Fracture Penetration Through an Interface

Abstract

Abstract This paper presents a combined theoretical and experimental investigation of fracture penetration through an interface. The results have application to hydraulic-fracture containment in sandstone or limestone reservoir strata bounded by shale layers. Several simplifying assumptions and approximations are made. We assume that the interface separates dissimilar but adhering materials that are elastic to first order. We consider only differences in material properties and take stresses to be locally uniform. Approximations are made that reduce the fourth-order equation of plane strain elasticity to the second-order Laplace equation. Crack shape is taken to be sinusoidal and fluid leak off is ignored. Additional simplifying assumptions are made about the shape of the crack tip as it passes through the interface. Using a virtual work analysis, we derive a relation for internal fluid pressure required to extend the crack through the interface. This pressure is related to the equilibrium pressure needed to hold the crack barely open. A simple relation is obtained involving only the shear modulus and surface energy of the materials on either side of the interface. The theory was tested in laboratory experiments with Plexiglas/resin bonds. Test blocks of several configurations were used with various kinds of external loading. Cracks were initiated by applying grease pressure in thin notches. Pressures required to hold cracks in equilibrium were compared with those required to penetrate interfaces. Results were consistent with the theory within limits of precision in measuring surface energy. We conclude that the theory explains field observations of containment in a number of reservoirs that have been fractured hydraulically. However, practical value is limited by inability to estimate surface energies from logging or other wellbore data. Introduction Fracture penetration through an interface is of fundamental importance in hydraulic fracturing operations. The question of how far a fracture grows vertically during a fracturing treatment is basic to all design and optimization considerations. In a fairly homogeneous formation, such as granite, unlimited vertical growth might be expected. This would lead to a penny-shaped crack of the kind expected for horizontal fractures. In layered, sedimentary rock, vertical growth requires penetration through interfaces between layers. If penetration is prevented at interfaces near the injection layer, the fracture will be contained and constant height thereafter. Constant-height fracture geometries have been assumed in most theories of fracture propagation. Field results, notably temperature logs, have long indicated that this constant-height assumption is reasonable. Many of these logs can be explained only by the existence of some kind of barriers to vertical fracture propagation. These considerations introduce the problem of crack penetration through an interface in a layered medium. This problem has received considerable attention already. It has been treated for both ideally elastic laminar materials and layered rock materials. Several studies have addressed the problem of a crack approaching an interface in a bonded-layer elastic material. These works have focused mainly on the nature of the singularity at the crack tip as it approaches the interface. The methods used have been based on the stress intensity concept introduced by Irwin. A similar approach has been used to treat the penetration problem in rock layers. Other studies have dealt with the fracture containment problem in reservoir rock be using the stress-intensity factor to evaluate penetration criteria. Our approach is much different. We use linear elasticity theory applied along the lines developed by Griffith for homogeneous materials. SPEJ P. 857^