Pipeline

Inputs

• Diameter: Internal diameter of the pipeline.
• Length: Total pipeline length.
• Elevation: Net elevation change between inlet and outlet.
• Relative Roughness: Pipe wall relative roughness. Height of wall irregularities divided by pipe diameter. Used in friction factor calculation.

Heat transfer inputs:

• External Temperature Specification:
  • Ambient temperature from process settings: Uses process-level ambient temperature.
  • Specified external temperature: Uses a single ambient temperature for the full pipeline.
  • Linear temperature gradient: Uses Temperature Inlet and Temperature Gradient.
• Ambient Temperature: Used when Specified external temperature is selected.
• Temperature Inlet: Used when Linear temperature gradient is selected.
• Temperature Gradient: Used when Linear temperature gradient is selected (K/km or K/m).
• Heat Ingress: External heat input per unit pipe length (W/m). Positive values add heat to the fluid, negative values remove heat.
• Heat Transfer Coefficient: Overall heat transfer coefficient for pipe wall, insulation etc. The heat transfer is calculated based on internal pipe diameter. Defaults to zero, resulting in an adiabatic pipe.

Outputs

• Outlet stream conditions are calculated as well as profiles along the flow path for pressure, temperature, density, flow speed and enthalpy.

Details

The steady-state pipeline module computes pressure losses along a pipeline segment for single- and two-phase flow. For single-phase flow, frictional pressure drop is calculated assuming homogeneous flow using the Darcy–Weisbach formulation accounting for relative wall roughness. For two-phase flow, frictional losses are evaluated using the Beggs and Brill correlation. Given the inlet flow rate, the module determines the outlet pressure by applying the calculated frictional pressure drop along the pipeline length.

Two-phase friction is calculating using the Beggs and Brill correlations ¹. The Beggs and Brill (1973) two-phase flow correlation is based on 584 experimental measurements covering a wide range of flow conditions and pipe inclinations. The experiments span gas flow rates from 0 to approximately 0.1 Nm³/s, liquid flow rates from 0 to approximately 2 L/s, system pressures of 2.4–6.6 bara, and pipe diameters of 1–1.5 in, using air–water mixtures with inclination angles from −90° to +90°. Currently the two-phase flow is considered homogeneous.

The pipeline unit operation is the only model that accounts for flow speed and changes in speed. Speeds outside the pipeline are assumed to be zero; therefore, for the exergy analysis to be consistent with the second law of thermodynamics, kinetic energy at the pipeline boundaries is converted to or from thermomechanical energy (pressure).

Net heat input to the fluid comes from heat exchange with ambient. Per unit length:

$$q' = U\,(\pi D)\,(T_{\text{amb}} - T_{\text{fluid}})$$

where $U$ is the heat transfer coefficient, and $\pi D$ is the internal pipe perimeter ($D$=diameter).

The pipe is discretized into 20 equally-spaced cells, conserving mass and energy.

References

Footnotes

1. Beggs, D.H. and Brill, J.P., A Study of Two-Phase Flow in Inclined Pipes, J. Pet. Technol. 25, 1973. ↩