Nonlinear Viscoelastic-Plastic Creep Model of Rock Based on Fractional Calculus

A rock creep constitutive model is the core content of rock rheological mechanics theory and is of great significance for studying the long-term stability of engineering. Most of the creep models constructed in previous studies have complex types and many parameters. Based on fractional calculus theory, this paper explores the creep curve characteristics of the creep elements with the fractional order change, constructs a nonlinear viscoelastic-plastic creep model of rock based on fractional calculus, and deduces the creep constitutive equation. By using a user-defined function fitting tool of the Origin software and the Levenberg–Marquardt optimization algorithm, the creep test data are fitted and compared. The fitting curve is in good agreement with the experimental data, which shows the rationality and applicability of the proposed nonlinear viscoelastic-plastic creep model. Through sensitivity analysis of the fractional order β2 and viscoelastic coefficient ξ2, the influence of these creep parameters on rock creep is clarified. The research results show that the nonlinear viscoelastic-plastic creep model of rock based on fractional calculus constructed in this paper can well describe the creep characteristics of rock, and this model has certain theoretical significance and engineering application value for long-term engineering stability research.

Field Application of Reaming-While-Drilling Technology in the Super Deep Composite Anhydrite-Salt Layers of Kuche Mountain Front in Tarim Oilfield

The implementation of drilling technique for multiple lithology interbeds and high-pressure anhydrite-salt in the complex Mountain Front area has been completed. The plastic creep of the anhydrite-salt layers, the losses of the low-pressure sandstone, the overflow of the high-pressure salt-water, the narrow mud density window and frequent pipe-stuck occurrence are significant issues, which trigger significant engineering challenges downhole. This study presents the application of the reaming-while-drilling (RWD) technology which has led to minimize the downhole non-productive time (NPT) and achieve successful results. The RWD technique was applied in the composite anhydrite-salt formation of the Kumugeliemu group. Through optimized combination of the RWD tools, bits, reaming blades, and the mechanical analysis the drill string with shock-absorbing design and hydraulics optimization to guarantee the bit and the reamer blades have the proper pressure drop, hydraulic horsepower and flow-field distribution, the RWD was used with the vertical seeking tool drilling technology, resulting in minimum vibration and/or stick-slip, and achieving the expected rate of penetration (ROP) as well as target inclination. It improved the operation efficiency significantly while avoiding the downhole complexities at the same time. Since the geological structure of the offset well Keshen X (no RWD) is similar to Keshen XX (RWD technology was applied), a comparison between the two wells was performed. The reaming meterage in the composite anhydrite-salt layers in Keshen XX was 791 m, spending 15 days, average ROP is 3.73 m/hr. There was no overflew or loss during the drilling. It was smooth, no pipe sticking when checking the reaming effect during the wiper trip and the tripping out. On the other hand, Keshen X spent 29 days with average ROP of 1.35 m/hr to drill the 449 m composite anhydrite-salt rock. Moreover, it was difficult to trip in and trip out during the drilling, and the pipe sticking happened frequently, back-reaming frequently as well. There were losses during both the drilling and the casing running. Due to the unsmooth wellbore, this well increased additional 3 runs of reaming after drilling operation and 4 clean-out runs. 13 days later after the reaming operation, the anhydrite-salt rock creep was checked and found that the hole was still smooth, no pipe sticking existing. Hence, RWD technology has accomplished both goals of preventing the downhole complexities and speeding up drilling. The novel RWD technology can be well illustrated by presenting all the details of its application in salt-base formations.

A Novel Method to Determine the Drilling Fluid Density for Gypsum-Salt Layer

The reservoir underneath the salt bed usually has high formation pressure and large production rate. However, downhole complexities such as wellbore shrinkage, stuck pipe, casing deformation and brine crystallization prone to occur in the drilling and completion of the salt bed. The drilling safety is affected and may lead to the failure of drilling to the target reservoir. The drilling fluid density is the key factor to maintain the salt bed’s wellbore stability. The in-situ stress of the composite salt bed (gypsum-salt -gypsum-salt-gypsum) is usually uneven distributed. Creep deformation and wellbore shrinkage affect each other within layers. The wellbore stability is difficult to maintain. Limited theorical reference existed for drilling fluid density selection to mitigate the borehole shrinkage in the composite gypsum-salt layers. This paper established a composite gypsum-salt model based on the rock mechanism and experiments, and a safe-drilling density selection layout is formed to solve the borehole shrinkage problem. This study provides fundamental basis for drilling fluid density selection for gypsum-salt layers. The experiment results show that, with the same drilling fluid density, the borehole shrinkage rate of the minimum horizontal in-situ stress azimuth is higher than that of the maximum horizontal in-situ stress azimuth. However, the borehole shrinkage rate of the gypsum layer is higher than salt layer. The hydration expansion of the gypsum is the dominant reason for the shrinkage of the composite salt-gypsum layer. In order to mitigate the borehole diameter reduction, the drilling fluid density is determined that can lower the creep rate less than 0.001, as a result, the borehole shrinkage of salt-gypsum layer is slowed. At the same time, it is necessary to improve the salinity, filter loss and plugging ability of the drilling fluid to inhibit the creep of the soft shale formation. The research results provide technical support for the safe drilling of composite salt-gypsum layers. This achievement has been applied to 135 wells in the Amu Darya, which completely solved the of wellbore shrinkage problem caused by salt rock creep. Complexities such as stuck string and well abandonment due to high-pressure brine crystallization are eliminated. The drilling cycle is shortened by 21% and the drilling costs is reduced by 15%.

Research on Construction and Operation Parameters of an Underground Oil Storage in Depleted Salt Caverns in the East of China

The crude oil price has been keeping at a low level in recent years, which made China's government put more efforts in the development of underground oil storages in depleted salt caverns. Under the initiative of "the Belt and Road", a more concrete concept which is "the Silk Road Economic Belt and the 21st-Century Maritime Silk Road" successfully connects Jiangsu Province in the east of China. Consisting of 20 depleted caverns, Huai'an project that is still under planning is one of the most successful examples that turn depleted salt caverns into underground crude oil storages in China. Each cavern takes up 24×104m3, while the project totally takes up 480×104m3. TDMA algorithm was adopted to solve the heat exchange model of oil, brine and surrounding rocks, revealing the relationship between temperature and cavern pressure. Salt rock safety factor, salt cavern shrinkage ratio, axial stress and ground subsidence were taken into consideration to establish a 3-dimension salt rock creep model for 19 depleted salt caverns, so that the caverns’ shapes were optimized. Hydrodynamics models were used to determine the oil's flow rate into and out of a 1000m deep cavern whose thermal field was simulated by software to reveal the temperature limit of oil and brine. Due to geothermal gradient and continuous heat transmission, the average temperature of oil and brine goes up from 35°C to 44.3°C within 7 years, while the inner pressure goes up from 12.96MPa to 21.93MPa in a depleted salt cavern. Salt creep ratio decreases as oil is stored in underground caverns for a longer period. Salt is hardly penetrated by oil, while the temperature change has a strong influence on caverns’ internal pressure. The thermal expansion factor and compressibility coefficient of crude oil and brine are both crucial to the temperature's effect on internal pressure. Caverns that have larger segments in their upper-middle or middle parts are more stable and resistant to salt creep than those that have larger segments in their lower parts. When oil is injected or pumped out, it is necessary to make the internal pressure lower than the static pressure of surrounding rocks. Hence, the most appropriate flow rate of crude oil is 4.5m/s. Crude oil that is stored in deep salt caverns may be heated up to 60°C due to the geothermal gradient, but the flammable gas in oil is rapidly gasified or even explodes when it is pumped out to the surface. To avoid accidents and air pollution, oil is cooled down before being delivered via pipelines. Oil tanks used to be applied by scale in China, however they are too obvious on the ground to comply with national strategic energy safety. Compared with oil tanks of similar volumes, the Huai'an underground oil storages may save the overall cost by 35.3%. It is the first time that the salt rock creep model is established in depleted salt caverns, while the conclusion overthrew the common preference of regular cylindrical caverns.

Analysis of Surrounding Rock Creep Effect on the Long-Term Stability of Tunnel Secondary Lining

The secondary lining failure of deep buried soft rock tunnel often occurs, which is obviously related to the time factor. The formation mechanism of this phenomenon is studied in this paper. Therefore, the combination of in situ stress measurement and neural network inversion is used to analyze the distribution characteristics of in situ stress. At the same time, the creep characteristics of surrounding rock are tested in laboratory, and the key parameters are obtained. Combined with the characteristics of surrounding rock, the calculation model is established by using discrete element simulation technology and considering the joints of surrounding rock. According to the above multiple information, the stress characteristics of the secondary lining in different time periods are analyzed creatively. Finally, the method of setting arch and adding anchor bolt in key parts is proposed, and significant effect results are obtained.

Experimental study on creep characteristics of infiltrated coal-rock under load

For the water-rich zone in the coal tunnel rock body perennial suffer from water infiltration destabilization destruction problem.In this paper, the influence of stress level and infiltration time on the creep properties of coal-rock was systematically studied after the water infiltration test, scanning electron microscope(SEM), water content test, uniaxial compressive strength test and creep mechanical properties test.The whole process of coal-rock creep is described by Hooke's body, Kelvin body and damage elastic-plastic body, and the total damage variable was introduced to show the weakening effect of the coupling effect of stress and water infiltration on the creep properties of coal-rock.A creep constitutive model of coal rock damage considering the weakening effect of water infiltration was established, besides, the influence law of stress level and infiltration time on creep parameters of coal rock was analyzed.The study shows that coal rocks underwent a process from surface drying and shrinkage to water absorption and swelling to water-filled infiltration damage in the infiltration test.With the increase of infiltration time, the water content of coal-rock tended to increase and eventually stabilizes, while the uniaxial compressive strength gradually decreased.With the increase of stress level and infiltration time, the stable creep strain of coal-rock kept increasing which accelerated creep advance, and its internal damage continued to accumulate and eventually led to destabilization damage.At the same stress level, the creep parameter E0 showed a tendency to increase and then decreased with the increase of infiltration time, while E1, η1, tF, E2 and ν continued to decrease.Combined with the microstructural changes of coal rocks in the water infiltration process, the change law of mechanical properties of infiltrated coal-rock and the intrinsic softening mechanism were revealed.Comparing the theoretical model of infiltrated coal rock creep with the experimental data, the model developed in this paper reflected the whole process of infiltrated coal-rock creep deformation and damage, and can characterize the influence of infiltration time and stress level on coal-rock creep properties, which verified the reasonableness of the model.

Study on long-term uniaxial compression creep mechanical behavior of rocksalt-mudstone combined body

Rocksalt and mudstone are usually under common stress in salt storage caverns, resulting in different mechanical properties from pure rocksalt and mudstone. To accurately obtain the creep mechanical characteristics of rocksalt-mudstone combined body, we have made three different combinations. The long-term creep experiment of bedded rocks can more closely reflect the long-term mechanical behavior of surrounding rock of salt storage caverns. The experimental results indicated that the long-term creep curve of the combined body includes initial and steady creep stages, and even includes accelerated creep stage. The strain of mudstone layer in the combined body was lower than that of rocksalt because of the higher strength. With the increase of the height ratio of mudstone, the creep strain of the combined body and each rock layer decreased, but the creep rate increased. A new nonlinear creep-damage constitutive model was proposed, which can well describe the creep evolution characteristics of the experiment. Compared with the fitting curves of classical Burgers and Nishihara creep constitutive models, it is revealed that the proposed model is most consistent with the experimental data. The duration of the long-term creep experiment under lower stress has a highly significant effect on the accuracy of predicting rock creep results. This research will contribute to a deeper understanding of the long-term creep characteristics of bedded rocks in salt storage caverns.