gas volume from liquid CO2

[bnrg]

Hello,
If I have a cylinder of carbon dioxide in liquid form at a given pressure and temp, how do I go about determining the volume of gas that I can obtain to power some pneumatic equipment?
Thanks,
Bob

 

[MintJulep]

Conservation of mass equation involving the density of liquid CO2 and the density at your discharge condition.

 

[mbeychok]

Bnrg:

Assuming that you know the weight (W) of CO2 in your cylinder, then:

For W in pounds:

(W/44)(379.48) = cubic feet of gas at 60 [°]F and atmospheric pressure

For W in kilograms:

(W/44)(22.414) = cubic meters of gas at 0 [°]C and atmospheric pressure

where: W = molecular weight of CO2


Milton Beychok
(Contact me at www.air-dispersion.com)

 

[25362]

A small typing error. 44 = mol. weight, not W.

 

[mbeychok]

25362:

Your are correct .. I did have a typo. Thanks for bringing it to our attention.

I wish these forums allowed the author of a message to make post-submission corrections ... as many other forums do.

Milton Beychok
(Contact me at www.air-dispersion.com)

 

[sailoday28]

I believe that MintJulip has given the answer to your question. I would note however, that the discharge pressure (which) probably will vary is not given.

Pressure and temp for liquid conditions allows calc of density.

 

[Montemayor]

bnrg:

One has to assume the CO2 cylinder is a nominal 50 lb (net content) U.S. compressed gas cylinder or its equivalvent 25 kg unit in Europe. In either case, one also has to assume that the cylinder has been filled with the pure CO2 after is has been evacuated of all residual air - which is not the usual, normal case. This is a prerequisite for determining the saturated liquid density and allowing for the vapor content over the saturated liquid - which is normally 80 - 90% of the total cylinder volume. The CO2 liquid and vapor densities can be obtained at the following web address:

http://webbook.nist.gov/cgi/fluid.c...it=Btu/lbm&WUnit=ft/s&VisUnit=cP&STUnit=lb/ft

Also be made aware that if you are proposing to simply connect the cylinder to a regulator and then feed the regulated CO2 gas to your pneumatic equipment, the temperature of the cylinder contents will be REDUCED below the existing ambient temperature you initially start off at -- depending on how fast (vapor draw-off rate) you remove the gas from the cylinder. This fact should be readily understandable by you since what you would be doing is forcing the liquid contents to vaporize (& subsequently cool) in order to maintain the vapor pressure above the liquid. Since the temperature would start to drop in the cylinder (easily observable by the water frost line formed on the outside cylinder walls) the liquid and vapor densities would be increasing -- something that will definitely have a bearing on the gas phase consumption and the way your downstream pneumatic equipments works. Many people who have charged their refrigeration cycles with make-up refrigerant gas from a compressed cylinder will recognize and confirm this fact.

This is why it is always smart to supply a constant heat input (or vaporizer on this type of operation. In the old days, when carbonated beverage bottlers used to use banks of HP CO2 cylinders to supply gas to their bottling machines, they sprayed water of kept the cylinders in a water bath to supply the need heat input to ensure constant vapor pressure and temperature in the CO2 gas draw-off operation.

Many engineers fail to take into consideration the simple Thermodynamic facts behind this type of liquified gas operation and take it for granted that it will behave very much like a purely compressed gas cylinder operation. It does not happen that way at all.

I hope this experience helps.

Art Montemayor
Spring, TX

 

[bnrg]

thsnks all for your help.
Bob

 

[MintJulep]

Montemeyer,

Well yes and no.

If there is a pressure regulator on the bottle then the temperature decrease and associated reduction in saturation pressure you describe will be essentially invisible to the system as long as the saturation pressure inside the bottle remains higher than the regulator setting.

If the temperature drop is sufficient to decrease the saturation pressure to near or below the regulator setting, then the flow will will reduce.

 

[25362]

To Art Montemayor, I'm well aware of your rich experience in this subject. Thus I'd appreciate your comments to the following notes.

Points about CO₂ when looking at a (Mollier) Pressure/Enthalpy chart.

1. If the bottle in question is warmed up beyond 32 deg C (just above the critical temperature) there wouldn't be any liquid, whatever the pressure in the bottle.

2. Saturated vapor at 25 ^oC (or supercritical vapor, i.e., above p_c and t_c) when throttled and expanded isenthalpically to a lower pressure, will cool down to very low temperatures and will re-enter the saturation envelope producing some liquid, and possibly even some dry ice.

3. When dealing with saturated vapor, only when the bottled gas is cooler than -20^oC would the isenthalpic expansion end up with a very cool gas and no liquid.

4. Superheated carbon dioxide at, for example, 20^oC and 35 bara, would surely end as a cool gas upon a free J-T expansion.

5. Thus the need to keep, at the same time, a cool bottle and a warm system at (and downstream of) the expansion valve, if one wishes to get gaseous CO₂ at a workable temperature.

6. Will the remaining liquid in the bottle solidify when not warmed up, if the pressure drops down to 5.18 bar, and -56.6^oC ?

Thanks.

 

[Montemayor]

This is a fun topic because it involves what we would normally classify as a mundane and ordinary procedurre involving a common, mundane "gas". It turns out that it isn't so; it really involves a compressed gas liquid that has extraordinary and interesting characteristics as it either cools down or heats up.

This is one thread that has certainly been posted in the CORRECT forum: Heat Transfer & Thermodynamics engineering. My compliments to bnrg for his insight. I will attempt to address the last two interesting posts:

MintJulep:
The best way I know how to prove what I stated is for you to rig up a CO2 cylinder with a pressure regulator set at approximately 50 psig and open the down stream valve 100% while placing the palm of your hand on the regulator's body. You will soon experience the absolute visibility of the system's lower temperature as the saturated gas is evacuated from the top of the cylinder. I know of no better way to prove what is clearly shown on the CO2 T-S (or Mollier) diagram. If you deplete the saturated gas in the cylinder faster than you can re-generate it by heat transfer through the cylinder steel walls, the pressure and the temperature will come down within the cylinder (& the system). And the effect will be very visible on the outside of the cylinder in the manner of ambient moisture freezing on the cylinders external surface and forming a "frost line" that can be clearly seen.

This is not theoretical Thermodynamics. This is the same process by which I have industrially produced thousands of tons of Dry Ice (solid CO2 @ -109 oF). I have done this starting with HP CO2 (like what exists in a cylinder) as well as with LP CO2 (Liquid CO2 @ -8 oF & 250 psig). This is still the way Dry Ice is produced today.

25362:
While I'm presently not at my customary library at home but helping my daughter move into a new home in Tucson, AZ, I'm still reminded of old problems and process headaches in reviewing your interesting 6 questions. I don't need access to my T-S diagram to identify the critical zone (or nightmare, as we used to call it) for CO2. I enjoy sharing my thoughts on this subject with you since I personally have read your many knowledgeable Thermodynamic discussions on this Forum for some years now. I don't think I can reveal any new Thermo knowledge to you.

Your first 2 questions have to do with theoretical and empirical findings regarding the supercritical zone. You are, as usual, correct in your analysis according to what I have witnessed in the field. For years, we called this nebulous zone "Mush" - or something similar.

Question 3 is temporarily out of my grasp since I don't have a T-S diagram to identify the phase site and the process path. The same applies to #4.

You have re-inforced my finding with #5. This is why the "old timers" used tap water (ambient temperature) - and not anything hotter - like steam - which could "pop" the cylinder's relief device. And, yes, if you want to heat up faster you can employ an inline heater downstream and also electrically trace the gas regulator.

#6 has been answered above. I can make Dry Ice by "evaporating" the saturated liquid's vapor pressue down to a temperature where, if you look on the T-S diagram, you will land on the horizontal equilibrium line connecting the saturated SOLID state (on the far left) and the saturated vapor curve (on the far right). This is the strength and simplicity demonstrated by the T-S diagram. Unfortunately the NIST data on their website doesn't identify the CO2 solid phase. For Dry Ice thermo data I resort to my own. In fact, the process vessels that were used for this purpose back in the old Liquid Carbonic Dry Ice Plants were called "evaporators" - simply because that was what was going on: a batch quantity of liquid CO2 was introduced into the vessel and then the vessel's saturated vapor was subjected to the suction of CO2 recompressors. The result was progressively colder and colder liquid CO2 that was eventually injected into a Dry Ice Press at a temperature and pressure just above it's "Triple Point". At that point, the remaining available saturated vapors were "sucked" out by the recompressors and the result in the Press chamber was solid, CO2 "snow" - which was ultimately compressed, using hydraulic rams, into a solid Dry Ice block.

I never like this method because I found it wasteful and slow. That's why I patented an automatic machine that produces pellet-sized Dry Ice on a continuous basis. This makes more sense and is far more economical and cost-effective.

I hope I furnished useful experience to your notes and I apologize for not being in a place with access to my files and databases.

Art Montemayor
Spring, TX

 

[MintJulep]

Art,

You are correct for the conditions stated in your last post.

In rereading my post I see that I wasn't very clear in defining the conditions I had in mind.
Unstated in my previous post was that the flow rate is lower than the rate at which liquid could boil off at whatever saturation temperature exists in the bottle.

Thus as long as the pressure in the bottle remains above the regulator setting (plus the pressure drop through the regulator) the FLOW will remain constant. There will of course be a temperature drop as the gas expands across the regulator.

I don't have access to a Mollier chart for CO2, but it seems that with only a throtteling valve on the discharge you could establish a steady-state condition where flow, pressure and heat transfer into the bottle all remain constant.

 

[25362]

Art Montemayor, thanks.

MintJUlep. As Montemayor says, CO₂ is a most interesting fluid. One can obtain a Mollier chart from the internet:

http://www.chemicalogic.com/download/mollier.html

From looking at it, it appears that if the bottle containing liquid CO₂ is kept by external means at, say, 20^oC and 57.2 bar, a steady isenthalpic expansion of the vapor through a throttling valve down to a pressure of above 75 psi, would produce a two-phase fluid (V+L).

When keeping the bottle warmer, at higher saturation temperatures and corresponding pressures, closer to the critical point, a slow and steady expansion would most certainly result in a V+L mix.

That's the reason I suggested to keep the valve and its downstream connections warm.

 

[MintJulep]

I imagine that I will eventually need to learn all about CO2 if it ever becomes a main stream refrigerant.

Don't have the time at the moment, and will get paid for the effort when necessary.

In the mean time I will follow this most interesting thread.