The effect of solid phase precipitation from a hydrothermal solution on the sealing of cracks and the permeability evolution of the system

The sealing of a hydrothermal crack or a system of such cracks due to solid phase precipitation in a hydrothermal solution is considered. A system of nonlinear equations describing this process for a solution flowing through a crack system in a cold rock: mass is derived. This system of equations determines the variation in the fluid temperature and the crack profile for a given variation in the fluid temperature at the crack entry. It is shown that, under specific conditions (a sufficiently high fluid flow velocity), the temporal variation in the width of a crack at its base is determined from a simple quadrature. The problem of the complete crack profile determination is more complicated and requires the solution of a nonlinear integro-differential equation. Various formulations of the problem are considered (a Poiseuille flow of the fluid with a relatively smooth variation in the crack profile and a given pressure drop, as well as the case with a given variation in the fluid flow flux with time). Analytical and approximate solutions are obtained for the fluid temperature varying in time by various laws and are used to estimate the permeability evolution of a hydrothermal system on a characteristic time scale of crack sealing due to silica precipitation in a hydrothermal solution. Relations describing the response of the system to periodical variations in the inlet fluid temperature are obtained.