Composite flows

Abstract

Composite flow models are an extension of the equations for a single compressible gas flows with multiple components, multiple phases, or multiple layers. Examples of such flows include the transport of oil, water, and polymers in porous reservoirs; separation of adsorbable solutes by chromatography; distillation columns; thermoclines in the ocean; multiphase flows in reactors; and separation of DNA fragments by electrophoresis. In many examples local equilibrium assumptions, such as Darcy's law or the Langmuir isotherm assumption, lead to nonlinear hyperbolic conservation laws which can be analyzed in terms of Riemann problems and elementary waves. In these cases front tracking algorithms show great promise for resolving very complicated wave interactions, in one dimension. We survey some of the recent developments in this field and present some computational examples. When local equilibrium assumptions are inappropriate, as is the case in many multiphase and multilayer flows, considerable difficulties, both theoretical and numerical, arise from the fact that the equations may be neither hyperbolic nor in conservation form. We give some examples of this and discuss the possibilities for analyzing these flows in terms of elementary and solitary waves.