This paper presents a derived stress ratio which permits the identification of the extent of the regional permits the identification of the extent of the regional tectonic forces acting upon a formation. Once identified, these tectonic forces allow certain inferences to be made about the maximum potential of natural fracturing present in a formation. Investigation of three gas producing formations in the Appalachian Basin shows that the Berea sandstone, the Clinton sandstone and the Devonian Shale all display a similar tectonic relationship. This leads to the conclusion that much of the Basin can be categorized into different stress regions with each region relating the degree of natural fracturing present.


The in-situ stress field acting upon a particular formation can be defined if the three principle stresses can be calculated (Figure 1). Hubbert, Kehle, Haimson and Fairhurst, and others have shown that the pressures obtained during hydraulic fracturing operations can be related to the magnitude of these in-situ earth stresses. This work provides a basis whereby selected dynamic and static treatment pressures are used to determine the principal stresses acting upon an induced vertical crack.

Once determined, these principal stresses can then be used to develop a regional stress ratio (or fracturing gradient). This stress ratio, in turn, provides a means of defining the degree of natural fracturing that exists in a formation by defining the degree of tensional relief present.


If the formation being hydraulically stimulated is an isotropic, elastic medium, a pressure-created vertical crack will propagate in a plane perpendicular to the minimum compressive in-situ principal stress. The pressure required to hold this vertical crack open will be a measure of the minimum horizontal stress acting normal to it. According to the solution for an elastic medium for a pressurized cylindrical cavity proposed by Hubbert and Haimson and Fairhurst, the proposed by Hubbert and Haimson and Fairhurst, the entire stress field can be calculated as follows:




where sigma HMAX is the maximum compressive stress in the horizontal plane, sigma HMIN is the minimum compressive stress in the horizontal plane and sigma V is the total overburden stress. The empirically derived values acquired from the hydraulic fracturing treatment to satisfy the equations are: the breakdown pressure (Pb) obtained early in the treatment after the initiation of the induced fracture, and the instantaneous shut-in pressure (Ps), obtained immediately at the termination pressure (Ps), obtained immediately at the termination of treatment when pumping ceases. The tensile strength (To), bulk density (), formation thickness (H), and pore pressure (Po) are formation-specific properties pore pressure (Po) are formation-specific properties and are readily available through standard techniques.

It should be noted that Equations (1) and (3) are valid only for instances where the fracturing fluid used does not penetrate the matrix of the formation to any significant degree. Also, Equations (1), (2), and (3) are not applicable if the vertical overburden stress (sigma V) is less than the minimum horizontal stress (sigma HMIN), in which case the induced fracturing will be in a horizontal direction.


Utilizing the above concept, a stress ratio can be determined for any formation or for any region, based on pressure data from hydraulic fracturing treatments. The basic conditions under which this analysis applies are that the fracture created:

  1. is essentially vertical and of constant heightduring propagation

  2. is in a quasi-elastic formation

  3. extends continuously when fluid is being pumped and stops growing when pumping stops

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