a trapping-controlled regime. Second, we study transport in correlated porous media. We show that particle motion describes a coupled CTRW that is parameterized in terms of the distribution of flow velocity and length scales. We show that disorder and correlation may lead to similar behaviors in terms of displacement moments, but the difference between these mechanisms is manifest in the distributions of particle positions and arrival times. Next, we study the relationship between flow and transport properties and the impact of different injection conditions on transport. To this end, the relationship between Eulerian and Lagrangian velocities is investigated. Lagrangian statistics evolves to a steady-state that depends on the injection conditions. We study the velocity organization in Darcy flows and we develop a CTRW model for transport that is parameterized in terms of flow and medium attributes only. This CTRW accounts for non-stationarity through Markovian velocity models. We study the impact of advective heterogeneity by considering different disorder scenarios. Finally, we quantify the impact of diffusion in layered and fibrous heterogeneous media by considering two disorder scenarios characterized by quenched random velocities and quenched retardation properties, respectively. These mechanisms lead to different, dimension-dependent disorder samplings that give rise to dual transport processes in space and time. Specifically, transport describes correlated Lévy flights in the random velocity model and correlated CTRWs in the random retardation model.