The present investigations on sealability evaluation for tubing and casing premium connections depend on the FEM with testing. This paper proposed a theoretical model to evaluate the sealability of a sphere-type premium connection based on make-up torque, which combines Hertz contact pressure and the von Mises yield criterion for calculating elastic–plastic contact pressure distribution on sealing interface and adopts the gas sealing criterion obtained from Murtagian’s experimental results for deducing gas sealing capacity. With the proposed model, the effects of additional make-up torque from the sealing interface on the sealing contact pressure distribution and key sealability parameters, including contact width, yield width, average contact pressure and gas sealing capacity, were analyzed and compared. The results show that additional make-up torque from the sealing interface closely influenced sealability parameters’ variation and gas sealing capacity. The gas sealing index based on the sealing contact energy theory should be recommended for sealability evaluation other than average contact pressure on the sealing interface. For improving gas sealability, make-up torque should be controlled accurately for ensuring enough average contact pressure and contact width but a proper yield width, and a lager sphere radius should be selected for reducing the risk of yield sticking.

This paper proposed a semi-theoretical model to quantitatively predict leakage rate of tubing and casing premium connections. The geometric parameters of the sealing surface profile approximated by a sinusoidal micro-convex surface were first obtained based on the random normal distribution sampling method. With the actual area prediction formula for elastic–plastic contact of an axisymmetric sinusoidal micro-convex body based on the equivalent simulation principle, the circumferential leakage width and radial average leakage height of the micro-leakage channel between sealing surfaces were then acquired with the surface roughness and geometric mean contact pressure. At last, the actual micro-leakage rate of the premium connection was derived by considering the non-uniform contact pressure distribution between sealing surfaces. An example was investigated to validate the model and reveal the sealing and leakage characteristics, and anti-leakage measures were proposed. The results show that average contact pressure, circumferential leakage width, and radial average leakage height between sealing surfaces were non-uniformly distributed. The leakage rate of a premium connection decreases exponentially with an increase in radial interference between sealing surfaces. In order to reduce leakage rate, it is beneficial to increase radial interference and lower sealing surface roughness.

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