We study nonlinear waves in two phase geochemical flow in one spatial dimension in porous media. We assume that each chemical species may flow in one or both phases with concentrations obeying thermodynamical equilibrium. We present a new methodology for reducing a number of equations applicable to injection problems for general systems of conservation laws in Geochemistry. This reduction is achieved by solving a nonlinear inverse problem. Nevertheless, we are able to perform a complete and explicit characteristic analysis, obtaining rarefaction and shock waves that are used to solve the representative Riemann problems, besides the main bifurcations structures appearing in the phase space are derived with explicit expressions. We illustrate the methodology by means of an example with four equations.
|Number of pages||49|
|Journal||Journal of Differential Equations|
|Publication status||Published - 2019|