Contaminant migration from an axisymmetric source in a porous medium

[1] This paper examines the problem of the nonreactive advective transport of a contaminant that is introduced at the boundary of a three-dimensional cavity contained in a fluid-saturated nondeformable porous medium of infinite extent. The advective Darcy flow is caused by a hydraulic potential maintained at a constant value at the boundary of the three-dimensional cavity. In order to develop a generalized solution to the problem the three-dimensional cavity region is modeled as having either a prolate or an oblate shape. Analytical results are developed for the time- and space-dependent distribution of contaminant concentration in the porous medium, which can also exhibit natural attenuation. The exact closed-form analytical results are also capable of providing solutions to advective transport problems related to spherical, flat disc-shaped and elongated needle-shaped cavities.

[1]  T. Chung.  Applied Continuum Mechanics , 1996 .

[2]  Wouter Zijl,et al.  Natural Groundwater Flow , 1993 .

[3]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[4]  D. Drew,et al.  Theory of Multicomponent Fluids , 1998 .

[5]  Jacob Bear,et al.  Transport Phenomena in Porous Media , 1998 .

[6]  E. J. Watson.  Laplace transforms and applications , 1980 .

[7]  Leah Edelstein-Keshet,et al.  Mathematical models in biology , 2005, Classics in applied mathematics.

[8]  Stephen Wolfram,et al.  The Mathematica book (3rd ed.) , 1996 .

[9]  G. Hedstrom,et al.  Numerical Solution of Partial Differential Equations , 1966 .

[10]  A.P.S. Selvadurai,et al.  Partial differential equations in mechanics , 2000 .

[11]  L. Billi,et al.  Unidirectional infiltration in deformable porous media: Mathematical modeling and self-similar solution , 2000 .

[12]  P. Kloeden,et al.  The periodic quasigeostrophic equations: existence and uniqueness of strong solutions , 1982, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[13]  Victor G. Ganzha,et al.  Computer-Aided Analysis of Difference Schemes for Partial Differential Equations: Ganzha/Computer-Aided , 1996 .

[14]  O. M. Phillips,et al.  Flow and Reactions in Permeable Rocks , 1991 .

[15]  Evgenii V. Vorozhtsov,et al.  Computer-Aided Analysis of Difference Schemes for Partial Differential Equations , 1996 .

[16]  P. Domenico,et al.  Physical and chemical hydrogeology , 1990 .

[17]  A.P.S. Selvadurai,et al.  The advective transport of a chemical from a cavity in a porous medium , 2002 .

[18]  E. Hobson.  The Theory of Spherical and Ellipsoidal Harmonics , 1955 .

[19]  Stanisław Ryszard Massel,et al.  Fluid Mechanics for Marine Ecologists , 1999 .

[20]  John Carroll,et al.  Rate equations in semiconductor electronics , 1985 .

[21]  Arnold Verruijt,et al.  Flow and transport in porous media , 1981 .

[22]  Arik Melikyan,et al.  Generalized characteristics of first order PDEs , 1998 .

[23]  J. M. Hill.  Differential Equations and Group Methods for Scientists and Engineers , 1992 .

[24]  I. N. Sneddon.  The use of integral transforms , 1972 .

[25]  Robert B. Banks.  Growth and diffusion phenomena : mathematical frameworks and applications , 1994 .

[26]  Stanisław Ryszard Massel.  Experimental Methods in Fluid Mechanics , 1999 .

[27]  A. P. S. Selvadurai.  The load–deflexion charateristics of a deep rigid anchor in an elastic medium , 1976 .

[28]  P. Morse,et al.  Methods of theoretical physics , 1955 .

[29]  C. Appelo,et al.  Geochemistry, groundwater and pollution , 1993 .

[30]  Kartic C. Khilar,et al.  Migrations of Fines in Porous Media , 1998 .

[31]  G. Ségol,et al.  Classic Groundwater Simulations: Proving and Improving Numerical Models , 1993 .

[32]  Parry Moon,et al.  Field Theory Handbook , 1961 .

[33]  G. Whitham.  Linear and non linear waves , 1974 .

[34]  A. Bejan,et al.  Convection in Porous Media , 1992 .

[35]  L. M. McDowell-Boyer,et al.  Particle transport through porous media , 1986 .

[36]  A. E. Gill.  Atmosphere-Ocean Dynamics , 1982 .