The rock- and fracture mechanics aspects of the modelling of induced hydraulic fractures in porous rocks are discussed. A classification of the various models of fracture geometry is given, and the geotechnical mechanisms which potentially control the preferential fracture growth in different directions are discussed. The modelling capabilities now include the effects of highly heterogeneous (layered) distribution of confining stress and the effects of large apparent fracture toughness on the field scale. These factors are shown to have a pronounced effect on the shape of hydraulically created fractures and therefore on the effectiveness of well stimulation.
The field technology for hydraulic fracturing and other completion techniques (acidizing, perforating etc.) has become more complex. In the current economic environment, the cost effectiveness and optimum use of this technology is crucial for the economic success of projects. One of the key elements for predicting the effectiveness of fracturing treatments is the computation of the extension of the fractures during injection. The same problem must be solved in geothermal applications and in injection operations above parting pressure. In general, the problem of predicting fracture geometry involves geo-mechanical aspects, fluid flow in porous media (leak-off), transport of non-Newtonian fluids, proppant slurries or acids in the fracture, and heat transfer. In this paper, we will discuss the geo-mechanical aspects only, with emphasis on the conventional fracturing treatment applications.
The methods for fracture geometry calculation originated in the theory of tensile cracks of Griffith (1921), and were later expanded for pressurized cracks by Sneddon(1946) and Barenblatt (1962). In this classic work, summarized by Sneddon and Lowengrub (1969), the crack extension was assumed to be controlled by the properties of the material (characterized by fracture toughness, specific energy or critical stress intensity factor). The first applications to high viscosity fluids were developed by Christianovic and Zheltov (1955), Geertsma and DeKlerk (1969), and by Perkins and Kern (1961). The first two works solved the problem in a horizontal plane (for a vertical fracture), while the last solved the fracture opening problem in the vertical plane. These two basic models are referred to, throughout this paper, as CGD and PK-type 2- dimensional models. Both types of two-dimensional models have been accepted in the oil industry and improved. In CGD model, Daneshy (1973) has made a further step toward the simultaneous solution of pressure and fracture opening by introducing analytical pressure profiles instead of step change. For the PK model, Nordgren (1972) has given a numerical integration method which simultaneously solves the pressure drop and fracture opening (width) along the fracture. Cleary (1980) has developed closed-form solutions for both CGD and PK geometries which are quite rigorous except for the "self-similar" assumption which allows the approximation of the time-derivative of the capacity (storage) of fracture volume. Numerical 2-D models with various assumptions were presented by Advani (1980), Biot (1982), Travis (1981) and others. Settari (1980) presented a more general model coupled with reservoir flow and heat transfer.
