NONREACTING CHEMICAL-TRANSPORT IN 2-PHASE RESERVOIRS - FACTORING DIFFUSIVE AND WAVE PROPERTIES

The vertical transport of mass, energy and n unreacting chemical speci es in a two-phase reservoir is analysed when capillarity can be ignore d. This results in a singular system of equations, comprising mixed pa rabolic and hyperbolic equations. We derive a natural factorisation of these equations into diffusive and wave equations. If diffusive or co nductive effects are important for only N - 1 of the chemical species, then there are N parabolic equations, and n + 2 - N wave equations. E ach wave equation allows for the corresponding variable to be disconti nous, or equivalently, for shock propagation to occur. Steady Rows wer e shown to allow for more than two (vapour and liquid dominated) satur ations for a given mass, energy and chemical flux, but when thermal co nduction and chemical diffusion are unimportant, only the vapour and l iquid dominated cases appear likely to occur. For infinitesimal shocks there is a continuous flux vector for each diffusive variable. The ex istence of these continuous flux vectors results in significant simpli fications of the corresponding wave equations. It remains an open ques tion if continuous flux vectors exist for finite shocks. General expre ssions are obtained for the diffusion and wave matrices, which require no knowledge of continuous flux vectors.