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Nonhomogeneous Two-Phase Flow in Pipes

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This type of flow is the most popular in pipes and wellbores. It results from the flowing phases having different in-situ velocities, namely, a nonzero slippage. In the case of gas-liquid flow, slippage is defined as the difference between gas and liquid in-situ velocities as follows,


In this case, the phases arrange in different types of flow patterns. Identifying the existing flow pattern in a pipe segment is the key for pressure drop and temperature profile predictions.

Nonhomogeneous Two-Phase Flow Models

Emperical Models

The empirical models use experimental data to correlate between dimensionless numbers. These models are short of capturing the physics of the flow, however, some of them are widely used in the industry, especially for steady-state flow, due to their simplicity.

Mechanistic Models

These models are more conserved to the physics of the flow and involve a hierarchy of mixed analytical solutions and empirical models. These models are more conservative to physics than the empirical models and are more accurate especially for those evaluated against experimental data. "To be simple, the mechanistic modeling approach captures the dominant physical phenomena and ignores the less important ones. Since mechanistic modeling simplifies nature, the resulting model must be verified by experiments to ensure its accuracy. " (Alsafran and Brill, 2017). Mechanistic models are widely used in the industry within code that simplifies the solution procedure.

Flow Calculation Procedure For Steady-State Flow

Al-Safran and Brill (2017) summarize the flow calculation procedure for the steady-state case as shown in fig. (1). The inputs for each pipe segment include fluid properties, pipe configuration, and flow conditions. The inputs are fed into the calculation models to identify flow patterns, based on the flow pattern, other calculation models are used to flow characteristics, e.g. liquid holdup and slug properties (if applicable). Then, the pressure gradient is found. In the case of a nonadiabatic flow, an iterative procedure is used to identify the temperature profile.

Figure 1. Nonhomogeneous two-phase flow calculation process (Alsafran and Brill, 2017)

Flow Patterns

The flow pattern is the geometric distribution of flow phases in the radial and the axial direction along the pipe. The main observed flow patterns observed in horizontal and near-horizontal pipes are dispersed, stratified, intermittent, and annular flows. Fig. (2) shows the two-phase flow patterns in horizontal and near-horizontal pipelines.

Figure 2. The two-phase flow patterns in horizontal and near-horizontal pipelines

Dispersed Flow

In this type of flows, one phase of a relatively lower flow rate is dispersed into a continuous phase that moves at a relatively high flow rate. Even though the flow rates are different, the mixture seems to travel at the same in-situ velocity. Thereby, the slippage or the difference between gas and liquid velocities are approximated at zero. Therefore, this flow pattern is effectively approximated with homogeneous flow models. There are two types of this flow.

1. Dispersed Bubble Flow: The liquid is the continuous phase while gas is dispersed. it occurs at the high liquid to gas flow rates. Due to the high liquid flow rate, the inertia forces of liquid significantly overcome the effects of interfacial tension of the gas. This leads the gas to shatter into small babbles. Also, the inertia forces of the liquid significantly overcome the buoyancy forces of the gas, which allows the gas bubble to disperse in all radial directions even at the bottom of the horizontal pipes.

2. Mist Flow: The gas is the continuous phase and the liquid travels as dispersed entrainments throughout the stream. Similar to dispersed bubble flow, the high inertia forces of the continuous phase, namely the gas, in this case, overcome the liquid body forces and disperses it all around the cross-sectional area.

Intermittent Flow

At lower liquid velocities relative to gas velocities, gas aggregates into large bubbles and move close to the top of the pipe inner wall. The following forms of intermittent flow patterns exist:

1. Plug Flow: short gas pockets separated with liquid plugs of low or no gas entrainments.

2. Slug Flow: longer gas pockets referred to as "Taylor bubbles" separated with liquid slugs of considerable gas entrainments.

3. Pseudo-slug flow: intermittent huge liquid waves.

Segregated Flow

Liquid and gas move in separated streams. Two main forms are identified:

1. Stratified Flow: the liquid moves as a continuous film at the pipe bottom side while the gas moves in a continuous passage above it. The interfacial surface might be smooth "Stratified Smooth" or contains small interfacial waves that form the "Stratified Wavy" flow.

2. Annular Flow: the liquid moves as a continuous film that covers the entire pipe circumference. Gas moves in the core as a continuous stream. In most cases, visually observed liquid entrainments fill up the gas core. Interfacial waves of different shapes and nature exist at the interface between liquid and gas.


Alsafran, M. and Brill J. 2017. Applied Multiphase Flow in Pipes and Flow Assurance. Society of Petroleum Engineers.

Shoham, O. 2006. Mechanistic Modeling of Gas-Liquid Two-Phase Flow in Pipes. Richardson, Texas: Society of Petroleum Engineers.