Experimental and thermal‐structure coupling analysis for oil and water‐swellable packer

It has been widely acknowledged that traditional packers will lose their elastic performance in the context of long periods of operation due to plastic deformation. This paper will introduce a swellable packer that can reduce the failure cases of production effectively. The deformation of the packer rubber in different media and temperatures has been analyzed. The pressure test of several packer rubber under different media is carried out in this paper. The reasonable expansion clearance between the rubber tube and the well wall is obtained by strength calculation to ensure the sealing reliability of the packer. Finally, the thermomechanical coupling calculation of the packer with different structural sizes is carried out. Experiments at different temperatures show that the higher saline concentration is associated with a lower expansion rate and a larger expansion rate in clear water. At the same time, the expansion of volume in clear water increases. In addition, the higher the external temperature is, the larger the temperature gradient is. When the temperature of the outer ring is between 100°C and 140°C, the internal temperature rises to 37°C under the thermomechanical coupling effect.

several packer rubber under different media is carried out in this paper. The reasonable expansion clearance between the rubber tube and the well wall is obtained by strength calculation to ensure the sealing reliability of the packer. Finally, the thermomechanical coupling calculation of the packer with different structural sizes is carried out. Experiments at different temperatures show that the higher saline concentration is associated with a lower expansion rate and a larger expansion rate in clear water. At the same time, the expansion of volume in clear water increases. In addition, the higher the external temperature is, the larger the temperature gradient is. When the temperature of the outer ring is between 100°C and 140°C, the internal temperature rises to 37°C under the thermomechanical coupling effect.

K E Y W O R D S
expansion rate, experiment, sealing, thermal-structure coupling

| INTRODUCTION
In the past 3 years, with a rapid increase in energy demand, various downhole tools have been innovated, especially the application of the packer has increased dramatically. [1][2][3] In high-pressure and high-temperature (HPHT) deepwater and ultra-deepwater drilling and completion projects, a sturdy dual barrier system is crucial for the integrity of oil wells and the identification of potential risks that may endanger wellbore integrity. Sealing components such as packers and cement sheaths serve as dual barrier components. [4][5][6] Birkle and Makechnie 7 and Su et al. 8 explored the failure types and mechanisms of cement sheaths using different wellbore operating procedures and tested the integrity of the upper and lower cement sheaths of the packer. Tests have shown that reducing the pressure and temperature inside the casing during the production phase is beneficial for maintaining the integrity of the cement sheath on the upper and lower parts of the packer. In the application of intelligent completion technology, formation water can easily flow around the packer through cracks/caves, leading to the sealing failure of the packer. Muradov and colleagues [9][10][11] proposed an optimization algorithm for the installation position of the packer in the horizontal well water control process by evaluating the impact of circulation isolation disturbance on the flow state of the completion reservoir. The number and location of the packer also depend on engineering technology and well conditions. Bosnjak and colleagues [12][13][14][15] studied the use of expansion packers in the completion and fracturing of hightemperature oil deep wells or natural gas reservoirs and proposed a sealing scheme using expandable thermoplastic vulcanized elastomers. The multistage fracturing pipe with improved packers was deployed into horizontal openings, and the results showed that the new scheme exhibited high strength, heat resistance, and structural integrity in high-temperature environments compared to traditional packers. Patel and colleagues [16][17][18][19] proposed a finite element method to evaluate the performance and service applicability of traditional rubber sealing components. Regulatory agencies and the industry have recognized the need to improve the design and certification of elastomeric packers, especially for HPHT applications. Zheng et al. 20 demonstrated the expansion performance of gel and the influence of the constrained swelling ratio of gel on the contact area (and its eccentricity), with pulling off the force and critical separation distance. Zhu and colleagues 21,22 found that the tensile properties and the hardness decrease significantly after corrosion. Ilseng and colleagues [23][24][25][26] claimed that the material was prone to failure when exposed to tensile loading at high temperatures. Variations in sealing pressure are studied for seal length, seal thickness, compression ratio, water salinity, swelling time, and type of well completion. The application of new packers has significantly increased due to the short service life and poor sealing performance of conventional compression packers. A swellable packer is a new type of self-expanding packer and its mechanism is the expansion of the rubber in the internal polymer structure to allow liquid hydrocarbons to enter into the polymer structure. The expansion is continuous and can be used to seal irregular wellbore and horizontal wellbore sections to replace cementing work. [27][28][29] Recently, compression packers have been widely used in fracturing operations. However, there are many reported failure accidents of compression packers due to their mechanical seat sealing overload. To solve the problem, this article develops a new type of expansion packer, which can effectively decrease the impact of mechanical seat sealing pressure and maintain the sealing function and increase the service life of packers in the fracturing industry. This article designs and analyzes the expansion-type packers. The deformation and compressive capacity of 2 7/8″-5 1/2″ swellable packers are tested in different media. Thermomechanical coupling research on rubber cylinders of different sizes has been conducted to provide swellable packers in situ. Detailed reference is provided for the use of the portable packers. The research results provide the experimental and theoretical basis for the selection of packers in fracturing operations.

| Advantage and sealing mechanism of swellable packer
In the sealing process of conventional packer rubber, the pressure head goes down first and the middle support ring moves down, the rubber ring will be extruded and deformed. This area contacts with the upregulating ring and the mantle ring, followed by the connection with the well wall or casing, forming a seal with the well wall or casing. As shown in Figure 1, plastic deformation will occur in the contact part between the indenter and the first rubber ring because of excessive stress and elastic deformation will be lost in the sealing process. 30 The chamfer position of the pressure ring and the support ring can lead to the protrusion of the rubber cylinder.
Compression packers have been widely used; however, they often cause rubber-cylinder compression failure accidents, such as rubber tube rupture or collapse, as shown in Figure 2.
It provides a swellable packer to reduce the failure of traditional packers in this paper. In the oil and gas well, sealing the formation through the swellable packers can provide a gas passageway for oil and gas at the project formation, as shown in Figure 3.
The sealing mechanism of convention packer rubber.

| Test methods and procedures
To improve the performance of the expandable packer and accurately determine the mechanical properties of the expandable rubber cylinder, this study conducted testing and research on the expandable rubber cylinder. The test research of packer rubber is based on an oil field issue in China. It is therefore paramount to test the expansion rule of oil/water-encountering rubber at the high temperature in the bottom hole. The expansion rate of rubber in water-based solutions with different salinity was compared. The test medium solutions are clear water, 20,000 ppm NaCl, CaCl 2 mixed solution, 50,000 ppm NaCl, CaCl 2 mixed solution, 100,000 ppm NaCl, and CaCl 2 mixed solution. For the comparison of rubber expansion rates at different temperatures, experiments were carried out at 70°C, 120°C, and 140°C, respectively.
In view of the different soaking environments of rubber in different oil-based media, the expansion rate of rubber was compared, and the expansion rate of rubber at different temperatures was observed. Take diesel oil, crude oil, and diesel oil solution with 5% and 20% oil content, respectively. The specifications of rubber in oil and water are the same: they are all cylindrical rubber samples; the size is 40 mm × 20 mm as shown in Figure 4.
Rubber samples are labeled to facilitate later measurement. Put the high-temperature roller furnace into the roller cylinders up to 120°C. The total measuring time is 48 h, 70°C, and 140°C. Preheat the roller furnace ( Figure 5A) and pour the prepared solution into the roller cylinders; into the roller furnace ( Figure 5B), put the rubber sample ( Figure 5C), and tighten the lid ( Figure 5D). Put the roller into the roller heating furnace, set the temperature, and expand at constant temperature.

| Test results and analysis
It is found that the oil content in the soaking medium is not directly related to the maximum expansion ratio of the rubber as shown in Figure 6 but to the expansion rate of the rubber. The hydrocarbon composition in the diesel oil solution with an oil content of 5% is absorbed with the expansion of rubber, and the oil content in the solution will gradually decrease. Thus, the rubber will continue to expand as long as there is oil. The oil content only affects the rate of expansion.
The height and expansion volume curves of rubber at different temperatures and media were obtained through a period of experiments as shown in Figure 7. The expansion image of rubber at 70°C showed that the expansion speed of rubber was high in 0-3 h when the salt content was between 20 and 100 g/L, and then it slows down in 3-48 h, and finally became stable; in clear water, the expansion speed of rubber was faster than that of rubber. The rubber expands fast in 0-6 h, with the speed slower in 6-48 h, and finally tends to be stable. Experiments at different temperatures show that the higher the salt concentration, the smaller the expansion rate, and at the same time, the most volume of expansion in clear water increases.
Expansion data of water rubber at 120°C and 140°C in Figures 8 and 9 shows that the higher the concentration of saline, the faster and higher the expansion rate is. It is found that the higher the temperature, the higher the expansion rate, and the expansion height will increase slightly. The expansion curves of rubber at 120°C and 140°C showed that the expansion rate of | 3057 rubber was gradually increasing in 0-100 g/L saline water within 0-24 h, then slightly descending in 24-48 h, and eventually tended to be stable.
The expansion rate of diesel is higher than its petroleum counterpart through a period of experiments at 120°Cand 140°C, as shown in Figures 10 and 11. The higher the concentration of diesel, the faster the expansion rate is. It is found that the temperature is associated with expansion rate.
After 48 h of expansion of rubber in water and oil, the data of volumetric ratio are sorted out, and the results are provided in Tables 1-3.
The data in Tables 1-3 are clear through the experiments of liquid rubber at 70°C, 120°C, and 140°C. When the temperature of water-expanded rubber is lower than 70°C, the expansion ratio at the 100,000 ppm of saline is not large, but when the temperature exceeds 100°C, the expansion ratio is high. With a certain increase, the expansion ratio reaches 2.12 times at 140°C, and there is a tendency to continue to increase.
The expansion ratio of oil-encountering rubber reaches 4.55 times at 120°C in diesel, while in previous tests at 70°C, the expansion ratio of oil-encountering rubber reaches only 2 times in 48 h in diesel. As the maximum expansion ratio of rubber can reach 5-6 times, it can reach the maximum expansion ratio at 70°C for 14 days. According to the rule of this experiment, it is estimated that the maximum expansion ratio can be achieved in 7 days after the temperature is higher than 100°C.

| Test and analysis of bearing capacity
To perform the pressure test in three different sizes of rubber cylinders, put them into the high-temperature heating furnace. Figure 12A is the dimension structure of a 5 1/2″ packer. Put them into the test equipment as shown in Figure 12B.
When the outer diameter of packer rubber is 2 7/8″-5 1/ 2″, the pressure capacity of packer rubber is increasing gradually with the length growth under 140°C as shown in Figure 13, and intended to maintain stability; finally when the outer diameter of packer rubber is 2 7/8″-5 1/2″, the maximum pressure capacity of packer rubber is close to 70 MPa; when the outer diameter of packer rubber is 3 1/2″, the maximum pressure capacity of packer rubber is close to 60 MPa; under different lengths of packer rubber and the diameter variation curves of the oil/water swellable rubber under different lengths, after 13 days testing, the swellable   | 3059 rate of water-swellable packer is larger than the oil swellable packer rubber; the diameter variation curves of the oil/water swellable packer rubber under high pressure are as shown in Figure 14. When the outer diameter of the swellable packer rubber is 5 1/2″, the outer diameter increases to 100 mm. The bigger the outer diameter of the swellable packer rubber, the larger the swellable rate of the packer rubber is.
Through the pressure test at high temperatures, the pressure capacity of 2 7/8″-5 1/2″ packers are between 55 and 70 MPa, and all of them can meet the pressure load of 5000-6000 m in the deep well.

| Material constitutive of rubber
Rubber can be modeled as a kind of hyperelastic material by means of the varied panoply of constitutive models such as the Heo-Hookean strain energy function, Exponential-Hyperbolic rule, Mooney-Rivlin model, and Ogden-Tschoegl model. 31,32 In this paper, the Mooney-Rivlin model was selected to describe the mechanical characteristics of rubber linings. The function can be expressed as follows 33,34 : where W is the strain energy density, C 1 and C 2 are the Mooney-Rivlin coefficient and I 1 and I 2 are the F I G U R E 11 The curves of height and expansion rate of oil packer at 140°C. first and second strain tensor invariant. The relationship between stress and strain can be expressed as follows: According to the rubber material, the linear elastic modulus It is confirmed that material constants of the Mooney-Rivlin model are related to the linear elastic modulus G, and G can be expressed as follows: According to the rubber compression test, C 1 = 1.87 MPa and C 2 = 0.47 MPa. The density of rubber ρ = 1200 kg/m 3 .

| Mathematical model of heat generation
The thermal source of the temperature field in the working process of packer rubber mainly comes from three aspects: downhole formation temperature is the main heat source affecting its temperature field, friction heat generation between the high-pressure drilling fluid and the inner wall of packer rubber cylinders; heat generated by hysteresis loss caused by viscoelastic material properties of rubber material. 35 According to the rule of stress and strain of rubber packer, the stress σand strain ε of rubber are In the formula, ω is the angular frequency and δ is the loss angle (i.e., the lag phase angle). According to the heat generation mechanism of packer rubber, the energy loss of each unit in the process of temperature propagation is as follows: In the formula, E′ is the loss modulus, E is the elastic modulus, and δ tan is the loss factor. The thermal analysis model of packer rubber needs to be completely consistent with the mechanical analysis model, and the node and unit numbers correspond one by one. The temperature field of packer rubber hysteresis can be regarded as a heat conduction problem with a heat source, and the heat conduction equation is In the formula, T ϕ is material temperature, K; K ij is the heat conduction coefficient in the specified direction, W/(m 2 K); Q is the heat generation rate in unit volume, J/(kg m 3 ); ρ is the material density, kg/m 3 ; c is the specific heat capacity, J/(kg°C). The convective heat transfer between the inner surface of rubber cylinders and the conveying liquid satisfies Newton's cooling equation In the formula, h is the convective heat transfer coefficient, W/(m 2 K); T r is the surface temperature of the inner chamber of the rubber cylinders, K; T f is the surrounding liquid temperature, K.

| Calculation of sealing and bearing capacity performance of rubber cylinder
To verify the reliability of the sealing performance of the expansion rubber cylinder under the action of 70 MPa downhole pressure, calculate the various parameters of the rubber cylinder sealing well wall and base pipe under different expansion clearances according to the working process of the expansion rubber cylinder. The working structure diagram of the rubber cylinder is shown in Figure 15.
According to the working environment of the downhole packer and the compressibility characteristics of the rubber, Figure 16 shows the four corresponding results under different expansion clearances and 70 MPa pressure. When the expansion gap is 12.5 mm, it is found from the sealing contact pressure diagram that the rubber cylinder is in close contact with the inner wall of the well and has good sealing performance. The maximum stress of the rubber cylinder itself is 7.52 MPa, the maximum displacement of the rubber cylinder is 7.95 mm, the maximum shear stress of the rubber cylinder is 4.14 MPa, and the maximum contact pressure of the rubber cylinder is 129.55 MPa, and these four maximum values are distributed at the extrusion position of the fixed ring and the rubber cylinder, which are the most susceptible to the load. However, the maximum stress does not exceed the required deformation range of rubber material.
To further intuitively compare the stress, shear stress, contact pressure, and displacement change rules of the inner and outer rings of the cylinder under different expansion gaps according to the finite element calculation results, select the node path of the inner and outer rings of the rubber cylinder according to the finite element model, as shown in Figures 17 and 18.
The stress, shear stress, contact pressure, and displacement curves of the inner and outer circles of the rubber cylinder can be obtained from the analysis of the above different expansion gaps, as shown in Figures 19 and 20. When the expansion gap is between F I G U R E 17 Finite element model.

F I G U R E 18
Nodes path of the inner and outer wall.
1.5 and 12.5 mm, the various parameters of the rubber cylinder gradually increase with the enlargement of the expansion gap. The stress, shear stress, contact pressure, and displacement of the rubber cylinder are small when the expansion gap is between 1.5 and 6.7 mm, and the rubber cylinder is relatively safe, but the sealing performance is not optimal. Although the sealing performance of the rubber cylinder is brilliant when the expansion gap is 12.5 mm, the stress and deformation are large, and the safety is reduced. When the expansion gap is between 9.6 and 12.5 mm, the difference in stress, shear stress, contact pressure, and displacement of the rubber cylinder is relatively small. The contact pressure is greater than the external pressure of 70 MPa on the main sealing path. Compared with other expansion gaps, the deformation and sealing performance of the rubber cylinder are relatively stable, and the expansion gap also meets the site operating requirements.
According to the above calculation and analysis results, the expansion rubber cylinder of 2 m length can meet the needs of on-site use when the expansion gap changes from 9.6 to 12.5 mm. To further analyze the strength and sealing performance of the rubber cylinder under the action of downhole high temperature, the thermal coupling analysis of the expanded rubber cylinder is also required.  Figure 21A.

| Computer model of finite element and boundary condition
When the working state of the rubber cylinders is stable, the inner and outer temperatures of the rubber cylinders are still equal to the downhole temperature, 36 which is taken as 100-140°C. The heat exchange between the outer surface of the rubber cylinders of the packer and the drilling fluid can be regarded as the convective heat exchange of fluid flow.
The temperature field distribution of packer rubber in the laboratory test under the normal temperature ranges from 100°C to 140°C without external pressure and is shown in Figure 21B. The higher the external temperature is, the larger the temperature gradient is. When the temperature is 140°C, the gradient is 15°C. The gradient is 11°C when the temperature is 100°C. In the context of the conventional temperature, the temperature has little effect on the rubber cylinders.
3.3 | Temperature distribution of the packer rubber Figure 22 demonstrates the distribution of the temperature field of the packer rubber cylinder with the consideration of its thermogenesis hysteresis when the formation temperature ranges from 100°C to 140°C and the hydraulic pressure of the production layer is 50 MPa. The maximum temperature increases gradually from outside to inside. When the outer ring temperature is between 100°C and 140°C, the internal temperature rises to 37°C under the thermomechanical coupling effect as shown in Figure 22.
The temperature field of packer rubber in a stable state is symmetrically strip-distributed in the middle of the rubber cylinders as shown in Figure 23, and the highest temperature zone is located in the center of the strip. When the temperature is 140°C in a stable environment, the maximum temperature can reach 172°C; under thermomechanical coupling, the increase in temperature is 22°C.
Compared with the initial data, the temperature gradient in stable conditions is smaller. Since the working performance of packer rubber is more sensitive to temperature, the equal wall thickness bushing has remarkable advantages in prolonging service life and improving the working performance of packer rubber.
In the context of practice, two kinds of rubber are often used together. This type of expansion packer is designed as a sleeve, which can be quickly installed on the site, and flexible adjustments are available at the last moment. The cured elastomer is bonded to the thin metal casing, which is fixed on the casing joint through the set screw. Figure 24 shows the working sealing state diagram of a certain type of expansion packer. The field application shows that the expansion packer designed in this paper is combined with multisection rubber. Compared with the single-section rubber packers, the multisection ones can withstand greater pressure load, with better sealing performance and higher resilience in operation conditions.

| CONCLUSION
(1) It is apparent that the higher the temperature is, the greater the expansion rate of rubber is through the experiments of liquid rubber at 70°C, 120°C, and 140°C.
(2) The effect of temperature increase on rubber expansion is distinct. The expansion ratio of oilencountering rubber reaches 4.55 times at 120°C in diesel; however, in previous tests at 70°C, the expansion ratio of oil-encountering rubber reaches only 2 times in 48 h in diesel. (3) Experiments in different temperatures show that the higher salt concentration is related to the lower expansion rate and the higher expansion rate in clear water. At the same time, the maximum volume of expansion in clear water increases. (4) The higher the concentration of diesel, the faster and larger the expansion rate is. Moreover, it is noted that the higher the temperature is, the higher the expansion rate. (5) After the thermal coupling analysis, it is evident that the distribution of the internal temperature field maintains even in the inflatable packer rubber with a certain length, lacking heat accumulation. Additionally, the packer rubber displays a brilliant performance in heat dispersion and the temperature differences intend to decline with the increased formation temperature, which can result in little effect on the reliability of the packer rubber to enhance its performance and extend service life.