Summary 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 factor, 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 operating conditions, pipe geometry, and fluid properties. Two sets of facilities, a small-scale facility with 51-mm internal diameter (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 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® (a commercial transient multiphase-flow simulator by Scandpower Petroleum used widely in the petroleum industry) performance was also presented. Literature Review 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 underestimation of pressure gradient will give a smaller pipe size than required, and the transportation capacity will be restricted; model overestimation of pressure gradient will result in an oversized pipeline, worse sweeping characteristics, and possible solids dropout and corrosion issues. In this section, some of the previous work on stratified flow were reviewed. Taitel and Dukler (1976) proposed a 1D two-fluid model that assumed a flat gas/liquid interface. A Blasius-type equation was used to calculate gas-wall and 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(1979) 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 dependent only on radial distance from the pipe wall. Akai et al.(1981) 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(1984) 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 the liquid phase. Issa(1988) 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.

Transient gas-liquid flow is a common phenomenon in the drilling, workover and gas/oil production processes. Any change in the operating conditions at the inlet or outlet will introduce a transient response. Operations such as liquid unloading, under balanced drilling with gasified fluid, well control, cementing, hole cleaning, pipeline startup and blowout may never reach a steady state. In order to simulate the flow system, several transient two-phase flow simulators have been developed in the past. However, these models are based on the two-fluid model approach. They are complicated and time consuming to run since they treat the gas and liquid phase separately in terms of pressure, temperature and velocity. In this paper a new transient two-phase flow model has been developed. In each time step, the two-phase flow regime, liquid holdup and pressure gradient are estimated with the empirical correlations which are well developed for the steadystate flow. A drift-flux equation was introduced to close the system. The model was validated against data collected from the public literature, field operations, and other transient software. Several field cases are used to illustrate the transient nature of pipeline production, underbalanced drilling (UBD), sand cleanout, and liquid unloading. The benefits of using the transient simulation for the operational design, training and job execution are also discussed.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractA 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.

Transient multiphase pipeline models have found wide use in upstream oil and gas production. Such models have been successfully used to estimate such transient events as flow ramp-up, pigging, and terrain slugging. However, it is not often appreciated how much can be done using steady-state multiphase models. Such models - along with minimal additional analysis - can be used to estimate liquid flow rate, liquid hold-up and pressure drop changes that are equivalent to full transient simulations. The focus of this paper will be on the use of steady-state models to estimate transient behavior, including estimates of ramp-up and pigging slugs, as well as terrain slugging severity (including slug size and frequency). Introduction Oil and gas production are, in most cases, gas-liquid multiphase flow rather than single-phase gas or liquid flow. Both transient and steady-state flow need to be simulated to properly design such a system and safely operate it. Intuitively, one would think that steady-state models should only be used for steady-state events; transient flow models would be required to simulate transient events, such as flow ramp-up, pipeline pigging, and terrain slugging. However, this may not be always true. This paper will discuss the use of steady-state models to estimate some transient events with some additional analysis, with accuracy comparable to transient simulations. By no means do the authors advocate the use steady-state models in all instances; transient flow models are definitely recommended where either too much analysis work is required, or the accuracy is significantly compromised through the use of steady-state models. Danielson et al. (2000) discussed in more detail where transient models should be used, and where steady-state models may suffice. Some exercises of using steady-state models to estimate transient events have been conducted by previous investigators (Cunliffe, 1978; Schmidt et al., 1985; Pots et al., 1987; and Xiao and Shoup, 1998). Cunliffe (1978) used steady-state liquid inventory to predict the ramp-up slug size and condensate flow rate at pipeline receiving end during a production ramp-up in a 107-km long, 0.5-m ID wet-gas pipeline. Comparison with actual condensate flow rate data showed errors within 15%. Schmidt et al. (1985) suggested that the existence of severe slugging in a pipeline-riser system can be determined using riser pressure drop - gas flow rate plot. If the curve has a negative slope, i.e. the riser pressure drop decreases with increasing gas flow rate, then the flow in riser is unstable and severe slugging may exist if other requirements are met. If the curve has a positive slope, i.e. the riser pressure drop increases with increasing flow rate, then the flow in riser is stable and severe slugging will not occur. Pots et al. (1987) argued that the relationship between unstable riser flow and severe slugging requires additional conditions be met in addition to the criterion of Schmidt. They proposed a dimensionless number, which is the ratio of pressure buildup rate in the pipeline to that in the riser. If the ratio is above one, which means the pressure buildup in the pipeline is faster than that in the riser, then severe slugging will not occur; if the ratio is less than one, severe slugging will take place. The smaller is this pressure build-up ratio, the more severe the slugging will be. Xiao and Shoup (1998) demonstrated that steady-state models can be used to extract important information such as pig transit time, liquid build up rate behind the pig, pig exit speed, the time for the pipeline to return to steady-state after pigging. Such information is of great importance to determine the slug catcher size and pigging frequency. This paper will focus on using steady-state models to predict slug size and liquid flow rate at pipeline receiving end during a production ramp-up, slug size from pigging a pipeline (both before and after the steady-state is reached in the pipeline), and severe slugging characteristics in a pipeline-riser system including its existence, slug size, and slug frequency. For comparison purpose, OLGA®5.3 (a transient multiphase flow simulator marketed and supported by SPT Group) was used for both the steady-state and transient simulations in the present study.