Measurement of tensile strength of well cement sheath in underground gas storage based on tensile failure method

During gas injection in gas storage, the inner pressure increase, potentially leading to tensile failure of the cement sheath. At present, the fracture strength of cement stone is measured using the Brazilian splitting method (BSM), which is prone to errors due to stress concentration at the loading point. To overcome this drawback, a novel test device and measurement method were developed to assess the tensile. This device utilizes the tensile failure method (TFM) to evaluate the sealing integrity of the cement sheath. The tensile strength tested by the BSM was found to be 40% higher than that tested by the TFM. Furthermore, based on the optimization of the cement slurry for underground gas storage (UGS) in the Jidong oilfield using both the TFM and the BSM. We found that using the BSM cannot optimize the cement slurry that meets the requirements for gas storage well cementing. The latex cement slurry was selected by the TMF for UGS well.

rocks and found that rocks typically exhibit cracking starting from the loading point, with relatively low tensile strength.Ayatollahi and Akbardoost 12 conducted a study on the influence of rock specimen size and geometric shape on the results of the splitting experiment.The findings indicated that the surface fracture toughness of the specimen increased with an increase in size.In the study conducted by Manchao et al., 13 the BSM was employed to test a large number of sandstones and mudstones.The results revealed that the tensile strength of rocks measured using different loading methods exhibited significant variations.Tong et al. 14 tested the tensile strength of sandstone, marble and granite by using the three-point bending method, and found that the bending tensile strength of the hard pad was twice that of the splitting tensile strength, while the bending tensile strength was 1.4 to 1.8 times higher than the splitting tensile strength of the soft pad.Huafeng et al. 15 studied the influence of the thickness to diameter ratio on the tensile strength of rock.The findings indicated that the tensile strength increased as the thickness to diameter ratio of the specimens decreased.
The aforementioned studies demonstrate that the tensile strength measured by BSM is influenced by various factors, including loading stress concentration, pad type, specimen geometry, specimen shape, and thickness-to-diameter ratio, which lead to the instability.These factors can contribute to the instability and variability in the measured tensile strength values obtained using the BSM.Therefore, some scholars have raised doubts ad concerns regarding the BSM for testing tensile strength.For example, Yong 16 put forward the belief that stress concentration at the loading point in the Brazilian splitting test can significantly impact the results, leading to specimen cracking and potentially causing substantial errors in the test outcomes.A comparison was made between the influence of the stretching method and the splitting method on the measurement of the tensile strength of rocks.The findings revealed that the stretching method was considered the most effective approach for measuring the tensile strength of rocks. 17Although it has been proposed and proved that the tensile failure method (TFM) is superior to the BSM, it has not been popularized to measure the tensile strength of rocks due to problems such as the processing of rock specimens.However, the cement stone differs from rock in that it can be obtained through the specialized curing molds, which resolves the challenges associated with specimen processing and fixation.
In this study, a new testing device and method of tensile strength of cement sheath (stone) for gas storage wells was developed.The use of this device and method can avoid the overestimation of measurement values caused by BSM testing.The sealing integrity test device of cement sheath will be used to verify the accuracy of the TFM and BSM.To validate the suitability of this method, the tensile strength and tension-compression ratio of various cement slurry were tested.Then, in practical application examples, the casing-cement sheath-formation elastic mechanics model was used to assess different cement slurry systems based on the tension-compression ratio.Finally, the optimization process focused on identifying a cement slurry that meets the specific production and operational requirements of gas storage in the Jidong oil field.

Tensile failure device
Figure 1 shows the tensile failure device used to evaluate the tensile strength of cement stone.It consists of three systems: dynamical system, testing mold, and data sampling.The dynamical system is a commonly used material testing machine utilized for testing the tensile strength of various materials.The testing mold is a very critical component for cement stone formation, consists of several parts: upper cup lid, upper cap, gasket, lower cap, lower cup lid, and tension sensor.The gasket features a circular hole in its center, which allows for control over the fracture position and cross-sectional area of the cement stone.The data acquisition system comprises a tension sensor and a data display for collecting and presenting the test data.

Methodology
The sequence of the experimental procedures can be described as follows: Step 1: Clean the cementing mold thoroughly and apply a thin, even layer of sealing grease on the inner wall of the slurry cylinder, the threaded buttons, and the end surface of the end cover.

F I G U R E 1
Tensile failure strength of cement sheath evaluation device and its schematic Step 2: Place the smaller end of the mold on the bonding test panel and firmly press it to ensure a leak-free seal of the cement slurry.
Step 3: Fill the mold with the cement slurry to be tested, cover the upper end cap of the slurry, and exhaust air and excess cement slurry.
Step 4: Place the mold filled with cement slurry into a high-temperature and high-pressure curing kettle, and subject it to the conditions of formation temperature and pressure for curing.
Step 5: Connect the steel wire rope between the pull sheath of the mold end cover and the bonding testing panel, ensuring a secure connection.
Step 6: Clamp the upper and lower rods of the mold in the respective upper and lower clamps of the material testing machine.Switch on the tensile data display, wait for the display meter to return to zero and start the material testing machine and conduct the test to measure the maximum tensile force at the moment of separation between the bonding panel and the cement stone specimen.
Step 7: Calculate the tensile failure strength of the cement sheath and the bonding panel using the following formula: where P is the tensile failure strength of the cement sheath, kPa; F is the maximum tensile force of cement stone specimen at the moment of separation, kN; and d is the inner diameter of the mold, m.

Sample preparation
The solid materials include API 18 class G oil well cement from the (Jiahua, China), a drag reducer (Hongshen, China), silica fume (Hongshen, China), polypropylene fibers (Chuangfeng, China) and expanding agent (Hongshen, China), self-healing agent (By self-innovate).The liquid materials include four admixtures: de-foamer (Chuanfeng, China), BSL 100 L (Hongshen, China), latex (Hongshen, China), water.The cement slurries are mixed at a density of 1.90 g/cm 3 , and the components of the basic cement slurry are 100% cement class G + 0.6% drag reducer +4.0% silica fume +4.0% filtrate reducer +0.3% defoamer + x% function materials (fiber, expanding agent, latex, self-healing agent) + y% water (x and y represent the addition amount of functional materials and water, respectively).The addition of function materials, along with the properties of the cement slurries, are shown in Table 1.Then, prepare the cement slurries according to the API standards.

F I G U R E 2
Sealing integrity test device of cement sheath

Experimental setup and method
Figure 2 shows the sealing integrity test device of cement sheath.The device is fitted with a strain gauge on the cement sheath, through which the stress on the cement sheath can be measured.The device applies pressure of 3 MPa through the gas at the bottom, while gas detection is located at the top.When the cement sheath fails under internal pressure, the gas will be detected.Record the stress on the cement sheath when gas is detected.

Verification results
In order to validate the accuracy of the TFM model, the circumferential stresses of the five cement slurries were measured at the moment of fracture, and the results are presented in Figure 3.As can be seen from Figure 3, the tensile strength measured by BSM is lower than the other two methods.Specifically, the tensile strength measured by TFM was found to be 8.3%, 3.3%, 3.4%, 7.1%, 6.5% higher than that measured by the sealing integrity device.Furthermore, the tensile strength measured by the sealing integrity device was 24.1%, 26.7%, 24.6%, 24.6%, and 24.0% higher than that of measured by BSM, respectively.These findings suggest that the tensile strength measured by TFM aligns more closely with the actual tensile strength under real conditions.

F I G U R E 4
The change of tensile strength of cement stones with curing time

Tensile strength of cement stone
The tensile strength of five cement slurries was tested using BSM and TFM shown in Figure 4.The test results not only enable the analysis of the relationship between the tensile strength of the TFM and BSM, but also serve to verify the reliability of the testing device and method used for the tensile test.The test results are shown in Figures 4 and 5.The results indicate that the inclusion of self-healing, expansion, latex and fiber materials can enhance the tensile strength of cement stone (Figures 4 and 5).The presence of fiber has a pronounced effect on enhancing the tensile strength of cement stone.Indeed, fibers possess both high tensile strength and the ability to undergo tensile deformation.Furthermore, fiber can effectively shield the stress field at crack tips with in the cement matrix, thereby enhancing the fracture toughness of cement stone. 19,20The tensile strength test using TFM on fiber-cement stone exhibited an increase of 45.8%, 45.7%, and 41.6% at 1, 2, and 7 days of curing, respectively.Meanwhile the tensile strength obtained using BSM increased by 51.5%, 52.9%, and 45.4%, respectively.It is noteworthy that the increase in tensile strength of fiber-cement stone cured for 7 days was lower than that for at 1 and 2 days.This can be attributed to the decrease in the tensile and deformation resistance of the fiber under high-temperature and high-pressure conditions with increased curing time, resulting in a reduction in the tensile strength of the cement stone.At different curing temperatures, the tensile strength of cement stones measured by TFM is greater than that of the BSM (Figure 6).The tensile strength measured using the TFM is found to be 1.35 to 1.47 times higher than the measurements obtained through the BSM (Figure 7).Among the samples tested, the fiber cement stone exhibits the highest tensile strength.The tensile strength measured by TFM shows an increase of 49.2% at 75 • C, 45.8% at 90 • C, 37.7% at 100 • C, and 33.8% at 130 • C. The tensile strength measured by the BSM increased by 51.6%, 52.9%, 33.8%, and 30.9%, respectively.Under the identical conditions, the tensile strength of cement measured using TFM is on average 40% higher compared to the BSM method, with a range of 30 to 1.48 times higher.This consistency between the tensile strength measurements obtained by TFM and BSM indicates the reliability of TFM device and method.

Tensile compression ratio of cement
The tensile compression ratio of cement stone, which represents the ratio of tensile strength to compressive strength, serves as an indicator of can reflect the toughness of cement stone.,A higher tensile compression ratio indicates the better toughness in the cement stone. 6To investigate the variation pattern of the tension compression ratio of cement stone, the compressive strength of five types of cement slurries was tested at different curing time (90 • C × 21 MPa) and curing temperature (21 MPa × 2 days).Subsequently, the tensile strength data was combined with the tensile strength to analyze the change pattern of the tensile compression ratio or different cement slurries concerning curing temperature and time.
The results are shown in Figures 8 and 9.Under different curing conditions, the tensile compression ratio measured by TFM for the cement stone ranges from is 0.054 to 0.076, while the range for the tensile compression ratio measured by BSM is 0.038 to 0.055.The tensile compression ratio of cement decreases with the increase of curing time or curing temperature.The tensile compression ratio of cement stone is affected by the degree of cement hydration.The more complete the cement hydration, the higher the brittleness of the cement, resulting in a smaller tensile compression ratio.Furthermore, it is important to note that many of the toughening materials in cement stone are organic polymer materials.
The performance and toughening effect of these materials tend to diminish as curing time or curing temperature increases.Consequently, this leads to a decrease in the tensile compression ratio of the cement stone. 21elf-healing, expansion, latex, and fiber materials have the potential to enhance the tensile compression ratio of cement stone.Among them self-healing and latex cement slurry can improve the tensile compression ratio of cement stone better, that is, they can obviously improve the toughness of cement stone.However, with the increase of curing time and temperature, the tensile compression ratio of latex cement slurry decreases more obviously, this is because latex will occur aging, affecting the toughness of cement stone.The tensile compression ratio of the self-healing cement slurry after 1, 2, and 7 days were increased by 12.5%, 10.3%, and 10.8%, respectively (Figure 8).At 75 • C, 90 • C, 100 • C, and 130 • C, the tensile/compression ratio of self-healing cement increased by 19.4%, 10.3%, 28.7%, and 25.8%, respectively (Figure 9).In the self-healing cement slurries, the adhesion between the self-healing particles and the cement skeleton is enhanced at high temperature, and the fracture energy required by the fracture propagation is absorbed, so as to increase the toughness of the cement stone. 22The tensile compression ratio of latex cement slurry for 1, 2, and 7 days increased by 14.5%,

F I G U R E 9
Ratio of tensile strength to compressive strength of cement stone at different curing temperature 11.6%, and 9.9%, respectively.When the curing temperature was 75 • C, 90 • C, 100 • C, and 130 • C, the tensile compression ratio of latex cement slurry increased by 16.4%, 11.6%, 30.2%, and 25.4%, respectively.In latex cement slurry, latex under the action of cement hydration, colloidal particles through the intermolecular force connection to form a layer of polymer film, disperse the stress concentration of cement stone, can greatly increase the deformation capacity of cement stone, improve the toughness of cement stone. 23

Evaluation index determination
Whether the tensile strength of cement sheath resistance can withstand circumferential tensile stress is a critical indicator for evaluating the sealing effectiveness during the cement sheath injection process.The distribution of circumferential tensile stress in the cement sheath can be obtained by analyzing the mechanics model of casing cement sheath with thick wall cylinder theory, and the circumferential tensile stress of cement sheath under different wellbore pressure conditions can be calculated.According to the common casing design standards, the model uses the following calculation parameters: the casing's elastic modulus and Poisson's ratio of the casing are 206 GPa and 0.3, respectively, with an inside diameter of 241.3 mm and outside diameter of 177.8 mm.The elastic modulus and Poisson's ratio of cement sheath are 8 GPa, 0.2 and 215.9 mm, respectively.The elastic modulus and Poisson's ratio of the stratum are 15 GPa and 0.25, respectively.The model is employed to calculate the distribution of circumferential tensile stress in the cement sheath for different internal pressure values of the casing, as shown in Figure 10.
Under the same radius of cement sheath, the circumferential tensile stress of cement sheath increases with the increase of the pressure inside the casing (Figure 10).Conversely, when the pressure inside the casing is held constant, the circumferential tensile stress of the cement sheath decreases with an increase in the radius of the cement sheath (Figure 10).The inner wall of cement sheath is subjected to the maximum circumferential tensile stress.If the tensile strength of the cement sheath is lower than the circumferential tensile stress on the inner wall of the cement sheath, tensile failure will occur at the inner wall of the cement sheath, resulting in the failure of the sealing integrity of the cement sheath.
During the production and operation of the gas storage in Jidong Oilfield, the maximum pressure inside the casing increases by 40 MPa.Consequently the circumferential tensile stress on the inner wall of the cement sheath reaches 1.88 MPa.Combined with the cement stone in Figure 8, the sealing effectiveness of the cement sheath of each slurry is evaluated, and the results are shown in Table 2 2).These values are all smaller than the circumferential tensile stress on the inner wall of the cement sheath.However, the tensile strength measured by tensile failure method is 1.90, 2.19, 1.89, and 2.38 MPa (Table 2), which are greater than the circumferential tensile stress of the inner wall of cement sheath.
If the BSM is used to evaluate the preferred cement slurry, the resulting cement sheath formed by these slurries will fail, resulting in the inability to select the cement slurry that meets the gas storage requirements.When the tensile failure method is used to optimize the slurry, the cement sheath formed by the self-healing, expansion, latex and fiber cement slurries will not suffer tensile damage and meet the sealing integrity requirements of the cement sheath.

Optimization of mechanical properties of cement slurry
The elastic deformation abilities of casing, cement sheath and formation is very different.When the internal pressure of the wellbore changes, it is difficult for the cement sheath to reach the same deformation as the casing and well wall, resulting in the formation of micro-annular gaps. 24Therefore, in the experimental design or slurry optimization of cementing cement slurry for gas storage, it is not only necessary to evaluate the tensile strength of cement, but also to consider improving the elastic deformation capacity of cement to reduce the risk of micro-annulus.Therefore, the TFM of cement sheath is premised on its circumferential tensile stress and the tensile ratio of cement stone is used to optimize the cementing slurry for Jidong gas storage.The results are shown in Figures 11 and 12.
The tensile strength and tension ratio of self-healing cement slurry initially increase and then decreased with the addition of self-healing agent.When the dosage of self-healing agent is 2.5%, the tensile strength and tension ratio of the cement reach their maximum values, which are 2.08 MPa and 0.0683 (Figures 11 and 12), respectively.A small amount of self-healing agent can improve the tensile strength of the cement, but more self-healing particles floating in the upper part of the cement slurry when the dosage is greater than 2.5%, resulting in the reduction of the tensile strength and F I G U R E 12 Influence of toughening materials on toughness of cement stone compressive strength of the cement.A small amount of self-healing agent can improve the tensile strength of cement, but when the dosage is greater than 2.5%, more self-healing agent floats in the upper part of cement slurry, resulting in the reduction of tensile strength and compressive strength of cement.The expansive material can obviously improve the tensile strength of cement.However, when excessive expansion agent is added, the internal structure of cement stone will be deteriorated, and the tensile strength and compressive strength will be reduced.When the expansion agent dosage is 5.0%, the tensile strength of the cement reaches the maximum of 2.25 MPa, but the improvement of the tensile compression ratio of the expansion material is not as good as that of the self-healing and latex material.When the expansion agent dosage is 7.5%, the tensile pressure ratio of cement reaches the maximum 0.0653.The tensile strength and tension ratio of latex cement slurry water increase with the addition of latex.When the amount of latex reached 10.0%, the tensile strength and tension ratio of cement were 2.15 MPa and 0.0747 (Figures 11 and 12), respectively.Although the improvement of the tensile strength of the latex cement slurry is not as good as that of the expanded cement slurry s, it can greatly improve the tensile compression ratio of the cement and improve the toughness of the cement.The self-healing, expansion, and latex cement slurries can meet the requirements of the circumferential tensile stress of the inner wall of the cement sheath when the internal pressure of the wellbore is increased by 20 MPa, but the latex cement slurry can significantly improve the tensile pressure ratio of the cement stone and improve the toughness of the cement stone.Therefore, when the internal pressure of Jidong gas storage increases by 20 MPa, the latex cement slurry with 10.0% latex addition can better ensure the sealing integrity of cement sheath.

CONCLUSIONS
In this study, a new testing device and method of tensile strength of cement sheath for UGS wells was developed.The sealing integrity test device of cement sheath was used to verify the accuracy of TFM and BSM.We used the device and method to evaluate the tensile strength of different types of cement slurries.The following are the results obtained: 1. Based on the stress characteristics of the cement sheath during gas storage operations, a novel device and method for measuring tensile strength has been developed.The device avoids the effect of stress concentration caused by the BSM.Through the evaluation of the tensile strength of different cement slurries, it has been observed that the tensile strength tested by TFM is approximately 40% higher than the BSM. 2. The tensile-to-compressive strength ratio of cement stone decreases with increasing curing time or curing temperature.
Compared to the net slurry, self-healing, expansive, latex, and fiber materials all improve the tensile-to-compressive strength ratio of cement stone.Among them, self-healing and latex materials are superior to the other materials.3. When designing a cement slurry system, the TFM is instead of the BSM, which may result in the inability to select a cement slurry that meets the requirements of oil and gas wells.

F I G U R E 3
Tensile strength of cement sheath (stone) measured by sealing integrity device, BSM and TFM.The cement sheath was cured at 90 • C and 21 MPa for 2 days.

F I G U R E 5
Ratio of tensile strength of TFM and BSM at different curing time F I G U R E 6 The change of tensile strength of cement stones with curing time F I G U R E 7 Ratio of tensile strength of TFM and BSM at different temperature.To prevent the strength decline of cement stone under high temperature conditions, affecting the test results.When the cement slurry is greater than 110 • C, 30% quartz sand is added.
(cement stone curing condition: 100 • C × 21 MPa × 48 h).When the F I G U R E 10 Circumferential tensile stress distribution of cement sheath

F I G U R E 11
Effect of toughening material on tensile strength of cement stone.Curing condition: 130 • C × 21 MPa × 2 days internal pressure is 40 MPa, the circumferential tensile stress on the inner wall of the cement sheath is 1.88 MPa.The tensile strength of the cement stone, measured using the Brazil method, are 1.33, 1.41, 1.56, 1.37, and 1.78 MPa for each respective slurry (Table 18 Composition of prepared experimental samples TA B L E 1

TA B L E 2
Evaluation results of tensile strength of cement set and effectiveness of cement sheath isolation