Simulation of Contaminant Transport in a Fractured Porous Aquifer

2007 ◽  
Vol 129 (9) ◽  
pp. 1157-1163
Author(s):  
Sergei Fomin ◽  
Vladimir Chugunov ◽  
Toshiyuki Hashida
Keyword(s):  
Solute Transport ◽  
Contaminant Transport ◽  
Time Derivative ◽  
Surrounding Rock ◽  
Time Dependent ◽  
Confined Aquifer ◽  
Closed Form Solutions ◽  
Advection Dispersion ◽  
Porous Aquifer ◽  
Fractional Time Derivative

Solute transport in the fractured porous confined aquifer is modeled by the advection-dispersion equation with fractional time derivative of order γ, which may vary from 0 to 1. Accounting for diffusion in the surrounding rock mass leads to the introduction of an additional fractional time derivative of order 1∕2 in the equation for solute transport. The closed-form solutions for concentrations in the aquifer and surrounding rocks are obtained for the arbitrary time-dependent source of contamination located in the inlet of the aquifer. Based on these solutions, different regimes of contamination of the aquifers with different physical properties are modeled and analyzed.

Application of Fractional Derivatives for Simulating Diffusion Into Porous Matrix in Mathematical Modeling of the Contaminant Transport in a Confined Fractured Porous Aquifer

2006 ◽  
Author(s):  
Sergei Fomin ◽  
Vladimir Chugunov ◽  
Toshiyuki Hashida
Keyword(s):  
Solute Transport ◽  
Contaminant Transport ◽  
Fractional Derivatives ◽  
Time Derivative ◽  
Porous Matrix ◽  
Confined Aquifer ◽  
Closed Form Solutions ◽  
Advection Dispersion ◽  
Porous Aquifer ◽  
Fractional Time Derivative

Solute transport in the fractured porous confined aquifer is modeled by the advection-dispersion equation with fractional time derivative of order γ, which may vary from 0 to 1. Accounting for diffusion in the surrounding rock mass leads to the introduction of an additional fractional time derivative of order 1/2 in the equation for solute transport. The closed-form solutions for concentrations in the aquifer and surrounding rocks are obtained for the arbitrary time-dependent source of contamination located in the inlet of the aquifer. Based on these solutions, different regimes of contamination of the aquifers with different physical properties are modeled and analyzed.

The effect of non-Fickian diffusion into surrounding rocks on contaminant transport in a fractured porous aquifer

2005 ◽  
Vol 461 (2061) ◽  
pp. 2923-2939 ◽  
Author(s):  
Sergei Fomin ◽  
Vladimir Chugunov ◽  
Toshiyuki Hashida
Keyword(s):  
Solute Transport ◽  
Contaminant Transport ◽  
Time Derivative ◽  
Surrounding Rock ◽  
Time Dependent ◽  
Fickian Diffusion ◽  
Confined Aquifer ◽  
Spatial Derivative ◽  
Closed Form Solutions ◽  
Porous Aquifer

Solute transport in a fractured porous confined aquifer is modelled by using an equation with a fractional-in-time derivative of order γ , which may vary from 0 to 1. Accounting for non-Fickian diffusion into the surrounding rock mass, which is modelled by a fractional spatial derivative of order α , leads to the introduction of an additional fractional-in-time derivative of order α /(1+ α ) in the equation for solute transport. Closed-form solutions for solute concentrations in the aquifer and surrounding rocks are obtained for an arbitrary time-dependent source of contamination located at the inlet of the aquifer. Based on these solutions, different regimes of contaminant transport in aquifers with various physical properties are modelled and analysed.

Dynamics of Infinite Beams Described by Fractional Time Derivatives

2003 ◽  
Author(s):  
Peter Ruge ◽  
Carolin Trinks
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Dynamic Stiffness ◽  
Time Derivative ◽  
Low Frequency ◽  
Internal Variables ◽  
Closed Form Solutions ◽  
Rational Polynomial ◽  
The Time Domain ◽  
Fractional Time Derivative

Closed-form solutions of infinite Bernoulli-Euler beams on a viscoelastic foundation are available for harmonic excitations with frequency Ω. For more general time-dependent loadings and beam-systems with local perturbations, for example caused by non-linear effects an overall treatment of the system in the time-domain is highly appropriated. Here the analytical dynamic stiffness of the infinite beam in the frequency-domain is approximated by a rational polynomial in the low frequency-domain and by an irrational part representing the asymptotic behaviour for Ω tending towards infinity. Thus, the corresponding description in the time-domain contains a fractional time derivative part and additonal internal variables due to splitting the rational polynomial into a linear system with respect to Ω.

Determination of time-dependent sources and parameters of nonlocal diffusion and wave equations from final data

2020 ◽  
Vol 23 (6) ◽  
pp. 1678-1701
Author(s):  
Jaan Janno
Keyword(s):  
Wave Equations ◽  
Fractional Laplacian ◽  
Source Term ◽  
Time Derivative ◽  
Sufficient Conditions ◽  
Time Dependent ◽  
Nonlocal Diffusion ◽  
Uniqueness Of Solutions ◽  
Fractional Time Derivative

Abstract Two inverse problems with final overdetermination for diffusion and wave equations containing the Caputo fractional time derivative and a fractional Laplacian of distributed order are considered. They are: 1) the problem to reconstruct a time-dependent source term; 2) the problem to recover simultaneously the source term, the order of the time derivative and the fractional Laplacian. Uniqueness of solutions of these problems is proved. Sufficient conditions for the uniqueness are stricter for the 2nd problem than for the 1st problem.

scholarly journals Numerical and experimental study on solute transport through physical aquifer model

2021 ◽  
Author(s):  
Muskan Mayank ◽  
Pramod Kumar Sharma
Keyword(s):  
Porous Media ◽  
Numerical Model ◽  
Solute Transport ◽  
Breakthrough Curves ◽  
Time Dependent ◽  
Environmental Concerns ◽  
Transport Parameters ◽  
Spatial Moments ◽  
Advection Dispersion ◽  
Simplifying Assumptions

Abstract Environmental concerns have drawn much research interest in solute transport through porous media. Thus, contaminants of groundwater permeate through pores in the ground, and adsorption attenuates the pollution concentration as the pollutants adhere to the solid surface. Mathematical models based on certain simplifying assumptions have been used to predict solute transport. The transport of solutes in porous media is governed by a partial differential equation known as the advection-dispersion equation. In this study, a two-dimensional numerical model has been developed for solute transport through porous media. Results of spatial moments have been predicted and analysed in the presence of both constant and time-dependent dispersion coefficients. Afterward, a numerical model is used to simulate experimentally observed breakthrough curves for both conservative and non-conservative solutes. Thus, transport parameters are estimated through numerical simulation of observed breakthrough curves. Finally, this model gives the best simulation of observed breakthrough curves, and it can also be used in the field scale.

Fractional abstract Cauchy problem on complex interpolation scales

2020 ◽  
Vol 23 (4) ◽  
pp. 1125-1140
Author(s):  
Andriy Lopushansky ◽  
Oleh Lopushansky ◽  
Anna Szpila
Keyword(s):  
Cauchy Problem ◽  
Time Derivative ◽  
Abstract Cauchy Problem ◽  
Initial Boundary ◽  
Sectorial Operator ◽  
Complex Interpolation ◽  
Bounded Domains ◽  
Initial Boundary Value Problems ◽  
Fractional Time Derivative ◽  
Initial Boundary Value

AbstractAn fractional abstract Cauchy problem generated by a sectorial operator is investigated. An inequality of coercivity type for its solution with respect to a complex interpolation scale generated by a sectorial operator with the same parameters is established. An application to differential parabolic initial-boundary value problems in bounded domains with a fractional time derivative is shown.

scholarly journals New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Mohamed S. Al-luhaibi
Keyword(s):  
Iterative Method ◽  
Analytical Solutions ◽  
Gas Dynamics ◽  
Time Derivative ◽  
Explicit Solutions ◽  
Fractional Partial Differential Equations ◽  
Approximate Analytical Solutions ◽  
Fractional Time Derivative ◽  
Burger's Equations ◽  
New Iterative Method

This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger’s equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.

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