scholarly journals ANALYTICAL SOLUTION FOR THE TWO-DIMENSIONAL LINEAR ADVECTION-DISPERSION EQUATION IN POROUS MEDIA VIA THE FOKAS METHOD

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Guenbo Hwang ◽  
Keyword(s):  
Porous Media ◽  
Analytical Solution ◽  
Dispersion Equation ◽  
Two Dimensional ◽  
Advection Dispersion ◽  
Fokas Method

ONE-DIMENSIONAL TEMPORALLY DEPENDENT ADVECTION-DISPERSION EQUATION IN POROUS MEDIA: ANALYTICAL SOLUTION

2010 ◽  
Vol 23 (4) ◽  
pp. 521-539 ◽  
Author(s):  
R. R. YADAV ◽  
DILIP KUMAR JAISWAL ◽  
HAREESH KUMAR YADAV ◽  
GUL RANA
Keyword(s):  
Porous Media ◽  
Analytical Solution ◽  
Dispersion Equation ◽  
One Dimensional ◽  
Advection Dispersion

scholarly journals Analytical Solution of 1D Advection-Dispersion Equation In Finite Groundwater Reservoir With Spatially Dependent Dispersivity And Two Inputs Sources With Source-Sink Term Impact

2021 ◽  
Author(s):  
Thomas TJOCK-MBAGA ◽  
Patrice Ele Abiama ◽  
Jean Marie Ema'a Ema'a ◽  
Germain Hubert Ben-Bolie
Keyword(s):  
Analytical Solution ◽  
Linear Function ◽  
Dispersion Equation ◽  
Source Term ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Liouville Problem ◽  
Finite Domain ◽  
Advection Dispersion ◽  
Sink Term

Abstract This study derives an analytical solution of a one-dimensional (1D) advection-dispersion equation (ADE) for solute transport with two contaminant sources that takes into account the source term. For a heterogeneous medium, groundwater velocity is considered as a linear function while the dispersion as a nth-power of linear function of space and analytical solutions are obtained for and . The solution in a heterogeneous finite domain with unsteady coefficients is obtained using the Generalized Integral Transform Technique (GITT) with a new regular Sturm-Liouville Problem (SLP). The solutions are validated with the numerical solutions obtained using MATLAB pedpe solver and the existing solution from the proposed solutions. We exanimated the influence of the source term, the heterogeneity parameters and the unsteady coefficient on the solute concentration distribution. The results show that the source term produces a solute build-up while the heterogeneity level decreases the concentration level in the medium. As an illustration, model predictions are used to estimate the time histories of the radiological doses of uranium at different distances from the sources boundary in order to understand the potential radiological impact on the general public.

Numerical treatment for solving two-dimensional space-fractional advection–dispersion equation using meshless method

2018 ◽  
Vol 32 (06) ◽  
pp. 1850073 ◽  
Author(s):  
Rongjun Cheng ◽  
Fengxin Sun ◽  
Qi Wei ◽  
Jufeng Wang
Keyword(s):  
Dispersion Equation ◽  
Convergence Rates ◽  
Dimensional Space ◽  
Energy Functional ◽  
Least Square ◽  
Approximation Schemes ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Moving Least Square ◽  
Advection Dispersion

Space-fractional advection–dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann–Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

Flow in Heterogeneous Hele-Shaw Models

1964 ◽  
Vol 4 (04) ◽  
pp. 307-316 ◽  
Author(s):  
R.A. Greenkorn ◽  
R.E. Haring ◽  
Hans O. Jahns ◽  
L.K. Shallenberger
Keyword(s):  
Porous Media ◽  
Analytical Solution ◽  
High Speed ◽  
Flow Behavior ◽  
Fluid Pressure ◽  
Large Field ◽  
Two Dimensional ◽  
Direction Parallel ◽  
Glass Plates ◽  
Flow Stream

Abstract This paper is a study of the effects of heterogeneity on flow in an analog of porous media, the Hele-Shaw model. A set of experiments in heterogeneous Hele-Shaw models showed streamlines through and around heterogeneities of various sizes, shapes and levels. (A level, we define as the ratio between the transmissibility of the heterogeneity and that of the rest of the model.) The heterogeneities were restrictions or expansions of the flow stream analogous to variations in the transmissibility of porous media. The experimental data agreed well with numerical results and with an analytical solution, which we derived for a circular heterogeneity in an infinite field. This study considers the flow-stream distortion due to the shape, size and level of heterogeneities. Size and level are much more important than shape provided the heterogeneity is not long and narrow. Our analytical solution shows that a circular heterogeneity in a large field can be replaced by an equivalent circle of either zero or infinite permeability. The radius of the. equivalent circle is a simple function of size and level of the actual circle. Introduction With the availability of high-speed computers and numerical procedures to predict reservoir behavior, we are faced with an important question. How much information about the reservoir do we need to justify the cost of the computer in any given case? To answer this question, we have to know how various reservoir parameters affect flow behavior. Reservoir heterogeneity is one of these parameters. In this study, we used a simple, two-dimensional model of porous media, the Hele-Shaw model, to investigate the effect of heterogeneity on flow behavior. We restricted ourselves to linear, single-phase, steady-state flow in a rectangular field with a single heterogeneity at its center. ANALOGY BETWEEN FLOW IN HELE-SHAW MODELS AND IN POROUS MEDIA HOMOGENEOUS HELE-SHAW MODELS The analogy between flow in Hele-Shaw models and in porous media is easily verified. Let us first consider a homogeneous Hele-Shaw model with constant plate separation h. (The Hele-Shaw model is constructed by placing two plates, usually glass, very close together and allowing liquid to flow between them. Streamlines are made visible by introducing colored fluid into the space between the plates at a number of points across the model.)We assume a cartesian coordinate system with its origin in the middle between the plates and the z axis directed perpendicular to the glass plates (Fig. 1). The fluid flow is always in a direction parallel to the glass plates and varies from a maximum value to zero in the very small distance from the middle (z = 0) to either plate (z = h/2).For slow motion of an incompressible fluid, neglecting inertia and body forces, we have the viscous flow equation: ......................(1) where p is the fluid pressure, mu the viscosity, andthe velocity vector with components u, v and w in the x, y and z directions, respectively. In our case and the derivatives of with respect to x and y are small as compared with the derivative in the z direction. Therefore, approximately, .............(2) with phi p and v being two-dimensional vectors in the x-y plane. SPEJ P. 307ˆ

Analytical Solution of Advection-Dispersion Equation with Spatially Dependent Dispersivity

2017 ◽  
Vol 143 (11) ◽  
pp. 04017126 ◽  
Author(s):  
Vinod Kumar Bharati ◽  
Vijay P. Singh ◽  
Abhishek Sanskrityayn ◽  
Naveen Kumar
Keyword(s):  
Analytical Solution ◽  
Dispersion Equation ◽  
Advection Dispersion

Application of the Fractional Advection-Dispersion Equation in Porous Media

2003 ◽  
Vol 67 (4) ◽  
pp. 1079-1084 ◽  
Author(s):  
Liuzong Zhou ◽  
H. M. Selim
Keyword(s):  
Porous Media ◽  
Dispersion Equation ◽  
Advection Dispersion
Sign in / Sign up

Export Citation Format

Share Document