The prediction of gas and liquid leak rate through packed stuffing boxes subjected to gas flow is a subject of very few studies in the literature. For better prediction of leakage, the change of porosity with length due to the non-uniform axial stress must be accounted for. There are few theoretical models on the prediction of leak rates in packing rings with capillary models. However, a model that incorporates the change of the capillary area with stress gives a better prediction.

In this paper, the first slip flow model is used to predict gas and liquid flow considering the straight capillaries and capillaries having an area dependent 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 uniform and non-uniform compressed yarned packings. 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 will be used to validate the models. The porosity parameters characterization will be conducted experimentally with helium at a reference gas at different gland stresses and pressures.

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