highly variable and dependent on construction techniques, pipe storage conditions and lenght of, , and of course length and size of the pipeline and definition of what 'clean' is for the line. For example, an ethylene pipeline will need to be much much cleaner than a crude oil pipeline.
I suggest you contact Bechtel Pipeline Group in Houston, Tx for any advice they might share.
A quick way is to compare the pressure drop from the expected drop in a clean (pigged) line. I don't remember the precise correllation but I think you should have enough data available to get close.
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As other posters have said, it will be variable based on construction practices and their cleaning procedures. For example, an oxygen line must be specially cleaned with certain chemicals prior to service while a line with hydrogen would face less stringent cleaning requirements. If there is no cleaning procedure you can expect pipe scale, welding slag, welding rods, etc. to be in the pipe.
What is your requirement for cleanliness in the line?
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Please kindly try the following: Consider the cross section of your gas pipeline as a cirle.Then assume the debries as a segement of a circle. Volume of the Debris = Area of Segment X Length of the Pipeline.
Standard equation for the Area and height of the sement of a circle will be ur guide.
Your contorl variable is the estimate of the avearge height of the Debris which is also the height of the segment.
The upper limit will be the volume of the <...gas Pipeline...>.
The lower limit will be zero.
This isn't the sort of thing that responds to a <...formula or equation...>, though it will respond to measurement.
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