It has always been an article of faith that if the density of the downstream piping were within 10% of the density of the upstream piping then the incompressible flow equations would provide adequate results in an inherently compressible fluid. When the downstream density is less than 90% of the upstream density then common practice was to segment the line until that 90% was realized. To get a feel for how valid this assumption is I wrote a MathCad program to bust up a flow problem with downstream density around 50% of upstream density for a single segment and then matched the (pipeline inlet - pipeline outlet) dP while segmenting the line finer and finer.
100% CH4 (MW 16.043, SG 0.5539)
Std weight 24 inch new steel pipe (ID 23.25 in, efficiency 0.95, absolute roughness 150E-06 ft)
No water standing in line
Temp constant at 520R
Upstream pressure 580 psia [40 bara]
Downstream pressure 290 psia [20 bara]
Line length 62 mi [100 km]
Guess segment downstream pressure
Calculate average pressure with the guess (using front-end loaded average)
Calculate compressibility at average and standard pressure
Calculate density at average pressure and standard pressure
Calculate viscosity at average pressure
Calculate Reynolds Number
Calculate Fanning Friction Factor
Using Isothermal Gas Flow Equation to calculate downstream pressure
If calculated downstream pressure more than 100 Pa from guess, iterate 1-9.
Move segment downstream pressure to upstream pressure and repeat 1-10
I ran the program for a number of different segments:
I found it interesting that above 90% the flow rate was unchanging. I re-ran this several times for flow rates increasing and found that below 90%, the flow rate changed with increasing segmentation, and above 90% a given dP gave the same flow rate. Changes above 30% were pretty small (more than the 0.016% above, but much smaller than the +/-10% accuracy we expect to get from this equation). My conclusion is that I will continue to use the 90% check, but certainly understand why someone would ignore it for pipeline calculations.
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