Nondissipative shock waves in two-phase flows

It is shown that the Korteweg-de Vries equation which describes dissipationless processes can occur also in the system of equations of multiphase hydrodynamics when dissipation is compensated by external supply of energy. Therefore all the phenomena which are characteristic for the Korteweg-de Vries equation (solitons, periodic waves, nondissipative shock waves) can occur also in multiphase hydrodynamics. The study analyzes in particular the phenomenon of formation of nondissipative shock waves. It is shown that multiphase filtration is accompanied by formation of a continuously expanding region with small scale undamping oscillations of phase composition and velocity. The analysis uses the Korteweg-de Vries equation which is derived from the system of conservation laws describing multiphase hydrodynamics in porous media. Obtained results are relevant for the analysis of multiphase filtration (viscous fingering in the hydrocarbon recovery process) and in the hydrodynamics of fluidized bed (formation of bubbles).