In-Situ Stress
In-situ stresses are one of the most important factors controlling hydraulic fracture behavior. These stresses exist naturally in the subsurface due to the weight of overlying rock layers and tectonic forces and are nominally compressive in all directions. The stress state of a reservoir determines how fractures initiate, propagate, and orient within the formation.
There are three mutually perpendicular principal stresses in the subsurface – the vertical stress, Svert, the horizontal maximum stress, SHmax, and the horizontal minimum stress, Shmin (Figure 3.4.1).
Figure 3.4.1: Subsurface rock element showing the relative orientations of the three principal stresses in the earth – Svert, SHmax, and Shmin.
Stress Regime and Hydraulic Fracture Orientation
Most commonly in the oilfield, the vertical stress is the most compressive stress and the sign convention is that compressive stresses are positive (tension is negative), such that Svert > SHmax > Shmin. When Svert is the most compressive, this is called the normal faulting stress regime because it favors normal slip on faults (Figure 3.4.2a). The other two stress regimes are reverse faulting (Fig. 3.4.2b), where the vertical stress is the least compressive, and strike-slip faulting (Fig. 3.4.2c), where the vertical stress is the intermediate magnitude stress.
Figure 3.4.2: Stresses for Andersonian Faulting Theory.
a) Normal faulting stress regime, where Svert > SHmax > Shmin. Normal faults strike perpendicular to the least stress, Shmin, the shortening direction is vertical (parallel to the most compressive stress), and the extension direction is horizontal parallel to Shmin (the least compressive stress).
b) Reverse faulting stress regime, where SHmax > Shmin > Svert. Reverse (or thrust) faults strike perpendicular to the most compressive stress, SHmax. The shortening direction is horizontal and parallel to SHmax (the most compressive stress), and the extension direction is vertical (parallel to the least compressive stress).
c) Strike-slip faulting stress regime, where SHmax > Svert > Shmin. Strike-slip faults strike oblique to the most compressive stress, SHmax. The shortening direction is horizontal parallel to SHmax (the most compressive stress), and the extension direction is horizontal parallel to Shmin (the least compressive stress).
Hydraulic fractures form in planes perpendicular to the least compressive stress because they naturally want to open in the direction that takes the least energy. For normal and strike-slip faulting stress regimes, this means the hydraulic fracture plane is perpendicular to Shmin. For the reverse faulting stress regime, Svert is the minimum stress, so under these conditions the hydraulic fracture plane is horizontal.
Figure 3.4.3: Expected orientation of hydraulic fractures relative to the principal stress directions. a) In the normal and strike-slip faulting stress regimes, ideal hydraulic fractures are vertical planes perpendicular to Shmin. b) In reverse faulting stress regimes, an ideal hydraulic fracture is horizontal, which is perpendicular to Svert.
The vertical stress is the overburden weight at any given depth, which is a function of the average bulk density of the rock. It can be calculated as
\[ S_{vert} = \bar{\rho}_b \cdot g \cdot z \tag{3.2} \]
where
- \( \bar{\rho}_b \) is the average bulk density of the rock to a given depth, \( z \), where bulk density includes both the grains and fluids that make up the rock,
- \( g \) is the gravitational constant,
- and \( z \) is the depth.
Accurate measurement of the in-situ stress field is essential for fracture design. Vertical stress is readily computed based on the density log, but determination of the horizontal stresses is more challenging. One commonly used method to measure Shmin at a particular depth is the Diagnostic Fracture Injection Test (DFIT), which analyzes pressure behavior during a controlled fluid injection that creates a hydraulic fracture. Log-based methods for stress characterization can predict the layer by layer stress characteristics that influence fracture height growth or containment.1Blanton, T. L., & Olson, J. E. (1999). Stress magnitudes from logs: Effects of tectonic strains and temperature. SPE Reservoir Evaluation & Engineering, 2(1), 62–68. https://doi.org/10.2118/54653-PA
Common In Situ Stress Gradients Magnitudes
It is recommended to make site specific measurements of in situ stresses for the sake of accuracy, but in most regions, it is safe to assume that the vertical stress, Svert, has a gradient of 1 psi/ft. The minimum horizontal stress, Shmin, can have a wide range. For normal and strike-slip faulting stress regimes, Shmin is expected to fall between 0.5 and 1.0 psi/ft. SHmax is the most difficult stress to constrain without downhole measurements, so no expected range will be offered here beyond the expected relative magnitudes specified in the caption of Figure 3.4.2.
