How to size a pressure tank for VFD pumping system?

As for the good performance of a well-controlled variable frequency drive (VFD) system tank capacity is not an issue, my own criteria is to dimension them as expansion tanks, to take water hammering, and expansion due to temperature raises -if pipes are exposed to the sun for e.g., or water heating tanks are in the line.

For domestic and small civilian uses, a bigger tank will prevent start-stop cycles due to small leakages, but this will highly depend on relationship between set point pressure and start up pressure, so the bigger tank will not have a dramatic effect as it has on traditional presostatic systems if this pressures are as close as you can get on VFD systems.

The first step is to determine the amount of working storage (Vw) needed to avoid short cycling of the pumps. The general equation for this is:

Vw = (min. allowable cycle time) * (pump output) / 4

For pumps started with full voltage, the minimum-allowable cycle time is around 15 minutes for most low-voltage motors (i.e. < 600 VAC), which corresponds to 4 starts per hour. In contrast, A VFD can provide a ramp start that greatly reduces the inrush current to the motor. Thus, with VFDs starting the motors, a 5-minute cycle time is used, which corresponds to 12 starts per hour.
Variable frequency drive
Pump output for a constant-speed pump is pretty straight forward to obtain. However, for variable-speed pumps, you want to use the output at minimum speed, for purposes of computing working storage.

If you were using an elevated tank for pressure regulation, you would base the size on the working storage requirement. However, when using a hydropneumatic tank, you typically require about 7 - 9 times the working volume, in order to maintain pressure within allowable limits. To calculate total tank volume, you use the relationship:

P1 * V1^gamma = P2 * V2^gamma

Gamma is 1.0 for isothermal expansion and 1.4 for adiabatic expansion. I typically use 1.4 because it yields a conservatively sized tank. Other engineers split the difference and use 1.2.

It is helpful to rearrange this equation with P1/P2 on the horizontal axis, and V1/V2 on the vertical axis. The ratio V1/V2, can then be determined by calculating P1/P2, and using the graph.

When you plot the graph of P1/P2 vs. V1/V2, you'll notice something important: a narrow operating pressure range requires a larger hydropneumatic tank. So, if you're trying to keep the tank size down, look into broadening the operating pressure range, if possible.

One more must convert all gage pressures to absolute pressure before plugging into the formula, above.

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