High pressure sealing characteristics of combined structure based on flexible graphite rings

Seal components made of flexible graphite have excellent resistance to temperature, while sealing of high pressure fluids is unsatisfactory. The sealing behavior of flexible graphite rings is characterized by the ratio of the contact pressure to the axial pressure. The FEA results show that the lateral pressure decreases roughly linearly along the direction of the sealing path, and the lateral pressure coefficient increases with increasing axial pressure. We design a combined seal structure based on flexible graphite rings, and extract the contact pressure along two sealing paths. The results imply that the self-sealing effect is more favorable when the pressure of the sealing fluid is increased. The effect of the friction coefficient on the contact pressure is not significant, except at the beginning of the sealing path. Sealing effects are tested under the coupling condition of 350°C and 50 MPa, which verify the sealing performance under high temperature and high pressure. The comparison of the test results of “kf” (the product of lateral pressure coefficient and friction coefficient) with those of the FEA validates the rationality of the analytical approach. The comprehensive coefficient “kf” can be easily obtained by testing, and can be used as a key parameter for seal design.


Introduction
In unconventional oil and gas resource development, high temperature geothermal extraction and utilization, underground coal gasification exploitation, equipment and tools are challenged by the high temperature and high pressure environments. The geological factors and operating conditions are complex, high temperature and high pressure are common in the downhole, the temperature may reach 350°C and may accompany pressure of more than 50 MPa under extreme conditions, in which sealing problem is one of the key technologies for downhole testing and operating tools. 1 At the same time, since the radial size of the downhole tool is mostly constrained by the bore size, the design of the sealing structure is also considerably limited, and rubber sealing is the preferred option when the temperature range is acceptable.
Rubber seals have the advantage of strong elasticity and simple sealing structure, but the maximum temperature of rubber seal elements for long-term stable working is limited. Mahankar and Dhoble summarized the selection reference of rubber seal materials under different working temperature ranges based on literatures, and even if the fluororubber of best temperature resistance is used, the maximum temperature for long-term stable operation is only about 230°C. 2 Degradation of seal life and deterioration of performance occurs at moderate to high temperatures. In fact, thermal effects and temperature resistance have ever been concerned for the sealing of rubber-based materials. [3][4][5] Metal-to-metal seals have the advantage of high temperature resistance and strong pressure bearing capacity, and are widely used in static seals for the aerospace and nuclear industries. Garfield and Mackenzie discussed the use of metal-to-metal seals in down-hole equipment under high temperature and pressure conditions. 6 Sufficient excitation force is required for metalto-metal sealing due to the poor resilience of metallic material. 7 Moreover, metal-to-metal contacts may have the tolerance fit change at high temperature differences, making it difficult to provide a reliable seal. 8 In order to improve the resilience and self-sealing performance, seal parts of different section shapes, such as O, C, and W shapes, have been discussed. 9,10 These section shapes of seals improve the sealing performance, but its manufacturing and installation accuracy requirements are quite strict, and the roughness of the sealing contact surface needs to be excellent handled. 11 Moreover, due to the limitations of the intrinsic mechanical properties of metals, the contact stress of the metal-to-metal sealing surface and the wear of the contact surface are a pair of contradictions that are difficult to resolve, and it is difficult to compensate after the contact surface wear. Therefore, metal seals are mainly used for static sealing, but rarely for dynamic sealing.
Flexible graphite is a good sealing material due to its high compressional resilience, low stress relaxation rate, and excellent resistance to temperature, radiation, and corrosion. 12,13 Flexible graphite ring seals have been widely used in the nuclear industry. 14,15 The resilience of flexible graphite is better than that of metal, but it is still not as excellent as that of rubber, and therefore a pre-tightening force is also required for flexible graphite sealing. Flexible graphite itself is also an excellent solid lubricant with a small friction coefficient, 16 and it is better suited for dynamic sealing requirements. Flexible graphite is commonly used for stuffing box seals, which are the most common type of pump shaft seals. The sealing mechanism of the flexible graphite stuffing box seal is formed as a combination of two successive hydraulic resistances: a pre-switch resistance and a contact seal. Leakage occurs due to looseness in the packing structure, shaft runout, local thermo-hydraulic effects, and other factors, and decreases with increasing contact pressure. 17 The interface contact pressure depends on several parameters including geometry, material and friction. 18 The mechanical behavior of a packing seal is characterized by the transmission ratio of the radial stress over the axial stress, known as the lateral pressure coefficient, which is one of the required parameters used to select packing seals. 19 Zhou et al. investigated the compressive resilience, radial contact stress, and sealing properties of graphite packing rings with different densities by testing, and results showed that the radial contact stress on the sealing surface is linearly and positively correlated with the axial load, with little effect of density. 20 Micro-mechanisms of compression and recovery behavior in flexible graphite have been examined involving the direct observations and measurements using synchrotron X-ray microtomography. The microstructural unit was found to be composed of thin expanded graphite discs with slightly misaligned basal planes of graphite. The macroscopic compression behavior of flexible graphite is attributable to a combination of bending and thickness reduction/ recovery of the discs. 21 For sealing structures, it is relatively simple to use rubber seals, which can be installed directly in the grooves, and retaining rings can be added to one or both sides of the seal to sustain higher fluid pressures. In addition, for high-pressure dynamic sealing, rubber seal rings are generally equipped with a hard-slip ring to form a combined seal. For metal-to-metal sealing, metal rings with different profiles are mainly used as static seals, which requires a large initial excitation force during seal installation. Therefore, the seal needs to be designed with a pre-loaded structure, for example, a high-pressure flange sealed by a metal ring that is directly pre-tightened by connecting bolts. For dynamic seals, however, metal-to-metal seal structures are generally more complex, typically consisting of a static ring and a dynamic ring, and rubber parts are still commonly used as auxiliary seals. Seal components made of flexible graphite materials are usually in the form of stuffing with flat or wedge-shaped rings, 17,22 and the sealing structure is relatively simple. Commonly, multistage seals are used, which also need to be pressed during installation, and the pressure needs to be maintained during working.
Flexible graphite seals have great temperature resistance, elasticity and lubrication properties and are suitable for sealing beyond the service temperature of rubber. However, the strength performance of seals made of flexible graphite is generally unsatisfactory and it is necessary to design a reasonable structure for sealing at high pressure. Typically, flexible graphite is made into rings and filled into a sealing box, known as a packing seal, which is loaded with sufficient axial compression force to generate lateral contact pressure to seal the fluid medium. In this paper, we focus on high-pressure radial sealing of shaft-cylinder and discuss the characteristics of the lateral pressure coefficient of flexible graphite rings. Based on this, we design a combined sealing structure for the high temperature and high pressure sealing requirements, and discuss its sealing properties by combining FEA and testing.

Mechanical analysis of sealing ring
The sealing performance is determined by the contact stress of the sealing surface, which should be larger than the pressure of the fluid being sealed. The contact stress acting on the sealing surface is generated by the axial compression force. Figure 1 shows the fundamental relations of the forces on the flexible graphite ring.
Equation (1) is the equilibrium equation for forces on the flexible graphite ring.
Where F 1 and F 2 are the frictional forces on the cylindrical surfaces corresponding to ''r 1 '' and ''r 2 ,'' respectively, and can be expressed as: Where p r 1 = k 1 p z and p r 2 = k 2 p z are the lateral pressures on the cylindrical surfaces corresponding to ''r 1 '' and ''r 2 ,''m 1 and m 2 are the friction coefficients, k 1 and k 2 are the lateral pressure coefficients, and p z is the axial pressure of the flexible graphite ring. By substituting the parameters, equation (1) can be written as follows.
À dp z p z = bdz ð3Þ By integrating equation (3), we can obtain p z = p 0 e Àbz . According to the sealing requirements, the corresponding lateral contact stress at axial (z . 0) shall not be less than the pressure of sealed fluid. Equation (4) shows the relation.
Where p i is the pressure of sealed fluid. Regardless of the difference of the friction coefficient and the lateral pressure coefficient on the two sides, the axial pressure at the starting position of the sealed fluid side shall obey the following relation: This expression can be used to guide the design of axial loading. In general, it is preferable to use the pressure of the sealed fluid to generate the axial pressure, that is, the effect of self-sealing. Unfortunately, it is difficult to obtain the lateral pressure coefficient directly, which is a key parameter. The FEA method is used to study the lateral pressure coefficient.
We use the ANSYS WORKBENCH software to construct an axisymmetric analytical model, as shown in Figure 2. Due to the complex mechanical properties of flexible graphite, the constitutive relations of flexible graphite in the FEA are approximately described by hyperelastic materials. Adopting the Neo-Hookean model, which has strong universality for large strains, only a few compressed experimental data are required to obtain the model parameters. The flexible graphite ring used has a density of 1.7 g/cm 3 , a compression rate of 10% and a recovery rate of 85%. The Neo-Hookean model is adopted for flexible graphite material, with model parameters u (initial shear modulus) and D 1 (incompressible parameter of material) calculated from the experimental compression data. By loading the flexible graphite ring with different axial pressures, the contact stress at the sealing surface (i.e. the lateral pressure) is calculated. The ratio of the lateral pressure to the applied axial pressure is defined as the lateral pressure coefficient.  The modeled flexible graphite ring has an outer diameter of 55 mm, an inner diameter of 49 mm, and a thickness of 5 mm. The friction effect between the flexible graphite ring and the sealing surface is taken into account and the value of the friction coefficient is set to 0.15-0.25. Axial pressure loading ranges from 5 to 70 MPa. Figure 3 shows the corresponding lateral pressure at different axial positions, with the friction coefficient set to 0.2. The lateral pressure decreases gradually along the axial direction, and the decreases approximately linearly except for an accelerated drop at the end. The variation of the lateral pressure along the axial direction is similar on the inner and outer sides of the seal ring. Figure 4 shows the lateral pressure distribution along the axial direction for different friction coefficients with an axial pressure loading of 50 MPa. The corresponding lateral pressure increases slightly when the friction coefficient is smaller. The lateral pressure is not a constant value along the sealing surface. For convenience of calculating the lateral pressure coefficient, the lateral pressure is averaged along the path of the sealing surface (z-direction). Figure 5 shows the average lateral pressure coefficient for different axial pressure loading. The average lateral pressure coefficient generally shows an upward trend with increasing axial pressure loading, varying from 0.78 to 0.90. When the axial pressure is less than 20 MPa, the variation of the average lateral pressure coefficient is less pronounced. The lateral pressure coefficient decreases when the friction coefficient increases for the same axial pressure loading.

Combined seal structure
The lateral pressure coefficient is less than 1, which means that the contact stress (lateral pressure) of the sealing surface is less than the seal ring axial pressure. If the axial pressure on the sealing ring is equal to the pressure of the sealing fluid, the resulting contact stress is insufficient to seal the fluid. Special design of the sealing structure is required to increase the axial pressure on the flexible graphite ring and to achieve self-sealing by relying on the pressure of the sealing fluid. The    design idea is to change the axial bearing area of the flexible graphite ring to increase its axial pressure. For the requirements, we design a combined seal structure that operates in high temperature and high pressure conditions, as shown in Figure 6. The combined seal consists of two support rings, two flexible graphite rings and a set of Belleville springs. The inner and outer flexible graphite rings are restrained during installation by a pair of support rings. When assembled, the two support rings are pressed from the top and bottom directions into the space between the inner and outer flexible graphite rings, which are constrained by the two support rings. The material of the support ring is commonly stainless steel (AISI 316L), and its hardness should be about 50HB lower than that of the sealing surface. Multiple groups of combined sealing components can be installed, with a set of Belleville springs arranged between the two groups. The Belleville spring is used to provide the initial pre-load to the sealing assembly.
In accordance with the sealing requirements, the lateral pressure and the sealing fluid pressure shall obey the following relations.
Where A i is the acting area of the sealed fluid pressure, A z is the axial sectional area of flexible graphite ring. Therefore, the area ratio should follow the condition: Based on the analysis of the lateral pressure coefficient, the dimensions of the outer and inner graphite rings have been designed by taking the value of ''k min '' at 0.78. The diameters are 49.5 and 55 mm of the outer flexible graphite ring, and those are 40 and 45.5 mm of the inner ring. The diameter of the support ring is slightly smaller than that of the flexible graphite ring, and the installation clearance should be considered to prevent scratching or even locking with the sealing surface during thermal expansion at high temperatures. The clearance can be calculated as follows.
Where d 0 is the initial installation clearance, which can be determined based on the clearance of the hydraulic cylinder O-ring seal, with a tolerance fit of H8/f7; Dd is an additional clearance, which is determined by the thermal expansion coefficient of the materials and the maximum working temperature, and can be calculated as follows.
Where a 1 and a 0 are the material thermal expansion coefficients of the support ring and the cylinder/shaft, DT is the temperature rise, and R 0 is the radius of sealing surface. The FEA model is shown in Figure 7, and model settings are similar to that of the FEA for the lateral pressure coefficient. The axisymmetric model is used for the FEA, and the quadrilateral mesh is used for meshing on the symmetric section. The mesh of the contact surface is refined and the mesh size is set to 0.2 mm. The contact surfaces between the flexible graphite ring and the support ring, as well as between the flexible graphite ring and the cylindrical surface of the cylinder and shaft, are set to be friction surfaces, which can define the value of the friction coefficient. There is an assembly clearance between the lateral side of the support ring and the cylindrical surface of the cylinder or shaft, which is set to be no-contact surface.

Results and discussions
In the combined seal structure, each flexible graphite ring has two sealing surfaces: one is the lateral contact surface, which is the main sealing surface; the second is  the contact surface between the seal ring and the highpressure side support ring, which belongs to the inner surface of the combined seal. Figure 8 shows the contact stress distribution on the sealing surface (the sealed fluid pressure is 50 MPa). The contact stress on the sealing surface near the high-pressure fluid side is relatively large and gradually decreases along the sealing path.
We extract the value of the contact pressure along the sealing path. Figure 9(a) and (b) show the change of contact pressure along the seal ring end surface (x direction), and Figure 9(c) and (d) show the change of contact pressure along the lateral contact surface (z direction), respectively. The contact pressure decreases along the sealing path in both directions, and the decrease is more pronounced at the end of the path. The larger the pressure of the sealed fluid, the more significant is the decrease of the contact pressure along the sealing path.
When the contact pressure is greater than the pressure of the sealed fluid, it is considered to be effectively sealed. When the pressure of the sealed fluid is large, the path length of the effective seal increases and the seal is more reliable. This implies that the self-sealing effect is more favorable when the pressure of the sealed fluid is increased. On the path (z direction) of the lateral sealing surface, when the pressure of the sealed fluid is lower than 10 MPa, the effective sealing path is short, and the sealing reliability should be paid attention to. For low-pressure sealing, it is recommended to reinforce the force of the Belleville spring when installing the combined seal, which increases the initial axial pressure on the flexible graphite ring.
The effect of the contact surface friction coefficient on the contact pressure is shown in Figure 10 (the sealed fluid pressure is 50 MPa). At the beginning of the sealing path, the greater the friction coefficient, the larger the contact pressure, while the effect of the  friction coefficient on the lateral pressure is reversed after leaving the beginning section of the path. The length of the sealing path where the friction coefficient has a noticeable effect on the contact pressure is short. In general, it can be considered that the friction coefficient has a limited effect on the contact pressure.

Sealing test device
The sealing test setup is shown in Figure 11 and consists mainly of a pressurization unit, heater, test assembly, cooling unit and back pressure unit. The test temperature of the device can be increased to 350°C, and the maximum test sealing pressure is 70 MPa, which can test static seal and a certain speed of sliding seal at high temperature and high pressure. Heat-resistant hydraulic oil is used as the sealing medium. During the test, first turn on the heater to heat the oil up to the target temperature and keeping it there, and then the pressure of the sealing medium is raised to the target value by using the hydraulic cylinder loading. The seal pressure is monitored by a pressure transducer to check if the seal is reliable.

Test results
We tested both static and sliding sealing at different temperatures, with a target value of 50 MPa for the pressure of the sealing liquid. Figure 12 shows the seal pressure fluctuations for different sliding speeds of the shaft. In the static sealing state (v = 0), the pressure is stable at different temperatures. When the shaft is sliding at a certain speed, the measured seal pressure fluctuates slightly, with a fluctuation rate between 2% and 4%. This fluctuation is stochastic, and the difference of the temperature and the sliding velocity has no appreciable tendency to affect the pressure fluctuations, which may be induced by the hydrodynamic forces induced by the velocity fluctuations. Since the pressure fluctuation is slight, it can be considered that the designed combined seal meets the operating requirements of temperature (350°C) and pressure (50 MPa), and indicates that the FEA results can provide a better guide for the combined seal design.
It is difficult to measure the friction coefficient and the lateral pressure coefficient separately, and we understand from the above FEA results that the lateral pressure coefficient is also affected by the friction coefficient. Thus the product of the lateral pressure coefficient and the friction coefficient is used as a comprehensive index (''kf'') to process the test data. Equation (10) shows the parametric relation.
Where p hc is the working pressure of the hydraulic cylinder whose piston area is A hc .   The differential value of the axial force (DFz) is calculated from the loading pressure and the sealing fluid pressure during the test. Figure 13 shows the comparison of the ''kf'' values between the test results and the FEA calculations. At static sealing, the ''kf'' test results are close to the ''kf'' curve obtained from the FEA, corresponding to a value of 0.2 for ''f''. When sliding at a certain speed, the ''kf'' test results lie between the ''kf'' curves obtained from the FEA with values of ''f'' between 0.15 and 0.2. Combining this test with the FEA results, it can be roughly inferred that the actual static friction coefficient is about 0.2 and the dynamic friction coefficient is between 0.15 and 0.2.

Conclusions
As a sealing material, flexible graphite has better temperature resistance than rubber and better elasticity than metal, and can be used in adverse working conditions beyond those of rubber and metal seals. A combined seal structure based on flexible graphite rings is designed by theoretical analysis and FEA. The static sealing and a certain speed of sliding sealing under high temperature (350°C) and high pressure (50 MPa) are effective by experimental verification.
The lateral pressure coefficient is a key parameter in the design of high pressure seals for flexible graphite. The lateral pressure gradually decreases along the sealing path of the lateral contact surface, and the average lateral pressure coefficient generally shows an upward trend with increasing axial pressure loading. The variation of the contact pressure with the sealing path of the combined seal is obtained from the FEA calculations, and the results imply that the self-sealing effect is more favorable when the pressure of the sealed fluid is increased.
The lateral pressure coefficient (''k'') and the friction coefficient (''f'') are not independent parameters, and the analysis shows that effects of the friction coefficient on the lateral pressure coefficient are different along the sealing path. It is difficult to measure these two coefficients separately, while the comprehensive parameter of ''kf'' can be easily obtained from the test, which has a guide for seal design. The combination of FEM analysis and ''kf'' testing is an effective design approach.

Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was funded by Sinopec Key Laboratory of cementing and completion, grant number 35800000-22-ZC0607-0040 and Hubei Engineering Technology Research Center of industrial internet of things intelligent sensing, grant number KXZ202101.