Hyperbolic Description of Contaminated Flow through an Unsaturated Wellbore

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.