Pressure change in a fixed volume as steam condenses 2

[BronYrAur]

In a fixed volume, such as a steam coil with a now closed steam valve on one end and a closed trap on the other end, and no vacuum breaker, how do I quantify the the pressure change in the coil as the steam condenses? Let's say I have 10 psig steam. I want to calculate the pressure after it condenses. I know that it goes into a vacuum, but how do I quantify it?

Same question if the steam is already in a vacuum, say 15" Hg. When it condenses, it will no doubt go into a deeper vacuum. I'm troubleshooting a vacuum steam system and think I may need a "vacuum breaker" between the steam side and the condensate side. They are both already in vacuum, but I an suspecting the steam side falls into a deeper vacuum when the steam condenses, thus preventing gravity drainage from the coil.

 

[zdas04]

PV=nRT. Every time for an ideal gas. What is the volume of the head space at time zero? How much mass is in the head space at time zero? What is the volume of the head space at the final time (often this will be effectively the same as time zero)? What mass is in the head space at the final time? Assuming isothermal condensation, the only unknown is final pressure.

If you assume that all the steam is gone and calculate a final pressure less than 0 psia, then your assumption is wrong and when you run out of pressure there is still some steam in the head space.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[Compositepro]

Assuming no air leaks, the pressure will be the vapor pressure of water at the hottest point in the tubing, which will be cooling to room temp.

 

[EmmanuelTop]

Just to add on top of the previous two posts: steam condensation parameters follow the tables for saturated steam. See for example:

http://www.engineeringtoolbox.com/saturated-steam-properties-d_457.html

or

http://www.tlv.com/global/TI/calculator/steam-table-temperature.html

for direct calculation.
If non-condensables are present in the steam, the actual pressure will be higher than that from the table. How much higher, depends on the amount (fraction) of non-condensables in steam.


Dejan IVANOVIC
Process Engineer, MSChE

 

[BronYrAur]

I appreciate several quick replies, but I am not following any of them.

I am not simply talking about the pressure-temperature relationship for saturated steam. I am looking at a fixed vessel containing steam, so my mass is also fixed. if the vessel is at 10 psig and the steam condenses, how do I calculate the resulting pressure? My vessel volume doesn't change, so I am not sure how the ideal gas law applies.

 

[EmmanuelTop]

I don't think there will be any alternative thermodynamics to follow except steam tables. Your case is (generally speaking) similar to steam-out conditions for process vessels, when steam flow is stopped at a certain point, and then vessel begins to cool down to ambient temperature. If no vent is provided, pressure inside the vessel will start to decrease, as a function of bulk condensate temperature inside (at the bottom of) the vessel. This condensation process occurs gradually so you won't be seeing steam condensate at ambient temperature immediately as steam flow is stopped - this temperature (and the corresponding pressure) will gradually decrease. The two phases must be in equilibrium always, in particular for slow processes.

A reverse example is LPG cylinder. It doesn't matter if you bleed off LPG to consumers, pressure inside the cylinder will always remain the same as long as there is liquid phase. The mass inside the vessel decreases, but pressure does not. It is vapor pressure of LPG at storage temperature. The same goes for steam inside closed system.

Dejan IVANOVIC
Process Engineer, MSChE

 

[IRstuff]

From PV = nRT

P₁/P₂ = T₁/T₂ IFF volume is constant

TTFN
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[BronYrAur]

but for the initial phase change from steam to condensate, my temperature doesn't change, yet my pressure dramatically decreases due to a reduction in steam volume (but not a reduction in vessel volume). Doesn't the ideal gas formula only work in the gas phase?

 

[BronYrAur]

I think I am understanding now ..... or maybe I'm confusing myself more.

So the pressure will "ride the saturation curve" and be at whatever pressure corresponds to the current cooled-off temperature, correct?

If that is right, then isn't my initial pressure irreverent? So no matter if I start with a vessel at 100 psig steam or 5 psig steam, if it is completely sealed, the equilibrium pressure will correspond to the saturation pressure at the cooler temperature?

 

[zdas04]

BronYrAur,
Your first statement about mass being constant is incorrect. The total mass in the vessel will be constant, but you don't care about the mass of liquid at any time, and your mass of steam is changing.

Your last paragraph is pretty close (assuming you meant "irrelevant" instead of "irreverent"). Problem is that your heat sink is probably colder than the saturation temperature at a near total vacuum (1 psia saturation temp is 102F).

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[EmmanuelTop]

This is a two-phase system in equilibrium so applying ideal gas law equations is not straightforward and can cause confusion. Ideal gas law applies to (ideal) non-condensible systems.

Steam (vapor) must always be in equilibrium with condensate (liquid) at any temperature. Looking at the steam T-P tables, you will find the equilibrium pressure for any temperature of interest. If there are other, non-condensible components in the steam, adjustments need to be made based on Dalton law.

Steam can also be superheated. If you start with steam at 100 psig and 500 degF, you can apply the ideal gas low till you reach the condensation point. Beyond this point, you need to follow steam tables.


Dejan IVANOVIC
Process Engineer, MSChE

 

[zdas04]

Dejan,
I'm moving towards his final conclusion. The amount of superheat, or even the original T&P do not matter in a real system. Eventually the trapped volume will reach heat sink temperature and pressure will be a function of that heat sink temp. If the heat sink is well below the freezing point of the condensate at 0 psia, then the answer is a little tough since the pressure before the onset of freezing will be close to absolute zero, but then the condensate volume will increase about 4% and raise the pressure a bit.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[EmmanuelTop]

Yes, his final conclusion is correct. "So the pressure will 'ride the saturation curve' and be at whatever pressure corresponds to the current cooled-off temperature, correct?" CORRECT (ET) - if steam is 100% pure, otherwise corrections are needed if other gases are present. Whenever you have a 2-phase system, you should follow steam tables.

Till the saturation point is reached (before that we have the superheated region), one can follow ideal gas law but with caution.

If heat sink temperature is below triple point of water (0 degc = 32 degF), water inside the coil will freeze.

Dejan IVANOVIC
Process Engineer, MSChE

 

[gruntguru]

"I think I am understanding now ..... or maybe I'm confusing myself more.

So the pressure will "ride the saturation curve" and be at whatever pressure corresponds to the current cooled-off temperature, correct?

If that is right, then isn't my initial pressure irreverent? So no matter if I start with a vessel at 100 psig steam or 5 psig steam, if it is completely sealed, the equilibrium pressure will correspond to the saturation pressure at the cooler temperature?"

Absolutely correct. Your final state is a saturated mixture (vapor and liquid). The pressure is uniquely defined by the temperature. The only thing that will change depending on the initial state will be the "quality" (ratio of vapor to liquid)

je suis charlie

 

[georgeverghese]

A temporary solution ( till you find some way of increasing the gravity head on this condensate leg) may be to install a small needle valve in parallel with this closed steam valve and set this for a small flow that will keep the vapor pressure from collapsing due to ambient cooling - check if this small flow / low heat load ( when the main line steam supply valve is closed) can be accomodated by the heating system.

 

[zdas04]

Georgeverghese,
I think he is talking about a strength of materials issue, not a current operational issue. With hundreds or thousands of tubes in a condenser, your solution would result in a lot of needle valves.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[dogtop]

check this action out: Mollier Diagram for water.

https://commons.wikimedia.org/wiki/File:HS-Wasserdampf_engl.png

 

[georgeverghese]

The OP clearly states he has a problem of draining the condensate leg at the bottom of a steam coil due to vapor space pressure approaching vacuum ?

The last thing you'd want to do is to introduce air into this coil to break the vacuum - the coil wont work after that with all the noncondensibles floating about.

 

[VerneE]

I have seen vessels and coils collapse since they were designed for pressure and not vacuum. Filling a body with steam, then letting the steam condense without a method to relieve the vacuum can be a problem. Also, condensate traps without sufficient head or back pressure will not allow the condensate to be removed - again causing problems in constant flow situations.

 

[itdepends]

What's controlling the pressure in the condensate system? Is it receiving condensate from other heating systems which are online? If so- you're out of luck. Once the steam in your offline coil condenses sufficiently to drop the pressure below the condensate system you won't be getting the condensate out without a pump, or breaking the vacuum by letting air in at the top and draining the condensate to ground.

Silly question time- why do you want to get the condensate out if the steam supply is switched off? Why do you care if the heating coil stays full of condy?

As a chem eng/metallurgist the first part of any answer I give starts with "It Depends"