Hydraulic fracture propagation under high compressive stresses in rock is considered. An ideal case of a Griffith crack propagating in an ideal material has been calculated by Dr. Joseph Walsh. This ideal case is used to estimate stepwise or continuous fracture propagation for different fracture fluids for a rock with stiffness and strength simulating a shale at a depth of about 6000 feet. More compressible fluids such as CO2 and nitrogen foam show larger stepwise propagation with steps of possibly tens of feet. Indeed rocks are not ‘ideal’ materials, nor are insitu stress magnitudes uniform and continuous. Nevertheless, the calculations here present interesting perceptions of the role of the compressibility of fracture fluids on hydraulic fracture propagation.
Hydraulic fracturing for oil/gas well stimulation involves fluid driven fractures that propagate under high compressive insitu stresses. The process is particularly complex in heterogeneous and discontinuous rock formations such as the shales. Because of the great importance of the problem, much research has been performed to model such fracture propagation. In the research, practitioners have attributed fluctuations in treatment records -- with varying amplitudes and frequencies -- as indicative of local or larger scale heterogeneity and consequent propagation complexity. However, in considering different time scales in the fracture propagation, other complexities exist with which we are familiar. For example, the so-called dry zone near the fracture tip is a classic situation where the fracture may grow faster than the fracture fluid can progress. After the fracture is arrested, the fracture fluid can partially or completely ”catch up” with the fracture tip, and another discrete propagation step may occur.