# Example 9: Calculate pressure drop for methane flow through pipeline in isothermal compressible flow

Background

The examples provide a comparison of AioFlo results with published data from well known and respected references that are generally accessible to engineers. This will allow prospective AioFlo users to validate its accuracy against a range of typical calculations. The worked examples can also be run by new users as part of their learning process. To learn more about AioFlo click on "Home" in the menu above.

Description

Flow calculations for methane (or natural gas) are frequently required in the sizing of pipelines. This worked example calculates the pressure drop over a line that is long enough for the minor losses (i.e. in pipe fittings and valves) to be neglected. The pipeline is assumed to be isothermal and there is no change in elevation.

Problem Reference

Coulson and Richardson's Chemical Engineering, Vol 1, 6th Ed, (1999), Page 168, Example 4.3

Fluid Details

 Fluid : Methane @ 405 kPa abs and 24°C Flow rate : 50.0 std m³/s @ MSC (*) = 33.85 kg/s Phase : Gas Density (upstream) : 2.69 kg/m³ Viscosity : 0.01 centipoise

(*) MSC = Metric Standard Conditions = 15°C and 101.325 kPa abs

Pipe Details

 Pipe ID : 0.6 m Roughness : 0.06 mm Length : 3000 m Fittings : Ignored

To be Calculated

Calculate the Reynolds Number and overall pressure drop

Comparison of Results

Calculated Item Reference AioFlo AioFlo
Fluid model Compressible Compressible Incompressible
Reynolds Number 7 180 000 7 180 000 7 180 000
Flow Regime Turbulent Turbulent Turbulent
Pressure Drop (kPa) 235 237 163

Discussion

This example should be considered in conjunction with Example 8. In Example 8 it was shown that because the pressure drop calculated for a gas with the incompressible model was less than 10% of the upstream absolute pressure, the result was sufficiently accurate for most purposes. However, the table of results above show that while the Reference and AioFlo results are very close when the Compressible model is used, the end column shows that the pressure drop for the methane flow would be badly under-estimated if the Incompressible (i.e. Liquid) model were used. The pressure drop calculated by the Incompressible model is 40% of the upstream absolute pressure, indicating that it is necessary to use the Compressible model.

In Example 8 the matter of considering the compressibility (i.e. variable density) of the gas while ignoring the compressibility factor (Z) was raised. In the current example the density of the methane varies significantly over the length of the pipe, resulting in the velocity increasing from 44 m/s at the inlet to 107 m/s at the outlet. But the compressibility factor (Z) varies by only 0.5% from inlet to outlet and the change is negligible in comparison with the other uncertainties involved.

Another area of confusion with pressure drop calculations for gases is the variability of the friction factor over the length of the pipeline. Some engineers recommend breaking the pipeline up into multiple sections and recalculating the friction factor for each section. In normal piping calculations this is totally unnecessary. The friction factor is fully defined by the Reynolds Number and the relative roughness. It can generally be assumed that the relative roughness is constant over the length of the pipeline, so the only question is whether the Reynolds Number remains constant as well.

In the Reynolds Number the velocity is multiplied by the density and because the velocity is inversely proportional to the density the product of the density and velocity remains constant, irrespective of the expansion model (eg isothermal or adiabatic) used. The gas viscosity is generally very insensitive to pressure changes and under the isothermal assumption the temperature is constant, making the viscosity, and therefore the Reynolds Number, constant over the length of the pipeline. Since the Reynolds Number and relative roughness are constant the friction factor can also be safely regarded as constant over the pipeline. In most cases involving gases the flow will be in the fully turbulent range and then the friction factor is independent of the Reynolds Number. In these circumstances the friction factor depends only on the relative roughness and can definitely be regarded as constant for the entire pipeline.

# AioFlo showing Input Data and Results for Example 9 