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Stochastic Solute Transport In Open Channel Flows
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Book Synopsis Stochastic Solute Transport in Open Channel Flows by : Tongbi Tu
Download or read book Stochastic Solute Transport in Open Channel Flows written by Tongbi Tu and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Solute transport in natural flows is a complex process, which is affected by various factors, such as channel roughness, river geometry, upstream inflow, lateral inflow, solute loadings. These factors are often spatiotemporally heterogeneous and uncertain. As a result, the solute transport process by rivers and stream flows in natural environment is full of uncertainties and has been approached as a stochastic process. Traditional transport governing equations are at point scale and cannot appropriately represent the stochastic dynamics of the transport process when applied in a reach scale or beyond. Upscaled governing equations of solute transport process in open channel flows are proposed in this dissertation to account for the uncertainties/heterogeneity in the transport process. One- and two-dimensional solute transport models are developed by upscaling the stochastic partial differential equations through their one-to-one correspondence to the nonlocal Lagrangian-Eulerian Fokker-Planck equations. The resulting Fokker-Planck equations are linear and deterministic differential equations, and these equations can provide a comprehensive probabilistic description of the spatiotemporal evolutionary probability distribution of the underlying solute transport process by one single numerical realization, rather than requiring thousands of simulations in the Monte Carlo simulation. Moreover, the proposed governing equations can explicitly indicate the effect of the corresponding drifts on the uncertainty of the transport process. Consequently, the ensemble behavior of the solute transport process can also be obtained based on the probability distribution. To illustrate the capabilities of the proposed stochastic solute transport models, various steady and unsteady uncertain flow and solute loading conditions are applied. The Monte Carlo simulation with stochastic flow and solute transport model is used to provide the stochastic flow field for the solute transport process, and further to validate the numerical solute transport results provided by the derived Fokker-Planck equations. The comparison of the numerical results by the Monte Carlo simulation and the Fokker-Planck equation approach indicates that the proposed models can adequately characterize the ensemble behavior of the solute transport process under uncertain flow and solute loading conditions via the evolutionary probability distribution in space and time of the transport process.
Book Synopsis One-dimensional Numerical Modeling of the Conservation Equation for Non-reactive Stochastic Solute Transport by Unsteady Flow Field in Stream Channels by : Lan Liang
Download or read book One-dimensional Numerical Modeling of the Conservation Equation for Non-reactive Stochastic Solute Transport by Unsteady Flow Field in Stream Channels written by Lan Liang and published by . This book was released on 2003 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Dynamics. Modeling Solute Transport in Porous Media by : Don Kulasiri
Download or read book Stochastic Dynamics. Modeling Solute Transport in Porous Media written by Don Kulasiri and published by Elsevier. This book was released on 2002-11-22 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas are explained in an intuitive manner wherever possible with out compromising rigor. The solute transport problem in porous media saturated with water had been used as a natural setting to discuss the approaches based on stochastic dynamics. The work is also motivated by the need to have more sophisticated mathematical and computational frameworks to model the variability one encounters in natural and industrial systems. This book presents the ideas, models and computational solutions pertaining to a single problem: stochastic flow of contaminant transport in the saturated porous media such as that we find in underground aquifers. In attempting to solve this problem using stochastic concepts, different ideas and new concepts have been explored, and mathematical and computational frameworks have been developed in the process. Some of these concepts, arguments and mathematical and computational constructs are discussed in an intuititve manner in this book.
Book Synopsis Predicting Solute Transport in Natural Streams by : Xueqing Zhou
Download or read book Predicting Solute Transport in Natural Streams written by Xueqing Zhou and published by . This book was released on 1995 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-fickian Solute Transport in Porous Media by : Don Kulasiri
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.
Book Synopsis Stochastic Analysis of Flow and Transport in the Vadose Zone by : Alexander Yishan Sun
Download or read book Stochastic Analysis of Flow and Transport in the Vadose Zone written by Alexander Yishan Sun and published by . This book was released on 2000 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis LONGITUDINAL SOLUTE TRANSPORT IN OPEN-CHANNEL FLOW - A Numerical Simulation Study on Longitudinal Dispersion, Surface Storage Effects, Transverse Mixing, Uncertainties and Parameter-Transferring Problems by : Wei Zhang
Download or read book LONGITUDINAL SOLUTE TRANSPORT IN OPEN-CHANNEL FLOW - A Numerical Simulation Study on Longitudinal Dispersion, Surface Storage Effects, Transverse Mixing, Uncertainties and Parameter-Transferring Problems written by Wei Zhang and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Civil Engineering
Book Synopsis A Generalization of One-dimensional Solute Transport by : C. S. Simmons
Download or read book A Generalization of One-dimensional Solute Transport written by C. S. Simmons and published by . This book was released on 1986 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Solute Transport in Open-channel Networks Under an Unsteady Flow Regime by : Mustafa M. Aral
Download or read book Solute Transport in Open-channel Networks Under an Unsteady Flow Regime written by Mustafa M. Aral and published by . This book was released on 1998 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Analysis Of Flow And Solute Transport In Heterogeneous Porous Media Using Perturbation Approach by :
Download or read book Stochastic Analysis Of Flow And Solute Transport In Heterogeneous Porous Media Using Perturbation Approach written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis of flow and solute transport problem in porous media are affected by uncertainty inbuilt both in boundary conditions and spatial variability in system parameters. The experimental investigation reveals that the parameters may vary in various scales by several orders. These affect the solute plume characteristics in field-scale problem and cause uncertainty in the prediction of concentration. The main focus of the present thesis is to analyze the probabilistic behavior of solute concentration in three dimensional(3-D) heterogeneous porous media. The framework for the probabilistic analysis has been developed using perturbation approach for both spectral based analytical and finite element based numerical method. The results of the probabilistic analysis are presented either in terms of solute plume characteristics or prediction uncertainty of the concentration. After providing a brief introduction on the role of stochastic analysis in subsurface hydrology in chapter 1, a detailed review of the literature is presented to establish the existing state-of-art in the research on the probabilistic analysis of flow and transport in simple and complex heterogeneous porous media in chapter 2. The literature review is mainly focused on the methods of solution of the stochastic differential equation. Perturbation based spectral method is often used for probabilistic analysis of flow and solute transport problem. Using this analytical method a nonlocal equation is solved to derive the expression of the spatial plume moments. The spatial plume moments represent the solute movement, spreading in an average sense. In chapter 3 of the present thesis, local dispersivity if also assumed to be random space function along with hydraulic conductivity. For various correlation coefficients of the random parameters, the results in terms of the field scale effective dispersivity are presented to demonstrate the effect of local dispersivity variation in space. The randomness of local.
Book Synopsis Selected Water Resources Abstracts by :
Download or read book Selected Water Resources Abstracts written by and published by . This book was released on 1991 with total page 962 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advances in Groundwater Flow and Solute Transport: Pushing the Hidden Boundary by : Hongbin Zhan
Download or read book Advances in Groundwater Flow and Solute Transport: Pushing the Hidden Boundary written by Hongbin Zhan and published by MDPI. This book was released on 2019-10-01 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Stochastic Methods for Flow in Porous Media by : Dongxiao Zhang
Download or read book Stochastic Methods for Flow in Porous Media written by Dongxiao Zhang and published by Elsevier. This book was released on 2001-10-11 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Methods for Flow in Porous Media: Coping with Uncertainties explores fluid flow in complex geologic environments. The parameterization of uncertainty into flow models is important for managing water resources, preserving subsurface water quality, storing energy and wastes, and improving the safety and economics of extracting subsurface mineral and energy resources. This volume systematically introduces a number of stochastic methods used by researchers in the community in a tutorial way and presents methodologies for spatially and temporally stationary as well as nonstationary flows. The author compiles a number of well-known results and useful formulae and includes exercises at the end of each chapter. Balanced viewpoint of several stochastic methods, including Greens' function, perturbative expansion, spectral, Feynman diagram, adjoint state, Monte Carlo simulation, and renormalization group methods Tutorial style of presentation will facilitate use by readers without a prior in-depth knowledge of Stochastic processes Practical examples throughout the text Exercises at the end of each chapter reinforce specific concepts and techniques For the reader who is interested in hands-on experience, a number of computer codes are included and discussed
Book Synopsis Selected Water Resources Abstracts by :
Download or read book Selected Water Resources Abstracts written by and published by . This book was released on 1991 with total page 1424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Solute Transport in Heterogeneous Geologic Media by : Tian-Chyi Jim Yeh
Download or read book An Introduction to Solute Transport in Heterogeneous Geologic Media written by Tian-Chyi Jim Yeh and published by Cambridge University Press. This book was released on 2023-02-28 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractal-based Stochastic Simulation and Analysis of Subsurface Flow and Scale-dependent Solute Transport by : Alberto Sangbong Ndumu
Download or read book Fractal-based Stochastic Simulation and Analysis of Subsurface Flow and Scale-dependent Solute Transport written by Alberto Sangbong Ndumu and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Modelling of Multi-scale Solute Dispersion in Porous Media by : Don Kulasiri
Download or read book Computational Modelling of Multi-scale Solute Dispersion in Porous Media written by Don Kulasiri and published by BoD – Books on Demand. This book was released on 2011-11-04 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph presents a mathematical approach based on stochastic calculus which tackles the "cutting edge" in porous media science and engineering - prediction of dispersivity from covariance of hydraulic conductivity (velocity). The problem is of extreme importance for tracer analysis, for enhanced recovery by injection of miscible gases, etc. This book explains a generalised mathematical model and effective numerical methods that may highly impact the stochastic porous media hydrodynamics. The book starts with a general overview of the problem of scale dependence of the dispersion coefficient in porous media. Then a review of pertinent topics of stochastic calculus that would be useful in the modeling in the subsequent chapters is succinctly presented. The development of a generalised stochastic solute transport model for any given velocity covariance without resorting to Fickian assumptions from laboratory scale to field scale is discussed in detail. The mathematical approaches presented here may be useful for many other problems related to chemical dispersion in porous media.
