Open AccessHYPERBOLIC DESCRIPTION OF CONTAMINATED FLOW THROUGH AN UNSATURATED WELLBORE
Author(s) -
Maria Laura MartinsCosta,
Rogério Martins Saldanha da Gama,
J. H. Carneiro de Araújo
Publication year - 2007
Publication title -
engenharia térmica
Language(s) - English
Resource type - Journals
ISSN - 1676-1790
DOI - 10.5380/reterm.v6i1.61810
Subject(s) - compressibility , mechanics , newtonian fluid , partial differential equation , flow (mathematics) , hyperbolic partial differential equation , non newtonian fluid , porous medium , nonlinear system , laminar flow , ladle , mathematics , porosity , materials science , mathematical analysis , physics , geology , geotechnical engineering , quantum mechanics , metallurgy
This work studies the flow of a mixture of two fluids – a Newtonian fluid and a pollutant – through a rigid cylindrical shell porous matrix. Aiming to build a preliminary local model for the flow of a Newtonian fluid containing a pollutant through a wellbore, a mixture theory approach is employed. The mixture consists of four overlapping continuous constituents: one solid (porous medium), one liquid (Newtonian fluid), the pollutant (solid, liquid or gas) and an inert gas included to account for the compressibility of the mixture as a whole. Assuming the flow on radial direction only, a set of three nonlinear partial differential equations describes the problem. Combining Glimm’s scheme with an operator splitting technique to account for the non-homogeneous part of the hyperbolic operator, the resulting nonlinear hyperbolic system is numerically approximated. Representative results illustrating the numerical methodology are presented.