Saturday, September 3, 2011
A close look at supercritical carbon dioxide CO2
I built a pressure vessel from aluminum and acrylic and filled it by placing pieces of dry ice inside. The dry ice melts under high pressure, and forms a liquid and gas phase. When the vessel is heated, the CO2 becomes supercritical -- meaning the liquid and gas phases merge together into a new phase that has properties of a gas, but the density of a liquid.
Supercritical CO2 is a good solvent, and is used for decaffeinating coffee, dry cleaning clothes, and other situations where avoiding a hydrocarbon solvent is desirable for environmental or health reasons.
If you have a suggestion for what I should do with the supercritical CO2, please leave a comment.
Here are a few engineering calculations that I used to determine the pressure capacity of the chamber:
1. Hoop stress in the aluminum ring:
The aluminum alloy and heat treatment is unknown unfortunately, which makes a huge difference in its material properties. Since it is a structural tube, I will assume 6061-T4, which has a yield strength of about 40 ksi.
Inner radius = 1.1", Outer radius= 1.5" (to the inner edge of the bolt circle)
Chamber pressure = 3000 psi
Hoop stress at inner edge = 10ksi
So, there is a safety factor of 4, but the additional material outside the bolt circle will actually add to this factor. In theory, the aluminum will yield at 12000 psi chamber pressure.
2. Bending force on the acrylic windows:
Acrylic ultimate strength: 10 ksi. It doesn't yield. It is elastic, then breaks. Modulus: 400 ksi
The plate is not a thin plate, but the results show only a 0.004" deflection at the center under a chamber pressure of 3000 psi.
This shows a stress of about 4.3 ksi for a 1.25" thick acrylic plate with 1.35" radius. The pressure-bearing radius is larger than the inner radius of the aluminum ring. This has a safety factor of 10/4.3 = 2.3. In theory the acrylic will break apart when the chamber reaches 7000 psi.
3. Stress on the bolts:
Total window area is about (pi)(1.35)^2 = 5.7", so total force when chamber pressure is 3000 psi is (5.7)(3000) = 17,200 pounds! I will use six bolts, so each bolt must hold 17,200/6 = 2860 pounds.
1/4-20 bolts are NOT strong enough -- even at grade 8!
5/16 bolts would be OK in grade 8, but I wanted a higher safety margin, and I don't like 5/16 bolts.
I chose 3/8" grade 8 bolts, which have a working load of almost 7000 pounds. I wanted to be sure bolt failure could not possibly be the failure mode that breaks the whole system. I also used grade 8 nuts, which should ensure the failure happens within the fastener, not by shearing the threads out of the nut or bolt. I am not positive about this, though.
4. Pipe threads:
I wasn't sure what 1/8" pipe threads are capable of holding, but McMaster sells such fittings that are rated for 5000 psi (like the gauge that I used), so I assume a brass part can hold such a load. I cut threads into the aluminum so it's possible that the pipe thread in aluminum could fail (ie the gauge or valve could be pushed out, shearing the threads right out of the aluminum ring). It might be possible to add up all of the area of the pipe thread cross-sectional area, but it seems silly and unlikely to be at all accurate.
5. Temperature concerns:
The acrylic has a glass transition temperature of at least 180*F, but it should not be heated anywhere near this temperature or else its ultimate strength rating may not be valid. I would say 130*F is the upper safe limit.
6. Effect of supercritical CO2 on the acrylic and O-ring:
I used buna-n O-rings, which may affected by exposure to SC CO2. They are very unlikely to fail in the short term, and I can change the O-rings for every experiment if I want.
The acrylic showed signs of crazing after just one supercritical CO2 cycle. I think the crazing is unlikely to affect the acrylic's ability to hold pressure, but there is a slight concern.
The most likely failure mode would occur when the acrylic reaches its ultimate strength, and suddenly breaks. Unlike pressure vessels made from ductile materials, which can be designed to yield and leak before breaking, the acrylic will suddenly blast apart without leaking first. If the equations and material specs are correct, 3000 psi should be OK, but I would not want to go much higher.