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# Thermal relief valve flow rate

## Thermal relief valve flow rate

(OP)
Hi all,

I've got a question here about how to calculate the mass flow / volume flow through a Thermal Relief valve (I don't know the size or orifice, but assume it's the smallest ones anyone makes for piping so maybe 1/2" x 1"?).

The piping in question had a surge type event a few weeks ago and it popped all the TRVs set at ~30 barg in cryogenic propane for approx 30 seconds duration.

Now people want to estimate the volume which escaped into the closed drain / vent system. So nothing escaped, but the volume needs to be reported.

Any clues?

Or things to try and find out?

I've had a look on line and on this site, but nothing obvious pops up for thermal relief valves.

Thanks

LI

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

### RE: Thermal relief valve flow rate

Hi,
From Internet (ref API 521 edition7th)

For liquid-full systems, expansion rates for the sizing of relief devices that protect against
thermal expansion of the trapped liquids can be approximated using Equation (1) in SI units

(1) q = alpha*phi/(1000 *d*c)
where
q is the volume flow rate at the relieving conditions, expressed in m3/s;
alpha is the cubic expansion coefficient for the liquid at the expected relieving conditions,
expressed in 1/°C;

phi is the total heat transfer rate, expressed in watts;

d is the relative density referred to water (d = 1.00 at 15.6 °C), dimensionless;
NOTE Compressibility of the liquid is usually ignored.
c is the specific heat capacity of the trapped fluid, expressed in J/kgꞏK

Pierre

### RE: Thermal relief valve flow rate

Hi LittleInch - I'm wondering if it is as simple as doing a PRV rated capacity calculation. You need to know the orifice size, rated coefficient of discharge*, and also the accumulated inlet pressure at the time of relief (ie., set pressure plus whatever overpressure was recorded at the time). Also, do you calculate as gas or liquid?

(* although a TRV, major manufacturers have had their TRV types type tested. If you can advise the manufacturer and model, the orifice and coefficient should be easy enough to find in the National Board NB-18 on-line document)

*** Per ISO-4126, the generic term 'Safety Valve' is used regardless of application or design ***

*** 'Pressure-relief Valve' is the equivalent ASME/API term ***

### RE: Thermal relief valve flow rate

(OP)
I've received a bit more data and think this is a D orifice at worst, so 0.11 in2. Coeff discharge - no idea, but can we choose something conservative?

Inlet pressure 30 barg, outlet <1 barg.

It's a triangle 1/2" x 3/4". No model no but will be ancient. UK supply so might not be in the NB system. But anything similar will do.

It's liquid at this stage, about 560 kg/m3.

It was used as an inadvertent relief valve during a process upset so not a classic what flow have I got - this is a what flow did it do with 30 odd bar inlet across a small orifice for 30 seconds??

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

### RE: Thermal relief valve flow rate

Assumed -25o C ---> 561 kg/m3
Liquid coefficient = 0.64
D orifice (0.110 in2)
27.3 barg set pressure
10% OP (30 barg sizing pressure)
Rated flow = 13,677 lb/hr (6204 kg/hr)
Actual flow = 15,197 lb/hr (6893 kg/hr)

If you want the IO file, email me.

Good Luck,
Latexman

### RE: Thermal relief valve flow rate

(OP)
Latexman,

Thank you very much - I really just needed an OOM estimate. That's great.

LI

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

### RE: Thermal relief valve flow rate

No problem, the company's PSV software made it PDQ, just a few minutes.

Good Luck,
Latexman

### RE: Thermal relief valve flow rate

The Triangle valve will probably have a pre code 0.06 in2 orifice. You'll also have to calculate it with the pre ASME 10% overpressure API-520 calculation, meaning you need to include a 0.6 overpressure correction factor as that formula is based on 25 & liquid overpressure. Low coefficient too so use 0.64 as already indicated.

*** Per ISO-4126, the generic term 'Safety Valve' is used regardless of application or design ***

*** 'Pressure-relief Valve' is the equivalent ASME/API term ***

### RE: Thermal relief valve flow rate

Thanks, Obturator. I couldn't find anything quickly on Triangle reliefs.

(0.06/0.11)2 x 6204 = 1846 kg/hr rated and 2051 kr/hr actual

LI, ASSuME wisely.

Good Luck,
Latexman

### RE: Thermal relief valve flow rate

(OP)
Thanks both of you - I was erring on the side of caution for the orifice size, but my initial estimate based on simple velocity through an orifice seemed rather high, so great to get "proper" numbers.

LI

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

### RE: Thermal relief valve flow rate

LittleInch,

A friend pointed out he got different numbers than I above. Turns out after I overrode the defaults in my program, with what I thought the defaults were, I got the same numbers as he:

Nozzle area = 0.110 in2; Rated coeff. = 0.640
Flowrate (lb/hr) = 20923 (rated) 23248 (actual)

Nozzle area = 0.060 in2; Rated coeff. = 0.640
Flowrate (lb/hr) = 11413 (rated) 12681 (actual)

Sorry for the confusion!

Good Luck,
Latexman

### RE: Thermal relief valve flow rate

(OP)
That's ok - actually feels a bit more realistic. I've sent you an e-mail.

It still results in less mass going through the system than the amount that triggers certain regulatory actions and reporting.

Still great that you did this - many thanks.

LI

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

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