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 force coefficients of annular seals operating with two-phase flow, a liquid in gas mixture or wet gas. Until now, a simple model for labyrinth seals (LSs) and the more modern pocket damper seals (PDSs) is not available, though these seal types find wide applications in subsea machinery. The paper develops a simple analytical model predicting the leakage and cavity pressures for LSs and PDSs operating with two-phase flow. The model adapts Neumann’s leakage equation for use with the physical properties of a homogeneous two-phase flow mixture. Predictions of leakage for a four-blade, eight-pocket, fully partitioned PDS operating under a low supply pressure (P_S = 2.3 bar and 3.2 bar) and a low rotor speed equal to 5250 rpm (surface speed = 35 m/s) agree well with experimental results procured for both a pure gas and a wet gas conditions (2.2% in liquid volume). Predicted leakage and cavity pressures also agree with those found by a multimillion node computational fluid dynamics (CFD) model. For an eight-blade, sixteen-pocket PDS supplied with air at P_S = 62.1 bar, discharge pressure P_a = 31.1 bar, and rotor speed of 15 krpm (surface speed = 91 m/s), the analytical model predicts leakage that is just 2% larger than a published CFD prediction. For the PDS supplied with an oil in gas mixture having gas volume fraction β_S = 0.92–0.98, the simple model delivers leakage that is up to ∼6% lower than published CFD results. An analysis of the two-phase leakage predictions via a modified flow factor reveals a loss coefficient (c_d) impervious to the range of supply and discharge pressures considered and growing in proportion to the liquid volume fraction (LVF). 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.