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

Published online by Cambridge University Press:  22 September 2017

Stephane Zaleski  and
Mikhail Panfilov Open the ORCID record for Mikhail Panfilov [Opens in a new window]
Stephane Zaleski
Affiliation:
Institut Jean le Rond d’Alembert – CNRS/Sorbonne Universités, UMR 7190, Paris, France
Mikhail Panfilov*
Affiliation:
Institut Jean le Rond d’Alembert – CNRS/Sorbonne Universités, UMR 7190, Paris, France Institut Elie Cartan – CNRS/Université de Lorraine, UMR 7502, Nancy, France
*
†Email address for correspondence: michel.panfilov@dalembert.upmc.fr
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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.

JFM classification

Multiphase and Particle-laden Flows: Gas/liquid flow Low-Reynolds-number flows: Porous media Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 829 , 25 October 2017 , pp. 659 - 680
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Copyright
© 2017 Cambridge University Press 

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