Calculate pressure 1

[MaxPlanck]

Dear all,

I want to calculate the pressure inside a small autoclave or pressure vessel.
It has an internal volume of 2000 ml and is filled with 350 ml of water. Then it is closed, placed in a furnace and heated up to 170 degrees Celsius. A two-phase equilibrium is established inside.

How can I calculate the pressure inside the autoclave at a temperature of 170 degrees Celsius? Or what more information do I need?

Thanks for your comments!

 

[Feric]

Hi there:

If I am not mistaken, you have heat adition at constant volume.

A steam diagram should inicate what the pressure is once the temperature is 170 [C].

Also, the steam diagram for such final state point will indicate what is (phase wise) inside the pressure vessel.

Thanks,

Gordan

http://engware.i-dentity.com

 

[JStephen]

If it was only water in there, you could just calculate density or specific volume and look it up in the steam tables, calculating quality as necessary. If it's a real problem (not a textbook problem), you also have the original 1650 ml of air in there that you have to deal with.

 

[Feric]

Hi there:

Since there is some air present initially -- the vessel volume is larger than the volume required by the water mass -- one can always try to do an ideal textbook problem.

Once the initial water mass and volume are known, the rest of the vessel volume can be assumed that is filled with standard air.

Therefore, keep the volumes split and hypothetically work with steam tables and/or T-s diagram following a constant volume process until temperature gets to 170 [C]. For the air part, use the ideal gas state equation to find out what the pressure is when the temperature is 170 [C].

An evaluation needs to be done on how to proceed and what the assumptions are if the final pressure values for steam and air are not the same ...

Also, another possibility is to have some vacuum in the vessel at the initial conditions so that there is no air present and the case is just what the steam tables would indicate ...

It turns out that this is not a straight forward problem, some assumptions need to be made and the problem needs to be simplified in order to get some meaningful numeric values and/or answers ...

Thanks,

Gordan

http://engware.i-dentity.com

 

[MaxPlanck]

Dear all,

Thank you for replying.

It is certainly not a textbook problem, but a real one in our lab. It is indeed not that straightforward to calculate the total pressure in this two-phase system.

Using a saturated steam table gives me a rational pressure.

"Therefore, keep the volumes split and hypothetically work with steam tables and/or T-s diagram following a constant volume process until temperature gets to 170 [C]. For the air part, use the ideal gas state equation to find out what the pressure is when the temperature is 170 [C]."

Can I just add up both pressures to calculate the total pressure?

Thanks for all the help!

 

[Feric]

MaxPlanck:

What I suggested, might make sense in the thermodynamics sense.

Since steam and air are at 170 [C], in order to solve the problem, one needs to focus on the mixing part of the problem.

Masses are known as well as the final temperature.

Total pressure is:

p = p' + p'' -- Dalton's Law

where

p' = (msRsT)/V

p'' = (maRaT)/V

ms - steam mixture mass [kg/s]
Rs - steam gas constant [kJ/kgK]

ma - air mass [kg/s]
Ra - air gas constant [kJ/kgK]

V - vessel overall volume [m^3]

This should give some initial meaningful values that need to be compared with the operational/lab conditions values that get measured.

Good luck!

Thanks,

Gordan

http://engware.i-dentity.com

 

[Feric]

MaxPlanck:

I need to provide you with a minor update.

I did not get the units right for steam and air masses -- it should be in [kg] (I have been working with streams and mass flow rates so that is the reason why I put [kg/s] which is wrong and does not apply to your case.

ms - steam mixture mass [kg]

ma - air mass [kg]

Thanks,

Gordan

http://engware.i-dentity.com

 

[MaxPlanck]

Dear Feric,

Yes, I noticed it before. Nevertheless thanks for the update and your contribution to the problem.

Best regards,
MaxPlanck

 

[MikeClay]

The answer depends on the initial composition of the vapor space. Assuming the vapor is air at 15.5C and remains in the vessel, the pressure will be about 9.4 bar instead of the saturation pressure of 7.9 bar.

--Mike--