The determination of tectonic stresses through analysis of hydraulic well fracturing

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The well-fracturing operation is modeled by a band of uniform pressure and two bands of uniform shear stress acting in a cylindrical cavity in an infinite body. Two interesting regions of induced stress are: either end of the pressurized interval where the tangential stress is zero (the vertical stress is approximately 95 per cent of the pressure) and the center of the packed-off interval where the tangential stress equals the pressure (the vertical stress is zero). The tectonic stresses are the overburden load and two unknown principal horizontal stresses that cause easily determined stress concentrations at the well bore. All calculated stresses are modified to account for the interstitial pore-fluid pressure. It is found that three situations are of interest: (1) the induced vertical stress is less than the overburden pressure; (2) the induced vertical stress and the instantaneous shut-in pressure are greater than the overburden pressure; (3) the induced vertical stress is greater than the overburden pressure but the instantaneous shut-in pressure is less than the overburden pressure. In (1) the fracture is vertical and the stresses are determinable. In (2) the fracture is horizontal and the stresses are indeterminate. In (3) the fracture is initially horizontal but becomes vertical as it propagates away from the well, the vertical and minimum horizontal compressions are determinable, and the other principal stress is bounded by a set of inequalities. Several examples are presented in which the tectonic stress states appear to be relaxed—approximately equivalent to the ‘hydrostatic’ pressure.