An integral method for predicting hydraulic fracture propagation driven by gases or liquids

Abstract

SUMMARYHydraulic fracture propagation is predicted by a general numerical procedure which satisfies the transport equations in a global or integral sense over theentire fracture and over a small control volume near the leading edge. At each discrete time step the pressure distribution is selected from a four-parameter family of profiles such that the stress intensity is equal to the critical value at the tip of the fracture and the integral equations are satisfied. Comparisons with previous analytical and numerical solutions indicate accuracy within 10 per cent for a variety of test problems include wedge-shaped and envelope-shaped fractures, laminar and turbulent flows, incompressible liquids and ideal gases, permeable and impermeable media, prescribed inlet pressure and prescribed flow rates. CPU time is typically a few seconds for a tenfold increase in fracture length. The method has been applied to explosively driven and propellant-driven gas fracturing problems as well as the traditional pumpdriven hydraulic fracturing problem.

On dynamic gas pressure induced fracturing

“…A number of experiments were conducted to validate an analytical/ numerical technique elaborated by Nilson (1986) and extended by Daehnke et al (1996) to model the gas flow in propagating fractures. For this purpose models were designed such that a single penny-shaped crack propagates from a centrally located borehole.…”

Rock fragmentation by blasting—a literature study of research in the 1980′s and 1990′s

“…Fracture extension can confidently be assumed to be due to pressurisation by combustion gases in these conditions. Physical modelling studies of such sophistication combined with a parallel theoretical explanation of the observed gas driven dynamic fracturing, based on the work of Nilson (1986) in which the dynamic material properties of PMMA were substituted, has reinforced currently accepted theory that give a primary role to the gas driven fracturing during blast fragmentation. The numerical model of blasting, given by Daehnke et al (1997) was also applied to the problem of confined well-bore stimulation, giving crack extension predictions for different rock properties, but is currently not appropriate to examine rock disaggregation processes that create blastpiles.…”

“…The ideal detonation codes of Braithwaite et al (1996) enable better estimates of starting conditions in the blast, while others (e.g. Nilson 1986, Munjiza et al 1999, have elaborated upon formulations for gas flow laws that will enable the incremental time history of the gas pressure within an expanding gas occupying and driving a growing network of fractures, to be approximated. The research is largely analytical theory combined with empirical constants that have been calibrated from experiments designed to determine the properties of the explosives.…”

Role of Turbulent Flow in Generating Short Hydraulic Fractures With High Net Pressure in Slickwater Treatments

“…Firstly, we acknowledge that there are almost certainly capabilities to model some form of turbulent flow in a number of proprietary hydraulic fracture simulators. Also, there is a small body of literature on gas-driven and other low-viscosity fluid-driven hydraulic fractures which account for high Reynold's number flow (Nilson 1981,1986, Emerman et al 1986, Huang et al 1990, Anthonyrajah et al 2013. But, this being said, the overall research direction driven by shale reservoir stimulation has been aimed at topics related to hydraulic fracture growth in naturally-fractured rock and from multiple injection points (e.g.…”