Problem

How can I calculate the "Pressure (gas preset)" for a hydropneumatic tank, for example based on an assumed initial bladder size? (gas volume)

Solution

When using a bladder-type hydropneumatic tank for a transient simulation in HAMMER, you must enter a gas preset pressure. This is the pressure inside the bladder before the tank is submitted to pipeline pressure; basically the pressure that you "precharge" it to, before installation. The preset pressure is typically a percentage of the pipeline pressure. Since the tank is not yet installed when the bladder is precharged, it means that the gas takes up the entire tank volume. So from this, HAMMER can calculate the initial gas volume inside the bladder (when submitted to pipeline pressure) based on the full tank volume, the preset pressure and the pipeline hydraulic grade.

The gas preset pressure is a user-defined value. If you do not know the value you need to use (either from regulations, tank manufacturer data, or engineering judgment), you can calculate this based on an assumed initial bladder size (gas volume).

Consider a case where you want the tank's bladder to be compressed to 200 liters when submitted to pipeline pressure (rather than assuming a percentage of pipeline pressure such as 5%) and would like to know what you would need to enter for the preset pressure to achieve this. Assume that the full tank volume or size is 500 liters and pressure head from the initial conditions calculation is 50 meters. 

First, calculate the K constant based on the gas law when the tank is installed, where the "P" is the initial pipeline pressure (50 m) and the "V" is the desired gas volume of 200 L (0.2 m^3):

K = (50m+10.33m)*0.2m^3 = 12.066.

Next, take this "K" and calculate the preset pressure that the bladder would need to be charged to before installed, where the bladder occupies the full volume (500L / 0.5 m^3). The gas law equation can be rearranged in this case to P=K/V:

P = (12.066 / 0.5 m^3)-10.33 = 13.8 m.

So, you would need to use a preset pressure of 13.8 m to achieve an initial gas volume of 200 liters in a system where the initial pipeline pressure is 50 m and the full tank volume is 500 L.

Note:

• The gas law exponent is assumed to be 1.0 in this particular calculation for finding the initial gas volume of the transient simulation. Once the transient simulation begins, the gas law exponent entered in the tank properties (which defaults to 1.2) is used for calculating changes in gas pressure/volume. See more details here.
• Since the gas law works with absolute pressures, atmospheric pressure head must be added in the calculation. HAMMER assumed atmospheric pressure head is 1.0 atm, which is the 10.33 m you see in the above example.

What if I get a negative value for preset pressure?

If you use the second approach above to calculate preset pressure based on assumed initial gas (bladder) volume, it is possible to end up with a negative preset pressure, if the initial pressure is less than atmospheric pressure. This can be a real situation because a slightly negative gage pressure is still a positive absolute pressure. Practically speaking, it means that your initial pressure is very low and the bladder would actually be slightly deflated in order to achieve the desired initial gas (bladder) volume. Under the assumption that the bladder fills the containing tank before being submitted to pipeline pressure, this deflated bladder would indeed experience a negative gage pressure in order for it to "stretch" to fill the containing tank. However there are still moles of gas inside the bladder, so it can still be compressed and follow the gas law relationship between volume and pressure. In this situation, check if the initial pressure, elevations and assumed initial bladder size are correct, as it would not be typical for a hydropneumatic tank to experience such low initial pressures.

See Also

Modeling Reference - Hydropneumatic Tanks

Use of the Gas Law Exponent During Initial Conditions vs. Transient simulation