Abstract
One of the main problems in hydraulic fracturing technology is the prediction of fracture height. In particular, the question of what constitutes a barrier to vertical fracture propagation is crucial to the success of field operations. An analysis of hydraulic fracture containment effects has been performed. The main conclusion is that in most cases the fracture will penetrate into the layers adjoining the pay zone, the depth of penetration being determined by the differences in stiffness and in horizontal in-situ stress between the pay zone and the adjoining layers. For the case of a stiffness contrast, an estimate of the penetration depth is given.
Introduction
Current design procedures for hydraulic fracturing of oil and gas reservoirs are based predominantly on the fracturing theories of Perkins and Kern, Nordgren, and Geertsma and de Klerk. In the model proposed by Perkins and Kern, and improved by Nordgren, the formation stiffness is concentrated in vertical planes perpendicular to the direction of fracture propagation, The fracture cross section in these planes is assumed elliptical, and the stiffness of the formation in the horizontal plane is neglected. In the model proposed by Geertsma and de Klerk, the stiffness of the formation is concentrated in the horizontal plane. The fracture cross section in the vertical plane is assumed rectangular, and the stiffness in the vertical plane is neglected. In both models, the fluid pressure is assumed a function of the distance from the borehole, independent of the transverse coordinates. The theory by Perkins and Kern is more appropriate for long fractures (L/H >1, where L and H are length and height of the fracture), whereas the model by Geertsma and de Klerk is applicable for short fractures, L/H less than 1. The main shortcoming of these fracture-design procedures is that they assume a constant, preassigned fracture height. H. The value of H has a strong influence on the result, for fracture length, fracture width, and proppant transport. Usually, the estimated fracture height is based on assumed "barrier action" of rock layers above and below the pay zone. This situation is rather unsatisfactory. Moreover, if these layers do not contain the fracture, large volumes of fracturing fluid may be lost in fracturing unproductive strata, and communication with unwanted formations may be opened up. Whether an adjacent formation will act as a fracture barrier may depend on a number of factors: differences in in-situ stress, elastic properties, fracture toughness, ductility, and permeability; and the bonding at the interface. We analyze these factors with respect to their relative influence on fracture containment. Differences in in-situ stress and differences in elastic properties affect the global or overall stress field around the fracture, and, hence, the three-dimensional shape of the fracture. This shape, together with the horizontal and vertical fracture propagation rates, determines the fluid pressure distribution in the fracture, which in turn affects the stress field around the fracture. Consequently, the elastic stress field, the fluid pressure field, and the fracture propagation pattern are intimately coupled, which makes the fracture propagation problem a complicated one. Whether at a certain point of the fracture edge the fracture will propagate is determined by the intensity of the stress concentration at that point. This stress concentration depends on the global stress distribution in and around the fracture, but it also is affected directly by local ductility, permeability, and elastic modulus in the tip region.
SPEJ
P. 341^
In-Situ Stress Measurements and Stress Accumulation Level Analysis of Coal Mines in Northern Ordos Basin
