Some Features of Fluid Filtration in a Hydraulic Fracture under Transient Well Operation Conditions

In this paper, exact analytic solutions of the set of equations describing fluid filtration in formations subjected to hydraulic fracturing are obtained under transient well operation modes. The cases, when the bottom hole pressure or the well flow rate changes were considered, taking piecewise constant values. These solutions are generalized for the case when the bottom pressure and the flow rate versus time are continuous functions. The solution makes it possible to determine the flow rate or bottom hole pressure according to the given pressure change law in the bottom or well flow rate and, as well as pressure evolution in the hydraulic fracture. In special cases, for example, with a pi-shaped change in the flow rate law, the solutions obtained from comparison of the field flow rate curves and bottom hole pressure make it possible to determine the conductivity of a hydraulic fracture. Good agreement is demonstrated between the theoretical pressure change curves constructed from the flow rate change data and results of field observations.