Numerical Investigation of Conjugate Flow, Heat and Chemical Transport Processes in Underground Cavities Partially Filled with Molten Rock

A transient numerical study of conjugate flow, heat and mass transfer by natural convection of gases - air, carbon dioxide, noble gases - within an underground cavity partially filled with molten rock is presented. The molten rock is initially considered to be at rest at an initial temperature and concentration. The molten rock is viscous and possesses strength that is temperature, viscosity, and crystal fraction dependent. Under natural conditions, convection cells are developed within the molten rock leading to circulation, mixing and degassing of the initially trapped gases. Furthermore, the molten rock as well the degassing enhances the conjugate convection flow in the air gap above the molten rock within the cavity and promote Bénard-Rayleigh-Taylor instabilities. We illustrate the onset of the different regimes of instabilities and their combined effect of flow, heat and mass transport of different gas species as function of the geometry of the cavity and the fraction of molten rock. The transient governing equations of mass, momentum, heat and chemical species were solved using the finite element method. Several numerical coupling schemes are presented, and numerical stability conditions are illustrated. We also present a sensitivity analysis of the effect of the outer cavity boundary condition on the heat loss and cooling to the adjacent rock formation and its effect on the convective mixing topology with the air gap and the molten rock.

This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.