An Analytical Two-Phase Flow Model for Prediction of Leakage in Wet Gas Labyrinth Seals and Pocket Damper Seals. Is Simplicity Still Desired?

Current and upcoming two-phase pump and compression systems in subsea production facilities must demonstrate long-term operation and continuous availability. Annular pressure seals, limiting secondary flow, also influence the dynamic stability of turbomachinery. Hence, it becomes paramount to quantify the leakage and dynamic performance of annular seals operating with a liquid in gas mixture (wet gas). The paper develops a simple analytical model predicting the leakage and cavity pressures for Labyrinth seals and pocket damper seals (PDSs) operating with two-phase flow. The model adapts Neumann's equation with a homogeneous flow model. Predicted leakage for a four-blade PDS operating under a low supply pressure (2.3 and 3.2 bar) and a low rotor speed (5,250 rpm) agree well with experimental results for both a pure gas and a wet gas conditions. For an eight-blade PDS supplied with air at 62.1 bar, discharge pressure 31.1 bar and rotor speed of 15 krpm, the analytical model predicts leakage that is just 2% larger than a CFD prediction. For the PDS supplied with an oil in gas mixture having gas volume fraction = 0.92 ~ 0.98, the simple model delivers leakage that is up to ~ 6% lower than published CFD results. Throughout the life of an oil well that sees radical changes in gas and liquid composition as well as pressure conditions, the expedient model, quick and accurate to estimate leakage in wet gases seals, can be readily integrated into an engineering routine or practice.