Investigation of the transition to instability of the water boiling front during injection into a geothermal reservoir

We discuss the stability problem for a boiling front moving at a constant speed in a porous permeable geothermal reservoir. We study the dispersion equation obtained by the method of normal modes. The decay of unstable small perturbations corresponding to large values of the dimensionless wave number is shown analytically. We construct neutral stability curves in the plane of the main parameters. The evolution of the neutral curves with changing parameters shows that an increase in the permeability and initial temperature, as well as a decrease in porosity and initial pressure, leads to an expansion of the instability region. We investigate the dependence of the critical dimensionless wave number on the permeability of a porous medium at which the transition to instability occurs. The obtained critical values give an estimate of the characteristic size of the most unstable perturbation, which varies depending on the process parameters. This size ranges from half a meter to several meters at characteristic values of the geothermal reservoir parameters. Possible types of transitions to instability of the interfaces in filtration problems are discussed.