Natural convection of water in thick geothermal layers, across which there are temperature differences as large as 345 K and pressure differences as great as 1 kbar, is investigated. Complete account is taken of the variable thermodynamic and transport properties of water as well as of non-Boussinesq effects. The increase of thermal expansivity with temperature by as much as a factor of 70 and the decrease of viscosity by more than 1 order of magnitude are primarily responsible for the enhanced instability to convection of a water-saturated porous layer compared with a porous layer saturated with a Boussinesq fluid having the constant properties of surface water. The critical Rayleigh number, critical wave number, and streamline and isotherm patterns are determined at the onset of convection for temperature gradients of 25, 50, 75, 100, 150, and 200 K/km in layers as thick as 10 km. The critical surface Rayleigh number is reduced by as much as a factor of 31 below the value of 4&pgr;2 appropriate for a constant property Boussinesq fluid. Variable water properties thus allow convection to occur for smaller vertical temperature differences in rock of a given permeability or for smaller permeability at a given temperature difference. The horizontal scae of convection is somewhat reduced, and the flow is concentrated toward the bottom of the porous layer by effects of variable expansivity and viscosity. |