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Should Specific Heat Capacity Ratio (k) In The Mach Number & Criti


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#1 JoeWong

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Posted 07 November 2007 - 10:06 AM

Dear all,

Specific heat capacity ratio (k) is included in the Equation [23] & [24] and [25] & [26] in API RP 521, 1997 where [23] & [24] and [25] & [26] are used to calculate the Mach number and Critical pressure of gas in the pipe respectively.

In the latest API Std 521 Jan 2007, Specific heat capacity ratio (k) has been removed from [27] & [28] and [29] & [30]...

I have made some surveys and derivation, k factor may be required in the equation. Read details HERE.

This issue has been highlighted to API committee incharge and the response is those equations in current revision (2007) are CORRECT (k factor should NOT appear in the equation).

Appreciate your advice and information.

JoeWong

#2 pleckner

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Posted 07 November 2007 - 12:10 PM

k should NOT be in the equation and it was an error in the previous edition. I'm happy to see it finally be corrected.

The equations given by API are specifically stated to be for ISOTHERMAL gas flow, NOT ADIABATIC gas flow. The ratio of specific heats is for ADIABATIC conditions, NOT ISOTHERMAL conditions.

#3 JoeWong

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Posted 08 November 2007 - 09:50 AM

QUOTE (pleckner @ Nov 7 2007, 12:10 PM) <{POST_SNAPBACK}>
k should NOT be in the equation and it was an error in the previous edition. I'm happy to see it finally be corrected.

The equations given by API are specifically stated to be for ISOTHERMAL gas flow, NOT ADIABATIC gas flow. The ratio of specific heats is for ADIABATIC conditions, NOT ISOTHERMAL conditions.



Phil,
Thanks for your response.

Per equation [6-116] in Perry's Chemical Engineering handbook,

T0/T1 = 1 - (k-1)/2 * M12

consider ISOTHERMAL gas flow,

T0 = T1 ==> k = 1

Can i say that k should still exist in the equation BUT it is equivalent to 1 due to ISOTHERMAL gas flow ?


JoeWong

#4 pleckner

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Posted 08 November 2007 - 06:22 PM

Simply put. an adiabatic term should not be used in an Isothermal equation Cp/Cv has no meaning in the Isothermal equation.

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Posted 19 December 2007 - 09:32 PM

As a supplement to this discussion could I ensure that you are aware that the 'real' Cp/Cv ratio data provided by HYSYS and other simulators should not be used in the RV sizing and capacity formulae in API-521. The API formulae are based on 'ideal' gas laws where Cv = (Cp-R) and using 'real' data can result in an undersized orifice, particularly at very high pressures.

Within HYSYS the 'real' data is used in a consistent manner for depressurisation modelling etc. but when data is extracted for use in sizing calculations based on API-521 then the alternative Cp/(Cp-R) data should be used.

#6 pleckner

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Posted 20 December 2007 - 06:21 AM

I assume you are referring to the evaluation presented in the article published in Chemical Engineering Magazine, November 2003 by Aubry Shackelford, "Using the Ideal Gas Specific Heat Ratio for Relief-valve Sizing"?

#7 JoeWong

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Posted 20 December 2007 - 09:55 AM

QUOTE (joe aiken @ Dec 19 2007, 09:32 PM) <{POST_SNAPBACK}>
As a supplement to this discussion could I ensure that you are aware that the 'real' Cp/Cv ratio data provided by HYSYS and other simulators should not be used in the RV sizing and capacity formulae in API-521. The API formulae are based on 'ideal' gas laws where Cv = (Cp-R) and using 'real' data can result in an undersized orifice, particularly at very high pressures.

Within HYSYS the 'real' data is used in a consistent manner for depressurisation modelling etc. but when data is extracted for use in sizing calculations based on API-521 then the alternative Cp/(Cp-R) data should be used.


joe aiken
Thanks for your input.

Are you saying we should use ideal K instead of real K in calculating Mach no and critical pressure ?

JoeWong

#8 pleckner

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Posted 20 December 2007 - 12:11 PM

@JoeW

Joe Aiken chimed in with a side-bar and has nothing to do with what your original post was about. Joe Aiken is referring to the PSV sizing equations given in API RP 520, not what is happening in the pipe! My original post not only still stands but I will defend it to my demise.

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Posted 27 March 2008 - 07:12 PM

QUOTE (joe aiken @ Dec 20 2007, 01:32 PM) <{POST_SNAPBACK}>
As a supplement to this discussion could I ensure that you are aware that the 'real' Cp/Cv ratio data provided by HYSYS and other simulators should not be used in the RV sizing and capacity formulae in API-521. The API formulae are based on 'ideal' gas laws where Cv = (Cp-R) and using 'real' data can result in an undersized orifice, particularly at very high pressures.

Within HYSYS the 'real' data is used in a consistent manner for depressurisation modelling etc. but when data is extracted for use in sizing calculations based on API-521 then the alternative Cp/(Cp-R) data should be used.


I know this is off topic but I can't help but reply to this:

API RP 520 Part I (7th, Jan 2000) Section 3.6.2 (p42)

C = coefficient determined from the expression of the ratio of specific heats (k=Cp/Cv) of the gas or vapor at inlet relieving conditions.

The API Standards Committee has the following to say regarding the above:

Yes. Section 3.6.2 recommends that the ratio of specific heats, k, in the sizing equations should be determined at the inlet relieving conditions. This is a departure from previous editions, which said that k should be based on standard conditions (i.e. 60ºF and atmospheric pressure).

And...

The ratio of specific heats, k, for most gases will become unstable near the critical point, and therefore the committee cautions users when the inlet conditions are near the critical point. Table 7 provides k values for some common gases at standard conditions. If the k at standard conditions is used, the resulting answer should be conservative.

The example calculations on page 44 and 45 do use the standard k values from Table 7. The committee will consider making changes to the text as well as the example problems to make it clearer to the reader that the actual values should be used and that the use of standard values as provided in Table 7 will be conservative in most cases.


API STD 521 (5th, Jan 2007) Section 5.15.2.2.2, Equation 10 (p42) echoes similar sentiment regarding the use of k at inlet relieving conditions.

Therefore, the Cp/Cv can be used directly from Hysys, as recommended by API.

#10 JoeWong

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Posted 28 March 2008 - 02:15 AM

QUOTE (rban @ Mar 27 2008, 08:12 PM) <{POST_SNAPBACK}>
....API STD 521 (5th, Jan 2007) Section 5.15.2.2.2, Equation 10 (p42) echoes similar sentiment regarding the use of k at inlet relieving conditions.

Therefore, the Cp/Cv can be used directly from Hysys, as recommended by API.


rban,
Welcome...

This is a bit off the topic... anyway...

You may be "right" (to certain extend) if you sit on API RP 520 Part I (7th, Jan 2000) Section 3.6.2 (p42) as basic document. API has admitted to certain condition (i.e. near critical condition), ideal Cp/Cv may be used. API has not addressed the pressure dip (low pressure region) in the PSV nozzle which potentially result k factor closer to ideal gas Cp/Cv...

Nevertheless, "Using the Ideal Gas Specific Heat Ratio for Relief-valve Sizing" published in Chemical Engineering Magazine, November 2003 by Aubry Shackelford has identified some event (Not all - inline with API), there is occasion where PSV is undersized by using Cp/Cv at inlet condition. Personally i have experienced in several occasions...

Being a professional engineer, i would encourage everyone not to give any chance on Pressure Relieving Device (PRD) as it is your last line of defense.

API STD 521 (5th, Jan 2007) Section 5.15.2.2.2, Equation 10 (p42) has discussed on different subject and context. It should not be referred in PSV sizing context.

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Posted 10 April 2008 - 11:38 PM

Sorry to extend this off-topic discussion but the point I was making is that HYSYS now calculates both Cv and Cp from 'real' simulated data (irrespective of the conditions) whereas Cv was previously calculated from Cp - R, where the Cp may be 'real' data but R is the Universal Gas Constant.

#12 JoeWong

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Posted 19 April 2008 - 04:09 PM

QUOTE (joe aiken @ Apr 10 2008, 11:38 PM) <{POST_SNAPBACK}>
Sorry to extend this off-topic discussion but the point I was making is that HYSYS now calculates both Cv and Cp from 'real' simulated data (irrespective of the conditions) whereas Cv was previously calculated from Cp - R, where the Cp may be 'real' data but R is the Universal Gas Constant.


For k factor, the (Cp-R)/Cp in HYSYS should be used to avoid potential undersized PSV.

#13 sheiko

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Posted 21 February 2009 - 05:26 AM

QUOTE (JoeWong @ Nov 7 2007, 04:06 PM) <{POST_SNAPBACK}>
Dear all,

Specific heat capacity ratio (k) is included in the Equation [23] & [24] and [25] & [26] in API RP 521, 1997 where [23] & [24] and [25] & [26] are used to calculate the Mach number and Critical pressure of gas in the pipe respectively.

In the latest API Std 521 Jan 2007, Specific heat capacity ratio (k) has been removed from [27] & [28] and [29] & [30]...

I have made some surveys and derivation, k factor may be required in the equation. Read details HERE.

This issue has been highlighted to API committee incharge and the response is those equations in current revision (2007) are CORRECT (k factor should NOT appear in the equation).

Appreciate your advice and information.

JoeWong


Dear Joe,

I think your demonstration is correct except that you made a mistake in the first equation (sonic velocity). The k factor should be ommited from sonic velocity under isothermal conditions as shown in the book: Darby R., "Chemical Engineering Fluid Mechanics", 2nd Ed., 2001.

See also: http://www.cheresour...?showtopic=7492

Regards



#14 JoeWong

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Posted 21 February 2009 - 06:23 AM

Dear Sheiko,
Thanks.

I have gathered more information and made some derivation. k factor should be omitted from the Mach number and critical pressure calculation.

Detail discussion in
Removal of Specific Heat ratio (k) in the Mach No. & Critical Pressure Calculation

Apologize. I should have include the follow up.

#15 sheiko

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Posted 21 February 2009 - 06:43 AM

QUOTE (JoeWong @ Feb 21 2009, 12:23 PM) <{POST_SNAPBACK}>
Dear Sheiko,
Thanks.

I have gathered more information and made some derivation. k factor should be omitted from the Mach number and critical pressure calculation.

Detail discussion in
Removal of Specific Heat ratio (k) in the Mach No. & Critical Pressure Calculation

Apologize. I should have include the follow up.


Joe,

I do know this article. I just want to point out that the k factor should also be removed from sonic velocity equation for ideal gas under isothermal conditions (not only critical pressure and Mach number).

For example, you made the mistake in your derivation (http://webwormcpt.blogspot.com/2007/11/another-descrepancy-found-in-api-std.html) which lead to wrong formulas for the critical pressure and Mach number...

Bye

#16 JoeWong

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Posted 21 February 2009 - 10:43 AM

Thanks. The equation [9] and [10] in here has already excluded the k factor.





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