Numerical calculation of stress rotation caused by salt creep and pore pressure depletion
7.2 STRESS ANALYSIS FOR A SUBSALT WELL
This section presents the results of the numerical analysis for a subsalt well, which penetrated a thick salt body.
The fundamental issue for a successful application of the numerical method in the analysis of stress orientation is the accurate entry of the pore pressure values encountered along the wellbore. A second issue affecting success is the accurate description of the 3D structure of the salt body and related formations, which are used in the calculation.
One-dimensional (1D) analytical software, such as the Drillworks® software, has proven to be a very powerful analytical tool used in the prediction of pore pressure for many well-bores around the world (Shen 2009). These kinds of tools have provided a good foundation for a successful 3D numerical analysis of stress orientation. Modern seismic technology can also provide accurate geological and structural information for the salt dome/canopy and related formations. Consequently, it is necessary and practical to perform a 3D numerical analysis on salt-body-related stress orientation surrounding a salt body.
7.2.1 Computational model
Fig. 7.1 shows the geometric profile of the model. Its width and thickness are both 10 km;
its height on the left side is 10 km, and its height on the right side is 9.6 km, which shows a variation of ground surface.
The geometry of the salt body was built as shown in Fig. 7.2. Its outer edge diameter is 7.01 km, and the maximum thickness is 1.676 km. Its upper surface has a 30° angle with the horizon. The depth of its top edge from the ground surface is 1.219 km.
The loads sustained by the model include gravity load distributed within the model body and pore pressure distributed in the formations. Because the salt body has no porosity or permeability, the pore pressure within the salt body is assumed to be zero. The pore pressure existing in the subsalt reservoir formation is given as 47 MPa, according to the software-predicted pore pressure value.
This analysis uses the modified Drucker-Prager yielding criterion. Values of material prop-erties are listed below and reference has been made to earlier works, specifically to Hunter et al., 2009; Infante and Chenevert 1989; Maia et al., 2005; Marinez et al., 2008; and Aburto and Clyde 2009. The values of strength parameters for salt adopted here by the Drucker-Prager model are d = 4 MPa, β = 44°, which correspond to values in the Mohr-Coulomb model, as c = 1.25 MPa, φ = 25°.
10 km
9.6 km 10 km
Figure 7.1. Model geometry: profile of the entire model.
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For the formation, the cohesive strength and frictional angle of Drucker-Prager model are given the following values: d = 1.56 MPa, β = 44°, which corresponds to values in the Mohr-Coulomb model, as c = 0.5 MPa, φ = 25°.
The creep law, given in Eq. 7.1 (Dassault Systems 2008), is adopted as follows:
εcr A
(( )
σσcrcr ntm (7.1) where εcr represents the equivalent creep strain rate; σcr represents the von Mises equivalent stress; t is the total time variable; A, n, m are three model parameters, which are given values of 2.5e-22, 2.942, and −0.2, respectively.Zero-displacement boundary constraints were applied in the normal direction of the four lateral surfaces and the bottom surface.
7.2.2 Numerical results
Fig. 7.3 through Fig. 7.8 show the numerical results of principal stress directions of the FEM. Fig. 7.3 through Fig. 7.5 show sectional views in the Cartesian XY plane at coordinate z = 5000 m, which is the central depth of the salt body. Fig. 7.6 through Fig. 7.8 are sectional views in the Cartesian YZ plane at coordinate x = 5000 m, where it also goes through the central position of the salt body.
Figure 7.3. Distribution of maximum principal stress component: z = 5000 m, Cartesian XY view.
30o
Salt body
Figure 7.2. Model geometry: profile of the salt body and its position in the model (sectional view).
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The sign convention used in these figures follows the convention used for solid mechanics, in which tensile stress is defined as positive, rather than that used for geoengineering. There-fore, the maximum principal stress is the minimum compressive stress.
As shown in Fig. 7.3, the direction of the maximum principal stress rotates with changes of the azimuth angle in the surrounding rocks of the salt body. At a certain distance from the salt body, as shown in Fig. 7.3, the maximum principal stress becomes normal, which is straight.
Fig. 7.4 shows the direction of the medium principal stress, and it appears to be perpendicu-lar to the direction of the maximum principal stress in this Cartesian XY view. Fig. 7.5 shows the direction of the minimum principal stress, and its vector appears to be very short because it is actually the vertical stress component.
Figure 7.4. Distribution of medium principal stress component: z = 5000 m, Cartesian XY view.
Figure 7.5. Distribution of minimum principal stress component: z = 5000 m, Cartesian XY view.
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Fig. 7.6 shows that the direction of the minimum principal stress in the Cartesian YZ plane changes from vertical to an inclined angle in the vicinity of a salt body and becomes vertical at a distance away from it. In Fig. 7.7 and Fig. 7.8, the orientations of the medium and maximum principal stresses are primarily horizontal.
Figure 7.6. Distribution of the minimum principal stress component: x = 5000 m, Cartesian YZ view.
Figure 7.7. Distribution of the medium principal stress component: x = 5000 m, Cartesian YZ view.
Figure 7.8. The finite element mesh used in the calculation.
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7.3 VARIATION OF STRESS ORIENTATION CAUSED BY INJECTION