Nonhomogeneous Two-Phase Flow in Pipes

Introduction

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,

....................(1)

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.

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)

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 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