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Abstract

A mechanistic two-fluid model with new closure relationships is proposed to predict liquid holdup and pressure gradient of stratified flow. The proposed closure relationships include correlations of wetted wall fraction, liquid-wall friction factor, and interfacial friction factor. An iterative calculation procedure is implemented to solve for liquid holdup and pressure gradient for a given set of operation conditions, pipe geometry, and fluid properties.

Two sets of facilities, a small-scale with 51-mm ID and a large-scale facility with 150-mm ID test sections, were used to tune the model. Superficial gas and liquid velocities were varied from from 5 to 25 m/s, and 0.00025 to 0.03 m/s, respectively in the small-scale facility while they were varied from 7.5 to 21 m/s, and 0.005 to 0.05 m/s, respectively in the large-scale facility.  The pipe inclination angle varied from -2˚ to 2˚. The liquid holdup was ranged between 0.003 and 0.12 emphasizing the low-liquid loading two-phase flow.

The tuned model performance was then benchmarked against the high-pressure (up to 90 bar) SINTEF stratified flow data. The model predictions agreed well with measured values of liquid holdup and pressure gradient. The comparison between the present model and OLGA performance was also presented.

Introduction

Stratified flow with a low liquid loading (< 1100 sm3/MMsm3) is a dominant flow pattern in wet-gas pipelines. A good prediction of liquid holdup and pressure gradient is critical to pipeline size selection and the design of downstream facilities (e.g., slug catcher). Model under-estimation of pressure gradient will give a smaller pipe size than required, and the transportation capacity will be restricted; model over-estimation of pressure gradient will result in an oversized pipeline, worse sweeping characteristics, and possible solids drop-out and corrosion issues.

Taitel and Dukler[1] proposed a one-dimension two-fluid model that assumed a flat gas-liquid interface. A Blasius-type equation was used to calculate gas-wall, liquid-wall friction factors. The effect of interfacial shear stress was taken into account. It was assumed that the interfacial friction factor was equal to the gas-wall friction factor for stratified-smooth flow, and 0.014 for stratified-wavy flow. Cheremisinoff and Davis[2] collected experimental data of air-water flow in a 63.5-mm ID horizontal flow loop. The liquid phase flow was modeled using an eddy viscosity expression developed for single-phase flow. To simplify the problem, the authors assumed that the shear stress was constant in the liquid region, and liquid velocity was only dependent on radial distance from the pipe wall. Akai et al.[3] solved the momentum equations for both phases. The turbulence effect was considered by using a modified model, which is applicable to low Reynolds number cases. Shoham and Taitel[4] numerically solved the liquid phase momentum equation, considering the gas phase as a bulk flow. The eddy viscosity model was applied to simulate the turbulence effect in liquid phase. Issa[5] solved the momentum equations for both gas and liquid phases to calculate pressure gradient and liquid holdup. The author used the two-equation model to simulate the turbulence effect in both phases.

Minami and Brill[6] investigated liquid holdup of horizontal gas-liquid two-phase flow. Two empirical correlations were developed. One is applicable only to wet-gas pipelines with a liquid holdup less than 0.35, and the other is more general, applicable to the whole range of liquid holdup in horizontal stratified flow.

Andritsos and Hanratty[7] found that interfacial friction factor increased linearly with superficial gas velocity, when it was larger than that needed to initiate waves. The interfacial friction factor was also affected by liquid viscosity and liquid flow rate, but was of secondary importance. An empirical correlation was proposed to estimate the interfacial friction factor of stratified-wavy flow.