Fractured water injection wells: Pressure transient analysis

In this paper we study the pressure drop in a hydraulic fracture after shut-in of a water injection well. The pressure transient behavior depends on fracture closure, lateral stress, rock elasticity and fracture fluid leak-off. Under the assumption that horizontal cross-sections of a vertical fracture do not depend on the vertical variable, we formulate a mathematical model which allows for determination of both pore pressure and elastic rock displacements jointly with the fracture aperture and fracture fluid pressure. An analytical consideration is performed for the case of an ideal very long fracture with the same aperture along its full length. In the general case, fracture closure is analyzed numerically.