# Scalability Analyses of Premium Connections Characterized by a Surface Fractal Function
## 4 Analysis of the Sealability of Premium Connections  
For a premium connection with a metal-to-metal sealing structure, achieving sealability relies predominantly on the distribution of contact pressure across the sealing surface. The influencing factors mainly include the geometric structure of the sealing surface, the properties of the metal materials, the properties of the sealing surface, the service environment, the load conditions, and whether a thread compound is used. The traditional design concept of sealability is that if the mean contact stress on the sealing surface surpasses the fluid pressure in the pipe, it will meet the requirements of sealability. However, sealing structures designed in line with this concept still leak [30]. Thus, this study utilized a model for sealing contact strength to assess the sealability of a premium connection.  
On the basis of the theory of sealing contact energy, [PERSON] established a weighted model of sealing contact strength to evaluate the sealability through experiments and a numerical simulation study [9].  
\[W=\int_{0}^{l}{p_{s}}^{m}dl={p_{av}}^{m}l \tag{23}\]  
Here, \(P_{av}\) is the average contact pressure (in Pa), \(W\) is the sealing strength (in m\(\cdot\)Pa\({}^{1.2}\)), \(l\) is the contact length of the sealing surface (in m) and \(m\) is the correlation index. If a thread compound is used, \(m=1.2\); if no thread compound is used, \(m=1.4\). In this case, we selected \(m=1.4\).  
\[W_{ac}=\left\{\begin{array}{l}1.843\times\left(\frac{p_{g}}{p_{a}}\right)^{1.177}(m\cdot Pa^{1.2})\\ 103.6\times\left(\frac{p_{g}}{p_{a}}\right)^{0.838}(m\cdot Pa^{1.4})\end{array}\right. \tag{24}\]  
Figure 14: Distribution of the contact pressure under internal pressure.  
Here, \(W_{ac}\) is the critical sealing strength (in m\(\cdot\)Pa\({}^{1.2}\)), \(P_{a}\) is the atmospheric pressure (in Pa, the standard atmospheric pressure here was \(1\times 10^{-5}\) Pa) and \(P_{g}\) is the pressure of gas to be sealed (in Pa).  
In order to effectively assess the sealing ability of a premium connection, [PERSON] optimized Equation (24) and established a model for the critical sealing strength of a cone-cone premium connection [31].  
\[W_{ac}=10\times\left(\frac{p_{g}}{p_{a}}\right)^{0.838}(m\cdot Pa^{1.4}) \tag{25}\]  
To ensure that a premium connection does not leak, it must meet the condition \(W\geq W_{ac}\).  
According to Equation (25), the critical sealing contact strength \(W_{ac}\) of a premium connection is \(3.12\times 10^{6}\) m\(\cdot\)Pa\({}^{1.4}\). According to the results of the above FEA and Equation (23), the sealing contact strength \(W\) of a premium connection under different axial forces and internal pressures can be calculated (as shown in Table 5). In the example shown in Figure 15, the sealing contact strength \(W\) under axial tension and internal pressure is greater than the critical sealing contact strength \(W_{ac}\), but there are still potential sealing failure points. For example, when the axial force is \(1.2\times 10^{6}\) N, the sealing contact strength \(W\) is reduced by 30%. Although the sealing contact strength \(W\) increases under the internal pressure, a large area of plastic deformation appears on the sealing surface when the internal pressure is \(1\times 10^{8}\) Pa (as shown in Figure 13). The strength failure can also lead to sealing failure on the sealing surface. Through the above analysis, it can be concluded that the premium connection in this study has a higher risk of sealing failure when the axial tension is \(1.2\times 10^{6}\) N or the internal pressure is \(1\times