Amount of heat required to produce 50 psig in pipe with water in it 4

[aeboarder]

I am wondering how much steam would have to be provided to a pipe (3 ft long, 2 in diameter, 316 SS) containing water to produce a vapor pressure of 50 psig. I'm assuming the pipe is half full of water (or 0.0325 cu. ft.) at 140F -- and that the water is stagnant and isolated (i.e. no flow and the pipe is then essentially a constant volume container). The pipe is heated via a steam jacket with steam at 327F and 85psig. The pipe is insulated so I've assumed heat loss to be negligable here. The problem I'm having is that I don't know how to take into account the fact that as the water inside the pipe vaporizes, the pressure builds. This increased pressure then increases the boiling point of the water which means additional heat would be required to vaporize the water.

The temperature of saturated vapor at 50 psig is 297 F if this helps.

Thanks so much in advance and please let me know if other information is needed!

 

[Latexman]

"I'm assuming the pipe is half full of water". What's the other half? Air? Water vapor?

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[aeboarder]

Well an air/water vapor mixture. The vapor content would be low before heating with the water content increasing as more water evaporates.

 

[racookpe1978]

Are you going to vent (or deliver to another process) that steam/vapor mix off of the top of the 1/2 full "boiler" ?
Are you going to regulate the pressure with a vent valve or a pressure relief valve?
How are you going to refill the water?

You no longer have a "pipe half full of water" ....
You now are building a "boiler" that is more easily capable of blowing up and killing nearby people than a terrorist's pipe bomb.

 

[LittleInch]

I don't think you need to worry about that - just use the energy values (enthalpy) for your start point (water at 140F) and then the energy values at your end point (steam at 50 psig and 297 and water at 297 using steam tables (I remember them from my youth...).

Your issue is more that the steam jacket will require a flow so there will be some temperature loss in the steam, but maybe not that much.

for such a small system I suspect there will be lots of other issues which mean your energy transfer is not ideal

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[aeboarder]

Yes, this is a safety concern, racookepe1978 -- Let me clarify, this scenario is certainly not something I'm trying to do, rather something I want to make sure is avoided It is a hypothetical "if this happened" exercise that is meant to avoid safety issues.

 

[LittleInch]

The question then is not "how much steam", but "how much energy". For a steam jacket to work it needs flow so not all the energy in the steam is transferred to the water.

So I'm not actually sure now what your question is and how you are going to measure it

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[aeboarder]

LittleInch, this neglects the enthalpy of the remaining liquid. I don't imagine all, or even most of the liquid will vaporize -- only enough to reach the point at which the vapor pressure reaches 50 psig. According to my calculations using just PV = nRT, if P = 50 psig (4.4 atm), T = 297F (147C), and V = 0.0325 ft3 (the remaining volume of the pipe) then the mass of the steam is only 2.1 grams.


Here's my thought process. Since at 50 psig, the boiling point of water is 125 C, I'm imaging the remaining liquid in the pipe to be at this temperature. At the point of reaching 50 psig, we have a small amount of steam at 147 C and the rest of the water at 125 C. I can then use the sum of these ethalpies to do as LittleInch suggested. Does anyone see flaws in this logic?

Thanks

 

[aeboarder]

The water inside the pipe is stagnant, the steam in the jacket would be flowing. I was planning on simplify my calculations by saying that the heat given to the water in the pipe is just the heat of vaporization lost from the condensing steam.

 

[LittleInch]

I'm a bit out of my depth when it comes to steam, but whether the steam actually condenses or not depends on the temperature it ends up as coming out of the jacket. Is this just barely saturated steam and not super heated in any way?

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[Compositepro]

Come on guys, this is a homework question, and there are no safety concerns in any case. The maximum that 327F, 85psig steam can heat can heat water to is 327F and 85 psig., which will not blow anything up.
Aeboarder, The boiling point of water is completely irrelevant to the problem. The total pressure in the pipe will be the partial pressure of air plus the partial pressure of water, which is equal to the vapor pressure of water.
There will be more heat used to heat up the pipe and water than to vaporize water. Remember to use absolute pressures and not gage pressures for your calculations.

 

[aeboarder]

Compositepro, wish it was a HW problem then I might just skip it and move on with my life The safety concern is not a pipe burst but rather the expansion of the pressurized gas if the downstream valve of the pipe were suddenly opened. I'm not concerned with the max the steam can heat to, but an intermediate point. The boiling point does seem relevant to me as this is what is producing the steam at the pressure I'm concerned with. can you elaborate why this does not matter?

LittleInch, the steam is saturated.

 

[bimr]

If the pipe is closed in, you also have to account for the pressure increased caused by the thermal expansion of the liquid.

 

[Compositepro]

Boiling point is is simply the temperature at which the vapor pressure equals the ambient pressure, so bubbles can form. It has no effect on the vapor pressure/temperature relationship. It seems you have the impression that bubbles must form and therefore pressure will suddenly increase. No, if pressure increases the bubbles collapse.
So what real world interest is there in knowing how much heat (calories) is required? If you open a valve you will vent a small amount of steam or hot water. What is the concern?

 

[aeboarder]

bimr, is this a significant expansion? The specific volume (m3/kg) of liquid water at 60C (140F) versus 147C (297F) is 0.0010172 and 0.0010850, respectively. To me this is not a significant expansion.

Composite, I found the boiling point relevant because this is the temperature I'm assuming liquid water to be when at this pressure. If I know this temperature, I can begin to calculate the amount of energy needed to bring it up to that temperature.

The real world interest is investigating if a small steam leak could provide enough heat to cause this to happen. If so, this would justify building in a pressure relief valve.

 

[Latexman]

A sketch of the real system/issue may be worthwhile here.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[Compositepro]

"The real world interest is investigating if a small steam leak could provide enough heat to cause this to happen. If so, this would justify building in a pressure relief valve."

It is not a question of heat. It is a question of temperature, and my first post explained why there is no safety issue. So please take a day or two and think a little before posting again. These are very elementary chemE concepts, which are admittedly somewhat complicated for non-chemE's who haven't thought about it before.

The expansion of liquid water is insignificant if there is a vapor space. It is very significant if there is no vapor space.
This could require a pressure relief.

"I found the boiling point relevant because this is the temperature I'm assuming liquid water to be when at this pressure. If I know this temperature, I can begin to calculate the amount of energy needed to bring it up to that temperature."
This statement is wrong and make no sense. If there were no air in the half-filled pipe, then any water in the pipe will always be at its boiling point, whatever the temperature. With air in the pipe the water can never reach a boiling point, whatever the temperature.

 

[bimr]

It is not clear what you are dealing with as far as your project, but 50 psig is a low pressure.

Thermal expansion is a concern only when a system is full of liquid, isolated and heated. You assumed that the pipe is half full so it should not be an issue except that thermal expansion should have a slight affect on the pressure.

If you pipe is full of liquid, it may be a big problem because liquid is incompressible.

http://abiquim.org.br/congresso/cong_cd/fullpapers/P171757.pdf

 

[LittleInch]

One of my posts didn't post yesterday, but you need to keep your units constant and use psia. Hence your note that boiling point of water at 50 psig is 125C is incorrect. At 50 psig (65 psia) boiling point is unsurprisingly the same as the saturated vapour pressure of steam, i.e. 147C/297F.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[25362]

If I'm not mistaken, at about 135[sup]o[/sup]C, the addition of both, air and steam pressures, would amount to about 4.4 atm absolute = 50 psig.