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PSV Calculation - Kd,Kc,Kb factor

Hi friends, how are you today? Hopefully, you are not already bored with my articles. Now, we will learn the concept of relief valve calculation. The spreadsheets not tell you anything, but we should know what really it does. After read this fully article, I hope you get a better understanding of the relief valve calculation concept, and then know well with your spreadsheet.

Pressure is equal to the force divided by the area (P~F/A). That is a very basic concept. I am sure you already familiar with this formula in the very beginning of junior high school. In talking PSV, the force is generated by mass relieving rate. I am sure, all of us know well that relieving rate is depends on cases that to be considered (e.g. fire, blocked discharge, gas blow by etc.)

We need some corrections since the fluid flows through a relief valve nozzle orifice rather than an ideal nozzle. For the same area, at certain condition, the flow capacity of relief valve orifice must be less compared with the ideal one – Its mean that more area is required to handle the same mass relieving rate -. That’s why, there are some correction factors are required such as; Kc, Kd, Kb, Kv, Kp, Kh, Kn etc.

Let’s focus to Kc, Kd and Kb. I will make other posting for the explanation of the other factors.

Effective Discharge – Kd

Kd is effective discharge coefficient used for the mass flux capacity correction for the real nozzle. The higher the Kd value, the closer the mechanical to an ideal design - ideal nozzle, Kd = 1-. It is very obvious that the PSV has Kd value lower than 1. For instance, API relief valve has Kd = 0.975 and 0.65 for gas and liquid respectively.

Kd is depends on the mechanical design. In other word, every vendor has a specific value of Kd. It is important to be realized, so you are not always input 0.975 in the spreadsheet whereas you use PSV other than API.

We can use API data as preliminary calculation only when we don’t have any reference of Kd value. We usually do this at proposal stage.

Some vendors have a better design PSV than standard API. In other word, they have Kd value higher than 0.975. So, I suggest you to ask your vendor the exact value of Kd, especially at project stage. There is potential that the smaller orifice area is required.

Combination with Rupture Disk – Kc

Kc is correction factor when rupture disk to be installed upstream of the PSV.

Rupture disk is required to be installed at upstream of the PSV for system contain solid that may plug the PSV over time. At HAZID/HAZOP, for toxic service, potential leaking of relief valve shall be considered, and then rupture disk at upstream PSV can be used as positive seal for the safeguard. That is why, based on my experience, the combination rupture disk and PSV is very seldom to be applied in the gas processing.

Actually, the Kc value is complex. But I am sure, we seldom use it. So, I am not too interest makes longer explanation. I understand many engineers hate with the long article with something not practical, me too. If you want to know more detail about Kc, please read API 520 part I by yourself.

Impact of Back Pressure – Kb

Back pressure is defined as a pressure existing at PSV’s outlet. It impact to opening pressure, reduction capacity, instability or may combination of all. Kb is required for correction of reducing capacity.

For the low back pressure system that the impact is not significant, conventional type can be used. And for the excessive back pressure service, pilot type PSV is required to overcome it. Then, imagine that low back pressure for the conventional type and no impact back pressure on pilot type due to mechanical design. That’s all, I think, very clear why Kb is required for balance below type only.

Note that the back pressure correction factor Kb for conventional and pilot type is not required, and then use Kb=1. Ask your vendor of Kb value –as graphic- for using below PSV type or refer to API 520 part 1 for preliminary design.
Actually, for conventional type, when the condition is non-critical due to superimposed back pressure, Kb is required. But for now, rather than it will make you confuse, forget it since there are not much system likes that.

The understanding of the back pressure is very important for process engineer. At this time, at least, we know why Kb is required. I will make a separate posting for explanation of back pressure for more detail. I have plan it will have been finished before the end of this month. Don’t miss it.

That’s all I can share this week. The required orifice area calculation procedure is covered in API 520 part I. The standard relief valve orifice is also already stated in API 526 and ASME Sec VIII. Please refer to those documents for the detail.

Thank you.

14 comments:

  1. In sizing PSV for steam relief - Kb can be greater then 1.0?

    ReplyDelete
    Replies
    1. I don't think so.
      The Kb is correction factor..(reducing capacity of the PSV due to back pressure)
      The greater the back pressure, the lower the PSV capacity.

      Delete
  2. This is such a great blog.Please do continue the good work as it is a lot of help for Process Engineers round the world...

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  3. Great job.Your articles are very helpfull.Thank you

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  7. Please correct like this: Note that the back pressure correction factor Kb for balanced bellow and pilot type is not required, and then use Kb=1. Ask your vendor of Kb value –as graphic- for using below conventional PSV type or refer to API 520 part 1 for preliminary design

    ReplyDelete
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  9. I am designing a flare system and the back pressure allowance for one of the valves is 0.9 bar which, but I am unable to reduce the backpressure below 1.08 bar. In aspen flare analyser help window it is said that pilot operated valves allow backpressure up to 75% of set pressure, but according to the API521 pilot operated valves allow 50% back pressure. Can you help me with this problem or can you please suggest some reliable reference material?

    ReplyDelete
    Replies
    1. Some Vendor confirmed that pilot operated valve allow back pressure up to 75%, some higher even 80%,.

      Delete
  10. I am quite interested to know more about the combination correction factor (kc) you have explained in this post. Actually i have a doubt, if coefficient of discharge (kd) for PSV is having different values for the state of fluid it is having at inlet of PSV. Why the factor of combination correction factor (kc) is fixed with one value?.. for an example, if i am sizing a PSV having a rupture disk (continental ULTRX) at inlet, the kc value given is 0.978 per manufacturer catalog. if my PSV is experiencing three scenarios
    1. Vapor relief
    2. Two-phase relief
    3. Liquid relief
    Do the capacity correction factor (kc) will be constant for all scenarios?

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    ReplyDelete
  11. Hi, can you explain in detail what is back pressure ?
    Thank you so much :)

    ReplyDelete
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