The salt rock samples of the Kumugeliemu Group were collected and prepared into 5 test samples with a size of 100 × 50 (mm × mm) (Table 1). The tests were carried out using the American MTS815 Flex Test GT rock mechanics test system (Rui et al., 2022a; Rui et al., 2022b). Creep tests require consideration of creep behavior under different confining pressures (axial compression) and temperatures, and the supplied salt rocks are highly rheological (Pan and Zhou, 2022). The test method is as follows: by controlling the principal stress σ1=125 MPa unchanged, starting from the initial stress σ3=120 MPa, σ1-σ3=5 MPa, the confining pressure (σ3) is reduced by 5 MPa in each stage and the axial pressure (σ1-σ3) is increased by 5 MPa, so as to ensure that the principal stress remains unchanged, and the pressure increases by 5 MPa step by step. Starting from 100°C, a total of 5 levels of temperature are designed, 110°C, 120°C, 130°C, and 140°C. The creep duration of the first 5 levels of deviatoric stress load is 3 h, and after 5 levels, it is changed to 2 h per grade.

Considering different factors such as effective stress and temperature, triaxial creep tests at high temperature were carried out under actual confining pressure (axial compression) and temperature (Tan et al., 2020; Tan et al., 2021). The experimental temperatures, stress differences and corresponding strain rates are shown in Table 2.

The results show that the creep displacement increases with the increase of temperature. When the temperature reaches more than 100°C, the creep displacement respectively reaches 100°C/22.14 mm, 110°C/26.09 mm, 120°C/31.59 mm, 140°C/53.32 mm, and the test result is rejected at 130°C because the sample is filled with oil. The results show that the temperature affects the overall strength of rock salt, resulting in weaker strength of samples (Figure 2). When the temperature is constant, the creep displacement increases with the increase of deviatoric stress; when the deviator stress is constant, the creep displacement increases with the temperature (Figure 3).

Comparing the creep test data of Tarim deep salt rock under high temperature and pressure with the creep test data at home and abroad, it is found that the differential stress of 10 MPa is an important contrast demarcation point. When the differential stress is less than 10 MPa, the creep rate of Tarim salt rock is higher than that of other blocks at the same temperature. When the differential stress is higher than 10 MPa, the creep rate is higher than that of most of the world’s salt rock creep experimental data (Figure 4).

Experimental data reveal the effect of temperature and differential stress on creep of salt rock. It can be seen that temperature and differential stress have a considerable magnitude of influence on the creep rate of salt rock, for example, the temperature ranges from 100°C–140°C, and the creep rate ranges from 3 × 10⁻⁶s⁻¹ to 1 × 10⁻⁵s^-1. While the differential stress varies from 5 to 40 MPa, the creep rate varies from 1 × 10⁻⁶s⁻¹ to 1 × 10⁻⁵s⁻¹.

According to the global mainstream knowledge, where the temperature is high and the stress value is relatively small, and the power law can be used to describe the steady creep of salt rock (Weertman, 1955), the steady creep rate of salt rock increase with the increase of temperature and differential stress (Li et al., 2022). Its expression can be summarized as a stress-independent power-law (non-Newtonian fluid flow) equation: ε ˙ = A 0 exp ⁡ ⁡ − Q R T σ 1 − σ 3 n (1)

The experimental data were fitted by the power-defect function. First, the exponent n is fitted as below: ln ε ˙ = ln A 0 − Q R T + n ln σ 1 − σ 3 (2) where ε ˙ is the steady creep rate of salt rock; A₀ is the material property parameter, fitted as 2.0543 MPa⁻¹ s⁻¹; Q is the activation energy, equal to 53,920 J mol⁻¹; R is the gas constant, equal to 8.314 J mol⁻¹ k⁻¹; T is the absolute temperature; σ1–σ3 is the deviatoric stress; n is the power-law exponent, fitted as 1.1333.

Then A 0 is fitted by Liang et al. (2022) as shown in Figure 5.

Numerical simulations based on core tests can extend the real experimental environment to a wider range of simulations. A numerical model of the same scale of the core experiment was established, and the stress-strain relationship obtained from the experiment was input into the software platform as the constitutive model. According to the environment and loading conditions of the core experiment, the numerical simulation of the influencing factors of salt rock creep was carried out. The simulation is mainly divided into three steps. First establish a model for numerical simulation of core specimens. Second, use the creep constitutive model obtained from experimental data under deep environmental conditions, to carry out numerical simulation under experimental isothermal pressure conditions. Third, compare the numerical simulation results with the field data. The comparison shows that the simulation results are basically consistent with the experimental results, which verifies the accuracy of the model.

By using the method of combining core experiment and core scale numerical simulation, this paper analyze the influence of temperature and differential stress (i.e., axial pressure) on creep, using creep power-law constitutive relations between temperature and pressure in deep layers. Combined with the actual on-site situation, four sets of simulations were set up, the creep deformation of 40 h was used, and then the deformation under different axial pressures was calculated respectively. The relationship between the creep rate and the combination of axial pressure and temperature was established (Table 3; Figure 6).

Creep simulations show an upward trend in creep rate with increasing differential stress and temperature combinations (Figure 7). From the data analysis, it can be seen that the creep rate increases from 0.4 × 10⁻⁷ s⁻¹ to 9.82 × 10⁻⁷ s⁻¹ as 100°C/5 MPa increases to 130°C/20 MPa, which shows a multiple growth.

The stress around the well is affected by the in-situ stress and the deviation angle, and the stress around the well can be obtained by calculating the in-situ stress according to the deviation angle. Therefore, the well deviation factor can also be considered as the change of differential stress in essence. Considering the influence of the well deviation angle (differential stress) and temperature on the creep, using the creep constitutive relations between temperature and pressure in deep layers, four sets of simulations were set up, the creep deformation of 40 h was used, and then the deformation under different conditions was calculated respectively. The relationship between the creep rate and the combination of temperature and well deviation was established (Table 4; Figure 8).

Creep simulations show that the creep rate tends to increase as the combination of well deviation and temperature increases. When the deviation ranges from0° to 90°, the effect on the creep rate is similar to the effect of 5–6 MPa differential stress increase (Figure 9). From the data analysis, it can be seen that the creep rate increases from 3.05 × 10⁻⁷ s⁻¹ to 8.04 × 10⁻⁷ s⁻¹ as 100°C/0° increases to 130°C/90°.

Through multi-factor comprehensive simulation, it can be seen that temperature and differential stress are the key controlling factors of creep, and well deviation angle has an important influence on creep. Its essence is to change the stress distribution around the well, which can be directly converted into the change of differential stress.

The wellbore stability of the composite salt-gypsum layers is affected by the rock mechanics, in-situ stress, well deviation and drilling fluid density. An integrated model of in-situ stress, the composite salt-gypsum layers, borehole and drilling fluid is established (Figure 10). Steps are as follows.

(i) Combining a stratigraphic model based on the superimposed relationship of multiple layers of mudstone and salt rock, with engineering data and creep mechanics test data, establish a mechanical model that reflects the vertical distribution of real stratigraphic lithology.

The creep shrinkage is simulated through the actual drilling and sticking situation on site. At a given reduction ratio, the drilling fluid density required to control creep is calculated.

According to the main deviation angle drilling through the composite salt-gypsum layer, when modeling the directional well, the angle is mainly set to 45° and 60° for simulation research. Table 5 illustrates the specific parameters at different deviation angles. Figure 11 shows the schematic diagram of the mechanical model at different deviation angles. Figure 12 shows the differential stress distribution at different deviation angles. Figure 13 shows the creep shrinkage results when the drilling fluid density is 2.3 g/cm³.

When the well deviation is 45°, the differential stress distribution of the model shows that the differential stress in the salt layers is very small (close to the isotropic stress condition), only about 0.03 MPa, while he differential stress of mudstone is 40–80 MPa, the maximum value of borehole shrinkage is 1.44 × 10⁻² m, and the shrinkage rate is about 11%. When the well deviation is 60°, the differential stress in the salt layers is also very small, about 0.06 MPa, while the mudstone differential stress is 60–90 MPa, the maximum value of borehole wall shrinkage is 1.70 × 10⁻² m, and the shrinkage rate is about 17%.

By establishing a two-dimensional mechanical model for deviated wells in composite salt-gypsum layers, the paper simulates the drilling fluid density that can resist salt rock creep with different depths and stresses under the conditions of 45° and 60° well deviation respectively (Table 6). Assuming that the creep shrinkage of salt rock that causes sticking is 5%, the drilling fluid density required to prevent sticking is calculated based on the field data of several wells, and the intersection chart of depth, stress, well deviation and creep-resistant density is established (Figures 14, 15).

The depth ranges from 5,500 to 6,000 m and the temperature ranges from 130°C to 150°C in this chart. Each colored line in the chart represents the three-dimensional in-situ stress of the salt rock, which is also the liquid column pressure required to balance the creep of the salt rock. The value of different colors is ranges from 140 to 180 MPa, and the ground stress of the same line is the same. The depth of sticking and the corresponding drilling fluid density data in the Bozi block are put into the chart. When the points with different colors are on the left side of the corresponding color curve, it means that the selected drilling fluid density is too small to resist salt rock creep. It also proved that the simulation was accurate.

The simulation chart shows that with the increase of the triaxial in-situ stress, that is, the increase of the formation depth, the density of the drilling fluid used to suppress the same shrinkage ratio increases, otherwise the sticking will show a more serious trend. Comparing the well deviation of 45° and 60°, under the same in-situ stress or depth, the density of drilling fluid required for 60° is slightly higher than that of 45° to maintain the same diameter reduction rate. It can be seen from the simulation results that the change of the well deviation angle will have an important influence on the creep shrinkage and jamming of the directional well in the composite salt-gypsum layers.

When the drilling fluid density is too high, it is easy to leak in the salt interlayer, so it is unreasonable to simply increase the drilling fluid density to resist the salt rock creep. Salt rock reaming was adopted in the field to deal with the problem of creep sticking. The fracture pressure was taken as the upper limit of drilling fluid density, and the salt creep rate under this density was calculated. The limit time of periodic reaming was calculated according to the creep variable of reduced diameter sticking, so as to prevent creep. Based on the creep model established in this study, 5% diameter reduction was set as the standard to judge stuck drilling, and the minimum reaming time was calculated under different drilling fluid densities. Drilling stuck occurred in Bz 9 well at a depth of 6,200–6400 m with 2.36 g/cm³ drilling fluid density. Actual drilling showed that the time from the first drilling through the stuck point depth to the occurrence of stuck was 41.7 h, within this time the bit successfully passed the stuck point. Under the condition of the simulated drilling fluid density of 2.36 g/cm³, the hole diameter at the stuck point reduced by 5% in an average time of 39.5 h, which corresponds well with the actual stuck time, verifying the practicability of this study.

This study establishes a model and method for numerical calculation of wellbore stability in two-dimensional directional wells, and it is an effective way to simplify the stress calculation. Three-dimensional modeling needs to be used in order to set up a more realistic model based on multiple parameters such as geostress distribution, well deviation angle, and azimuth angle. Due to the three-dimensional borehole mechanics calculation and demonstration along the shaft axis direction and each depth section direction in directional well are complicated, the three-dimensional mechanical analysis of wellbore creep will be carried out in the future study.