Semianalytical solutions for fluid flow in rock joints with pressure-dependent openings

Abstract

If fluid is injected into joints in rock masses, the pressure required might result in changes in the joint space between rock blocks that accommodate the fluid transport. At one extreme, very low injection rate and pressure, the joint space is unaffected, and the fluid pressure follows the usual law of linear diffusion. At the opposite extreme, very high injection rates, as used, for example, during hydraulic fracturing, the pressure is so high as to overcome the original Earth stress holding the rock blocks in contact. They "lift off," resulting in huge changes in joint space, and the flow equation then becomes so nonlinear that pressure pulses are no longer transmitted in a smooth, diffusive manner but more like a propagating shock wave. In between these extremes, at more modest pressure, the result is not liftoff, but nevertheless, the effective stress tending to close the joint space is reduced; this space dilates, and the effective permeability and storativity of the joint will increase. While the pressure wave will not propagate quite as sharply as it does for liftoff, nonlinearities greatly influence the results, exhibiting behavior far from that predicted by linear diffusion.