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VARIATION OF STRESS ORIENTATION CAUSED BY INJECTION AND PRODUCTION

Numerical calculation of stress rotation caused by salt creep and pore pressure depletion

7.3 VARIATION OF STRESS ORIENTATION CAUSED BY INJECTION AND PRODUCTION

This section investigates the stress rotation caused by water injection and/or oil production.

A two-dimensional (2D) model is used. The influence of the anisotropic property of per-meability is numerically simulated and investigated. The numerical results presented in this chapter have visualized the change of stress pattern from its original isotropic stress pattern to a specific form after injection and production.

7.3.1 The model used in the computation

Fig. 7.8 shows the finite element mesh used in the calculation. There are a total of 3201 nodes and 1024 CPE8RP quadratic plane strain elements used in the mesh. Pore pressure and nodal displacement are two types of primary variables. The width and length are 1600 m. One well in the center of the model is represented by a dot. Injection and production are simulated with concentrated flow at the well location. A constant initial pore pressure of pp = 10 MPa was given to all of the nodes of the model, including the boundary nodes.

The following material parameters were used:

• Young’s modulus E = 1 × 1010 Pa, Poisson’s ratio v = 0.3

• Initial geostress is set as isotropic, i.e., σx= σy= 10 × 106 Pa, and plane strain status is set with εz= 0

• Initial porosity φ = 0.25

Normal displacement constrains were applied to the four sides of the model.

In the following paragraphs, the numerical results of principal stresses include both values and directions for four different cases, and will be given in the following sequence:

• Isotropic permeability with injection.

• Isotropic permeability with production.

• Orthotropic permeability with injection.

• Orthotropic permeability with production.

The convention used for solid mechanics signs is followed, i.e., positive for tensile stress and negative for compressive stress.

It is obvious that the direction of the initial in-plane maximum principal stress is in the horizontal direction, and the direction of the initial in-plane minimum principal stress is in the vertical direction in the 2D planar space. Thus, the visualization of their distributions is neglected here.

7.3.2 Numerical results

7.3.2.1 Numerical results of stress rotation with isotropic permeability and injection

The following results are obtained with isotropic permeability k = 100 Darcy. Although this number is rather high, it is physically possible; consequently, it is a reasonable value to be used in this example. The maximum injection pressure is controlled with a limit of ppmax= 1.335 × 107 Pa.

Fig. 7.9 shows the distribution of pore pressure after injection. The highest pore pressure is at the center of the field. The visualization of the in-plane maximum principal stress in Fig. 7.10 shows that the direction of the maximum principal stress is in the circumferential direction, which uses the position of well as the center of the circle. Fig. 7.11 shows that the minimum principal in-plane stress is in the radial direction of the circle. These figures show the drastic change of principal directions after injection.

7.3.2.2 Numerical results on stress rotation with isotropic permeability and production The following results are obtained with isotropic permeability and production. The values of parameters used here are the same as those used for injection simulation. The minimum production pressure is controlled with a limit of ppmin= 6 × 106 Pa.

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Fig. 7.12 shows that the distribution of pore pressure after production is similar to that after injection, but with the opposite gradient of pore pressure: the lowest pore pressure is at the center of the field. Fig. 7.13 provides a visualization of the in-plane maximum principal stress and shows that the direction of the maximum principal stress is in the radial direction, which uses the position of well as the center of the circle. Fig. 7.14 shows that the minimum principal in-plane stress is in the circumferential direction of the circle. These figures demon-strate the drastic change of principal directions after injection.

Figure 7.9. Distribution of pore pressure after injection.

Figure 7.10. Distribution of direction of maximum in-plane principal stress after injection.

Figure 7.11. Distribution of direction of minimum in-plane principal stress after injection.

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7.3.2.3 Numerical results on stress rotation with orthotropic permeability and injection The following results are obtained with orthotropic permeability k

x= 100 and ky= 400 Darcy.

Although these numbers are rather large, they are physically possible. Consequently, it is are reasonable to use them in the example. The maximum injection pressure is controlled with a limit of ppmax= 1.163 × 107 Pa.

Figure 7.12. Distribution of pore pressure after production.

Figure 7.13. Distribution of direction of maximum in-plane principal stress after production.

Figure 7.14. Distribution of direction of minimum in-plane principal stress after production.

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In Fig. 7.15, the distribution of pore pressure after injection is not isotropic because it is influenced by its orthotropic property of permeability: the pore pressure increase in the y-direction occurs more quickly than the increase that occurs in the x-direction. The contour of the pore pressure distribution in the field becomes elliptical. Consequently, in the visu-alization of the in-plane maximum principal stress, shown in Fig. 7.16, the direction of the maximum principal stress appears to be in the circumferential direction of the ellipse, which uses the position of well as the center. Fig. 7.17 shows that the minimum principal in-plane stress is in the radial direction of the ellipse. These figures demonstrate the drastic change of Figure 7.15. Distribution of pore pressure after injection.

Figure 7.16. Distribution of direction of maximum in-plane principal stress after injection.

Figure 7.17. Distribution of direction of minimum in-plane principal stress after injection.

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principal directions after injection and the significant influence from the anisotropic property of its permeability.

7.3.2.4 Numerical results on stress rotation with orthotropic permeability and production The following results are obtained with orthotropic permeability and production. The val-ues of parameters used here are the same as those used for the orthotropic permeability and injection simulation. The minimum production pressure is controlled with a limit of ppmin= 8.366 × 106 Pa.

In Fig. 7.18, the distribution of pore pressure after production is not isotropic because it is influenced by its orthotropic property of permeability: the pore pressure decrease in the y-direction occurs more quickly than the decrease that occurs in the x-direction. The contour of the pore pressure distribution in the field is elliptical. Consequently, in the visualization of the in-plane maximum principal stress, shown in Fig. 7.19, the direction of the maximum principal stress appears to be in the radial direction of the ellipse, which uses the position of well as its center. Fig. 7.20 shows that the minimum principal in-plane stress is in the Figure 7.18. Distribution of pore pressure after production.

Figure 7.19. Distribution of direction of maximum in-plane principal stress after production.

Figure 7.20. Distribution of direction of minimum in-plane principal stress after production.

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circumferential direction of the ellipse. These figures illustrate the drastic change of principal directions after production and the significant influence from the anisotropic property of its permeability.

7.3.3 Remarks

The following conclusions can be derived from the previously described numerical results of flow-induced stress re-orientation:

• The direction of principal stress varies drastically from its initial direction during the transient injection/production process. Consequently, it is important to account for the influence of injection/production activities of nearby wells in the analysis process of wellbore stability or stimulation design.

• The anisotropy of permeability of a field will influence the effect of the injection design:

pore pressure distributed in the direction that has greater permeability will be greater than that with lesser permeability values. This occurrence will cause a non-uniform distribution of pore pressure in the process of injection/production.

7.4 VARIATION OF STRESS ORIENTATION CAUSED BY PORE PRESSURE