scholarly journals Two-Dimension Hydrodynamic Dispersion Equation with Seepage Velocity and Dispersion Coefficient as Function of Space and Time

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Abdon Atangana ◽  
S. C. Oukouomi Noutchie
Keyword(s):  
Dispersion Equation ◽  
Dispersion Coefficient ◽  
Analytical Techniques ◽  
Hydrodynamic Dispersion ◽  
Seepage Velocity ◽  
Transform Method ◽  
Space And Time ◽  
Advection Dispersion ◽  
Homotopy Decomposition ◽  
Geological Formation

The contamination through the geological formation cannot move and disperse with the same speed and dispersion coefficient, respectively, due to the variability of the geological formation. This paper is therefore first devoted to the description of the hydrodynamic advection dispersion equation with the seepage velocity and dispersion coefficient as function of space and time. Secondly the equation is solved via two analytical techniques: the homotopy decomposition method and the differential transform method. The numerical simulations of the approximated solutions are presented.

scholarly journals Generalized Analytical Solutions of The Advection-Dispersion Equation with Variable Flow and Transport Coefficients

2021 ◽  
Vol 13 (14) ◽  
pp. 7796
Author(s):  
Abhishek Sanskrityayn ◽  
Heejun Suk ◽  
Jui-Sheng Chen ◽  
Eungyu Park
Keyword(s):  
Dispersion Equation ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Transient Flow ◽  
Dispersion Coefficient ◽  
Transport Coefficients ◽  
Variable Coefficients ◽  
Dispersion Coefficients ◽  
Transform Method ◽  
Advection Dispersion

Demand has increased for analytical solutions to determine the velocities and dispersion coefficients that describe solute transport with spatial, temporal, or spatiotemporal variations encountered in the field. However, few analytical solutions have considered spatially, temporally, or spatiotemporally dependent dispersion coefficients and velocities. The proposed solutions consider eight cases of dispersion coefficients and velocities: both spatially dependent, both spatiotemporally dependent, both temporally dependent, spatiotemporally dependent dispersion coefficient with spatially dependent velocity, temporally dependent dispersion coefficient with constant velocity, both constant, spatially dependent dispersion coefficient with spatiotemporally dependent velocity, and constant dispersion coefficient with temporally dependent velocity. The spatial dependence is linear, while the temporal dependence may be exponential, asymptotical, or sinusoidal. An advection–dispersion equation with these variable coefficients was reduced to a non-homogeneous diffusion equation using the pertinent coordinate transform method. Then, solutions were obtained in an infinite medium using Green’s function. The proposed analytical solutions were validated against existing analytical solutions or against numerical solutions when analytical solutions were unavailable. In this study, we showed that the proposed analytical solutions could be applied for various spatiotemporal patterns of both velocity and the dispersion coefficient, shedding light on feasibility of the proposed solution under highly transient flow in heterogeneous porous medium.

Analytical Solution for Advection-Dispersion Equation of the Pollutant Concentration using Laplace Transformation

2021 ◽  
Vol 4 (1) ◽  
pp. 33-40
Author(s):  
Keshav Paudel ◽  
Prem Sagar Bhandari ◽  
Jeevan Kafle
Keyword(s):  
Analytical Solution ◽  
Dispersion Equation ◽  
Laplace Transformation ◽  
Dispersion Coefficient ◽  
Oxygen Demand ◽  
Pollutant Concentration ◽  
One Dimension ◽  
Advection Dispersion ◽  
State Case ◽  
Saturated Oxygen

We present simple analytical solution for the unsteady advection-dispersion equation describing the pollutant concentration C(x; t) in one dimension. In this model the water velocity in the x-direction is taken as a linear function of x and dispersion coefficient D as zero. In this paper by taking k = 0, k is the half saturated oxygen demand concentration for pollutant decay, we can apply the Laplace transformation and obtain the solution. The variation of C(x; t) with different times t upto t → ∞ (the steady state case) is taken into account advection-dispersion equation in our study.

Using the Fractional Advection Dispersion Equation to Improve the Scale Effect in the Sampling Process of Column Tests with Lateritic Soils

2015 ◽  
Vol 365 ◽  
pp. 188-193 ◽  
Author(s):  
Ricardo Mendonça de Moraes ◽  
André Luís Brasil Cavalcante
Keyword(s):  
Dispersion Equation ◽  
Contaminant Transport ◽  
Dispersion Coefficient ◽  
Breakthrough Curves ◽  
Column Tests ◽  
Lateritic Soils ◽  
Advection Dispersion ◽  
Sampling Process ◽  
Heterogeneous Soil ◽  
Heavy Tailed

Breakthrough curves (BTCs) obtained from column tests in heterogeneous soils are not satisfactorily simulated with the advection-dispersion equation (ADE) for some heavy tailed cases. Furthermore, the dispersion coefficient calculated with the ADE for heavy tailed BTCs are scale dependent when simulating columns of soil larger than the original test depth. In this paper we compare the usage of a fractional ADE (FADE) and the classical ADE to fit column tests BTCs made with Brazilian lateritic soils, discussing both contaminant transport theories and underlying stochastic models. The FADE can more accurately simulate heavy tailed BTCs, and when applying the adjusted FADE parameters to longer depths of soil, the FADE also predicts a more realistic scenario of contaminant transport through heterogeneous soil. The addition of fractional calculus in the advection-dispersion equation proves to improve contaminant transport predictions based on column tests over the classical ADE, with the use of a constant fractional dispersion coefficient that is scale independent.

scholarly journals Modelling solute transport in homogeneous and heterogeneous porous media using spatial fractional advection-dispersion equation

2018 ◽  
Vol 13 (No. 1) ◽  
pp. 18-28 ◽  
Author(s):  
G. Moradi ◽  
B. Mehdinejadiani
Keyword(s):  
Sensitivity Analysis ◽  
Solute Transport ◽  
Dispersion Equation ◽  
Dispersion Coefficient ◽  
Breakthrough Curves ◽  
Heterogeneous Porous Media ◽  
Average Pore ◽  
Advection Dispersion ◽  
Estimated Parameters ◽  
Heterogeneous Soil

This paper compared the abilities of advection-dispersion equation (ADE) and spatial fractional advection-dispersion equation (sFADE) to describe the migration of a non-reactive contaminant in homogeneous and heterogeneous soils. To this end, laboratory tests were conducted in a sandbox sizing 2.5 × 0.1 × 0.6 m (length × width × height). After performing a parametric sensitivity analysis, parameters of sFADE and ADE were individually estimated using the inverse problem method at each distance. The dependency of estimated parameters on distance was examined. The estimated parameters at 30 cm were used to predict breakthrough curves (BTCs) at subsequent distances. The results of sensitivity analysis indicated that average pore-water velocity and dispersion coefficient were, respectively, the most and least sensitive parameters in both mathematical models. The values of fractional differentiation orders (α) for sFADE were smaller than 2 in both soils. The scale-dependency of the dispersion coefficients of ADE and sFADE was observed in both soils. However, the application of sFADE to describe solute transport reduced the scale effect on the dispersion coefficient, especially in the heterogeneous soil. For the homogeneous soil, the predicting results of ADE and sFADE were nearly similar, while for the heterogeneous soil, the predicting results of sFADE were more satisfactory in comparison with those of ADE, especially when the transport distance increased. Compared to ADE, the sFADE simulated somewhat better the tailing parts of BTCs and showed the earlier arrival of tracer. Overall, the solute transport, especially in the heterogeneous soil, was non-Fickian and the sFADE somewhat better described non-Fickian transport.

Hydrodynamic Dispersion Coefficient of Urea in Silty Loam Soil

2019 ◽  
Vol 6 (04) ◽  
Author(s):  
RAM PAL ◽  
H C SHARMA ◽  
M IMTIYAZ
Keyword(s):  
Transport Phenomenon ◽  
Porous Medium ◽  
Contaminant Transport ◽  
Dispersion Coefficient ◽  
Hydrodynamic Dispersion ◽  
Soil Columns ◽  
Soil Medium ◽  
Adverse Health Effects ◽  
Silty Loam ◽  
Loam Soil

The modern theme of agriculture is not only to increase production but also to minimize undesirable environmental effects. Leaching of surface-applied fertilizer is the major source of groundwater pollution. Nitrogenous fertilizers are the most popular among the Indian farmers, which on leaching reach the groundwater in different forms (NH4-N, NO3-N, etc). NO3-N leaches faster than other types, remains in-reactive in groundwater, moves with the velocity of groundwater and contaminates it. Contamination arises when NO3-N accumulates in groundwater and consumed in high amount by humans and animals, may result in adverse health effects. For the study of contaminant transport phenomenon in porous medium, a general convection dispersion equation is used, in which dispersion coefficient is one of the primary parameters necessary to be determined for a particular soil. Keeping it in view a study was conducted to assess different available techniques to determine the dispersion coefficient with the help of soil columns having silty loam soil as soil medium. The value of the dispersion coefficient obtained for silty loam soil, by this method was equal to 0.00576 m2.

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