Evolution of Filtration Pressure Waves in a Hydraulic Fracture during Transient-Well-Operation Modes

At present, a significant part of oil is extracted from difficult-to-develop reservoirs with low permeability. Hydraulic fracturing is one of the most important methods of production stimulation. Scientific articles do not describe the connections between the flow-rate in the well and the change in pressure in the hydraulic fracture or between the changing pressure in the well and the pressure in the hydraulic fracture, except in some cases of constant fluid-flow in the well and constant production. We obtained both the exact analytical solutions and the simple approximate solutions which describe the connection between the well-fluid flow-rate and the pressure evolution in a fracture. The work has also solved the inverse problem: how to determine the parameters of a hydraulic fracture, knowing the change in well flow-rate and the change in fluid-flow. The results show good comparison with practical data.