On the Modeling of Gas and Liquid Leaks Through Packed Glands

The prediction of gas and liquid leak rates through packed glands is overlooked and the very few studies available in the literature focus on the packing axial stress distribution. For better prediction of leakage, the change of porosity with length due to this nonuniform axial stress must be accounted for. Our previous theoretical model on leakage predictions are based on uniform capillaries. In this paper, a new model that accounts for the change of the capillary diameter with the axial stress for gaseous leak and a straight capillary model for liquid leaks are developed. The first slip flow condition is used to predict gas and liquid flow considering straight capillary model and a nonuniform capillary model the area of which dependents on the axial stress in the packing rings. An approach that uses an analytical-computational methodology based on the number and the size of pores obtained experimentally is adopted to predict gas and liquid leak rates in both the uniform and nonuniform compressed packed gland models. The Navier–Stokes equations associated with slip boundary condition at the wall are used to predict leakage. Experimental tests with helium, argon, nitrogen, and air for gazes and water and kerosene for liquids are used to validate the models. The porosity parameters characterization is conducted experimentally with a reference gas, namely, helium at different gland stresses and pressures.