5.1. Orthogonal Optimization Analysis of Slip Structure
According to the simulation data in
Figure 12 and
Table 2, it can be seen that all teeth on the slip have uneven forces and different biting depths, and there are great differences, as shown in the red curve in
Figure 15, and the number of the teeth is shown in
Figure 12. There are many factors affecting the uniformity of the depth of the slip teeth, such as the number of cemented carbide teeth installed, the diameter of the spacing of the installed cemented carbide teeth, the wedge angle of the slips, the installation angle of the cemented carbide teeth, the number of slips, the stability of the setting load of the packer, and whether the machining and installation of the slips are standard. In order to solve the uniformity of bite depth and improve the overall setting performance of the sidetracking packer, the orthogonal optimization analysis of the structural parameters of the sidetracking packer was carried out on the basis of the furrow effect [
19,
20,
21].
According to the design requirements of the sidetracking packer slips, four factors that have a significant impact on slip performance, including slip tooth installation spacing
L (factor A), the slip tooth installation angle
α (factor B), the slip tooth diameter
d (factor C), and the slip wedge angle
β (factor D), are selected for the orthogonal test [
22,
23], and their parameters are shown in
Figure 16. According to the principle of orthogonal test [
24,
25,
26], a four-factor and three-level orthogonal test scheme L
9 (3
4) [
27,
28] was designed. The test parameters are shown in
Table 3 to explore the influence rule of these four test factors on the slip performance of sidetracking packer.
Numerical simulation is carried out on slips of nine different schemes under setting load (
T = 76.5 kN) and axial load (
F = 73.5 kN) conditions. The variation law of bite depth of slip teeth under nine different schemes is shown in
Figure 17. The numerical simulation results of the orthogonal test are shown in
Table 4. The standard deviation of the data of each bite depth of the slips into the casing was used as the standard to measure the uniformity of each bite depth. As can be seen from
Figure 17, the bite depth of the slip teeth in scheme 4 and scheme 7 is relatively large, and the bite depth of each tooth in scheme 4 varies greatly. The bite depth of the tooth from #1 to #7 increases significantly, and the bite depth of #7 is almost twice as deep as that of #1. The bite depth of slip teeth in scheme 2 and scheme 9 is relatively small.
Range analysis is also known as an intuitive analysis method and has the advantages of being simple to calculate, having intuitive imaging, being simple to understand, and so on. It is the most commonly used method for analyzing the results of an orthogonal test. Range analysis is converted into a single index orthogonal experimental design, and the larger the range, the greater the influence weight of the selected level under this factor on the test index [
29,
30]. According to the calculated data in the table, the influence of the four factor levels on the three test indicators can be obtained.
Table 5 shows the range analysis results for the maximum stress of slip teeth;
Table 6 shows the range analysis results for the maximum bite depth; and
Table 7 shows the range analysis results for the uniformity of bite depth. According to the range analysis results, the influence of maximum stress on alloy teeth is D > A > B > C, from large to small; the influence of maximum bite depth is A > B > D > C, from large to small; and the influence of bite depth uniformity is A > B > C > D, from large to small.
Therefore, the optimal combination analysis results of objective functions are shown in
Table 8.
Through orthogonal test analysis, it is found that the optimal combination of the two optimization objective functions [
31,
32,
33]—the optimal uniformity of bite depth and the optimal stress of slip tooth—is consistent. Therefore, the optimal combination parameters of slips can be obtained as follows: the slip tooth installation spacing
L = 10 mm, the slip tooth installation angle
α = 80°, the slip tooth diameter
d = 10 mm, and the slip wedge angle
β = 6°. This set of slip parameters does not appear in the orthogonal test scheme in
Table 3, so another set of simulation tests needs to be added. The simulation result for the optimal slip combination parameters is shown in
Figure 18. As can be seen from
Figure 18, the maximum stress of the slip teeth decreases from 3925 MPa to 3219 MPa, with a percentage of 17.99% decrease, and the stress distribution of each tooth is relatively uniform. By comparing
Figure 14 and
Figure 19, it can be seen that the bite depth of each tooth, when it bites into the casing before optimization, is unevenly distributed. The bite depth above the casing is small, while the bite depth below the casing is large. After optimization, the shape and bite depth of each tooth are basically the same. Meanwhile, as can be seen from
Figure 15, the bite depth of each tooth after optimization is significantly reduced compared with that before optimization, but the change range of the bite depth of each slip tooth is small, and the standard deviation of the bite depth uniformity of each slip tooth is reduced from 0.1366 to 0.0349, which is 74.45% lower than that before optimization.
5.2. Experiment Study
In order to verify the accuracy of the furrow effect and the simulation results, in the case study of Sidetracking Well 2, Block Wen 116, Zhongyuan Oilfield in China, the inserted tooth slip sidetracking packer is employed to carry out the experiment on the casing with a diameter of 139.7 mm, steel grade of P110, and wall thickness of 7.72 mm, as shown in
Figure 20. The purpose of the experiment is to verify the reliability of the setting process of the inserted tooth slip, and to observe whether the slip will slide down. The basic parameters of the experiment include a set pressure of 25 MPa, total load time of 220 s, and total WOB of 310 kN. The loading time history is shown in
Figure 21.
The application test indicates that the inserted tooth slip sidetracking packer does not slide down and has achieved a reliable setting. The application test results also show that the FEA model and calculated results of the inserted tooth slip sidetracking packer, considering the furrow effect and the adhesion effect, are correct in this paper and that the requirements of engineering applications are basically met. Therefore, in the theoretical research and simulation analysis of the slip, the furrow effect and the adhesion effect between the friction surfaces of the slips and the casing need to be considered at the same time.