Hydrotest Volume Calculations

[Katelyn]

I am doing volume calculations for hydrotests, updating a procedure at work. Our procedure has different equations for buried vs. unburied pipe and I can't seem to validate them - I can only find one equation for Fpp and Fpt.

Fpp (factor to correct for volume cahnge in pipeline due to pressure increase from 0psi to test pressure, P):
The equation from Pipeline Rules of Thumb Handbook is as follows:
Fpp = 1 + [(D/t)*(0.91P/30000000)]+[0.0000036*(t-60)]
Our original procedure has a different equation whether the pipe is buried or unburied (or unrestrained, and restrained). But I cannot confirm the equation for unburied pipe. The equation our procedure has is
Fpp = 1 + [( D/t) x ( P/24000000)] but I can't find one source validating this.

Same goes for Fpt (factor to correct for change in pipe volume due to thermal expansion of the pipe from base temp of 60F).
Fpt = 1 + [( T - 60 )* Em] where Em= .0000182 for unrestrained pipe or .0000121^-6 for restrained pipe. / deg F. However I can only validate Em = 0.0000182.

 

[zdas04]

OH MY GOD. All of that together will be a tiny percentage of the water left in the hoses which is a tiny percentage of the amount of short-sticking that the truck drivers do when loading their trucks.

I've done dozens of hydro tests based on the empirical relationship:

Volume (in 42 gallon barrels per 1000 linear ft) = [Pipe ID (in inches)]^2

It is a stupid coincidence that this relationship works, but it does (all the unit conversions and constants work out to about 1.0). It gives you a quantity that is a few percentage points higher than an explicit volume calculation, but that gets left in hoses, gets splashed on the ground and accounts for short-sticking. One warning: don't try to convert this equation to any other units, the coincidental unit conversion won't fall out. You need to convert your DIN or mm numbers to inches, square them, and convert the result to volume/unit length in the units you like.

The arithmetic in the OP is kind of hard to evaluate without units, but I know that it is going to give you a number that is mathematically elegant and practically worthless.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[SNORGY]

Katelyn,

Does the procedure have a signature sheet on the front from which you can track down the original author? Is there a list of references or bibliography that you can track from footnote numbers? You might then be able to ask where the equations come from. I have not attempted the derivations myself, but on first glance the equations appear to be (and perhaps indeed ought to be) the result of combining the effects of circumferential and longitudinal pipe strain due to pressure and temperature rise with the effects of the compressibility of water. Probably quasi-theoretical and quasi- empirical. I suspect that the "restrained" case should depend to some extent on soil conditions and virtual anchor length, which will vary from place to place.

I view it is unfortunate that equations of this nature find their way into documents of this type but that the source of these equations gets lost. It is my belief that the author(s) ought to provide either the sources or the derivations. When I have written certain documents or reports that include an equation for something in support of the text, I always include an appendix that shows either the source or the actual derivation. Otherwise, you end up in a situation like the one you are in: a bright engineer asking "Where did this come from?" in a company where nobody knows the answer. That produces, over time, a "Design By Xerox" mentality. People get psyched into thinking, "Ooooh...look at that equation...it's complicated and hard...it *must be* right...it *must have* come from really smart people and lots of science.". (much like the API 14E correlation for erosion velocity limits, I imagine). And, well, maybe it did, or maybe it didn't, or maybe it's wrong. What I will offer you is this: good on ya for checking it thoroughly in an effort to understand it.

How much time are they providing you with for this task and to what level of detail do they want you to check it out? If you have a couple of days, you could prepare your own spreadsheet that compares various methods: the one you have in the procedure versus the one proposed by zdas04 versus your own first-principles derivation versus those that you might obtain from textbooks that deal with piping and pipelines versus those that might be published in Codes and Standards versus those that are used by pipeline construction company guidelines. If they compare closely, you then have succeeded in verifying with reasonable level of comfort that the equations in the procedure are valid. Or, you might find yourself in a position where you can conclude that the much simpler correlation proposed by zdas04 is valid and you will have the pages of your validation effort to prove it.

I recently wrote a technical report in which I came up with a calculation methodology to quantify the prediction of erosion rates ceased by entrained frac (and / or formation) sand in flowing gas wells. Basically, the end result was something incredibly simple: if [number A] is this, go up one nominal pipe size; if [number A] is this, go up two nominal pipe sizes; otherwise install [facilities]. I got there after reading fourteen papers, reading two failure reports, reading a couple of textbook chapters, creating a custom spreadsheet and performing 40 pages of calculations - but I got there. A colleague for whom I have great respect and who holds a PhD in chemical engineering, said that the simpler the answer, the better the guideline. Keep the calculation records to be produced on request, but meanwhile, only publish the little table of [number A] versus [do this].

In other words, in your position, I would make it as simple as possible, and maybe tie it back to a reference document that, if necessary, captures the proof of why it boils down to something that simple. You will only need to do that once or twice before people start saying, "Holy crap is this person smart.".

 

[SNORGY]

"...caused by..." as opposed to "...ceased by...".
Stupid iPad.

 

[zdas04]

The Pipeline Rules of Thumb book is the ultimate "designed by Xerox" document. After about the third time I got burned for using something from it without confirmation I started verifying everything I used from it. Finally that evolved to where I kind of stopped using it for anything.

If you were figuring something hard, SNORGY's advice is excellent. Ordering hydrotest water is not hard. If you worked for me and came in with a detailed spreadsheet on this topic I would politely ask you if you didn't have anything value-adding to do (the first time you did it that is, the second time I would politely ask you to clean out your desk). We tend to assume that an Engineer can determine a volume of a cylinder in appropriate units to order water (which is never measured very closely on delivery). In other words if the delivered volume is +/- 15%, you are not adding value by computing a 0.5% change in volume from expansion of the pipe during pressurization.

If you are trying to figure the amount of water you can add after the start of the test due to expansion STOP IT. Temperature gains and losses with be at least an order of magnitude more important than pipe expansion. Water is more compressible than the steel is flexible (both numbers are pretty small), pipe expansion gets lost in the other effects.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[EnergyMix]

David (zdas04)

While you make a great argument for common sense, Katelyn may be in some megacorporation that has to have a procedure to turn the lights on in the morning (in other words, common sense doesn't apply.) So she may be stuck with having to spend at least some amount of time coming up with a justification. Doesn't mean you're not right, just means she might work for a bureaucracy. (Of course, sometimes these assignments are given out as training to younger engineers to see who can separate the wheat from the chaff.)

 

[SNORGY]

I think zdas04 is used to a work environment where the answers have to come fast, simple, no-frills attached, just get it done. Probably a tough guy to work for but a good guy to work for at the same time. Maybe the best move on this one might be to show the equations to the person who asked for the work to be done and ask, "How closely do you want me to look at this level of detail?". If the person is anal, he might say, "Prove the validity of those equations.". If the person is zdas04' the answer might be more like, "The pipe's a long cylinder, so knowing how long and how big around it is, tell me how much water to get and add a bit.".

That defines the scope of the assignment.

 

[zdas04]

I actually have no problem with revisiting the gray areas (and at some level in the experience curve you only get the gray stuff). I think the erosive velocity exercise SNORGY mentioned above was Engineering at its best. There is a lot of stuff we don't know enough about and I spend a lot of my life trying to get good enough answers to that stuff (all of my patents are pretty far outside the box). I just don't have to prove that the area of a circle is ([π]/4 * ID² to accept that it is true. There are far too many hard questions to spend a lot of time on an easy one.

Back in the slide rule days we had to understand that if you were trying to read a number off the right-hand end of the scale it was going to be impossible to be very precise and we were not encouraged to try to get numbers "outside the accuracy of the calculation". The OP looked to me like trying to take a fairly loose number (e.g., do you really know the volume of all the fittings in the system?) out to 6 decimal places when the quality of the data makes the confidence in the digit in the 10's column questionable.

About 1/3 of the people who ever worked for me hated my guts and are still waiting patiently for me to die a painful and lingering death. The other 2/3 still complain to me about their subsequent bosses. I never lied to my staff, and I worked hard to make sure that they fully understood what I expected of them. Some people like that. Others don't. So yeah, I was hard and easy to work for, just depended on what you were looking for.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[MintJulep]

The format of the the equations presented have the appearance of empirical equations. In all likelihood a best fit line through a hand full of data points plotted by hand on quad paper with a crayon.

A big number in the denominator, and another coefficient with a bunch of zeros before any significant digits - as zdas notes the result will be a small number.

 

[EnergyMix]

About 1/3 of the people who ever worked for me hated my guts and are still waiting patiently for me to die a painful and lingering death. The other 2/3 still complain to me about their subsequent bosses.

I'm not sure if that quite describes me; hoever, I'm constantly being told that I need to work on my communication skills (while at the same time, my boss acknowledges that my message needs to be said.)

 

[rconner]

Just a comment -- maybe from a practical standpoint all systems hydrotested contain a certain amount of air, and when so they are subject to all the solution and gas law behaviors/vagaries thereof (relative e.g. to water). Try as one might or want, I therefore feel it may be difficult to precisely/theoretically/dependably? model the issue discussed on paper or computer, particularly if/when one doesn't know exactly what this volume of air inside the pipe or vessel actually is. In such cases perhaps (to any extent vetted) rules of thumb (or experience?) may be at least helpful in establishing reasonable expectations?