Due to the complexity of sealing surface topography, it is difficult to take the surface topography into consideration when building a leakage rate model theoretically. Therefore, a theoretical model for estimating the leakage rate of metal-to-metal seals based on the fractal theory of porous medium, which can objectively reflect the influence of sealing surface topography from a microscopic perspective, is proposed in the present work. In the approach, fractal parameters are adopted to characterize the sealing surface. The sealing interface is supposed to be a porous medium space and the intrinsic parameters are obtained through rigorous theoretical derivation. The results show that the topography parameters of the sealing surface have a significant effect on the intrinsic parameters of the pore space and lead to a significant influence on the leakage rate of metal-to-metal seals. Specifically, the smoother the sealing surface, the lower the leakage rate of the metal-to-metal seal. Moreover, the leakage rate decreases with an increase in the contact pressure, and, if the fluid pressure difference is too large, the sealing performance will be seriously reduced. The proposed model provides a novel way to calculate the leakage rate of metal-to-metal seals.
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