Ball valve for throttling minor dp

In theory, yes, in practice no and is very common. The controllability though is not high and a better way might be use of suitably sized orifice plates to balance out your system or use of butterfly valves.

For a ball valve so long as it is more than 30-40% open when throttling, the increase in velocity is not big enough to cause any damage.

The majority of quarter turn taps in your house are ball valves.... Remind them of that when you talk next.

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You likely want to throttle on the outlet side of these units and not the inlet.
There are actually ball valves with special balls that are designed for some throttling,

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P.E. Metallurgy, consulting work welcomed

To balance the flow, your best and least expensive option is to consider "restriction" orifices in the pipe to the two units experienceing the dominant flows.

You'll need the piping layout, the various pressures, fluid properties, and desired flows to each unit.

You are only trying to balance the flows, so, it is entirely possible that you only need two plates.

In the case of minor changes in the pressure distribution bast for each tower, you should have to worry about complexities of high pressure drop restrictions.

What kind of ball valves are they and exactly how do they say the gas flow will damage the valves? I can see some argument being made that floating ball valves may see some vibration due to pressure fluctuations when throttled, perhaps wearing at the downstream sealing seat and/or the stem packing. If they are trunnion ball valves, though, I certainly do not see that as a possibility.

If this is a short-term measure, go for it. As LI said, if you need a fixed dP for the long run, orifice plates are the way to go. Also, manual ball valves that are partially throttled have a tendency to become "unthrottled" when nobody is looking (i.e. new guy comes in, sees a partially open valve on an online system, and opens the valve fully because he doesn't know any better and thinks it should be open).

As mentioned, one may throttle the typical ball valve to reduce the flow but can't adjust the flow similar to a "control" valve.
IMO, the potential damage of the valve seat could be a risk issue to the process or operation which need to be discussed and documented.

At low dp, if a soft seat ball valve is all you've got to enable flow balancing on these lean amine lines, use it.
In the long term, flow control would be better, with metal seated ball valves.

You could try using a reduced bore valve in the ones needing throttling or a full bore valve in your one with lowest flow if they are all reduced bore?

That might be enough to make a difference.

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Dirt accumulation in some valve's the seat space may make a tight shut off difficult and erosion is more likely when partially open. You will have to make a significant change in %Open to see any decrease in flow, so you may be significantly exposing a valve's critical parts.

You can easily calculate the different flow rates you get through the valves with a few psi difference using the Cv or Kv coefficients. Normally a few psi does mot even make any significant theoretical difference in flow, unless the valves are small. Whether it does make a difference or not is mostly related to diameter.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

@ChemEngHeriot
Some ball valves have a dissimilar dedicated design. I have positive experience with control valves 3 psi (20 kPa) dP (at norm conditions) either in gas and liquid services. Consult a reputable vendor for details, we dealt with Emerson

Note that you don't need an excellent accuracy and all range of Cv curve. Combination of accuracy and rangebility is an important info for a vendor's tech support in your case.

Also look up V ball valves if you want to go this way.

E.g.
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.