A robust type curve solution for analyzing pressure-transient behaviours of both vertical and horizontal fracture systems

Although there have been many analytical studies on pressure-transient behavior of hydraulic fracture systems, no single analytical solution capable of describing both vertical and horizontal fracture transient state behaviors has been developed. The purpose of this work is to develop a single analytical solution that is robust enough to fit this need. This paper presents a type curve solution for a well producing from a solid bar source in an infinite-acting reservoir with impermeable upper and lower boundaries. Computation of dimensionless pressure reveals that the pressure-transient behavior of any hydraulic fracture system is governed by two critical parameters (i) aspect ratio, m, and (ii) dimensionless length, L_D. Analysis of a typical log-log plot of p_wD vs. t_Dxf indicated the existence of four distinct flow periods (i) vertical linear flow period, (ii) fracture fill-up period causing a typical storage dominated flow, (iii) transition period, and (iv) radial flow period. As aspect ratio tends to zero, the first and second fracture fill-up periods disappear resulting in typical fully/partially penetrating vertical fracture pressure response. This analytical solution reduces to the existing fully/partially penetrating vertical fracture solution developed by Raghavan et al¹ as aspect ratio tends to zero, and a horizontal fracture solution is obtained as aspect ratio tends to unity.