Mathematical Model of Fluid Exchange between Reservoirs and Hydraulic Fractures and Its Application

Hydraulic fractured wells are commonly applied to low permeability reservoir development. The numerical model of fractured wells flowing in reservoirs was established to describe the law of the fluid exchange. The 2-D reservoir model and the 1-D fracture model coupled to a whole by the coefficient of the fluid exchange. And the numerical model was solved by the finite difference method. For the reservoir whose permeability is 1 × 10^-3 μm² and the flow conductivity of hydraulic fractures is 1 D.cm, the drainage capacity of fractures is lower than fluid supply capacity of reservoirs. While the reservoir permeability is 1 mD and the flow conductivity of hydraulic fractures is 10 D.cm, the drainage capacity of fractures is equivalent with the fluid supply capacity of reservoirs. With the increase of the flow conductivity of hydraulic fractures, the cumulative productions of fractured wells increase. But with the conductivity increases to a value, the increasing range of cumulative productions is not significant. Therefore, for the reservoir of certain a permeability, there is a economical range of fracture conductivity.