scholarly journals A fractional dispersion model for overland solute transport

2006 ◽  
Vol 42 (3) ◽  
Author(s):  
Zhi-Qiang Deng ◽  
João L. M. P. de Lima ◽  
M. Isabel P. de Lima ◽  
Vijay P. Singh
Keyword(s):  
Solute Transport ◽  
Dispersion Model

A time-space Hausdorff derivative model for anomalous transport in porous media

2019 ◽  
Vol 22 (6) ◽  
pp. 1517-1536 ◽  
Author(s):  
Yingjie Liang ◽  
Ninghu Su ◽  
Wen Chen
Keyword(s):  
Porous Media ◽  
Solute Transport ◽  
Water Flow ◽  
Dispersion Model ◽  
Mathematical Formulation ◽  
Breakthrough Curves ◽  
Flow In Porous Media ◽  
Time And Space ◽  
Time Space ◽  
Constant Diffusion

Abstract This paper presents a time-space Hausdorff derivative model for depicting solute transport in aquifers or water flow in heterogeneous porous media. In this model, the time and space Hausdorff derivatives are defined on non-Euclidean fractal metrics with power law scaling transform which, respectively, connect the temporal and spatial complexity during transport. The Hausdorff derivative model can be transformed to an advection-dispersion equation with time- and space-dependent dispersion and convection coefficients. This model is a fractal partial differential equation (PDE) defined on a fractal space and differs from the fractional PDE which is derived for non-local transport of particles on a non-fractal Euclidean space. As an example of applications of this model, an explicit solution with a constant diffusion coefficient and flow velocity subject to an instantaneous source is derived and fitted to the breakthrough curves of tritium as a tracer in porous media. These results are compared with those of a scale-dependent dispersion model and a time-scale dependent dispersion model. Overall, it is found that the fractal PDE based on the Hausdorff derivatives better captures the early arrival and heavy tail in the scaled breakthrough curves for variable transport distances. The estimated parameters in the fractal Hausrdorff model represent clear mechanisms such as linear relationships between the orders of Hausdorff derivatives and the transport distance. The mathematical formulation is applicable to both solute transport and water flow in porous media.

Solute transport in dual conduit structure: experiment and modelling

2020 ◽  
Author(s):  
Chaoqi Wang ◽  
Xiaoguang Wang ◽  
Samer Majdalani ◽  
Vincent Guinot ◽  
Hervé Jourde
Keyword(s):  
Solute Transport ◽  
Peak Concentration ◽  
Dispersion Model ◽  
Tracer Tests ◽  
Breakthrough Curves ◽  
Physical Models ◽  
Length Ratio ◽  
Tracer Transport ◽  
Transport Parameters ◽  
Total Length

<p>An important phenomenon often encountered when interpreting tracer tests in karst aquifers is the occurrence of dual-peaked breakthrough curves (BTCs). The dual-peaked BTCs are usually attributed to tracer transport through a conduit system consisting of a dual-conduit structure: an auxiliary conduit that deviates from the main conduit at the upstream and converges back at the downstream. In order to understand how the geometric configuration of the dual-conduit structure influences the BTCs, laboratory experiments utilizing plastic tubes were conducted. The physical models were constructed by varying: 1) the total length of the conduits, while fixing the length ratio; 2) length ratio between the two conduits, while fixing the length of the main conduit; and 3) conduits connection angle. The tracer experiments are then fitted by a Multi-Region Advection Dispersion model and a Transfer Function model to derive effective transport parameters. This allows us to quantitatively compare the experimental results, and thus to analyse the conduit geometry effects on solute transport and to compare the performance of the two models.</p><p>Results show that the dual-conduit structure causes the double peaks of BTCs. Keeping the length ratio of the two conduits and increasing their total length leads to a larger separation of the two peaks of the BTCs. Keeping the length of main conduit while increasing the length of the secondary conduit causes similar effects. As (θ<sub>1</sub>-θ<sub>2</sub>) increases, the first peak concentration value decreases, the second peak concentration value increases.</p><p><strong>Keywords</strong>: karst, lab experiment, dual-peaked BTCs, modelling</p>

Jacobi Spectral Collocation Method for the Time Variable-Order Fractional Mobile-Immobile Advection-Dispersion Solute Transport Model

2016 ◽  
Vol 6 (3) ◽  
pp. 337-352 ◽  
Author(s):  
Heping Ma ◽  
Yubo Yang
Keyword(s):  
Fractional Derivative ◽  
Solute Transport ◽  
Collocation Method ◽  
Dispersion Model ◽  
Time Variable ◽  
Spectral Collocation Method ◽  
Variable Order ◽  
Spectral Collocation ◽  
Advection Dispersion ◽  
Variable Order Fractional Derivative

AbstractAn efficient high order numerical method is presented to solve the mobile-immobile advection-dispersion model with the Coimbra time variable-order fractional derivative, which is used to simulate solute transport in watershed catchments and rivers. On establishing an efficient recursive algorithm based on the properties of Jacobi polynomials to approximate the Coimbra variable-order fractional derivative operator, we use spectral collocation method with both temporal and spatial discretisation to solve the time variable-order fractional mobile-immobile advection-dispersion model. Numerical examples then illustrate the effectiveness and high order convergence of our approach.

An Integrated Finite-Element Approach to Mechanics, Transport and Biosynthesis in Tissue Engineering

2004 ◽  
Vol 126 (1) ◽  
pp. 82-91 ◽  
Author(s):  
Bram G. Sengers ◽  
Cees W. J. Oomens ◽  
Frank P. T. Baaijens
Keyword(s):  
Finite Element ◽  
Solute Transport ◽  
Dispersion Model ◽  
Finite Element Approach ◽  
Cyclic Compression ◽  
Functional Development ◽  
Element Approach ◽  
Velocity Pressure ◽  
Transport Of Macromolecules ◽  
Small Solute

A finite-element approach was formulated, aimed at enabling an integrated study of mechanical and biochemical factors that control the functional development of tissue engineered constructs. A nonlinear biphasic displacement-velocity-pressure description was combined with adjective and diffusive solute transport, uptake and biosynthesis. To illustrate the approach we focused on the synthesis and transport of macromolecules under influence of fluid flow induced by cyclic compression. In order to produce net transport the effect of dispersion was investigated. An abstract representation of biosynthesis was employed, three cases were distinguished: Synthesis dependent on a limited small solute, synthesis dependent on a limited large solute and synthesis independent of solute transport. Results show that a dispersion model can account for augmented solute transport by cyclic compression and indicate the different sensitivity to loading that can be expected depending on the size of the limiting solute.

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