Calculating leakage rates

[jberrio]

I am trying to calculate the leakage rate from a high pressure system to a low pressure system.
I have a closed loop, high pressure (2000psi) system which has a cooling system attached. The cooling system, basically, is a pump and heat exchanger with inlet and outlet isolation valves connected across the high pressure system. Both systems contain water.
The maximum pressure in my low pressure system is 400psi.
About every eight hours, the pressure in my low pressure system approaches 400psi and we end up draining water to reduce the pressure to 50psi. Eight hours later we repeat.

The obvious answer would be to measure the amount of effluent and this would give me my leakage rate but due to piping design, sizing of tanks, accuracy of level indicators, I cant get a good volume estimate.

Is there a way, knowing the volume of the system, the size of piping, and the working fluid, to calculate the amount of water needed to change the pressure in the system?
The only measurable parameters I have available are the sizes of the system, initial and final pressures, and temperature.

I have considered different things such as the overall increase in volume of the system, due to pressurizing the piping (pipe diameter changes), changes in specific volume due to pressure changes. I have also looked for books on hydraulics to try to find how to calculate pressure changes as a function of added volume but have been unsuccessful.

 

[pumpbhoy]

Why try to calculate leakage rate ? Do you not wish to prevent leakage occuring in first instance ?
To help answer basic question you have to detail where leakage is occuring. i.e. is it between flat faces or an annular clearance ? System diagram would be very helpful. If you can provide more detail there may be a relatively simple answer.

 

[tblaser]

I agree with henrick67, why not stop the leak?

or

If there is no hazardous materials in the water, you could install a relief valve set to maintain the proper pressure in your low pressure system.

Attempting to calculate the leakage using liquid compressibility and metal deformation is the hard way to do it and will not be sufficiently accurate to justify the time involved, especially if the system is more than a few gallons in volume.

It would be easier and less time consuming to use a bucket and a stop watch( or hourglass - slow leak) if you really need to know.

 

[jberrio]

Of course I would like to prevent the leakage in the first place, thats why we have valves which isolate the systems. The problem is finding which valves are the leakers. I have a set of 10" isolation valves and check valves and a whole array of 1" sampling piping which is cross connected to other piping and other high pressure systems. I also have an accumulator which is connected to system via the sampling piping and shows a drop in level but I dont know if the loss of level in the accumulator corresponds too accurately with the amount of water that is leaking into the system. Hence, if I can determine the amount of water required to raise pressure, I can either validate or rule out the accumulator as a source of leakage and try to locate other sources.

Basic diagram

---------------------------------------------
2000 psi
---------------------------------------------
|x| <----valves----------------->|x|
| | | |
| | 10&quot; piping 200 ft long | |
| | | |___ other piping and accumulators
| |________________________| |
|___________________________|

pressure change 50 to 400 psi

The water is hazardous and we do have relief valves but we want to maintain our inventory. I dont have the ability to use a bucket and stopwatch.

My question is specifically directed at calculating a leakage rate and whether there are factors other than liquid compressibility and metal deformation need to be taken into consideration.

Basically, how can I calculate the most accurate leakage rate into the system knowing only the volume and pressure change.

 

[uncleal]

Why don't you just do a compessability calc using bulk modulus with your dP. Is the temperature constant in this system??? Also what is the volume magnitude of this system???

 

[GGW]

jberrio,

In your June 6 post you ask the question, &quot;Is there a way, knowing the volume of the system, the size of piping, and the working fluid, to calculate the amount of water needed to change the pressure in the system?&quot;

You state that the pressue change in the low pressure system goes from 50 to 400 psig. I assume gage pressure.

Now, if you take the isothermal compressibility which is the change in volume that results in the change in pressure while the temperature remains constant and integrate this over the pressure interval you will be able to calculate the change in water density over that pressure interval. Multiplying this density change by the total volume of your low pressure system, you will come up with the amount of water that entered the low pressure system to raise it from 50 to 400 psig. I assumed that the temperature of the water was 60 F and did the calculation and found that the change in density from 50 to 400 psig is 0.071 lb / ft3. If you know the volume of the low pressure system which I read from your post that you do, the result is the water in lb that entered the system to raise the pressure 350 psi. If the temperature I assumed is significantly different than the actual, I would be more than willing to use that
temperature and recalculate the density change. For your information, I used the equation of state as developed by Keenan, Keyes, Hill and Moor (Steam Tables (c) 1969) which is a very complicated equation of state but is good for both liquid (including compressed liquid) and vapor. The equation was used to calculate the isothermal compressibility and yields results with a high degree of certainty that can be used in engineering calculations.