13 replies to this topic

[klequet]

Dear all,

I am a junior process engineer and I have a question on PSV sizing for the protection of two vessels.

problem: Imagine that two equipments are protected by a common PSV. According to API calculation of the heat absorbed by one vessel is Q=C.F.A^0.82 with A the total wetted surface.

What is the application of this formula for two equipments?

[1] Q=C.F.(A₁^0.82 + A₂^0.82)

OR

[2] Q=C.F.(A₁+A₂)^0.82

In my minds, it seems to be logical that heat absorbed is only proportional to the wetted surface whatever the fragmentation of this surface so [2] should be applicable.
But if I consider a PSv for each equiment I have Q1=C.F.A₁^0.82 and Q2=C.F.A₂^0.82 so Q=Q₁+Q₂ and [1] is applicable.

I don't understand why 10m² of wetted surface on one vessel should be different of 10m² on several vessels?


Thank you for your help

[fallah]

klequet,

If two connected vessels have the conditions per UG133© of ASME Sec. VIII, they can be considered as one vessel and [2] formula is applicable.

If each vessel has its own PSV, no need to consider summation of absorbed heat and each PSV has to be sized based on its relevant vessel conditions.

Fallah

Edited by fallah, 01 August 2012 - 03:37 AM.

[klequet]

Fallah,

Indeed UG133 ASME Sec. VIII can be resume as follow:
if many equipments are protected by a single PSV and if there is no valve between these equipments, they can be consider as ONE UNIT.

I agree with you that it can be interpreted using equation [2].


Thank you for the fast answer,

Kévin

[Robert Montoya]

Hello Klequet
Option 1 is the fact that mathematically applies, it is known as exponents rule:
Q1 = CFA₁^0.82 and Q1 = CFA₂^0.82 if C and F are equal, we write: Q = CF (A₁^0.82+ A₂^0.82). In the attachment is an example relating to the case being discussed.

Attached Files

•  Relief Valve heat.pdf   595.54KB   77 downloads

Edited by Robert Montoya, 01 August 2012 - 08:53 AM.

[fallah]

Robert,

As per my specifying (red rectangular) in attached, you can see that the method is conservative and i think the main reason is this fact that the term (A₁^0.82 + A₂^0.82) is always greater than (A₁+A₂)^0.82 , otherwise for two connected vessels with the same environment factor (F) which is protected by one common PSV and engulfed in same pool fire, using [2] equation is more logical. On the other hand, in fire case due to having no protection by PSV there is no need to be conservative in PSV size.

Would you please introduce the reference from which you did upload one page as your post attachment.

Fallah

Attached Files

•  Relief Valve heat.pdf   600.91KB   32 downloads

Edited by fallah, 02 August 2012 - 01:57 AM.

[Robert Montoya]

Hello, Fallah

The approach referred to in the attached article is about the scenarios and the calculation of total relief flow in a distillation column (tower, reboiler, cooler and accumulator drum) and that the analysis should consider performing the dynamic simulation for the if electrical failure (stopping pumps reflux). However if two vessels are interconnected and between them there is no valve that separates them, the venting system of the two systems is designed as a single, this refers to the example shown, the case fire reboiler and the distillation column, therefore PSV must be designed to withstand the heat in both cases and the total heat flow will be the sum of both.
The bibliographic reference is: APPLIED INSTRUMENTATION IN PROCESS INDUSTRIES

[CMA010]

Robert,

As per my specifying (red rectangular) in attached, you can see that the method is conservative and i think the main reason is this fact that the term (A₁^0.82 + A₂^0.82) is always greater than (A₁+A₂)^0.82 , otherwise for two connected vessels with the same environment factor (F) which is protected by one common PSV and engulfed in same pool fire, using [2] equation is more logical. On the other hand, in fire case due to having no protection by PSV there is no need to be conservative in PSV size.

Would you please introduce the reference from which you did upload one page as your post attachment.

Fallah

Equation 2 is mathmatically incorrect.

[fallah]

Equation 2 is mathmatically incorrect.

CMA010,

What's the incorrectness in mathematical point of view?

Fallah

[CMA010]

Equation 2 is mathmatically incorrect.

CMA010,

What's the incorrectness in mathematical point of view?

Fallah

High school math: x^z + y^z does not equal (x + y)^z

[fallah]

Equation 2 is mathmatically incorrect.

CMA010,

What's the incorrectness in mathematical point of view?

Fallah

High school math: x^z + y^z does not equal (x + y)^z

CMA010,

Before jumping to a thread read the thread history. If you had it done you had seen the below statement in my post (post#5):

"...the term (A₁^0.82 + A₂^0.82) is always greater than (A₁+A₂)^0.82 ..."

Indeed it is strange that no one in this thread claimed that above two terms should be equal and the reason you are going to prove they aren't equal isn't known. For your information the main issue is that among two equations which one is applicable for the case which OP has specified.

Fallah

[Robert Montoya]

Fallah;
The manner in which should join is Q₁ + Q₂, but when you want to do some elementary algebra Q₁ + Q₂ = F₁C₁A₁^0.82 + F₂C₂A₂^0.82, if C₁ = C₂ and F₁ = F₂ the before equation is summarized Q₁ + Q₂ = CF (A₁^0.82 + A₂^0.82). The result is not related that (A₁ + A₂) ^0.82 is greater than (A₁^0.82+ A₂^0.82 ).

[CMA010]

Equation 2 is mathmatically incorrect.

CMA010,

What's the incorrectness in mathematical point of view?

Fallah

High school math: x^z + y^z does not equal (x + y)^z

CMA010,

Before jumping to a thread read the thread history. If you had it done you had seen the below statement in my post (post#5):

"...the term (A₁^0.82 + A₂^0.82) is always greater than (A₁+A₂)^0.82 ..."

Indeed it is strange that no one in this thread claimed that above two terms should be equal and the reason you are going to prove they aren't equal isn't known. For your information the main issue is that among two equations which one is applicable for the case which OP has specified.

Fallah

Same applies to you regarding your accusation me not having read the thread history.

It makes no sense whatsoever that the duty absorbed by two vessels when combined is different (either larger or smaller) from the sum of the individual duties, commom logic dictates that these duties should be equal. Something that Robert realised but you didn't. It was merely pointed that equation 2 is mathematically incorrect (Robert had already mentioned this) and subsequently equation 1 is applicable (there you have to link with the original query). This in contradiction to your statements that equation 2 is the more logical one and is applicable.

[fallah]

CMA010,

Every one can submit his/her idea about this matter and seems you believe the equation 1 is applicabe to the issue. No problem, but the matter that is strange to me: you did mention that the equation 2 is mathematically incorrect! while each of two equations is stablished based on relevant physical view on the matter: two vessels are engulfed in one common pool fire and are protected by one PSV. One physical view leads to summing two wetted areas and putting it in the equation and another view leads to look at each vessel such that it is protecting with its own PSV and doing separate heat absorbed calculations then summing the two values of heat absorbed. Everybody could be able to look precisely to this matter realize that no mathematical logic come into play and two equations are different merely due to difference in physical views on the matter.

Fallah

[kkala]

"Basically the equations we all use are based on full-scale fire tests conducted in the 1940s using various petroleum fuels. The familiar coefficients for heat flux were determined from a series of plots. Do they have any real relevance? Only for the fuels they were derived from and only for non-reactive systems. Are we conservitive or not if we use them? The answer is both yes and no (clear as mud).
There is nothing that says we have to follow these simplified equations. Indeed, the authors of reference (2) suggest a more performance-based approach,..."
Post No 3 by Phil pleckner in "Reliability of Fire case Heat Load Equations", http://www.cheresources.com/invision/topic/3838-reliability-of-fire-case-heat-load-equation/.

1. x^z + y^z is lower than (x + y)^z if z>1, but higher than (x+y)^z if z<1, such as z=0.82 (clarified in post No 5). Difference is not so great, (x^0.82+y^0.82)/(x+y)^0.82 has a max value of 1.13 (when x=y). Uncertainty of API equations used for heat input seems much higher.
2. Attached publication "Relief valve heat.pdf" in post No 4 clearly recommends x^0.82 +y^0.82 , which is more conservative.
3. I would not risk the interpreatation of (x+y)^0.82 , which could cause another issue to the inspector (among others) in case of a relevant fire accident. Extra cost (if any) is not much. Both cases [1] or [2] probably require same size of PSV, or the "conservative" interpretation [2] may result in next higher size.
4. In conclusion I would base the design on interpretation [2] and write the relevant documents accordinly.
5. Actual examples from cases already designed are welcomed.

Note: Same environmental factor C is assumed for the two vessels. The case that fire "sees" all sides of both vessels may be rear but possible.

Edited by kkala, 10 August 2012 - 01:32 PM.