32 replies to this topic

[PaoloPemi]

The isentropic nozzle model (see the attached Excel file nozzle.xls) available in Prode Properties (sizing of relief valves with critical and two-phase flow with isentropic nozzle model HEM) calculates required area and estimates the discharging temperature in two steps, a isentropic flash to choked pressure and then adiabatic flash to outlet pressure,
according Prode this rigorous method is applicable to both gas and gas+liquid (HEM method) flows.
I have tested this method for many years comparing results against single isentropic and adiabatic flash (with specific corrections) and the constant energy flash (available in Prode Properties) and the results seem more accurate than the other options that I have investigated.
I have been informed that different software applications (as Aspen Flarenet) utilize similar procedures.
Since the determination of discharging temperature can have a large impact in plant's design (selection of materials etc.) and different methods may produce very different estimates it would be interesting to know if a specific method or procedure has been discussed in standards,
does anyone know if some standard (API etc.) do include a discussion about this specific topic (determination of discharge temperature) ?

Attached Files

•  nozzle.xls   140.5KB   1694 downloads

Edited by PaoloPemi, 03 September 2012 - 11:40 AM.

[flarenuf]

Paolo
I posted this last year on the subject ...................

I read with interest recently various postings on this site about whether a PSV should be modelled as isenthalpic,isentropic or a combination of both. Various people expressed various views and the concensus seemed to be an isentropic flash from inlet pressure to sonic velocity & pressure at the Vena Cava , ie a nozzle. Then an isenthalpic flash from the VC to the valve outlet. Little or no loss in the outlet due to friction.

Being a user of AspenHYSYS and Flarenet I did some comparison runs at various inlet pressures, temps and MW's using a combined flash and the good old fashioned isenthalpic flash ( ie as a control valve). In HYSYS assumed a perfect isentropic flash with 99% of heat recovery in the kinetic energy recovery zone

summary of results
a simple isenthalpic flash gives exit temperatures 1-2% higher than the complex model.
at high pressure drops across the valve this can increase to 5%.
the complex model does predict the throat temperature nicely which could impact on the choice of metallurgy, but this is down to the valve vendor surely.

In Aspen Flarenet selecting the option to compensate for the change in kinetic energy from inlet to outlet gives results closer to the complex model values. The use of this option is encouraged.
The optional isentropic method in Flarenet gives ridiculously low exit temps and should not be used as it could give incorrect metallurgy selection. ( you only need an isentropic efficiency of 0.005 to match the complex model). In my opinion its not worth using it.

Conclusions

I agree with the thinking that a combined isentropic/isenthalpic model is the absolute correct way to model a PSV, given the tools available this is possible but...
..to all extents and in the real engineering world it doesnt make any difference. We are talking tenths of a degree difference in the outlet temps.
Given all the other errors in data prediction taht could occur when sizing a PSV the old fashioned method of simulating as a valve with an isenthalpic flash seems not too bad away to do it after all.

a reply from JOe Wong was
The thermodynamic path that an engineer would like to consider is subject to what he really wanted to look at and how conservative he would like to design for. If you intended to derive low temperature limit, certainly you can not ignore the isentropic path. However, from back pressure aspect probably an pure isenthalpic path would be better.

I do not disagree with your statement the difference may be minor in some event, an engineer should always keep in mind the thermodynamic path would be a mix of both, imagine how this mix affect their design and provide necessary margin if a particular approach has been taken.

Just to correct you Flarenet does not do the double flash method, its one or the other.
I attach an excel spreadsheet showing the differences.

Flar e nuf

Attached Files

•  PSV 035 - Isenthalpic vs tropic.xls   33.5KB   1148 downloads

[PaoloPemi]

Flar e nuf,
thank you for the comment,
I wrote this post to see if this specific topic has been discussed in some standards (API etc.)
I agree that isentropic nozzle model produces accurate results, from your description I guess the option to compensate for the change in kinetic energy in Aspen Flarenet should be similar to the Constant Energy Flash available in Prode Properties.
As said I have tested this model for many years and compared the results against alternative formulations,
in my opinion results are reasonably reliable (at least in the cases which I have tested).
The attached file nozzle.xls (see above) includes a little VBA procedure which one can easily modify (Prode Properties exports a set of methods for solving temperature (or pressure) at specifed enthalpy, entropy, volume and temperature (or pressure)) and it's easy to introduce variants.
I have not been able to compare Prode with your results since you do not provide compositions,
it doesn't seem you make a iterative calculation to detect the pressure for maximum flux (as the simple procedure in nozzle.xls does) but just compare results, a iterative procedure is required to detect that point which is not constant.
Prode has a specific operating unit (NOZZLE) which solves the isentropic nozzle model but I prefer the VBA code in nozzle.xls which I can easily adapt according my needs.
I think it's a very easy to use procedure directly in Excel and I recommend this procedure for all critical applications as supercritical or two phase where the HEM (Homogeneus Equilibrium Model) is applicable, Prode has another option to deal with cases where HEM is not applicable.
For the usual applications simple formulations as API for gas or vapor relief (based on integration of constant, ideal k) are much more simple and yet give accurate results, it doesn't make sense to run a complex model except for purposes of comparing results, for example to discover that entering the real k (cp/cv) calculated at pin,tin can produce wrong results in many cases.

Edited by PaoloPemi, 03 September 2012 - 11:44 AM.

[pter]

thanks for the information

[fallah]

Hi,

I, same as Flar e nuf, agree with the fact that a combined isentropic/isenthalpic model is a better way to model a PSV. Of course, it should be noted that VC just ocuurs in sharp edge orifice rather than nozzle and because flow restricting area of a PSV is closer to a nozzle than an orifice, then the PSV nozzle throat (or a point neat there) would be the transformation point from ISENTROPIC to ISENTHALPIC process while a flow is passing through the PSV. In fact, the process from PSV inlet to mentioned point as a short and frictionless (the minor frictional loss is ignored) passage is thermodynamically considered REVERSIBLE (ISNTROPIC) and from mentioned point to PSV outlet due to expansion process is considered ISENTHALPIC (IRREVERSIBLE). Anyway these fact should be considered to find PSV downstream temperature using any software.

Indeed, as far as i know there is no specific points/discussion in the standards such as API,.. in this regard.

Fallah

Edited by fallah, 04 September 2012 - 04:45 AM.

[PaoloPemi]

thanks fallah,
indeed I wasn't able to find any specific information (about this topic) in API codes.
While for natural gas mixtures (C1 > 0.7) discharging temperature as calculated with adiabatic or isentropic+adiabatic flash can show little variations (depending from C1 properties) the same is not true for many other fluids,
consider for example the mixture 0.9 Water 0.1 Ammonia,
if I model a PSV discharging this mixture at 40 Bar.@ 530K (vapor phase) I get very different values (for discharging temperature) from a single adiabatic flash (486K) or isentropic+adiabatic flash (428K) so it seems to me that the selection of proper method has importance.

Attached Files

•  psvmodel.jpg   89.15KB   173 downloads

[chemdoc]

interesting discussion,
just to add my contribute:
1) as far as I know this specific point is not mentioned in API code
2) the results shown by Flar e nuf are not valid for fluids as water (and many others), for many fluids isentropic and adiabatic path are VERY different as the resulting final temperatures

[PaoloPemi]

thanks for the comments,
I agree about the different results of adiabatic, mixed (isentropic+adiabatic) and isentropic flash,
that is true for many fluids,
I attach two examples of simulation
the first psvwater.jpg for a PSV discharging steam at 170 Bar.a and 700 K with model IAPWS 95 (included in Prode Properties) results are

553 K for single adiabatic flash
373 K for single isentropic flash (with a very low error in VLE outlet being 0.76 gas + 0.24 liquid)
482 K for mixed (isentropic+adiabatic flash)

note that if I set in Prode Properties the Extended Peng Robinson or another model I get similar results.
the second psvoxygen.jpg for a PSV discharging oxygen at 70 Bar.a and 288 K with model Extended Peng Robinson available in Prode Properties, results are

265 K for single adiabatic flash
90 K for single isentropic flash
220 K for mixed (isentropic+adiabatic flash)

in absolute values there is about 20% error (265 K - 220 K ) / 220 K from adiabatic and mixed model (I do not consider the single isentropic flash)
however from the point of view of metallurgists while 265 K in most cases is an acceptable temperature, 220 K may be a limiting value

Note that I see similar or higher differences with two-phase flow,
as said the Excel page nozzle.xls is capable to model rigorously (accepting the limits of HEM model) relief valves with two-phase flow (with pure fluids and mixtures),
I can provide some additional test case if someone is interested

Attached Files

•  psvwater.jpg   99.61KB   68 downloads
•  psvoxygen.jpg   97.33KB   46 downloads

Edited by PaoloPemi, 05 September 2012 - 03:46 AM.

[frpe]

interesting information,
thank you

[staffel]

great post !
Can you provide some additional information comparing the rigorous model against API formula with ideal and real cp/cv values ?
According some authors the use of 'real' ratio for orifice sizing can result in under-sized orifices.

[PaoloPemi]

Staffel,
as suggested in API for gas streams I run the rigorous model when discharging (pd,td) conditions are in critical region,
cp values may become very high in this area and integrating with constant cp/cv (API formulation) can produce unreliable results.
In general with API formulation for gas the ideal cp/cv produces more reliable results.
I include (see image psv07C2H603C4H10.jpg) an example for a stream composed by 0.7 Ethane and 0.3 nButane , model Soave Redlick Kwong

I have defined the discharging conditions at 40 Bar.a , 348 K (far from critical point in vapor region)
Prode Properties calculates these properties
cp/cv = 1.77
compare this value with that calculated at 1 Bar.a
cp/cv = 1.13
the calculated areas are
2.34 cm2 (with cp/cv = 1.77)
2.74 cm2 (with cp/cv = 1.13)

when I run the rigorous model (see the attached file) I get
required area = 2.64 cm2

so the area calculated with real cp/cv is understimated of about 10%
setting the discharging conditions more close to the critical point we will observe increasing values for cp and cp/cv and possibly larger differences in values.

there are many cases where API with real and ideal cp/cv and rigorous model give different results, in all these cases I utilize the values calculated with rigorous model

Attached Files

•  psv07C2H603C4H10.jpg   117.2KB   52 downloads

Edited by PaoloPemi, 08 September 2012 - 04:16 PM.

[pathensey]

thanks,
very good information !

[staffel]

Paolo,
I think I have a similar case,
fluid Acetylene, vapor phase (supercritical), discharging pressure 1000 psia temperature 110 F
could you verify the results with rigorous model ?

Edited by staffel, 07 September 2012 - 01:35 AM.

[PaoloPemi]

I have converted Psia and F units to Bar.a and K , flow has been defined at 4.3 Kg/s (15480 Kg/h)
the first figure psvacetylene_Case1a,jpg shows the results for your test case
as you see due to the large values calculated for cp/cv (Prode Properties with Soave-Redlich-Kwong model calculates 23.46 for cp and 1.69 for cv) there is a large difference between the area calculated with real cp/cv 1.09 cm2 and ideal 1.94 cm2
the rigorous model calculates a value of 2.19 cm2 ,
the area calculated with real cp/cv is understimated of about 50%

however observing the value of the specific volume calculated at 47.453 Bar.a (0.007 m3/kg) we realize that it's not all vapor phase, possibly it's some supersaturated state,

In my opinion a more correct test should consider a stream with properties of vapor within the valve,
to obtain that condition with the same pressure (1000 Psia or 68.94 Bar.a) we can increase the temperature from 313 K to 325 K (125.33 F)
the second figure psvacetylene_Case2a,jpg shows the results for this test case
the specific volume calculated at 44.147 Bar.a 294 K is that of vapor state (0.012 m3/kg)
There is a quite large difference (about 30%) for the values calculated with real cp/cv and ideal cp/cv
Also in this case the area calculated with ideal cp/cv (2.63 cm2) is close to that calculated with rigorous model (2.67 cm2) while the area calculated with real cp/cv is understimated of about 30%

Please note that the rigorous model permits to evaluate also the state of the fluid within the valve (see the above notes) which may be of importance in many cases

Attached Files

•  psvacetylene_Case2a.jpg   111.32KB   22 downloads
•  psvacetylene_Case1a.jpg   111.35KB   18 downloads

Edited by PaoloPemi, 08 September 2012 - 04:08 PM.

[latexman]

Paolo,

I do not recall having seen or heard of these calculation method details being discussed in any public standard.

From my understanding of compressible flow where Mach 1, or at least transonic flow, is achieved at the end of the flow nozzle, there will be a corresponding shock wave at the flow nozzle exit. The classical approach to this is for the stagnation enthalpy (h₀) to be the same just upstream of the discontinuity (x) and just downstream of the discontinuity (y). This is represented in the form:

h_x + V_x²/2 = h_y + V_y²/2 = h₀
h = enthalpy
V = velocity

Is this what you mean by ”then adiabatic flash to outlet pressure"? Somehow, I think not.

This approach sounds like what Flarenuf described, "In Aspen Flarenet selecting the option to compensate for the change in kinetic energy from inlet to outlet gives results closer to the complex model values."

Edited by latexman, 09 September 2012 - 06:41 AM.

[Bobby Strain]

If you can program in VB or VBA, then you can write your own program. You can automate by using HYSYS or ProII or similar OOP simulators to perform the flash calculations, which I recommend.
I always specify flashing or two-phase flow valve sizing based on my own calculations; I don't depend on vendor results. And I always perform adiabatic flashes to do the calculations. The difference from isentropic is always positive, giving a conservative valve size, but not by much. HEM is a very complex procedure, and you should not use a spreadsheet for sizing. Get something hard coded, compiled, and locked. I recommend the HEM method for supercritical fluid relief, too. Where vendors have the capability to correctly size the valve, like vapor or liquid, you should make them responsible for sizing the valve. Don't take on any unwanted liability for you employer.
As a general rule, I abhor spreadsheets for any engineering calculation. No control whatsoever.

Regards,
Bobby

[pter]

Paolo,
the information provided is very interesting and useful for psv design and rating,
thank you !

Bobby Strain,
please review the results shown by Paolo,
the evaluation, comparation and discussion of results should be the work of engineers...
if you have different data please show it and we'll be pleased to comment...

Edited by pter, 08 September 2012 - 12:41 AM.

[twell]

This is a VERY interesting thread !
if I may add a little contribute, there is a paper "Proper relief-valve sizing requires equation mastery" Hydrocarbon Processing 2011, where the authors discuss a method for sizing pressure-relief valves (critical flow of gases or vapors) , they evaluated the contribute of real gas specific heat ratio (in API formulation) and came to the conclusion that "The real gas specific heat ratio already accounts for the value of the compressibility factor and non-ideality at high pressure conditions. Therefore, when the real gas specific heat ratio is used in the sizing equation, the compressibility factor is not necessary. If one uses the real gas specific heat ratio in Eq. 1, the compressibility factor will be accounted for twice. This may result in inadequate relief valves, as addressed in API-520"
The paper includes several numerical examples.

The procedure is very simple and could be easily coded in Excel but it requires a simulator to calculate the properties (as the authors did) and it is applicable to gases or vapors only,
by comparison the numerical solution of isentropic nozzle model discussed in this thread (and presented as Excel page) is applicable to both gas and gas+liquid flows.

[PaoloPemi]

I have that paper in my library,
I have also compared the results with the example included in the article,
10,000 kg/h of saturated n-hexane vapor (M = 86.18) at a relief pressure of 1,807.38 kPa and a relief temperature of 474 K,
see the attached image psvnhexane.jpg ,
there are three cases, the third adopts the equation 7 proposed by authors,

the rigorous procedure calculates an area of 5.55 cm2

the first with real cp/cv (1.25) and zv 0.65 gives an area of 4.58 cm2
the second with ideall cp/cv (1.044) and zv 0.65 gives an area of 4.90 cm2
the third with real cp/cv (1.25) and zv 1.0 gives an area of 5.68 cm2
(the author report for equation 7 a value of 567 mm2)

in this case the value calculated with this method is very close to that calculated with rigorous method
in other cases there are differences (up to 10-15%), see the attached example with nHexane at 27 Bar.a 500 K

Attached Files

•  psvnhexane.jpg   112.92KB   30 downloads
•  psvnhexane_case1.jpg   112.07KB   18 downloads

Edited by PaoloPemi, 08 September 2012 - 04:19 PM.

[staffel]

Paolo,
could you share the Excel xls page utilized to solve the three different procedures ?
I wish to compare the results for a range of values

[PaoloPemi]

sure,
I attach the Excel page psvcompare1.xls

this page permits to compare different procedures

Discharging temperature (PSV outlet)
1) calculated with isentropic + adiabatic flash (the default in nozzle.xls)
2) calculated with adiabatic flash
3) calculated with isentropic flash

Calculated Area
1) rigorous numerical solution of isentropic nozzle
2) API formulation for gas and vapors, ideal cp/cv
3) API formulation for gas and vapors, real cp/cv
4) API formulation for gas and vapors, real cp/cv, Zv = 1

all the required properties are calculated by Prode library , for personal/academic use you can download a free -with limited number of components- copy from www.prode.com

I utilize the unit conversion methods available in Prode Properties to convert from and to different units
UMCR() converts the different values entred by user to the units required by formulation (Pa.a,K,Kg/s)
UMCS() converts the calculated area (cm2) to the units required by the user
StrMw(1) returns the Molecular weight
the formulations are those of API and ISO standards, with different parameters as discuused,
you can easily introduce variants if you wish to compare different methods

the relative errors are calculated as difference with rigorous solution


good luck
Paolo

Attached Files

•  psvcompare1.xls   146KB   829 downloads

Edited by PaoloPemi, 11 September 2012 - 08:24 AM.

[staffel]

Paolo,
thank you very much for the Excel page.

[twell]

Paolo,
according the authors the method presented in "Proper relief-valve sizing requires equation mastery" (psv sizing for gas and vapors based on Zv = 1 and real cp/cv ) gives results more accurate of std. procedure based on real Zv, ideal cp/cv ,
your Excel page shows that this is true in most cases

[serra]

very useful thread,
thank you all !

[marchem]

latexman,
I would presume that the procedure in nozzle.xls solves the energy balance across the orifice (in = inlet, o = orifice)
hin+1/2*vin^2 = ho+1/2*vo^2
where vo is the speed of sound for choked flow
the solution is iterative taking in account the properties of real fluids as calculated with EOS