Generating Valve Characteristic Curve Using Iterations

First you need to know the valve type, then pressure and temperature for determination if any gas is present...purity of the chlorine, pipe restriction total...

https://www.copely.com/tools/pressure-drop-calculator/

Vendor has provided me something like this for following valve:

Now the procedure of reaching my objective is as follows:

1) Cl2 has 1% O2 (humidity in ppms so forget it)

2) Gas densities & other properties I can get at normal conditions

3) Its a fairly straight DN200 line (10m) from compressor with few pipe ancillaries. However inlet pressure to valve will be 2.5 barg while Cl2 enter HCl synthesis furnace at 0.5barg after valve. So its a 2bar delta across valve

4) I can follow Crane TP-410 or I found this to be more straightforward:

I am supposed to use 2nd equation

Flow principles | Tameson.com

Seems like once you figure out the pressure drop, which depends on the temperature, you can calculate the gas density....and the possibility of your valve freezing?

I think I have not made myself clear enough. This particular valve is a part of pressure loop so outlet pressure user decide (based on vendor recommended pressure value) which is 0.5barg max. So pressure drop is set! I will see what JT effects such pressure drop entails

1. There are no figures on the photo of the nameplate
2. On the graph of stroke vs flow, which of the curves applies to your valve?
3. 2nd equation should read ΔP > P₁/2. Don't forget P₁ is absolute pressure = 3.5bara.
4. It's not unusual to apply a swaging factor to the tabulated Kv, particularly if the valve size is less than pipe size, which it often is for a control valve. Typically 0.8 for butterfly valves. Don't know about your valve.
5. γ =1.4 for most diatomic gases eg air. You might need to check for chlorine.
6. Assuming have chosen the Kv curve and you know T, you then have the inputs you need to estimate flow (and that's all it will be). You most likely want mass flow, but it's easy to calculate that from Q_n.
7. You haven't said what's controlling what, but if you want a certain flow and there's a flow meter somewhere, the valve can adjust accordingly. In that case, as long as you're in the valve design range, the flow at a particular Kv isn't that critical.

1- The nameplate shows Kv & that its equal% valve, the graph I took from valves literature.

2- Equal% (curve 1)

6- I will deal with mass flows exclusiely. Bcz Cl2 will generate HCl (with raw H2) so from production point of view I will used mass flows

7- An overview of circuit (I have skipped manual ancillaries)

• Cl2 from compressor at 2.5barg is at upstream of PRV (delta P of 2bar)
• Cl2 buffer tank of ~3m^3 is at downstream of PRV operating at 0.5barg
• Buffer tank has PT & TT (pressure / temperature sensors)
• Downstream of buffer tank is FCV (flow control valve)
• Downstream of FCV is flow metering device (Orifice meter with pressure / temperature correction signals from Cl2 buffer tank sensors)
• Cl2 enters HCl synthesis unit

Now I just want to know is my valve suitable enough to handle Cl2 flow. What i have read butterfly control valves should control flows b/w 20 - 70% opening

I haven't worked on control valves for some years, but looking at this in more detail.

Your equations are wrong. The 2nd, when ΔP > P₁ should be

Q_n = 256*Kv*P₁/√(γ*T) where γ is gas density kg/m³ at 1 atm, 0°C (not C_p/C_v!) You check this online.

You then have all the information.

You know Cl₂ mass flow, convert this to Q_n, m³/h. You know P₁ (bara), γ and T (in K). From the 2nd equation, calculate Kv. Check that Kv is less than your 100% figure, if not your valve is too small! Divide Kv by your 100% Kv, and find relative stroke from curve 1.

It's true that butterfly control valves should control flows b/w 20 - 70% opening, but yours is not a butterfly valve. But with the uncertainty over swaging factor etc, I wouldn't want to go outside those limits in your case, hopefully nearer the middle opening %.

Just to be correct, where I said "The 2nd, when ΔP > P₁ should be..." I meant "The 2nd, when ΔP > P₁/2 should be...."

Where Tameson are wrong is their bottom line, it should be √(γ*T/293) so

Q_n = 30.8*√293*Kv*P₁/(2√γ*T) = 263*Kv*P₁/(2√γ*T)

I said earlier 256*Kv*P₁/(2√γ*T), the constant can vary depending on the figure for standard temperature - 0, 15, or 20°C. Also some valve manufacturers use gas density kg/m³, others use SG relative to air = 1. I can't be bothered to go through all that, above is near enough for what you need.

I contacted Tameson and rather to my surprise, they acknowledged there is a mistake in the equations. They will make corrections. So you can wait for that or use my formula