Steady state and transient liquid gas pipe flow models

Abstract

Two-phase ow analyses are critical to successful design and operations of liquid-gas pipe ow applications found in major industrial fields, such as petroleum, nuclear, chemical, geothermal and space industries. Due to diffculties in obtaining analytical solutions, approximate solutions have been applied to two-phase flows. However, several limitations still exist, and categorised into three prediction models, namely: ow regime, pressure gradient, and transient models. Previous studies show that existing ow regime models and maps for horizontal flows under-predicts transition from stratified to annular flow. Furthermore, there is requirement to include criteria for identifying mist and plug flows in unified flow regime model. In order to improve under-prediction in stratified to annular prediction, nondimensional liquid lm height in original criterion is replaced with nondimensional liquid holdup. This shifts stratified to annular transition line towards higher gas superficial velocity thus improving prediction. Using experimental data available in literature, a simple flow rate dependent criterion is proposed for identifying the existence of mist flow. Two criteria are proposed for identifying plug flow in horizontal and inclined flows. The first criterion is the exact criterion for identifying bubble flow in vertical flows. The second criterion is also based on bubble flow criterion but fitted to experimental data. Transition criterion for the existence of dispersed-bubble flow is also proposed, based on stability of gas bubble in liquid ow. These flow regime criteria are combined in a solution algorithm to obtain a unified flow regime model, which has been verified using existing unified flow regime models and map, and validated using experimental data. Mechanistic or phenomenal methods are generally applied in predicting pressure gradient in two-phase liquid-gas pipe flow. These methods relies on prior knowledge of prevalent flow regime, and subsequent application of flow regime specific pressure gradient model. This approach is susceptible to error should wrong flow regime be selected. In order to overcome this problem, a Single Equation Two-Phase Mechanistic (SETM) model is proposed. SETM is obtained by combining: liquidgas momentum equations, existing and modified flow regime criteria, and new flow regime boundaries at the initiation and completion of transition to annular flow. Thus, SETM implicitly determines pressure gradient and flow regime in liquid-gas pipe flow, and also captures liquid-gas interface transition from at to curved interface. SETM is applicable to all pipe inclination, and has been validated using experimental data available in literature. Further, prediction of flow characteristic features per ow regime, such as identified flow regime, liquid holdup in slug lm region, ratio of slug regions, and apparent liquid heights, have been verified against theoretical limits for different flow regimes. Alternative to SETM, modified homogeneous pressure gradient model is also proposed for liquid-gas pipe flow. Existing homogeneous models are applicable to dispersed bubble flow, and slug flow with low or negligible liquid-gas slip. The modified homogeneous model is obtained by correcting mixture fanny friction factor using error between experimental pressure gradient and unmodified homogeneous pressure gradient; observed error is particularly large at high liquid-gas slip values. The modified homogeneous model is therefore applicable to all flow regimes, including stratified, annular, and mist flows. The modified model has been verified against existing homogeneous model, and validated using published experimental data. Transient analysis is critical to liquid-gas pipe flow design. Rigorous analytical solution is generally not available. Alternative solution method is full numerical solution approach, which is subject to high demand on computational resources and time, especially for long pipelines. Hence simplified transient methods are sort. Existing simplified transient liquid-gas pipe flow models assume quasi-steady state conditions for liquid-gas momentum equations, thus neglecting convective terms in the momentum equations. The simplified transient liquid-gas pipe ow model proposed in this study include: (a) transient liquid-gas continuity equations, (b) transient convective terms of liquid-gas momentum equations, and (c) steady state pressure gradient terms of liquid-gas momentum equations. The proposed transient model captures gas and/or liquid flow variations at coarse pipe discretisation, and has been validated against published experimental data and verified with a proprietary program (OLGA).