Plasticity Effects in Hydraulic Fracturing
Authors: Medlin W.L. , Masse L. 
Published: December 2007

Summary
The importance of reservoir rock plasticity in fracturing operations has been investigated by laboratory experiments and field results. A Lagrangian formulation for crack propagation provided the basis for the laboratory experiments. A simple crack propagation experiment showed that plasticity effects can be observed and that the importance of plasticity depends on the relative magnitudes of surface energy and energy plasticity depends on the relative magnitudes of surface energy and energy dissipated in plastic deformation of the reservoir rock. The latter can be evaluated by laboratory measurements of a plasticity coefficient, et, which comes out of the Lagrangian analysis. To measure et, we developed a triaxial system for applying tensile stress to rock cores under confining pressure at strain rates characteristic of fracturing operations. Strain pressure at strain rates characteristic of fracturing operations. Strain gauges mounted on each core were used with a servo-controlled press to apply strain at a linear rate between 10–4 and 10–6 seconds -1 and to obtain stress/strain data to the point of tensile failure. To distinguish between plasticity and nonlinear elastic phenomena, we also obtained strain hysteresis data. These methods were used to evaluate et in a variety of cores from reservoirs where fracturing treatments had been conducted. This survey showed that severe plasticity can be found in some, but not many, cases. The Lagrangian theory predicts that plasticity will show up in fracturing records as abnormal treating pressures and will result in fractures that are shorter and wider than normal. All these effects have been observed in massive fracture treatments in the Piceance basin, and modest treating-pressure increases have been observed in Muddy-J fracture treatments in the Denver basin. We found only slight plasticity, however, in well cores from these formations. Severe plasticity was found in some deep carboniferous cores from the Oldenberg field in north Germany. However, the expected fracturing problems were found in only one well. We attribute this to sampling problems connected with inhomogeneous formation properties. We conclude that plasticity can explain fracturing problems in properties. We conclude that plasticity can explain fracturing problems in some, but not many, reservoirs and that core analysis is not a very practical means of anticipating it. practical means of anticipating it.

Introduction
The effect of rock plasticity in hydraulic fracturing has generally been ignored. The importance of plasticity in shales has been recognized by Perkins, who considered effects in competent rock unimportant. All the Perkins, who considered effects in competent rock unimportant. All the commonly used theories of fracture propagation treat reservoir rocks as ideally elastic materials. Even surface energy effects in crack extension have been neglected except in some early work by Perkins and Bartlett and Perkins and Krech. Probably the chief reason for ignoring these phenomena is that they are not easily incorporated into the theoretical phenomena is that they are not easily incorporated into the theoretical approaches previously used. The Lagrangian method, which is presented in an earlier paper, provides a means of including plasticity and surface energy in fracturing provides a means of including plasticity and surface energy in fracturing theory. However, to apply it we must have a basic understanding of plastic behavior in reservoir rock under tension. The literature contains little information on this subject. Essentially, all the work on plastic deformation of rocks has been done in compression. This paper presents experimental results from both field and laboratory work to provide at least a start in understanding the tensile plastic properties of rock materials. We have used these results along plastic properties of rock materials. We have used these results along with the Lagrangian method to evaluate the practical importance of plasticity in conventional fracturing operations. Our conclusions are less plasticity in conventional fracturing operations. Our conclusions are less than definitive. It appears that plasticity is important in some, but not many, reservoirs of modest depth. As fracturing methods are extended to greater depths and more unconventional types of rock formations, however, we can expect plasticity effects to become more important. Therefore, refinement of the theory and collection of additional experimental data are clearly worthwhile.

The Separation Energy
The separation energy was introduced in the Lagrangian analysis of fracture propagation presented earlier. It appears there as a consequence of the propagation presented earlier. It appears there as a consequence of the virtual work principle and has been formulated as consisting of two parts, a surface energy, and a plasticity term, :
............................(1)
This relation is consistent with the principle of energy conservation. The crack extension energy is the sum of the energy required to generate new surface at the crack tip and the energy spent in plastic deformation before tensile failure occurs. The surface energy is twice the surface tension, defined by Griffith and others because two surfaces of unit area are created per unit length of crack extension. p. 995