A case study of mud weight design with finite element method for subsalt wells
6.5 STRESS PATTERN ANALYSIS FOR SALTBASE FORMATION
The goal of this section is to perform an analysis on the stress pattern in terms of the numeri-cal results obtained with the global model by using FEM. As a measure of the stress pattern, the effective stress ratio between three normal stress components of a stress tensor will be vis-ualized and analyzed for the subsalt section of a wellbore. The effective stress ratio is one of the essential parameters used with 1D analytical tools for MWW design, such as Drillworks.
Therefore, the stress pattern analysis in terms of the effective stress ratio will provide further understanding and useful information that can be referenced by the 1D MWW design. Focus has been put on the stress pattern in the sectional area where the wellbore trajectory was included. The red vertical line shown in Figure 6.14 is selected as Path-1, along which the stress distribution will be plotted.
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Pressure gradient /Pa/m
TVD depth /m
SFG 3D
FG 3D
pp
Figure 6.13. Numerical results of the SFG and FG values obtained with the secondary submodel.
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For the convenience of analysis, which is based on mathematical description in the framework of solid mechanics, the sign convention and unit convention of solid mechanics will be adopted in the following contexts: a negative sign is used for compression and the stress is shown in the unit of Pa.
Figure 6.15 shows the variations of the total stress components with z-depth from the top surface along with the pore pressure distribution. Non-zero pore pressure occurs at the top of the reservoir formation and at the salt exit of the wellbore trajectory. The effective stress component, σz, is provided solely for the purpose of comparison. A close-up view of Figure 6.15, which focuses on a 2-km depth interval around the salt-formation interface is shown in Figure 6.16. As illustrated in Figure 6.16, the vertical stress component, σz, is the minimum stress component in this depth interval.
Figure 6.17 shows the distribution of effective stress along Path-1. The distribution of the effective stress ratios along Path-1 is shown in Figure 6.18. A close-up view around the salt-reservoir interface for the curves in Figure 6.18 is shown in Figure 6.19. For points in the salt base along Path-1, the effective stress ratios are significantly greater than 1. This result, however, is only true for the Path-1. For a different path, the effective stress ratio will be dif-ferent. As shown in Figure 6.19, there is a range of 1.5 km within which the effective stress ratio is greater than 1. Because the absolute values of stress components are in the sequence of σx>σy>σz, its stress pattern is the reverse faulting pattern, even though no fault structure exists there.
Figure 6.14. Path-1 along which the stress distribution will be plotted.
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Z-depth staring from seabed along path1 /m
Total S11 Total S22 Effective S33 PP-zcoord Total stress Sig33
Figure 6.15. Variation of stress components with z-depth from the top surface.
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Zoomed view
Z-depth staring from seabed along path1 /m
Total Sig11 Total Sig22 Effective S33 PP-zcoord Total stress Sig33
Figure 6.16. Zoomed-in view of stress variation with depth.
Effective stresses
Figure 6.17. Distribution of effective stress ratio along Path-1.
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Figure 6.18. Distribution of effective stress ratio along Path-1.
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To better explain the range of area in which the reverse faulting stress pattern exists within the subsalt formation, investigations of the distribution of stress components along Path-2 and Path-3 are presented in the following contexts.
As shown in Figure 6.20, Path-2 is selected within the salt body. Figure 6.21 shows that the stress distribution along Path-2 inside the salt body is in the order of σz>σy>σx, which indicates a normal faulting stress pattern.
As shown in Figure 6.22, Path-3 is chosen within the subsalt formation and is horizontal.
Figure 6.23 shows the distribution of stress components along Path-3. Figure 6.23 illus-trates a region (marked with a blue-dashed circle) whose stress components is in the order of σx>σy>σz, which represents the reverse faulting stress pattern. Other locations outside the reverse faulting circle are normal fault regions, where σz>(σy and σx).
To investigate the stress pattern within the salt base formation, Figure 6.24 shows the distribution of the effective stress ratio along Path-3. The effective stress ratio varies signifi-cantly from 0.65 to 1.23 with horizontal coordinates of the points investigated.
Figure 6.25 and Figure 6.26 show the numerical results of the sectional distribution of the minimum principal stress obtained by 3D FEM. Figure 6.25 and Figure 6.26 show that the direction of minimum principal stress vector in the area of the salt body varies significantly from place to place. Consequently, these are the causes of effective stress ratio variation within formations. In summary, the effective stress ratio is by far not a constant, and cannot be represented by any constant value.
With reference to the numerical results shown in Figure 6.19, Figure 6.23, and Figure 6.24, it can be concluded that the stress pattern of reverse faulting causes the discrepancy between the MWW results obtained by using 3D FEM and those obtained with the 1D method.
Because no faulting structure exists in the subsalt formation, it is difficult to relate its stress pattern to the form of reverse faulting. Consequently, in the input data of the 1D calculation
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z-depth starting from stop surface
Ratio s11/s33 Ratio s22/s33 Subsalt: SigH>Sigh>OBD
Reverse faulting, 1500 m
Figure 6.19. Distribution of effective stress ratio along Path-1: Zoomed-in view around the salt-reservoir interface.
Figure 6.20. Illustration of Path-2.
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for the MWW, the effective stress ratio can usually be classified as normal faulting. However, this kind of stress pattern can be discovered using 3D FEM numerical calculations, although it is not used as input data there.
Figure 6.27 shows an example of mud weight logging data reported by Shen (2009). The mud weight used in the drilling of the subsalt wellbore section (the black curve) is greater than the overburden gradient. This indicates that the minimum horizontal stress component is greater than the vertical component and, consequently, provides an example of a reverse faulting stress pattern in the subsalt formation.
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s22 s33 s11
Figure 6.21. Distribution of effective stress components along Path-2.
Figure 6.22. Illustration of Path-3.
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Figure 6.23. Distribution of stress components along Path-3.
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Effective stress ratio
s22/s33 s11/s33
Figure 6.24. Effective stress ratio along horizontal Path-3.
Figure 6.25. Finite element results: the sectional view of the minimum principal stress at the salt base formation with TVD = 6142 m (z-coordinate = 2858 m) in 3D space.
Figure 6.26. Finite element results: the sectional view of the minimum principal stress in the plane which is normal to the central axis of salt body in 3D space.
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6.6 ALTERNATIVE VALIDATION ON STRESS PATTERN WITHIN SALTBASE