Hydraulic Fracture Propagation in Layered Formations

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Abstract
This paper reports theoretical and experimental developments involving propagation of hydraulic fractures in layered formations. Unobstructed fractures are shown experimentally to propagate with a decreasing fracturing fluid pressure. This general trend is in agreement with pressure. This general trend is in agreement with theoretical predictions. Restrictions in fracture propagation result in an increase in fluid pressure. propagation result in an increase in fluid pressure. The relative fracturability of rocks can be determined by a direct experiment, the results of which are clear, easy to interpret, and include all pertinent parameters, such as physical and pertinent parameters, such as physical and mechanical properties of rocks, as well as the reactions between formation and fracturing fluid (for example, leak-off). Fracturing experiments with layered samples show that with strong bonding between rocks it is difficult to contain a fracture in a formation totally. The strength of the interface between adjacent formations is shown theoretically to be an important factor in fracture containment. With a weak bonding, fracture containment is possible and is associated with slippage at the interface. The pattern of propagation then will depend on the relative propagation then will depend on the relative mechanical properties of fractured formations. Introduction: Most industrial hydraulic fractures are created in layered formations. During propagation, these fractures encounter various formations with different physical and mechanical properties. This paper physical and mechanical properties. This paper discusses the effect of those properties on propagation of the fracture. propagation of the fracture.Most of the theoretical studies on fracture propagation have been extensions of Griffith's propagation have been extensions of Griffith's work. Based on an energy criterion, Griffith developed a relationship among fracture shape, material properties, and the external force needed for fracture propagation. The energy source in hydraulic fracturing is the fluid pressure inside the fracture. The relationship between this pressure and material properties is (1) (2) in which L = fracture extent (length of a two-dimensionalfracture or radius of a penny-shapedfracture) E = Young's modulus of material mu = Poisson's ratio of material gamma = effective fracture surface energy of material sigma = least in-situ principal stress A similar equation for a three-dimensional fracture is derived in Appendix A in the form of (3) in which hf = fracture height E(k) = complete elliptic integral of the secondkind K(k) = complete elliptic integral of the first kind k = parameter of the elliptic integrals Eqs. 1 through 3 show p to decrease with increasing L (Fig. 1) As the fracture becomes larger, it needs less pressure for propagation. In deriving these equations, no allowance has been made for fluid leak-off into the formation. SPEJ P. 33

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