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Pressure reduction during contraction
3

Pressure reduction during contraction

Pressure reduction during contraction

(OP)
Hello,

I was asking how to accurately estimate pressure reduction during contraction. I saw some experienced engineers using the formula P2=(rho1/rho2)*P1 to estimate the pressure after contraction of 40 barg saturated steam to saturated water but i cannot find where it comes from...Is it correct?

Thanks in advance

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

Your formula is just a simplification of the ideal gas law - assuming the temperature is constant. It will certainly not be accurate (or even relevant) if the second state involves a liquid. Also, be aware that saturated steam at 40 bar has a compressibility of around 0.82, so the ideal gas law becomes suspect even if you stay with gas phases.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

RE: Pressure reduction during contraction

(OP)
Yes Z=0.872 for steam at 40 barg

So?
considering Z and that:
State 1 is saturated steam at 40 barg
state 2 is saturated liquid
what would be the correct approximation for determining P2?
 

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

P2 is determined by the vapour pressure of the liquid at T2.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

RE: Pressure reduction during contraction

(OP)
BTW katmar says "Your formula is just a simplification of the ideal gas law - assuming the temperature is constant."
Using the ideal gas law would lead to the formula P2=(rho2/rho1)*P1  and not P2=(rho1/rho2)*P1 ...

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

The formula you should be using for the first cut is Bernoulli's equation.  In the contraction, the velocity increases rapidly and the pressure decreases (the equation assumes a constant density).

Then you can use Joule-Thomson coeeficients to get the temperature change to calculate the probable change in density.  Finally you can use your equation.

Typically Bernoulli is close enough for this sort of calculation, but if you need more precision this will get you there.

David

David Simpson, PE
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RE: Pressure reduction during contraction

(OP)
Thank you zdas04,

Could you please tell me where does  the relationship P2=(rho1/rho2)*P1 come from (different from ideal gas law which wuold lead to P2=(rho2/rho1)*P1...)?

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

Well, I don't really know.  If I were to bastardize Bernoulli by saying that the density isn't constant and assuming velocity and elevation are constant, you would get P2/rho2=P1/rho1 so I don't have a clue where thay could have come from beyond a long-lived typo.

David

RE: Pressure reduction during contraction


Steam tables show that below 40 barg, the saturated steam line shows that the products P.v are about constant (with an error of less than 5%) down to, say, 10 Bar.

where P are absolute pressures and v specific volumes = 1/ρ of saturated steam.

P.v = P/ρ

Is this sheiko's intention ?  

RE: Pressure reduction during contraction

(OP)
Thanks 25362,

However your relationship still leads to P2/rho2=P1/rho1 while some engineers use the relationship P2/rho1=P1/rho2 to estimate the pressure reduction during contraction...

So:
1/ Where does this expression come from?

2/ In the case i mentionned:
State 1 is saturated steam at 40 barg (rho1=19.46 kg/m3)
state 2 is saturated liquid (rho2=799.36 kg/m3)
Is this expression valid?

Please.

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

(OP)
Also i considered:
T1=Tsat=250°C, Z1=0.872 and
rho2 is obtained from specific volume in steam tables at same temperature T2=T1=Tsat=250°C (maybe it is wrong...)

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

Guys, we are talking at cross purposes here. I took sheiko's "contraction" to be "contraction during cooling" and David has assumed it is a flow process through a reducer. These are two very different situations and require different analyses. Even with the information now presented I cannot say that I know what the problem actually is. I must admit that I did not check carefully enough to see that the formula was upside down compared with the ideal gas law.

Sheiko, what actually are you trying to do?

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

RE: Pressure reduction during contraction

(OP)
Thanks,

I'm trying to check if the minimum design pressure of a 40 barg steam pipe is low enough. So i considered the formula that i presented you in order to figure out the pressure reduction during condensation.

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

If you fill your pipeline with 40 barg steam and isolate it and let it cool down the pressure will be determined by the vapour pressure of water at the temperature reached. The temperature reached will depend on the time and the external weather conditions, but if you left it long enough in freezing conditions the pressure in the pipe would get down to below 1 kPa absolute.  Effectively full vacuum.

You may well find that your steam traps will work as vacuum breakers. Depends what type you are using and what your condensate piping looks like.

Off topic - but if you are talking saturated 40 barg steam your density is wrong.

Harvey

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

RE: Pressure reduction during contraction

(OP)
For saturated steam at 40 barg:
rho1=4100000*18/(0.872*8314.5*(250+273.15))=19.46 with real gas law and rho1=19.95 using steam tables at 250°C.

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

(OP)
In addition, Katmar, what about using the Joule-Thomson coeeficients to get the temperature change to calculate the probable change in density?

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

The process is constant volume; therefore, just follow a line of constant specific volume on your steam charts/tables until you reach the equilibrium temperature.

I2I

RE: Pressure reduction during contraction

[quote sheiko]In addition, Katmar, what about using the Joule-Thomson coeeficients to get the temperature change to calculate the probable change in density?[/sheiko]

If it's a closed system, there is no change in density.

I2I

RE: Pressure reduction during contraction

(OP)
How can the volume be constant during a contraction (which is by definition a volume reduction)? Also does condensation always produce a contration?

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

You have a two-phase vapor-liquid mixture.  The portion that condenses to a liquid takes up less space; however, the amount that remains vapor takes up more space as it expands with the corresponding decrease in pressure.  The average specific volume of the complete mixture remains the same.

I2I

RE: Pressure reduction during contraction

(OP)
How do you link this average specific volume to the specific volumes of saturated steam and water, respectively vf and vg in steam tables? and which volume to follow on the line of constant specific volume of steam charts/tables to determine the equilibrium temperature?

Reminder:
Initial state is saturated steam at 40 barg (and T=250ºC)
Final state is saturated liquid. What is the final T?

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

Quote (insult2injury):

If it's a closed system, there is no change in density

Think of a 200 mile long gas pipeline that is at 80F and 1,400 psig at the head and 55F and 600 psig at the foot.  The density of 0.6 SG gas at the head is 4.2346 lbm/ft^3 and 1.9247 lbm/ft^3 at the foot--less than half.

Mass flow rate is constant for the two points.  This is accomplished in the face of declining density by increasing velocity.

David

RE: Pressure reduction during contraction

zdas04:  Now I'm confused.  I thought that he was considering a case where the line is blocked in, initially filled with steam, and wanted to determine the final pressure after the temperature equalized.  Reading back, I'm not sure that it is ever clearly defined whether this is a blocked in line or a normal operating process line with heat transfer.

sheiko:  
1st approach (blocked in line, initially filled with steam)
- look up the specific volume corresponding to the initial state
- follow the line of constant specific volume corresponding to the initial state specific volume
- from this line, you can determine the quality and pressure of the mixture at the temperatures of interest
- how much the temperature changes is a function of the ambient temperature and heat transfer coefficients
- if left sufficiently long, the pipe will equalize in temperature with the surroundings
- to determine the pressure, look up the pressure value corresponding to the initial (and final) state specific volume and ambient temperature

2nd approach (flowing process line with heat transfer)
- the pressure difference will equal the two-phase frictional flow losses, several correlations have been published for this case

I2I

RE: Pressure reduction during contraction

If we are considering a blocked line that is cooling the pressure will follow the saturation line as the steam cools.
The practical answer is: Can the line withstand total vacuum without collapsing, if not, install a vacuum breaker set at a pressure above the collapse pressure.  

RE: Pressure reduction during contraction

The blocked line case is trivial.  If there is no flow then pressure (within a few seconds of shut in) is the same on both ends of the contraction.  As the line cools, pressure drops on both sides of the contraction.

The question only makes sense if the line is flowing.

David

RE: Pressure reduction during contraction

(OP)
It was dealing with blocked in line.
My conclusion is that, as i want to check the pipe against vacuum, maybe i should account for full vacuum, as even with a final temperature close to room temp, the vapour pressure will be substantially zero.

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

I am not sure about your formula but you can do this in the following way unless the entire steam is condensed.

Suppose, you have 1cu.mtr of pipe volume filled with steam at 40barg and it started condensing. At 40barg the density is about 20.6078kg/cu.mtr. If 10 kgs of steam is condensed then you have about 10.6078kgs of steam left to occupy a volume of approximately 1cu.mtr (actually, water specific volume at 40barg is 0.00125cu.mtr/kg, so 10kgs of water occupies 0.0125cu.mtr or 10.6078kgs of steam occupies 0.9875cu.mtr and density should be 10.6078/0.9875 = 10.74kg/cu.mtr)

Now, get a steam table program like steam tab and go use the saturation temperature corresponding to 40barg and go on varying the pressure till you end up with 10.74kg/cu.mtr density. This will give you the pressure of 23.75bara.

The important point is to first calculate the heat loss and then use that data to check the rate of condensation and then using the above method, you can check the pressure at intervals.

RE: Pressure reduction during contraction

(OP)
Quark,
Could you please clarify/explain your last sentence "The important point is to first calculate the heat loss and then use that data to check the rate of condensation and then using the above method, you can check the pressure at intervals. ", because i don't really see how to perform that...

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

(OP)
Moreover,

1/ Why the fact that the entire steam is condensed invalidates your method?

2/ Why did you make all your calcs assuming steam and water at 40 barg while the pressure is suppose to vary?

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 

RE: Pressure reduction during contraction

I would allow for full vacuum and at the end of the day it probaly make little difference considering the wall thickness you are using for 40 bar - this should have a wall thickness well in excess of requirements for a full vacuum.

RE: Pressure reduction during contraction

Quote (sheiko):

Could you please clarify/explain your last sentence
Suppose, xkw/m2/k is the heat transfer coefficient and y kJ/kg is the latent heat of steam at the given conditions, then the amount of condensate formed in one hour from 1 m2surface area of the pipe and with 1K temperature difference is x*3600/y.

Quote (sheiko):

Why the fact that the entire steam is condensed invalidates your method?
When the entire steam condenses then it will be the vapor pressure at the condensate temperature.

Quote:

Why did you make all your calcs assuming steam and water at 40 barg while the pressure is suppose to vary?
I just showed one example. You can better split the process into no. of intervals and do the calcs as your time permits.

However, like earlier suggested, if the steam quantity trapped is insignificant compared with the exposed area and if it happens for a longer periods of time then full vacuum is a better assumption.
 

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