Rayleigh convection, mass transport, and change in porosity in layers of sandstone

Abstract

The critical Rayleigh number for the onset of thermal convection in a quartz‐rich sandstone layer is discussed for different thermal boundary conditions. The mass transfer of silica due to Rayleigh convection is computed, assuming that the solution is saturated with respect to quartz and that the silica concentration is a function of temperature only. Since quartz solubility increases with temperature, silica is dissolved from the sandstones in the lower part of the layer where the fluid is being heated and precipitated in the upper part where it is cooled. The change in porosity is found as function of the vertical coordinate, valid for small values of time. It is shown that for small supercritical Rayleigh numbers the time for the porosity to change up to 10% of its initial value is of the order 10 m.y. The spatial variation in porosity should be a characteristic signature of Rayleigh convection and should be easy to recognize if convection has taken place for significant geological time.