Convective instabilities in vertical fractures and faults

Abstract

Natural convection of water contained in a vertical fracture or fault in which the temperature increases with depth is strongly influenced by the heat transport processes not only within the water itself but also by the heat transferred to and from the surrounding rock mass. The results of a linear stability analysis indicate that the critical Rayleigh number R* is time dependent. For spontaneous neutral stability, R*(t = 0) ≅ 10(h/a)2, where h and a are the fault height and aperture, respectively. Since h ≅ a, R*(0) is several orders of magnitude greater than the value 4π2 that would pertain to the same situation without the influence of the surrounding rock masses, e.g., a porous bed with large horizontal dimensions. The resultant cell motion consists of rolls about axes parallel to the aperture. These rolls are of height h and closely spaced in the strike direction. Cases of spontaneous instabilities in fractures or faults are expected to be infrequent, but initially subcritical convection could be fostered by other means such as tectonic displacements at the fault. Because R* diminishes as time−½, eventually, this subcritical convection becomes unstable, and exponential growth ensues. As the heat of the surrounding rock is depleted and an isothermal state is approached, the convection eventually dampens until a period of thermal recovery allows its resumption.