While many factors may influence fracture-height evolution in multilayer formations, the consensus is that the so-called “equilibrium height belonging to a certain treating pressure” provides an upper limit, at least for nonnaturally fractured media. The authors have revisited the “equilibrium-height problem,” and their theoretical and numerical investigations led to a new model that fully characterizes height evolution amid various formation properties.
Introduction
Solutions for the equilibrium-height problem have been known since the 1970s, and several models have been developed for calculating hydraulic-fracture height. However, because of the complexity of the algebra involved, the equations used in these early models were overly simplified and gave unreliable results.
The authors developed an improved, mathematically rigorous model that, for the first time, solves the equilibrium height under various formation-property conditions and fluid properties. The authors started from the definition of fracture toughness, incorporated the effects of hydrostatic pressure, and considered nonsymmetric variations of layered formation properties.
