Unsteady flow in a reservoir with a main fracture crossing an injection or production well

The problem of instantaneous injection or withdrawal of Newtonian fluid through an injection or production well into an infinite reservoir with a vertical main fracture of constant width at a given constant bottomhole pressure and constant reservoir pressure is considered. Analytical solutions are obtained for the pressure fields in the fracture and reservoir during injection or withdrawal of fluid, as well as for the flow velocity in the fracture. An explicit expression for the fluid leak-off (leak-in) from the fracture into the reservoir (from the reservoir into the fracture) and equations of particle trajectories in in the fracture and reservoir are obtained. For the solutions obtained, graphs are plotted for the pressure fields, fluid velocity distributions in the fracture, and fluid leak-off from the final fracture into a finite reservoir for different reservoir permeabilities.