It is generally accepted within the petroleum industry that hydraulic fractures propagatealong a vertical plane at depth due to the stress fields which exist in the earth. The capability also exists for predicting the degree of containment which can be expected during ahydraulic fracturing operation, given reservoir and fluid properties, and anticipated injection rates and pressures.
The question of the prediction of the azimuth of fracture propagation, however, is one Which has only recently been addressed by the industry. Various methods have been employed to predict and/or measure the azimuth of fracture propagation. Amoco's experience is that the method ofmeasuring borehole deformation through the useof oriented four arm caliper logs will allow an analysis of the horizontal stresses which exist within the earth. Once the orientation and relative magnitude of these stresses is known, it becomes possible to predict the azimuth of induced fractures.
The method is simple, inexpensive, and appears to show a high degree of reliability.
The production implications have been demonstrated in published studies which show potential recovery increases up to 25 percent in tight gas sands if the well pattern and spacing are adjusted to take advantage of hydraulic fractureorientation. Preliminary studies also indicate that waterflood oil recovery can be increased by proper location of wells with respect to fracture azimuth. The theory and method for using the four arm caliper tool are discussed with specific reference to field applications.
In order to appreciate the concept of using borehole deformation to predict hydraulic fracture azimuth it is necessary to have a basicunderstanding of the stresses which can occur in the earth and the manner in which these stresses control fracture azimuth and borehole deformation.
Stress is similar to pressure; it is a force per unit area. What differentiates stress from pressure is the fact that stress is a force per unit area in a given direction whereas pressurehas no orientation. Stress is a tensor quantity; pressure is a scalar quantity.
The concept of stress as used in rock mechanicsis very similar to that which is used in the theory of elasticity and continuum mechanics. However, in rock mechanics, compression is usually assigned a positive sign convention and tension a negative sign. This is opposite to the convention normally used in the theory of elasticity and continuum mechanics.
Consider the general case of a small, square body such as that shown in Figure No.1 subject to the stresses σx, σy, Tyx and T xy (For amore detailed derivation of these equations see References 1 and 2.) In order for equilibrium to exist the sum of all the compressive and shear stresses which act upon this body must equal zero. Therefore T must be equal to T. Now if a new series of axes x1, yl are considered, rotated at some angle e from the x axis (Figure No.2) the equations of stress on an infinitesimal unit square can be rewritten as follows:
