Relation of Formation Rock Strength to Propping Agent Strength in Hydraulic Fracturing
Authors: McGlothlin B.B. , Hutt J.L. 
Published: December 2007

Abstract
The introduction of new fracture propping agents that are brittle but much stronger than sand created the problem of what loading strength is required for a propping agent to be effective in a given formation. It is shown that the load at which the propping agent crushes should exceed the load at which total embedment in the fracture faces is possible. Simple laboratory tests to determine loading strength of the propping agent and embedment in the fracture faces, and use of these data in selecting a propping agent for a given formation, are discussed.
Introduction
One of the most important factors in the design of hydraulic fracturing treatments is the selection of a propping agent that can effectively provide the fracture flow capacity needed for stimulation of a well. Sand, once generally accepted as being synonymous with propping agent in hydraulic fracturing, is now recognized as having limited effectiveness in many formations because of its low resistance to crushing. Sand particles are brittle and have relatively low strength. Because of this property, sand particles are crushed in rocks that offer high resistance to the penetration of fracture faces by the proppant particles when the fracture attempts to close under the action of the overburden load. For rocks that offer a high resistance to penetration, deformable particles are more effective propping agents than sand. However, for this same type of rock, a propping agent that does not deform, yet does not crush, is often more effective. Thus, a rigid propping agent with sufficient strength to prevent crushing is desirable. A method for determining the strength required for a rigid propping agent to function effectively in given formations is discussed.
BEHAVIOR OF RIGID PROPPANTS AND FRACTURE FACES RELATED STUDIES
An early qualitative description of the reaction of propping sand in fractures was given by Hassebroek et al. In discussing fracturing in deep wells, the authors mentioned that even though propping sand entered the fractures, a high flow capacity did not result due to crushing or embedding of the propping sand. Dehlinger et al. in discussing the reaction of propping sand surmised that, because of the hardness of sand particles, deformation occurred in the fracture faces contacting the propping sand. In later studies," methods of determining the embedment of propping sand in fracture faces of soft rock and the critical load at which propping sand is crushed by the fracture faces in hard rock were discussed. In working with deformable proppants, Kern et al. considered proppant articles to be deformed into cylindrical disks by action of the overburden and then pressed slightly into the fracture faces by further action of the overburden. Rixie et al. reported on embedment pressure and presented a method of selecting a propping agent for use in given formations. The propping agents included sand, walnut shells and aluminum pellets. All these studies have contributed materially to a better understanding of propping agent behavior; however, the strength of brittle proppants (sand, glass and ceramics) required to result in embedment rather than crushing has not been discussed. This topic will be covered in the ensuing discussion.
PROPPANT PARTICLE CRUSHING-EMBEDMENT
For this discussion, a rigid propping agent is considered to be one that is brittle and fails under tensile stress when loaded to a critical value. In an earlier study it was shown that the Hertzian loading theory could be applied to a spherical brittle propping agent if the propping agent and fracture faces behaved elastically. At the failure of the proppant, the ratio of the load to the square of the diameter of the particle should be constant for a given material combination, or:
(1)
A partial derivation of this equation from proppant and formation properties is included in the Appendix. Should a rigid particle not be crushed as a load is applied, it embeds in the fracture faces. A study of particle embedment in fracture surfaces has been published. The embedment can be described by an equation based on Meyer's metal penetration hardness relationships:
(2)
In Eq. 2, B and m are constants that are characteristic of the rock; the significance of the other terms is shown in Fig. 1.
JPT