TEMPORALLY DEPENDENT DISPERSION THROUGH SEMI-INFINITE HOMOGENEOUS POROUS MEDIA: AN ANALYTICAL SOLUTION

Size: px
Start display at page:

Download "TEMPORALLY DEPENDENT DISPERSION THROUGH SEMI-INFINITE HOMOGENEOUS POROUS MEDIA: AN ANALYTICAL SOLUTION"

Transcription

1 IJRRAS 6 () February 5.pdf TEMPORALLY EPENENT ISPERSION THROUGH SEMI-INFINITE HOMOGENEOUS POROUS MEIA: AN ANALYTICAL SOLUTION R.R.Yadav, ilip Kumar Jaiswal, Hareesh Kumar Yadav & Gulrana epartment of Mathematics and Astronomy Lucknow University, Lucknow-67, India Corresponding authors: yadav_rr@yahoo.co.in, dilip3jais@gmail.com ABSTRACT An analytical solution is obtained for two-dimensional dispersion through semi-infinite homogeneous porous medium. Point source concentration of pulse type is considered at the origin. Nature of pollutant is chemically nonreactive. Initially the domain is not solute free. The seepage velocities are considered exponentially decreasing function of time along both directions (longitudinal and lateral). ispersion coefficient is assumed proportional to seepage velocity. First order decay is also considered which is proportional to dispersion coefficient. Laplace technique is used to obtain the analytical solution. Key Words: Advection; ispersion; Groundwater; Point source; Seepage velocity.. INTROUCTION In last few years, modeling of solute transport in porous media remain a key issue in the area of soil physics, hydrogeology and environmental science, because anthropogenic chemicals frequently enter the soil, subsoil, aquifers and groundwater either by accident or by human activities, and resulting chemical residues pose hazards to the environment and groundwater. The advection-dispersion equation is the most common method of modeling solute transport in subsurface porous media. This equation includes terms that describe the physical process governing advective transport with flowing groundwater, molecular diffusion, hydrodynamic dispersion, retardation, first order decay, zero-order production and equilibrium or non-equilibrium exchange with the solid phase if reactive solutes are involved. The transport and mixing of contaminants in conduits is governed by advection, dispersion, and decay. Several models/solutions are available to trace the transport of such constituents and most assume that the principal mechanisms for transport are advection and reaction only. A number of analytical solutions have been developed to describe one-dimensional convective dispersive solute transport. Elder [8] by using Taylor's approach and assuming a logarithmic velocity distribution, derived an expression for the longitudinal dispersion coefficient for an infinitely wide open channel. Fischer [] derived another expression for longitudinal dispersion coefficient assuming that the velocity distribution in lateral direction was the primary mechanism responsible for longitudinal dispersion. Marino [6], van Genucheten [3], Banks and Jerasate [3], Rumer [8] and Yadav et al. [5] considered dispersion along unsteady flow. Al-Niami and Rushton [] considered uniform flow where as Kumar [4] took unsteady flow against the dispersion in finite porous media. Most of these works have included the attenuation effect due adsorption, first order radio-active decay and / or chemical reactions. Shen [] presented a generalized closed form solution for three-dimensional dispersion in saturated ambient porous media resulting from sources of finite extent with time-dependent input concentration. Winter et al. [4] defined one- and two-dimensional formation analytically, relate the dispersion parameter to the statistics of the hydraulic conductivity spatial distribution. Batu [5] discussed time-dependent linearized twodimensional infiltration and evaporation from non-uniform and non-periodic strip source. Latinopoulos et al. [5] studied the chemical transport in two-dimensional aquifer. Ellosworth and Butters [9] discussed three-dimensional solutions used for transport problems involving arbitrary Cartesian coordinate systems. Aral and Liao [] examined solutions to two-dimensional advection-dispersion equation with time-dependent dispersion coefficients. In particular, they developed instantaneous and continuous point source solutions for constant, linear, asymptotic, and exponentially varying dispersion coefficients. Stenbacka et al. [] employed a two-dimensional analytical model for estimating the first-order degradation rate constant of hydrophobic organic compounds (HOCs) in contaminated groundwater under steady-state conditions. Massabo et al. [7] gave some analytical solutions for a two-dimensional advection equation with anisotropic dispersion. Chemical decay or adsorption-like reaction inside the liquid phase is considered. Basha and Malaeb [4] presented a method for simulating the advection-dispersion-reaction process of constituent transport in water networks and using Eulerian-Lagrangian method where dispersion term in the governing equation is approximated using finite differences and the resulting first-order partial differential equation is then integrated using the method 58

2 IJRRAS 6 () February of characteristics. Essa et al. [] investigated the dispersion of pollutants from a point source, analytically taking into consideration the vertical variation of both wind speed and eddy diffusivity. Shapiro and Bedrikovetsky [9] proposed a new approach to transport of the suspensions and tracers in porous media. The approach is based on a modified version of the continuous time random walk (CTRW) theory. In the framework of this theory they derived an elliptic transport equation. The new equation contains the time and the mixed dispersion terms expressing the dispersion of the particle time steps. Jaiswal et al. [] and Kumar et al. [3] obtained analytical solutions for temporally and spatially dependent solute dispersion in one-dimensional semi-infinite media. The objective of the present paper is to obtain an analytical solution for prediction of concentration distribution in shallow aquifer with time-dependent dispersion coefficient. Porous domain is considered homogeneous, isotropic, semi-infinite and non-reactive. Both components (longitudinal and lateral) of dispersion coefficient and flow velocity are considered. Seepage velocities are function of time. Point source and pulse type input concentration is considered at origin. Initially the domain is not solute free. There is no solute flux at end of both boundaries. ispersion is proportional to seepage velocity which is taken as time-dependent. First order decay term which is proportional to dispersion coefficient and retardation factor are also considered. Analytical solutions are obtained with the help of Laplace technique. Two-dimensional problem is used to demonstrate the different water and solute profile, for surface and surface line / non-point irrigation. Realistic approach of the obtain results are illustrated by different graphs.. MATHEMATICAL FORMULATION OF THE PROBLEM The two-dimensional parabolic partial differential equation describing hydrodynamic dispersion in adsorbing homogenous, isotropic porous medium can be written as (Schiedegger, []), S + c = t t x + y u t v t γ(t)c () where S is the adsorbed concentration, c is the dissolved concentration and γ is first order decay term. From relation S = K d c, where K d is distribution coefficient which is defined as ratio of the adsorbed contaminant concentration to the dissolved contaminants. In case no adsorption K d =. So that, S = K t d Eq. () becomes, c t ( + K d ) c t = x R c t = x + y + y u t u t v t γ(t)c (3) v t γ(t)c (4) where + K d = R, which is the retardation coefficient accounting for equilibrium linear sorption processes. Let u = u exp mt, v = v exp ( mt) (5) where u and v are initial velocity components along x and y axis respectively and m is flow resistance coefficient. Its dimension is inverse of time. Ebach and White [7], have established that the dispersion coefficient vary approximately directly to flow velocity, for different types of porous medium. So let us considered x = au and y = av (6) where a is a constant depends upon pore geometry of the medium. ispersion and decay term can be written by using expression from (5) and (6), as x = x exp mt, y = y exp mt and γ = γ exp ( mt) (7) where x = au and y = av are initial dispersion coefficient components along two respective directions and γ is the first order decay constant. Initial and boundary conditions for the present paper are, c = C i, t =, x, y (8) where C i is resident concentration in domain. c = C, < t t, x =, y = (9), t > t c c and =, = t, x, y () A pulse-type input condition represented by (9) in which t is the time span of the contaminant release (assuming release starts at time zero) and C is the constant concentration of the pulse at the inlet boundary. When considering the contamination release and discharge problem in industrial sites, this situation is realistic in the sense that generally industries or waste sites release pollution in a finite time period, either because industrial firms have a finite life or the pollution problem is controlled after a certain time with the awareness of the contamination or government regulation. Boundary condition (), indicate that there are no solute flux at end of the both boundaries. Using Eqs. (5) and (7) the differential equation (4) can be written as, () 59

3 IJRRAS 6 () February V t = t x + y u v γ c () exp mt where V t =. R Introducing the new time variable T by following transformation (Crank, [6]) t T = V t dt t or T = exp mt /R dt = exp ( mt) () mr For an expression exp mt which is taken such that exp mt = for m = or t =, the new time variable obtained from Eq. () satisfies the conditions T = for t = and T = for m =. The first condition ensures that the nature of the initial condition does not change in the new time variable domain. Thus Eq. () can be written as, = T x + y u v γ c (3) Let us introduced new variable as, X = x + y y (4) Eq. (3) reduces into c = c c T X U γ X c (5) where = x + y ; U = u + v y The initial and boundary conditions (8)-() in terms of new variables become, c = C i, T =, X (6) c = C, < T T, T > T, X = (7) c =, T, X (8) X Using the following transformation c X, T = K X, T exp U U X + γ 4 T (9) and applying Laplace technique, we get following boundary value problem, pk C i exp U X = d K () dx K X, p = C exp p p α α T ; X =, () and dk dx + U K =, X () where p is Laplace parameter, α = U + γ 4 and β = U. 4 The solution of boundary value problem ()-() in Laplacian domain may be written as, K X, p = C p α α T exp X p β (3) Applying inverse Laplace transformation on (3) and using Eq. (9), the solution in terms of c X, T written as, c X, T = C i F X, T + C F X, T, < T T (4a) c X, T = C i F X, T + C F X, T C F X, T T, T > T (4b) where F X, T = exp γ T X UT erfc T X F X, T = exp β β +γ exp UX C i p β X+UT erfc T erfc X U +4γ / T T, p + C U iexp X + exp β + β +γ / X β = U, = 4 x + y, U = u + v y erfc X+ U +4γ / T T, T = Rm exp ( mt) and X = x + y y,. 6

4 IJRRAS 6 () February.. Particular cases (i) For steady flow The solution for steady in horizontal plane, can be obtained by putting m = in Eq. (4) c X, t = C i F X, t + C F X, t, < t t c X, t = C i F X, t + C F X, t C F X, t t, t > t (5a) (5b) where F X, t = exp γ t/r RX Ut erfc Rt UX exp RX+Ut erfc Rt, F X, t = exp β β +γ X erfc RX U +4γ / t Rt + exp β + β +γ / X erfc RX+ U +4γ / t Rt. (ii) One-dimensional solution along unsteady flow The solution for one-dimensional dispersion along unsteady flow through semi-infinite porous medium can be obtained by putting y = and v = in (4), c x, T = C i F x, T + C F x, T, < T T (6a) c x, T = C i F x, T + C F x, T C F x, T T, T > T (6b) where F x, T = exp γ T F x, T = exp β β +γ erfc x u T T exp u x x erfc x+u T T, erfc x u +4γ / T T where β = u 4 T will remain same as in (4). + exp β + β +γ / x erfc x+ U +4γ / T T,, u and x are initial velocity and dispersion coefficient along longitudinal direction (x-axis) and 3. RESULT AN ISCUSSION To illustrate the concentration distribution of the obtained analytical solution (4) in two-dimensional homogeneous porous medium in semi-infinite domain, an example has been chosen in which the different variables are assigned numerical values, where u =.5 (m/day), v =.5 (m/day), x =.5 (m /day) and y =.5 (m /day) respectively. The lateral velocity dispersion component are considered one-tenth of the longitudinal component. Lateral dispersion is also an essential factor to predict the temporal behavior of the contaminant. The ratio of longitudinal to lateral dispersivity in an aquifer is an important factor to determine the behavior of the contaminant. The flow resistance coefficient m =. (day - ), retardation coefficient R =.4 and first order decay constant γ =.4 have been chosen. Figure () and () are drawn for solution (4a) and (4b) with different time t =.3,.6 and.9 (days) in time domain t t and at t = 3., 3.4 and 3.7 (days) in time domain t > t, respectively. 6

5 IJRRAS 6 () February t =.3 t =.6 t =.9 c/c R = x y.8 Figure. istribution of solute concentrations of f mt = exp ( mt) at different time for solution (4a)..8 t = 3. R =.4 t = 3.4 t = 3.7 c/c.4..4 x y.6.8 Figure. istribution of solute concentrations of f mt = exp ( mt) at different time for solution (4b). In domain t t, the concentration behavior of solute at particular position increases with increasing time while in time domain t > t, solutes concentration decreases with increasing time. It means as the time increases dispersion process goes on dominating over the transport due to convection. Concentration distribution behavior are shown for different R =.4 and.8 at time t =.6 (days) in domain t t and t = 3.6 in domain t > t by Figs. (3) and (4) respectively. 6

6 IJRRAS 6 () February t =.6 R =.8 R =.4 c/c x.8..4 y.6.8 Figure 3. Comparison of solute concentration for different retardation coefficient at time t =.6 (days) for solution (4a)..9.6 t = 3.6 R =.8 c/c R = x.8 y.6.8 Figure 4. Comparison of solute concentration for different retardation coefficient at time t = 3.6 (days) for solution (4b). We observe that the contaminant concentration decreases with increasing retardation coefficient. The time-dependent behavior of solutes in subsurface is of interest for many practical problems where the concentration is observed or needs to be predicted at fixed positions. These solutions have practical application for many field problems. For example, many pipe or conduits carrying contaminated fluids exits in the country. Leakage from those pipe/conduits can contaminate the aquifer/soil below them. These contaminations problems where pipe/conduits are simulated as line/point source. Problems of solute transport in two-dimension involving sequential first order decay reactions and retardation coefficient frequently occurs in soil and groundwater systems, for example the migration of simultaneous movement of interacting nitrogen species, organic phosphate transport and the transport of pesticides and their metabolites. The accuracy of the numerical method is validated by direct comparisons with the analytical results. For a complex source area or non-steady-state plume, a superposition of analytical models that incorporate longitudinal and transverse dispersion and time may be used at sites where the centerline method would not be applicable. 4. CONCLUSION In this work, an analytical solution is obtained for two-dimensional dispersion through semi-infinite homogeneous porous medium. Point source concentration of pulse type is considered at the origin. Initially the domain is not solute free. The seepage velocities are considered exponentially decreasing function of time along both directions (longitudinal and 63

7 IJRRAS 6 () February lateral). ispersion coefficient is assumed proportional to seepage velocity and first order decay is also considered which is proportional to dispersion coefficient. The analytical solutions of two-dimensional dispersion problem may help to determine the position and time to reach the minimum / maximum or harmless concentration and it is very useful for design and interpretation of experiments in laboratory and possibly some homogeneous aquifers and for the verification of complicated numerical models. Obtained result may also be useful as a predictive tool in environmental / groundwater management and applies to real-world applications in which retardation rates are much faster than the rates of advection and dispersion. Multi-dimensional solutions are more widely applicable to transport problems encountered in the field because of the fact that a solute will disperse in any direction that a concentration gradient is present. 5. ACKNOWLEGEMENT Second author is gratefully acknowledged for giving financial assistance as UGC-r. S. Kothari Post octoral Fellowship. 6. REFERENCES []. Al-Niami, A.N.S. and K.R. Rushtom (977). Analysis of flow against dispersion in porous media. J. of Hydrology, 33, []. M. M. Aral and B. Liao. Analytical solutions for two dimensional transport equation with time dependent dispersion coefficients. J. of Hydrologic Eng.,-,-3, (996). [3]. R.B. Banks and S. Jerasate. ispersion in unsteady porous media flow. J. of Hydroul.iv.,9,3-3, (96) [4]. H. A., Basha and L. N. Malae. Eulerian Lagrangian Method for Constituent Transport in Water istribution Networks. Journal of Hydraulic Engineering, 33(), 55 66, (7). [5]. V. Batu. Time-dependent. linearized two-dimensional infiltration and evaporation from non-uniform and non-periodic strip sources. Water Resources Research, 8, , (98). [6]. J. Crank. The Mathematics of iffusion. Oxford Univ. Press, London, nd edition, (975). [7]. E.H. Ebach and R.White. Mixing of fluids flowing through beds of packed soils. J.ofAmer. Inst.Chem. Eng., 4, 6-64, (958). [8]. J. W. Elder. The dispersion of marked fluid in turbulent shear flow. J. Fluid Mech. 5, , (959). [9]. T.R. Ellsworth and G.L. Butters. Three-dimensional analytical solution to the advection- dispersion equation in arbitrary cartesian coordinate. Water Resour. Res., , (993). []. K. S. M. Essa, S. M. Etman and M. Embaby. New analytical solution of the dispersion equation Atmospheric Research, 84, , (7). []. H. B. Fischer. The mechanics of dispersion in natural streams. J. Hydraul. iv. ASCE, 93 (HY6), 87-6, (967). []..K. Jaiswal, A. Kumar, N. Kumar and R.R. Yadava. Analytical solutions for temporally and spatially dependent solute dispersion of pulse type input concentration in one dimensional semi-infinite media. Journal of Hydro-environment Research,, 54 63, (9). [3]. A. Kumar,.K. Jaiswal and N. Kumar. Analytical solutions to one-dimensional advection-diffusion with variable coefficients in seme-infinite media. Journal of Hydrology, 38(3-4), , (). [4]. N. Kumar. Unsteady flow against dispersion in finite porous media with unsteady velocity distribution. Nordic Hydrol., 4,67-78, (983). [5]. P.. Latinopoulos, Tolikas and Y. Mylopoulos. Analytical solution for two dimensional chemical transport in aquifer. J. of Hrdrol., 98, -9, (988). [6]. M.A. Marino. isrtibution of contaminants in porous media flow. Water Resour. Res., (5), 3-8, (974). [7]. M. Massabo, R. Cianci and O. Paladino. Some analytical solutions for two- dimensional Convection dispersion equation in cylindrical geometry. Environmental Modelling and Software,, , (6). [8]. R. Rumer. Longitudinal dispersion in steady flow. J. of Hydrul. iv., 88(4), 47-7, (96). [9]. A. A. Shapiro and P. G. Bedrikovetsky. Elliptic random-walk equation for suspension and tracer transport in porous media. Physica A, 387, , (8). []. A. F. Scheidegger. General theory of dispersion in porous media. J. of General Theory Res., 66,, (96). []. H. T. Shen. Transient dispersion in uniform porous media flow. J. of Hydraul. iv., (6), 77-75, (976). []. G. A. Stenbacka, S. K. Onga, S. W. Rogersa, and B. H. Kjartanson. Impact of transverse and longitudinal dispersion on first order degradation rate constant estimation. Journal of Contaminant Hydrology, 73, 3 4, (4). [3]. van Genuchten, M. Th. Analytical Solutions for chemical transport with Simultaneous adsorption, zero-order production and first order decay. J. of Hydrology, 49, 3-33, (98). [4]. C.L. Winter, C.M. Newman, and S.P. Newman. A perturbation expansion for diffusion in randam velocity field. SIAM J. Appl. Math., 44(), 4-44, (984). [5]. R. R. Yadava, R. R. Vinda, and N. Kumar. One dimensional dispersion in unsteady flow in an adsorbing porous medium: An analytical solution. Hydrological Processes, 4, 89 96, (99). 64

Pollution. Elixir Pollution 97 (2016)

Pollution. Elixir Pollution 97 (2016) 42253 Available online at www.elixirpublishers.com (Elixir International Journal) Pollution Elixir Pollution 97 (2016) 42253-42257 Analytical Solution of Temporally Dispersion of Solute through Semi- Infinite

More information

O.R. Jimoh, M.Tech. Department of Mathematics/Statistics, Federal University of Technology, PMB 65, Minna, Niger State, Nigeria.

O.R. Jimoh, M.Tech. Department of Mathematics/Statistics, Federal University of Technology, PMB 65, Minna, Niger State, Nigeria. Comparative Analysis of a Non-Reactive Contaminant Flow Problem for Constant Initial Concentration in Two Dimensions by Homotopy-Perturbation and Variational Iteration Methods OR Jimoh, MTech Department

More information

1906 Dilip kumar Jaiswal et al./ Elixir Pollution 31 (2011) Available online at (Elixir International Journal)

1906 Dilip kumar Jaiswal et al./ Elixir Pollution 31 (2011) Available online at   (Elixir International Journal) 196 Dilip kumar Jaiswal et al./ Eliir Pollution 31 (211) 196-191 ARTICLE INF O Article history: Received: 21 December 21; Received in revised form: 16 January 211; Accepted: 1 February 211; Keywords Advection,

More information

IOSR Journal of Mathematics (IOSRJM) ISSN: Volume 2, Issue 1 (July-Aug 2012), PP

IOSR Journal of Mathematics (IOSRJM) ISSN: Volume 2, Issue 1 (July-Aug 2012), PP IOSR Journal of Mathematics (IOSRJM) ISSN: 78-578 Volume, Issue (July-Aug ), PP - Analytical Solutions of One-Dimensional Temporally Dependent Advection-Diffusion Equation along Longitudinal Semi-Infinite

More information

International Research Journal of Engineering and Technology (IRJET) e-issn: Volume: 04 Issue: 09 Sep p-issn:

International Research Journal of Engineering and Technology (IRJET) e-issn: Volume: 04 Issue: 09 Sep p-issn: International Research Journal of Engineering and Technology (IRJET) e-issn: 395-56 Volume: 4 Issue: 9 Sep -7 www.irjet.net p-issn: 395-7 An analytical approach for one-dimensional advection-diffusion

More information

Journal of Applied Mathematics and Computation (JAMC), 2018, 2(3), 67-83

Journal of Applied Mathematics and Computation (JAMC), 2018, 2(3), 67-83 Journal of Applied Mathematics and Computation (JAMC) 8 (3) 67-83 http://www.hillpublisher.org/journal/jamc ISSN Online:576-645 ISSN Print:576-653 Analysis of two-dimensional solute transport through heterogeneous

More information

Chemical Hydrogeology

Chemical Hydrogeology Physical hydrogeology: study of movement and occurrence of groundwater Chemical hydrogeology: study of chemical constituents in groundwater Chemical Hydrogeology Relevant courses General geochemistry [Donahoe]

More information

Computational modelling of reactive transport in hydrogeological systems

Computational modelling of reactive transport in hydrogeological systems Water Resources Management III 239 Computational modelling of reactive transport in hydrogeological systems N. J. Kiani, M. K. Patel & C.-H. Lai School of Computing and Mathematical Sciences, University

More information

ABSTRACT INTRODUCTION

ABSTRACT INTRODUCTION Transport of contaminants from non-aqueous phase liquid pool dissolution in subsurface formations C.V. Chrysikopoulos Department of Civil Engineering, University of California, ABSTRACT The transient contaminant

More information

Numerical Solution of the Two-Dimensional Time-Dependent Transport Equation. Khaled Ismail Hamza 1 EXTENDED ABSTRACT

Numerical Solution of the Two-Dimensional Time-Dependent Transport Equation. Khaled Ismail Hamza 1 EXTENDED ABSTRACT Second International Conference on Saltwater Intrusion and Coastal Aquifers Monitoring, Modeling, and Management. Mérida, México, March 3-April 2 Numerical Solution of the Two-Dimensional Time-Dependent

More information

Lecture 16 Groundwater:

Lecture 16 Groundwater: Reading: Ch 6 Lecture 16 Groundwater: Today 1. Groundwater basics 2. inert tracers/dispersion 3. non-inert chemicals in the subsurface generic 4. non-inert chemicals in the subsurface inorganic ions Next

More information

1D Verification Examples

1D Verification Examples 1 Introduction 1D Verification Examples Software verification involves comparing the numerical solution with an analytical solution. The objective of this example is to compare the results from CTRAN/W

More information

dynamics of f luids in porous media

dynamics of f luids in porous media dynamics of f luids in porous media Jacob Bear Department of Civil Engineering Technion Israel Institute of Technology, Haifa DOVER PUBLICATIONS, INC. New York Contents Preface xvii CHAPTER 1 Introduction

More information

Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing.

Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing. Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing. Thus, it is very important to form both a conceptual understanding and a quantitative

More information

RADIONUCLIDE DIFFUSION IN GEOLOGICAL MEDIA

RADIONUCLIDE DIFFUSION IN GEOLOGICAL MEDIA GEOPHYSICS RADIONUCLIDE DIFFUSION IN GEOLOGICAL MEDIA C. BUCUR 1, M. OLTEANU 1, M. PAVELESCU 2 1 Institute for Nuclear Research, Pitesti, Romania, crina.bucur@scn.ro 2 Academy of Scientists Bucharest,

More information

7. Basics of Turbulent Flow Figure 1.

7. Basics of Turbulent Flow Figure 1. 1 7. Basics of Turbulent Flow Whether a flow is laminar or turbulent depends of the relative importance of fluid friction (viscosity) and flow inertia. The ratio of inertial to viscous forces is the Reynolds

More information

Evaluation of hydrodynamic dispersion parameters in fractured rocks

Evaluation of hydrodynamic dispersion parameters in fractured rocks Journal of Rock Mechanics and Geotechnical Engineering. 2010, 2 (3): 243 254 Evaluation of hydrodynamic dispersion parameters in fractured rocks Zhihong Zhao 1, anru Jing 1, Ivars Neretnieks 2 1 Department

More information

Solving Pure Torsion Problem and Modelling Radionuclide Migration Using Radial Basis Functions

Solving Pure Torsion Problem and Modelling Radionuclide Migration Using Radial Basis Functions International Workshop on MeshFree Methods 3 1 Solving Pure Torsion Problem and Modelling Radionuclide Migration Using Radial Basis Functions Leopold Vrankar (1), Goran Turk () and Franc Runovc (3) Abstract:

More information

Analytical solution of advection diffusion equation in heterogeneous infinite medium using Green s function method

Analytical solution of advection diffusion equation in heterogeneous infinite medium using Green s function method Analytical solution of advection diffusion equation in heterogeneous infinite medium using Green s function method Abhishek Sanskrityayn Naveen Kumar Department of Mathematics, Institute of Science, Banaras

More information

A semi-lagrangian scheme for advection-diffusion equation

A semi-lagrangian scheme for advection-diffusion equation EPiC Series in Engineering Volume 3, 2018, Pages 162 172 HIC 2018. 13th International Conference on Hydroinformatics Engineering A semi-lagrangian scheme for advection-diffusion equation Ersin Bahar 1,

More information

Abstract. Introduction

Abstract. Introduction Stability Criterion for Explicit Schemes (Finite-Difference Method) on the Solution of the Advection-Diffusion Equation L.F. León, P.M. Austria Mexican Institute of Water Technology, Paseo Cuauhnáhuac

More information

EFFECT OF CHANNEL BENDS ON TRANSVERSE MIXING

EFFECT OF CHANNEL BENDS ON TRANSVERSE MIXING NIJOTECH VOL. 10. NO. 1 SEPTEMBER 1986 ENGMANN 57 EFFECT OF CHANNEL BENDS ON TRANSVERSE MIXING BY E. O. ENGMANN ABSTRACT Velocity and tracer concentration measurements made in a meandering channel are

More information

The distortion observed in the bottom channel of Figure 1 can be predicted from the full transport equation, C t + u C. y D C. z, (1) x D C.

The distortion observed in the bottom channel of Figure 1 can be predicted from the full transport equation, C t + u C. y D C. z, (1) x D C. 1 8. Shear Dispersion. The transport models and concentration field solutions developed in previous sections assume that currents are spatially uniform, i.e. u f(,y,). However, spatial gradients of velocity,

More information

v. 8.0 GMS 8.0 Tutorial RT3D Double Monod Model Prerequisite Tutorials None Time minutes Required Components Grid MODFLOW RT3D

v. 8.0 GMS 8.0 Tutorial RT3D Double Monod Model Prerequisite Tutorials None Time minutes Required Components Grid MODFLOW RT3D v. 8.0 GMS 8.0 Tutorial Objectives Use GMS and RT3D to model the reaction between an electron donor and an electron acceptor, mediated by an actively growing microbial population that exists in both soil

More information

RT3D Double Monod Model

RT3D Double Monod Model GMS 7.0 TUTORIALS RT3D Double Monod Model 1 Introduction This tutorial illustrates the steps involved in using GMS and RT3D to model the reaction between an electron donor and an electron acceptor, mediated

More information

RT3D Rate-Limited Sorption Reaction

RT3D Rate-Limited Sorption Reaction GMS TUTORIALS RT3D Rate-Limited Sorption Reaction This tutorial illustrates the steps involved in using GMS and RT3D to model sorption reactions under mass-transfer limited conditions. The flow model used

More information

1 of 7 2/8/2016 4:17 PM

1 of 7 2/8/2016 4:17 PM 1 of 7 2/8/2016 4:17 PM Continuous issue-4 January - March 2015 Abstract The similarity solution of Diffusion equation using a technique of infinitesimal transformations of groups The similarity solution

More information

RT3D Double Monod Model

RT3D Double Monod Model GMS TUTORIALS RT3D Double Monod Model This tutorial illustrates the steps involved in using GMS and RT3D to model the reaction between an electron donor and an electron acceptor, mediated by an actively

More information

Extreme Mixing Events in Rivers

Extreme Mixing Events in Rivers PUBLS. INST. GEOPHYS. POL. ACAD. SC., E-10 (406), 2008 Extreme Mixing Events in Rivers Russell MANSON 1 and Steve WALLIS 2 1 The Richard Stockton College of New Jersey, School of Natural Sciences and Mathematics,

More information

EVALUATION OF CRITICAL FRACTURE SKIN POROSITY FOR CONTAMINANT MIGRATION IN FRACTURED FORMATIONS

EVALUATION OF CRITICAL FRACTURE SKIN POROSITY FOR CONTAMINANT MIGRATION IN FRACTURED FORMATIONS ISSN (Online) : 2319-8753 ISSN (Print) : 2347-6710 International Journal of Innovative Research in Science, Engineering and Technology An ISO 3297: 2007 Certified Organization, Volume 2, Special Issue

More information

SOLUTE TRANSPORT. Renduo Zhang. Proceedings of Fourteenth Annual American Geophysical Union: Hydrology Days. Submitted by

SOLUTE TRANSPORT. Renduo Zhang. Proceedings of Fourteenth Annual American Geophysical Union: Hydrology Days. Submitted by THE TRANSFER FUNCTON FOR SOLUTE TRANSPORT Renduo Zhang Proceedings 1994 WWRC-94-1 1 n Proceedings of Fourteenth Annual American Geophysical Union: Hydrology Days Submitted by Renduo Zhang Department of

More information

A Decomposition Method for Solving Coupled Multi-Species Reactive Transport Problems

A Decomposition Method for Solving Coupled Multi-Species Reactive Transport Problems Transport in Porous Media 37: 327 346, 1999. c 1999 Kluwer Academic Publishers. Printed in the Netherlands. 327 A Decomposition Method for Solving Coupled Multi-Species Reactive Transport Problems YUNWEI

More information

Advanced numerical methods for transport and reaction in porous media. Peter Frolkovič University of Heidelberg

Advanced numerical methods for transport and reaction in porous media. Peter Frolkovič University of Heidelberg Advanced numerical methods for transport and reaction in porous media Peter Frolkovič University of Heidelberg Content R 3 T a software package for numerical simulation of radioactive contaminant transport

More information

On the advective-diffusive transport in porous media in the presence of time-dependent velocities

On the advective-diffusive transport in porous media in the presence of time-dependent velocities GEOPHYSICAL RESEARCH LETTERS, VOL. 3, L355, doi:.29/24gl9646, 24 On the advective-diffusive transport in porous media in the presence of time-dependent velocities A. P. S. Selvadurai Department of Civil

More information

Application of Green Function Method for Solution Advection Diffusion Equation of Nutrient Concentration in Groundwater

Application of Green Function Method for Solution Advection Diffusion Equation of Nutrient Concentration in Groundwater Annals of Pure and Applied Mathematics Vol. 7, No. 2, 2014, 1-5 ISSN: 2279-087X (P), 2279-0888(online) Published on 26 August 2014 www.researchmathsci.org Annals of Application of Green Function Method

More information

2. Conservation of Mass

2. Conservation of Mass 2 Conservation of Mass The equation of mass conservation expresses a budget for the addition and removal of mass from a defined region of fluid Consider a fixed, non-deforming volume of fluid, V, called

More information

Integrating tracer with remote sensing techniques for determining dispersion coefficients of the Dâmbovita River, Romania

Integrating tracer with remote sensing techniques for determining dispersion coefficients of the Dâmbovita River, Romania Integrated Methods in Catchment Hydrology Tracer, Remote Sensing and New Hydrometric Techniques (Proceedings of IUGG 99 Symposium HS4, Birmingham, July 999). IAHS Publ. no. 258, 999. 75 Integrating tracer

More information

EXAMPLE PROBLEMS. 1. Example 1 - Column Infiltration

EXAMPLE PROBLEMS. 1. Example 1 - Column Infiltration EXAMPLE PROBLEMS The module UNSATCHEM is developed from the variably saturated solute transport model HYDRUS-1D [Šimůnek et al., 1997], and thus the water flow and solute transport parts of the model have

More information

Energy Pile Simulation - an Application of THM- Modeling

Energy Pile Simulation - an Application of THM- Modeling Energy Pile Simulation - an Application of THM- Modeling E. Holzbecher 1 1 Georg-August University, Göttingen, Germany Abstract Introduction: Energy piles, i.e. heat exchangers located within the foundation

More information

V (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t)

V (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t) IV. DIFFERENTIAL RELATIONS FOR A FLUID PARTICLE This chapter presents the development and application of the basic differential equations of fluid motion. Simplifications in the general equations and common

More information

SAFETY ASSESSMENT CODES FOR THE NEAR-SURFACE DISPOSAL OF LOW AND INTERMEDIATE-LEVEL RADIOACTIVE WASTE WITH THE COMPARTMENT MODEL: SAGE AND VR-KHNP

SAFETY ASSESSMENT CODES FOR THE NEAR-SURFACE DISPOSAL OF LOW AND INTERMEDIATE-LEVEL RADIOACTIVE WASTE WITH THE COMPARTMENT MODEL: SAGE AND VR-KHNP SAFETY ASSESSMENT CODES FOR THE NEAR-SURFACE DISPOSAL OF LOW AND INTERMEDIATE-LEVEL RADIOACTIVE WASTE WITH THE COMPARTMENT MODEL: SAGE AND VR-KHNP J. B. Park, J. W. Park, C. L. Kim, M. J. Song Korea Hydro

More information

Analytical solutions for water flow and solute transport in the unsaturated zone

Analytical solutions for water flow and solute transport in the unsaturated zone Models for Assessing and Monitoring Groundwater Quality (Procsedines of a Boulder Symposium July 1995). IAHS Publ. no. 227, 1995. 125 Analytical solutions for water flow and solute transport in the unsaturated

More information

v GMS 10.4 Tutorial RT3D Double-Monod Model Prerequisite Tutorials RT3D Instantaneous Aerobic Degradation Time minutes

v GMS 10.4 Tutorial RT3D Double-Monod Model Prerequisite Tutorials RT3D Instantaneous Aerobic Degradation Time minutes v. 10.4 GMS 10.4 Tutorial RT3D Double-Monod Model Objectives Use GMS and RT3D to model the reaction between an electron donor and an electron acceptor, mediated by an actively growing microbial population

More information

Code-to-Code Benchmarking of the PORFLOW and GoldSim Contaminant Transport Models using a Simple 1-D Domain

Code-to-Code Benchmarking of the PORFLOW and GoldSim Contaminant Transport Models using a Simple 1-D Domain Code-to-Code Benchmarking of the PORFLOW and GoldSim Contaminant Transport Models using a Simple 1-D Domain - 11191 Robert A. Hiergesell and Glenn A. Taylor Savannah River National Laboratory SRNS Bldg.

More information

CHARACTERIZATION OF HETEROGENEITIES AT THE CORE-SCALE USING THE EQUIVALENT STRATIFIED POROUS MEDIUM APPROACH

CHARACTERIZATION OF HETEROGENEITIES AT THE CORE-SCALE USING THE EQUIVALENT STRATIFIED POROUS MEDIUM APPROACH SCA006-49 /6 CHARACTERIZATION OF HETEROGENEITIES AT THE CORE-SCALE USING THE EQUIVALENT STRATIFIED POROUS MEDIUM APPROACH Mostafa FOURAR LEMTA Ecole des Mines de Nancy, Parc de Saurupt, 54 04 Nancy, France

More information

NATURAL ZEOLITE AS A PERMEABLE REACTIVE BARRIER

NATURAL ZEOLITE AS A PERMEABLE REACTIVE BARRIER NATURAL ZEOLITE AS A PERMEABLE REACTIVE BARRIER PREDICTION OF LEAD CONCENTRATION PROFILE THROUGH ZEOLITE BARRIER N. Vukojević Medvidović, J. Perić, M. Trgo, M. Ugrina, I. Nuić University of Split, Faculty

More information

Contaminant Fate and Transport in the Environment EOH 2122; Lecture 6, Transport in Surface Waters

Contaminant Fate and Transport in the Environment EOH 2122; Lecture 6, Transport in Surface Waters Contaminant Fate and Transport in the Environment EOH 2122; Lecture 6, Transport in Surface Waters Conrad (Dan) Volz, DrPH, MPH Bridgeside Point 100 Technology Drive Suite 564, BRIDG Pittsburgh, PA 15219-3130

More information

VISUAL SOLUTE TRANSPORT: A COMPUTER CODE FOR USE IN HYDROGEOLOGY CLASSES

VISUAL SOLUTE TRANSPORT: A COMPUTER CODE FOR USE IN HYDROGEOLOGY CLASSES VISUAL SOLUTE TRANSPORT: A COMPUTER CODE FOR USE IN HYDROGEOLOGY CLASSES Kathryn W. Thorbjarnarson Department of Geological Sciences, San Diego State University, 5500 Campanile Drive, San Diego, California

More information

In all of the following equations, is the coefficient of permeability in the x direction, and is the hydraulic head.

In all of the following equations, is the coefficient of permeability in the x direction, and is the hydraulic head. Groundwater Seepage 1 Groundwater Seepage Simplified Steady State Fluid Flow The finite element method can be used to model both steady state and transient groundwater flow, and it has been used to incorporate

More information

350 Int. J. Environment and Pollution Vol. 5, Nos. 3 6, 1995

350 Int. J. Environment and Pollution Vol. 5, Nos. 3 6, 1995 350 Int. J. Environment and Pollution Vol. 5, Nos. 3 6, 1995 A puff-particle dispersion model P. de Haan and M. W. Rotach Swiss Federal Institute of Technology, GGIETH, Winterthurerstrasse 190, 8057 Zürich,

More information

POINT SOURCES OF POLLUTION: LOCAL EFFECTS AND IT S CONTROL Vol. II - Contaminant Fate and Transport Process - Xi Yang and Gang Yu

POINT SOURCES OF POLLUTION: LOCAL EFFECTS AND IT S CONTROL Vol. II - Contaminant Fate and Transport Process - Xi Yang and Gang Yu CONTAMINANT FATE AND TRANSPORT PROCESS Xi Yang and Gang Yu Department of Environmental Sciences and Engineering, Tsinghua University, Beijing, P. R. China Keywords: chemical fate, physical transport, chemical

More information

Research Article An Analytical Solution of the Advection Dispersion Equation in a Bounded Domain and Its Application to Laboratory Experiments

Research Article An Analytical Solution of the Advection Dispersion Equation in a Bounded Domain and Its Application to Laboratory Experiments Applied Mathematics Volume 211, Article ID 49314, 14 pages doi:1.1155/211/49314 Research Article An Analytical Solution of the Advection Dispersion Equation in a Bounded Domain and Its Application to aboratory

More information

Solute transport through porous media using asymptotic dispersivity

Solute transport through porous media using asymptotic dispersivity Sādhanā Vol. 40, Part 5, August 2015, pp. 1595 1609. c Indian Academy of Sciences Solute transport through porous media using asymptotic dispersivity P K SHARMA and TEODROSE ATNAFU ABGAZE Department of

More information

MHD Flow Past an Impulsively Started Vertical Plate with Variable Temperature and Mass Diffusion

MHD Flow Past an Impulsively Started Vertical Plate with Variable Temperature and Mass Diffusion Applied Mathematical Sciences, Vol. 5, 2011, no. 3, 149-157 MHD Flow Past an Impulsively Started Vertical Plate with Variable Temperature and Mass Diffusion U. S. Rajput and Surendra Kumar Department of

More information

A Boundary Condition for Porous Electrodes

A Boundary Condition for Porous Electrodes Electrochemical Solid-State Letters, 7 9 A59-A63 004 0013-4651/004/79/A59/5/$7.00 The Electrochemical Society, Inc. A Boundary Condition for Porous Electrodes Venkat R. Subramanian, a, *,z Deepak Tapriyal,

More information

Transactions on Ecology and the Environment vol 7, 1995 WIT Press, ISSN

Transactions on Ecology and the Environment vol 7, 1995 WIT Press,   ISSN Non-Fickian tracer dispersion in a karst conduit embedded in a porous medium A.P. Belov*, T.C. Atkinson* "Department of Mathematics and Computing, University of Glamorgan, Pontypridd, Mid Glamorgan, CF3

More information

Numerical Solution of One-dimensional Advection-diffusion Equation Using Simultaneously Temporal and Spatial Weighted Parameters

Numerical Solution of One-dimensional Advection-diffusion Equation Using Simultaneously Temporal and Spatial Weighted Parameters Australian Journal of Basic and Applied Sciences, 5(6): 536-543, 0 ISSN 99-878 Numerical Solution of One-dimensional Advection-diffusion Equation Using Simultaneously Temporal and Spatial Weighted Parameters

More information

A Numerical Algorithm for Solving Advection-Diffusion Equation with Constant and Variable Coefficients

A Numerical Algorithm for Solving Advection-Diffusion Equation with Constant and Variable Coefficients The Open Numerical Methods Journal, 01, 4, 1-7 1 Open Access A Numerical Algorithm for Solving Advection-Diffusion Equation with Constant and Variable Coefficients S.G. Ahmed * Department of Engineering

More information

Fundamentals of Transport Processes Prof. Kumaran Indian Institute of Science, Bangalore Chemical Engineering

Fundamentals of Transport Processes Prof. Kumaran Indian Institute of Science, Bangalore Chemical Engineering Fundamentals of Transport Processes Prof. Kumaran Indian Institute of Science, Bangalore Chemical Engineering Module No # 05 Lecture No # 25 Mass and Energy Conservation Cartesian Co-ordinates Welcome

More information

Modelling of decay chain transport in groundwater from uranium tailings ponds

Modelling of decay chain transport in groundwater from uranium tailings ponds Modelling of decay chain transport in groundwater from uranium tailings ponds Nair, R.N., Sunny, F., Manikandan, S.T. Student : 曹立德 Advisor : 陳瑞昇老師 Date : 2014/12/04 Outline Introduction Model Result and

More information

6. Continuous Release - Point Source

6. Continuous Release - Point Source 1 6. Continuous Release - Point Source A scalar released continuously into a moving fluid and from a discrete point will form a plume that grows in the lateral dimension through diffusion and extends downstream

More information

Theories for Mass Transfer Coefficients

Theories for Mass Transfer Coefficients Mass Transfer Theories for Mass Transfer Coefficients Lecture 9, 5..7, r. K. Wegner 9. Basic Theories for Mass Transfer Coefficients Aim: To find a theory behind the empirical mass-transfer correlations

More information

Comparison of Heat and Mass Transport at the Micro-Scale

Comparison of Heat and Mass Transport at the Micro-Scale Comparison of Heat and Mass Transport at the Micro-Scale E. Holzbecher, S. Oehlmann Georg-August Univ. Göttingen *Goldschmidtstr. 3, 37077 Göttingen, GERMANY, eholzbe@gwdg.de Abstract: Phenomena of heat

More information

Chapter 2 Theory. 2.1 Continuum Mechanics of Porous Media Porous Medium Model

Chapter 2 Theory. 2.1 Continuum Mechanics of Porous Media Porous Medium Model Chapter 2 Theory In this chapter we briefly glance at basic concepts of porous medium theory (Sect. 2.1.1) and thermal processes of multiphase media (Sect. 2.1.2). We will study the mathematical description

More information

1.061 / 1.61 Transport Processes in the Environment

1.061 / 1.61 Transport Processes in the Environment MIT OpenCourseWare http://ocw.mit.edu 1.061 / 1.61 Transport Processes in the Environment Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 6.

More information

Spatial moment analysis: an application to quantitative imaging of contaminant distributions in porous media

Spatial moment analysis: an application to quantitative imaging of contaminant distributions in porous media Spatial moment analysis: an application to quantitative imaging of contaminant distributions in porous media Ombretta Paladino a,b, Marco Massabò a,b, Federico Catania a,b, Gianangelo Bracco a,c a CIMA

More information

NUMERICAL SOLUTION OF TWO-REGION ADVECTION-DISPERSION TRANSPORT AND COMPARISON WITH ANALYTICAL SOLUTION ON EXAMPLE PROBLEMS

NUMERICAL SOLUTION OF TWO-REGION ADVECTION-DISPERSION TRANSPORT AND COMPARISON WITH ANALYTICAL SOLUTION ON EXAMPLE PROBLEMS Proceedings of ALGORITMY 2002 Conference on Scientific Computing, pp. 130 137 NUMERICAL SOLUTION OF TWO-REGION ADVECTION-DISPERSION TRANSPORT AND COMPARISON WITH ANALYTICAL SOLUTION ON EXAMPLE PROBLEMS

More information

RAM C. ACHARYA, ALBERT J. VALOCCHI, THOMAS W. WILLINGHAM, AND CHARLES J. WERTH

RAM C. ACHARYA, ALBERT J. VALOCCHI, THOMAS W. WILLINGHAM, AND CHARLES J. WERTH PORE-SCALE SIMULATION OF DISPERSION AND REACTION ALONG A TRANSVERSE MIXING ZONE IN TWO-DIMENSIONAL HETEROGENEOUS POROUS MEDIUM COMPOSED OF RANDOMLY DISTRIBUTED CIRCULAR AND ELLIPTICAL CYLINDERS RAM C.

More information

Analytic Solution of Two Dimensional Advection Diffusion Equation Arising In Cytosolic Calcium Concentration Distribution

Analytic Solution of Two Dimensional Advection Diffusion Equation Arising In Cytosolic Calcium Concentration Distribution International Mathematical Forum, Vol. 7, 212, no. 3, 135-144 Analytic Solution of Two Dimensional Advection Diffusion Equation Arising In Cytosolic Calcium Concentration Distribution Brajesh Kumar Jha,

More information

Contaminant Modeling

Contaminant Modeling Contaminant Modeling with CTRAN/W An Engineering Methodology February 2012 Edition GEO-SLOPE International Ltd. Copyright 2004-2012 by GEO-SLOPE International, Ltd. All rights reserved. No part of this

More information

Solving the One Dimensional Advection Diffusion Equation Using Mixed Discrete Least Squares Meshless Method

Solving the One Dimensional Advection Diffusion Equation Using Mixed Discrete Least Squares Meshless Method Proceedings of the International Conference on Civil, Structural and Transportation Engineering Ottawa, Ontario, Canada, May 4 5, 2015 Paper No. 292 Solving the One Dimensional Advection Diffusion Equation

More information

Solute dispersion in a variably saturated sand

Solute dispersion in a variably saturated sand WATER RESOURCES RESEARCH, VOL. 39, NO. 6, 1155, doi:10.1029/2002wr001649, 2003 Solute dispersion in a variably saturated sand Takeshi Sato Department of Civil Engineering, Gifu University, Yanagido, Gifu,

More information

SIMILARITY SOLUTION FOR DOUBLE NATURAL CONVECTION WITH DISPERSION FROM SOURCES IN AN INFINITE POROUS MEDIUM

SIMILARITY SOLUTION FOR DOUBLE NATURAL CONVECTION WITH DISPERSION FROM SOURCES IN AN INFINITE POROUS MEDIUM Proceedings NZ GeothermalWorkshop SIMILARITY SOLUTION FOR DOUBLE NATURAL CONVECTION WITH DISPERSION FROM SOURCES IN AN INFINITE POROUS MEDIUM A.V. and A. F. Geothermal Institute, The University of Auckland,

More information

Physicochemical Processes

Physicochemical Processes Lecture 3 Physicochemical Processes Physicochemical Processes Air stripping Carbon adsorption Steam stripping Chemical oxidation Supercritical fluids Membrane processes 1 1. Air Stripping A mass transfer

More information

STEADY SOLUTE DISPERSION IN COMPOSITE POROUS MEDIUM BETWEEN TWO PARALLEL PLATES

STEADY SOLUTE DISPERSION IN COMPOSITE POROUS MEDIUM BETWEEN TWO PARALLEL PLATES Journal of Porous Media, 6 : 087 05 03 STEADY SOLUTE DISPERSION IN COMPOSITE POROUS MEDIUM BETWEEN TWO PARALLEL PLATES J. Prathap Kumar, J. C. Umavathi, & Ali J. Chamkha, Department of Mathematics, Gulbarga

More information

11280 Electrical Resistivity Tomography Time-lapse Monitoring of Three-dimensional Synthetic Tracer Test Experiments

11280 Electrical Resistivity Tomography Time-lapse Monitoring of Three-dimensional Synthetic Tracer Test Experiments 11280 Electrical Resistivity Tomography Time-lapse Monitoring of Three-dimensional Synthetic Tracer Test Experiments M. Camporese (University of Padova), G. Cassiani* (University of Padova), R. Deiana

More information

On steady hydromagnetic flow of a radiating viscous fluid through a horizontal channel in a porous medium

On steady hydromagnetic flow of a radiating viscous fluid through a horizontal channel in a porous medium AMERICAN JOURNAL OF SCIENTIFIC AND INDUSTRIAL RESEARCH 1, Science Huβ, http://www.scihub.org/ajsir ISSN: 153-649X doi:1.551/ajsir.1.1..33.38 On steady hydromagnetic flow of a radiating viscous fluid through

More information

An Introduction to COMSOL Multiphysics v4.3b & Subsurface Flow Simulation. Ahsan Munir, PhD Tom Spirka, PhD

An Introduction to COMSOL Multiphysics v4.3b & Subsurface Flow Simulation. Ahsan Munir, PhD Tom Spirka, PhD An Introduction to COMSOL Multiphysics v4.3b & Subsurface Flow Simulation Ahsan Munir, PhD Tom Spirka, PhD Agenda Provide an overview of COMSOL 4.3b Our products, solutions and applications Subsurface

More information

5. Advection and Diffusion of an Instantaneous, Point Source

5. Advection and Diffusion of an Instantaneous, Point Source 1 5. Advection and Diffusion of an Instantaneous, Point Source In this chapter consider the combined transport by advection and diffusion for an instantaneous point release. We neglect source and sink

More information

Kabita Nath Department of Mathematics Dibrugarh University Dibrugarh, Assam, India

Kabita Nath Department of Mathematics Dibrugarh University Dibrugarh, Assam, India Influence of Chemical Reaction, Heat Source, Soret and Dufour Effects on Separation of a Binary Fluid Mixture in MHD Natural Convection Flow in Porous Media B.R.Sharma Department of Mathematics Dibrugarh

More information

arxiv: v1 [physics.flu-dyn] 18 Mar 2018

arxiv: v1 [physics.flu-dyn] 18 Mar 2018 APS Persistent incomplete mixing in reactive flows Alexandre M. Tartakovsky 1 and David Barajas-Solano 1 1 Pacific Northwest National Laboratory, Richland, WA 99352, USA arxiv:1803.06693v1 [physics.flu-dyn]

More information

Studies on flow through and around a porous permeable sphere: II. Heat Transfer

Studies on flow through and around a porous permeable sphere: II. Heat Transfer Studies on flow through and around a porous permeable sphere: II. Heat Transfer A. K. Jain and S. Basu 1 Department of Chemical Engineering Indian Institute of Technology Delhi New Delhi 110016, India

More information

Total Thermal Diffusivity in a Porous Structure Measured By Full Field Liquid Crystal Thermography

Total Thermal Diffusivity in a Porous Structure Measured By Full Field Liquid Crystal Thermography Proceedings of the International Conference on Heat Transfer and Fluid Flow Prague, Czech Republic, August 11-12, 2014 Paper No. 89 Total Thermal Diffusivity in a Porous Structure Measured By Full Field

More information

Study on Estimation of Hydraulic Conductivity of Porous Media Using Drag Force Model Jashandeep Kaur, M. A. Alam

Study on Estimation of Hydraulic Conductivity of Porous Media Using Drag Force Model Jashandeep Kaur, M. A. Alam 26 IJSRSET Volume 2 Issue 3 Print ISSN : 2395-99 Online ISSN : 2394-499 Themed Section: Engineering and Technology Study on Estimation of Hydraulic Conductivity of Porous Media Using Drag Force Model Jashandeep

More information

Charging and Transport Dynamics of a Flow-

Charging and Transport Dynamics of a Flow- Charging and Transport Dynamics of a Flow- Through Electrode Capacitive Deionization System Supporting information Yatian Qu, a,b Patrick G. Campbell, b Ali Hemmatifar, a Jennifer M. Knipe, b Colin K.

More information

Second-Order Linear ODEs (Textbook, Chap 2)

Second-Order Linear ODEs (Textbook, Chap 2) Second-Order Linear ODEs (Textbook, Chap ) Motivation Recall from notes, pp. 58-59, the second example of a DE that we introduced there. d φ 1 1 φ = φ 0 dx λ λ Q w ' (a1) This equation represents conservation

More information

Chapter 4 Transport of Pollutants

Chapter 4 Transport of Pollutants 4- Introduction Phs. 645: Environmental Phsics Phsics Department Yarmouk Universit hapter 4 Transport of Pollutants - e cannot avoid the production of pollutants. hat can we do? - Transform pollutants

More information

Module 2 Lecture 9 Permeability and Seepage -5 Topics

Module 2 Lecture 9 Permeability and Seepage -5 Topics Module 2 Lecture 9 Permeability and Seepage -5 Topics 1.2.7 Numerical Analysis of Seepage 1.2.8 Seepage Force per Unit Volume of Soil Mass 1.2.9 Safety of Hydraulic Structures against Piping 1.2.10 Calculation

More information

Application of the random walk method to simulate the transport of kinetically adsorbing solutes

Application of the random walk method to simulate the transport of kinetically adsorbing solutes Groundwater Contamination (Proceedings of the Symposium held during the Third IAHS Scientific Assembly, Baltimore, MD, May 1989), IAHS Publ. no. 185, 1989 Application of the random walk method to simulate

More information

Numerical Analysis of MHD Flow of Fluid with One Porous Bounding Wall

Numerical Analysis of MHD Flow of Fluid with One Porous Bounding Wall Numerical Analysis of MHD Flow of Fluid with One Porous Bounding Wall Ramesh Yadav 1 & Vivek Joseph 2 1Assistant Professor, Department of Mathematics BBDNITM Lucknow U P 2Professor, Department of Mathematics

More information

Lecture Note for Open Channel Hydraulics

Lecture Note for Open Channel Hydraulics Chapter -one Introduction to Open Channel Hydraulics 1.1 Definitions Simply stated, Open channel flow is a flow of liquid in a conduit with free space. Open channel flow is particularly applied to understand

More information

Safety assessment for disposal of hazardous waste in abandoned underground mines

Safety assessment for disposal of hazardous waste in abandoned underground mines Safety assessment for disposal of hazardous waste in abandoned underground mines A. Peratta & V. Popov Wessex Institute of Technology, Southampton, UK Abstract Disposal of hazardous chemical waste in abandoned

More information

Corresponding Author: Kandie K.Joseph. DOI: / Page

Corresponding Author: Kandie K.Joseph. DOI: / Page IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 13, Issue 5 Ver. 1 (Sep. - Oct. 2017), PP 37-47 www.iosrjournals.org Solution of the Non-Linear Third Order Partial Differential

More information

Freezing Around a Pipe with Flowing Water

Freezing Around a Pipe with Flowing Water 1 Introduction Freezing Around a Pipe with Flowing Water Groundwater flow can have a significant effect on ground freezing because heat flow via convection is often more effective at moving heat than conduction

More information

Biological Process Engineering An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems

Biological Process Engineering An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems Biological Process Engineering An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems Arthur T. Johnson, PhD, PE Biological Resources Engineering Department

More information

Solving One-Dimensional Advection-Dispersion with Reaction Using Some Finite-Difference Methods

Solving One-Dimensional Advection-Dispersion with Reaction Using Some Finite-Difference Methods Applied Mathematical Sciences, Vol., 008, no. 53, 6-68 Solving One-Dimensional Advection-Dispersion with Reaction Using Some Finite-Difference Methods H. Saberi Naafi Department of Mathematics, Faculty

More information

Hydromagnetic oscillatory flow through a porous medium bounded by two vertical porous plates with heat source and soret effect

Hydromagnetic oscillatory flow through a porous medium bounded by two vertical porous plates with heat source and soret effect Available online at www.pelagiaresearchlibrary.com Advances in Applied Science Research, 2012, 3 (4):2169-2178 ISSN: 0976-8610 CODEN (USA): AASRFC Hydromagnetic oscillatory flow through a porous medium

More information

12 SWAT USER S MANUAL, VERSION 98.1

12 SWAT USER S MANUAL, VERSION 98.1 12 SWAT USER S MANUAL, VERSION 98.1 CANOPY STORAGE. Canopy storage is the water intercepted by vegetative surfaces (the canopy) where it is held and made available for evaporation. When using the curve

More information

Stokes Flow in a Slowly Varying Two-Dimensional Periodic Pore

Stokes Flow in a Slowly Varying Two-Dimensional Periodic Pore Transport in Porous Media 6: 89 98, 997. 89 c 997 Kluwer Academic Publishers. Printed in the Netherlands. Stokes Flow in a Slowly Varying Two-Dimensional Periodic Pore PETER K. KITANIDIS? and BRUCE B.

More information