Modeling of the fluid filtration for hydraulic fracture conditions

We research the process of fluid filtration to bore under the hydraulic fracture conditions. This fracture is presented as the thin ellipsis crossing the bore. Use the theory of complex- valued functions allows finding the accurate solution of this problem and obtaining the analytic expression for the skin factor value which shows the influence of hydraulic fracture on well efficiency. In conclusion we introduce the simple formulation of this problem, when the hydraulic fracture is presented as zero-thickness notch having the finite conductivity.