Model of kinematic waves for gas–liquid segregation with phase transition in porous media

Abstract

We consider the problem of gas–liquid flow with phase transition in a porous medium, governed by the buoyancy force. Free gas releases due to continuous pressure decrease. We take into account the gas expansion and the dissolution of chemical components in both phases controlled by the local phase equilibrium. We have developed an asymptotic model of flow for low pressure gradients in the form of a nonlinear hyperbolic system of first order with respect to the liquid saturation and the total flow velocity, which is the extended non-homogeneous Buckley–Leverett model. In two asymptotic cases determined by two different ratios between the characteristic times, this model is completely decoupled from pressure, i.e. the pressure enters in this model as a parameter determined through an independent formula. The segregation problem with phase transition in a bounded domain is solved for two cases of boundary conditions. The saturation behaviour is described in terms of nonlinear kinematic waves, whose evolution follows a complex segregation scenario, which includes the wave reflection and formation of shocks. The macroscopic gas–liquid interfaces are described in terms of shock waves. The comparison with numerical simulations shows satisfactory results.