The Energy Balance Concept of Hydraulic Fracturing

This paper explains the concept of a damaged region arising from high stress concentration at the leading edge of a hydraulically created fracture. Approximate stresses near the tip of the crack are calculated, and it is shown that a stable crack shape is possible for which all stresses are finite. A new energy balance is derived incorporating these thoughts, and it is shown that predicted fracturing pressures (using surface energies determined by cleavage) agree with experimental fracturing pressures determined in models. All calculations apply to the case of a nonpenetrating fluid. It is concluded from these studies that in some cases, particularly in small laboratory models, these phenomena significantly affect extension pressures and crack widths. Introduction One of the perplexing questions about hydraulic fracturing that has not been satisfactorily answered is, what pressure is necessary to extend a fracture? For many engineering problems involving failure, it is sufficient to calculate those loading conditions which would bring a stress or elastic strain within the material to a level that could not be tolerated. However, this approach is not useful when considering a sharp-edged crack; calculated stresses and elastic strains always reach infinitely large values near the tip of the crack if fluid pressure is applied all the way to the crack extremity. This difficulty has led to the concept of cohesiveness or absorption of surface energy, implying that behavior near the tip of the crack is not purely elastic. Additional note of the nonideal behavior of rocks will be made in this paper. Then, by simplifying and dealing with an average stress in an inelastic region, the approximate stress distribution around a hydraulic fracture will be calculated and the conditions under which a stable fracture can exist will be shown. A new energy balance equation is then derived incorporating the modified stress picture. Finally, predicted fracture extension pressures are compared with breakdown pressures obtained in laboratory models. This comparison shows that surface energies measured by the cleavage technique are consistent with those values manifested during fracture extension. PROBLEMS OF INDUCED STRESS It will be revealing to consider first the calculated stresses around a penny-shaped line crack, assuming that the rock behaves as a linear, elastic material. Fig. 1 shows the stress distribution in the plane of the crack as calculated with Sneddon's equation. If pressure p is applied uniformly within the crack, then infinitely large tensile stresses would be induced in the rock near the crack tip. Such stresses could not be sustained in a real material. Two approaches have been proposed to explain this dilemma. SPEJ P. 1ˆ