Download Free Stochastic Dynamics Modeling Solute Transport In Porous Media Book in PDF and EPUB Free Download. You can read online Stochastic Dynamics Modeling Solute Transport In Porous Media and write the review.

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.
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 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.
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.
This book is an ensemble of six major chapters, an introduction, and a closure on modeling transport phenomena in porous media with applications. Two of the six chapters explain the underlying theories, whereas the rest focus on new applications. Porous media transport is essentially a multi-scale process. Accordingly, the related theory described in the second and third chapters covers both continuum‐ and meso‐scale phenomena. Examining the continuum formulation imparts rigor to the empirical porous media models, while the mesoscopic model focuses on the physical processes within the pores. Porous media models are discussed in the context of a few important engineering applications. These include biomedical problems, gas hydrate reservoirs, regenerators, and fuel cells. The discussion reveals the strengths and weaknesses of existing models as well as future research directions.
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.
This book addresses the key issues in the modeling and simulation of diffusive processes from a wide spectrum of different applications across a broad range of disciplines. Features: discusses diffusion and molecular transport in living cells and suspended sediment in open channels; examines the modeling of peristaltic transport of nanofluids, and isotachophoretic separation of ionic samples in microfluidics; reviews thermal characterization of non-homogeneous media and scale-dependent porous dispersion resulting from velocity fluctuations; describes the modeling of nitrogen fate and transport at the sediment-water interface and groundwater flow in unconfined aquifers; investigates two-dimensional solute transport from a varying pulse type point source and futile cycles in metabolic flux modeling; studies contaminant concentration prediction along unsteady groundwater flow and modeling synovial fluid flow in human joints; explores the modeling of soil organic carbon and crop growth simulation.
This book covers theoretical aspects as well as recent innovative applications of Artificial Neural networks (ANNs) in natural, environmental, biological, social, industrial and automated systems. It presents recent results of ANNs in modelling small, large and complex systems under three categories, namely, 1) Networks, Structure Optimisation, Robustness and Stochasticity 2) Advances in Modelling Biological and Environmental Systems and 3) Advances in Modelling Social and Economic Systems. The book aims at serving undergraduates, postgraduates and researchers in ANN computational modelling.
In response to the exponentially increasing need to analyze vast amounts of data, Neural Networks for Applied Sciences and Engineering: From Fundamentals to Complex Pattern Recognition provides scientists with a simple but systematic introduction to neural networks. Beginning with an introductory discussion on the role of neural networks in