Effects of altitude on liquid CO2 utilization

[MrFreezeMiser]

Based on equilibrium vapor pressure data, the temperature of the solid-vapor mixture coming out of the tubing should be about 8 F cooler for Denver than for Detroit (say, -117 F vs -109 F). The streams should have about the same mass fractions solid (pretty low). Based solely on these temperature of the streams, the water freezing at Denver should be more rapid than the water freezing at Detroit.

We know that the vapor flow rate affects the heat transfer. How do you know that the mass flow rates were approximately the same. given that, as the tank empties, the pressure in the tank decreases so that, at a given valve opening, there is decreasing flow as the tank empties.?

These are good questions, and I can’t answer them.

The tank seems to maintain pressure throughout use. It has a dip tube (unlike normal CO2 tanks), so you keep the tank vertical and LCO2 is forced up the dip tube and out. As I get closer to the tank being empty (maybe 2-3 lbs LCO2 remaining), all you get thru the pipe freeze connection is CO2 gas. Pressure doesn’t seem to ever decrease, rather only CO2 vapor remains in the tank and the dip tube doesn’t allow every last bit. Otherwise, throughout the process, you get a crackling noise—like bacon sizzling and popping—and snow pops out of various places.

What you can’t see in the photo here are the orange, rubber-like seals inside the C-clamps that get squeezed around the pipe. These C-clamps (various sizes for various pipes) are first placed around pipe and then you tighten a bolt to close the rubber seals firmly on the pipe. This keeps the LCO2 somewhat regulated/contained to the effected area. The manufacturer designed it so it’s loose enough that pressure won’t build. In some cases, it’s fairly quiet (or at least for awhile) and then will suddenly pop open a minor stream here/there or even where you connect the hose adapter to the C-clamp.

Shown in this photo is 3/4” CPVC pipe (installed circa 1996) plug-freeze in place holding back 65-psi branched-off a 2” CPVC main. I froze this for 28-minutes just to be 100% certain...but it cost nearly 15-lbs of LCO2. Mind you it was about 7ºF outside and the tank was subjected to -9ºF on my truck the previous night. I had to warm it considerably prior to use to even get LCO2 vs. vapor at ambient/as-was.

 

[Chestermiller]

According to the p-H diagram I presented in post #16, the pressure in the tank will be about 800 psia at room temperature (70 F), and will be about 240 psia at 0 F. So more liquid CO2 can flow out of the tank per unit time at the higher temperature than the lower temperature.

Do you have any idea what the flow geometry is in the region where the CO2 is flowing in the gap between the water pipe and the clamped zone to the pipe? It should be something like an annulus, with half the fluid flowing along the water pipe in each direction. Do you have any idea what the gap is, or the length of water pipe that the CO2 contacts? It is possible to estimate this from the inlet CO2 pressure and the flow rate.

 

[MrFreezeMiser]

I think your assumption is correct: there is no choked flow. On that really cold day in Denver, I could only get vapor to flow. I didn’t even connect it to the pipe clamp adapter.

According to the p-H diagram I presented in post #16, the pressure in the tank will be about 800 psia at room temperature (70 F), and will be about 240 psia at 0 F. So more liquid CO2 can flow out of the tank per unit time at the higher temperature than the lower temperature.

Do you have any idea what the flow geometry is in the region where the CO2 is flowing in the gap between the water pipe and the clamped zone to the pipe? It should be something like an annulus, with half the fluid flowing along the water pipe in each direction. Do you have any idea what the gap is, or the length of water pipe that the CO2 contacts? It is possible to estimate this from the inlet CO2 pressure and the flow rate.

I’ve only spoken to the manufacturer/tech support once to discuss high usage/different yields in Denver. Everything it has tested I’m sure is closer/at sea level, but I suppose I could circle back and ask if there is any more data available.

Unfortunately, I don’t have any means of collecting flow rates and/or pressures. Furthermore the manufacturer does make it easy to install here/there any metering/measuring devices. To its credit, the device is fire-and-forget—very simple. I am attaching some additional photos to show how the C-clamp adapters (”clamps”) attach to the pipe. These clamps seem to form snug seals but then their flexibility “gives” under pressure as needed so as to prevent pipe/device damage. It’s a very simple, clever design in one sense but otherwise there is no adjustability for changing conditions. Also, attaching pictures of the tank hose and both ends. Interestingly, I just noticed the hose orifice closer to the tank is much smaller than the adapter port that connects to clamps. This could theoretically induce a reduction pressure and cause more liquid to turn to gas? In the picture of the hose that connects between tank and clamp, the adapter on the left connects to clamp and the small brass (female) end attaches to the tank’s valve via a small 1/4” compression adapter (not shown). Otherwise this is it.

 

[MrFreezeMiser]

The more I become educated by everyone contributing here and now looking at the bigger diameter of the adapter outlet going into the clamp, the more I think this could be part of the problem—especially at altitude. This larger orifice and clamp zone in general (at least until it becomes frozen with light, fluffy ice) is the first larger volume area LC02 arrives in and consequently becomes a low pressure zone ===> more LCO2 turning gas than remaining liquid?

 

[Chestermiller]

To get a better handle on this problem, we need to be more precise as to what is happening to the water as it freezes, and what the flow and heat transfer are to the CO2 as it flows in the interstices (annular gap) between the outside of the pipe and the clamp.

As far as the water is concerned, it starts out at, say, room temperature. When it is in contact with the CO2, the temperature drops to a much lower value at the outside radius. The freezing takes place from the outside radius inward toward the center, while the liquid water inside has a temperature that varies radially, with the lowest temperature at 0C at the freezing interface. We need to do calculations for this freezing process.

The temperature at the outside of the pipe can approach -80 C, assuming infinite heat transfer coefficient between the CO2 and the outside wall. We need to decide what we consider "freezing' of the water plug. Do we consider it to be the point where the ice fills the pipe, and the temperature at the centerline of the pipe is 0 C, or do we consider it when the temperature of the entire ice plug approaches -80 C? (The times for reaching these two states can be significantly different). Is it reasonable to assume an initial water temperature of 20 C for the cases in Denver and Dallas?

As far as the flow and heat transfer in the CO2 stream within the space between the clamped adapter and the pipe outside, is it reasonable to assume a small gap, say 1/64" between the outside of the pipe and the clamp?

 

[MrFreezeMiser]

To get a better handle on this problem, we need to be more precise as to what is happening to the water as it freezes, and what the flow and heat transfer are to the CO2 as it flows in the interstices (annular gap) between the outside of the pipe and the clamp.

As far as the water is concerned, it starts out at, say, room temperature. When it is in contact with the CO2, the temperature drops to a much lower value at the outside radius. The freezing takes place from the outside radius inward toward the center, while the liquid water inside has a temperature that varies radially, with the lowest temperature at 0C at the freezing interface. We need to do calculations for this freezing process.

The temperature at the outside of the pipe can approach -80 C, assuming infinite heat transfer coefficient between the CO2 and the outside wall. We need to decide what we consider "freezing' of the water plug. Do we consider it to be the point where the ice fills the pipe, and the temperature at the centerline of the pipe is 0 C, or do we consider it when the temperature of the entire ice plug approaches -80 C? (The times for reaching these two states can be significantly different). Is it reasonable to assume an initial water temperature of 20 C for the cases in Denver and Dallas?

As far as the flow and heat transfer in the CO2 stream within the space between the clamped adapter and the pipe outside, is it reasonable to assume a small gap, say 1/64" between the outside of the pipe and the clamp?

In both locations (Denver and Detroit), the temperature of the incoming water is somewhat similar at 48ºF-55ºF (closer to 10ºC) depending on season.

Looking at the “Freeze Head” (what I’ve been calling clamp) there is quite a bit of space (interstice) that does fill with dry ice. I measured the “Injector” (what I‘ve been calling the adapter) gap with some putty at approx 2.3mm or 3/32 in. From field observations of 3/4” CPVC (see pic), the freeze-effected zone appears to be approx two times the diameter of the pipe, so plug is approx 1-1/2” long x 3/4” diameter.From the manufacturer: “-110°F ice pack is strong enough to withstand 7,000-PSI (500 bar).”

This week I called ColdShot tech support, and it is going to forward some of my high altitude questions/concerns to product engineers in UK. In the meantime, it suggested to try removing the second sintered brass filter in the head of the injector. Tech said it can clog or even freeze up causing problems. So I removed it (1) to inspect it and (2) evaluate next freeze performance without it. Surprisingly, it did have some sort of white contamination partially covering surface of filter. Looked like mineral residue; however putting some citric acid on it gave no reaction. Interestingly, upon disassembly and looking right after where LCO2 goes through second filter, it goes through a very tiny hole (see pic) before leaving the much larger diameter brass nozzle of the injector. In a pic, I stood up the two identical nozzles to show how small the hole is LCO2 enters and then much larger hole coming down the brass nozzle. Also, I included pic of what the interstice-filled space looks like after removing Freeze Head after a freeze. What I find fascinating is the dry ice outside the pipe is so light and fluffy vs. the super strong, dense ice inside the pipe.

Injector components (incl 2nd filter) and 3/4”-sized Freeze Head
Injector nozzle different angles (big hole is outlet/smaller is inlet)

Freeze Head with Injector inserted

Picture of dry ice on pipe after removing Freeze Head

Cross-section of ice plug inside 3/4” CPVC

 

[Chestermiller]

This is going to be a crude analysis of the transient radial heat transfer to the water within the tube. Assume that the initial temperature of the water within the tube is 10 C, and the outside wall of the tube is suddenly dropped to -110 F (-79 C) and held at that temperature for all time. How long does it take for essentially all the water in the tube to freeze, and reach -79 C.

The freezing starts out at the outer radius R of the tube and propagates inward. There is going to be a heat flux discontinuity and phase change at the inward-moving radial location at which the temperature is 0 C, and where 333 J/gm is released. To approximate the thermal inertia effects of this discontinuity, we average the discontinuity over the entire temperature range between -79 C and +10C. The heat capacity of the liquid water is taken as 4.184 J/gC and the heat capacity of the ice is taken as 2.108 J/gC. So the enthalpy change of the water/ice between -79 C and 10. C is about $$\Delta H=(79)(2.148)+333+(10)(4.184)=543.\ J/g$$And, thus, we take the average heat capacity as $$C_p=\frac{543}{89}=6.10\ J/gC$$Most of the temperature variation is going to be within the ice, where the thermal conductivity is 2.22 W/mC, and the density is going to be close to 1.0 gm/cc for both the solid ice and the liquid water. So the average thermal diffusivity will be $$\alpha=\frac{k}{\rho C_p}=\frac{0.0222}{(1)(6.1)}=0.0036\ cm^2/sec=0.000564\ in^2/sec$$

Bird, Stewart, and Lightfoot in their book Transport Phenomena, show that transient heat transfer in a cylinder is essentially complete when the time t is given by: $$t=\frac{0.5R^2}{\alpha}\tag{1}$$For our value of the average thermal diffusivity, this becomes $$t=14.8 R^2$$where R is the inside radius of the pipe in inches.

The figure below shows a comparison between the lower-bound freeze times estimated from Eqn. 1 and the actual Cold-Shot data for steel tubes taken from their promotional material.

According to the figure, the observed time for steel tubes is about twice that produced by our lower-bound equation. This is expected because the model equation neglects the heat transfer resistance of the tube wall and the convective heat transfer resistance outside the tube. Also, the slope of the model equation is exactly 2.0, while that of the data is 1.6. This is another indicate of heat transfer resistance beyond the inside radius of the tube.

In subsequent analysis, I will discuss the determination of the tube-wall- and convective heat transfer resistance (the latter of which is affected by the flow rate of the CO2).

 

[MrFreezeMiser]

Modestly ”crude”, Chestermiller. It is amazing to me and hopefully others. Thank you

 

[Chestermiller]

It is puzzling to me that, while the thermal conductivity of copper is much higher than steel and the wall thicknesses for the copper tubes is much less than the wall thicknesses of the steel tubes (implying lower resistance to heat transfer for the copper tubes than the steel tubes), the freeze times for the water in the steel tubes is shorter than the freeze time for the water in the copper tubes. Do they have any explanation for this. Have they gotten the observations reversed?

 

[Bystander]

Interior surface roughness/finish?

 

[MrFreezeMiser]

It is puzzling to me that, while the thermal conductivity of copper is much higher than steel and the wall thicknesses for the copper tubes is much less than the wall thicknesses of the steel tubes (implying lower resistance to heat transfer for the copper tubes than the steel tubes), the freeze times for the water in the steel tubes is shorter than the freeze time for the water in the copper tubes. Do they have any explanation for this. Have they gotten the observations reversed?

It’s a great question. I was surprised by this, too—moreso when instructions state freezing plastic (even lower thermal conductivity) takes considerably even longer. Clearly, thermal conductivity matters, but what else is at play here? Lots! it turns out—including altitude—as I am learning. I will query Cold-Shot (CS) for its take. In the meantime, I have a couple of hunches.

Given the same size freeze heads used for similar trade sizes (1/2”, 3/4”, 1”, etc.) of copper and steel, with steel, the LCO2 is striking more mass at the injector (in surface area and thickness) albeit vs. matter that is significantly lower in thermal conductivity. However, with same ID but thicker walls and bigger OD of steel pipe, the interstice is significantly smaller with steel. So, with steel, does this translate into: (1) less time and LCO2 to fill the smaller interstice with dry ice and (2) less CO2 blowing out everywhere with smaller OD of copper pipe? As you are freezing, initially you get a lot of popping and dry ice shooting out. This goes on until the interstice is full, and then everything quiets down a bit and you get these blowouts from random places where seals are max’ed out and relieving pressure. Conclusively, maybe with smaller OD copper, it’s just more inefficient despite higher thermal conductivity.

I have never frozen galvanized iron pipe (GIP) to compare results. GIP is pretty rare to find and generally a poor choice for potable water distribution. We would replace it vs. try to repair it.

 

[Chestermiller]

It’s a great question. I was surprised by this, too—moreso when instructions state freezing plastic (even lower thermal conductivity) takes considerably even longer. Clearly, thermal conductivity matters, but what else is at play here? Lots! it turns out—including altitude—as I am learning. I will query Cold-Shot (CS) for its take. In the meantime, I have a couple of hunches.

Given the same size freeze heads used for similar trade sizes (1/2”, 3/4”, 1”, etc.) of copper and steel, with steel, the LCO2 is striking more mass at the injector (in surface area and thickness) albeit vs. matter that is significantly lower in thermal conductivity. However, with same ID but thicker walls and bigger OD of steel pipe, the interstice is significantly smaller with steel. So, with steel, does this translate into: (1) less time and LCO2 to fill the smaller interstice with dry ice and (2) less CO2 blowing out everywhere with smaller OD of copper pipe? As you are freezing, initially you get a lot of popping and dry ice shooting out. This goes on until the interstice is full, and then everything quiets down a bit and you get these blowouts from random places where seals are max’ed out and relieving pressure. Conclusively, maybe with smaller OD copper, it’s just more inefficient despite higher thermal conductivity.

I think what you are saying is that, for the same set of freeze heads, the ODs of the steel pipes and the copper pipes are sufficiently different that the CO2 flow velocities and convective heat transfer coefficients outside the pipes can be significantly different. Is this what you mean?

 

[MrFreezeMiser]

That‘s my guess. It would be interesting to conduct testing with a slightly smaller freeze head designed just for copper.

 

[Dullard]

A contributing factor:
Longitudinal heating. The (relatively) poor thermal conductivity of steel allows a lot less heat to migrate (down the length of the pipe) into the area of interest. Anyone who has ever welded steel and aluminum on the same day can probably testify - you don't just 'locally heat' aluminum (or copper) the way that you do with steel.

 

[MrFreezeMiser]

As a welder myself you use a lot more power/heat welding aluminum (even adding a touch of CO2 to my gas mix for penetration) and often you have to back it with stainless steel to act as a heat sink to avoid melting everything. It’s an interesting point, Dullard, basically you’re stating: the superior thermal conductivity of copper is dissipating the cooling quickly (and well beyond) the local target zone. The thought of filling a 5-gallon bucket with a firehose comes to mind…very inefficient at full blast!

 

[Chestermiller]

The dimensions of PVC pipes are the same as steel pipes of the same nominal diameter. But the thermal conductivity of PVC is 100 x lower than steel. This would result in significant resistance to heat transfer through the wall in PVC pipes. Based on this, I estimate that the freeze times with PVC pipe will be on the order of about 5X those of steel. Is this what is observed experimentally?

 

[MrFreezeMiser]

The dimensions of PVC pipes are the same as steel pipes of the same nominal diameter. But the thermal conductivity of PVC is 100 x lower than steel. This would result in significant resistance to heat transfer through the wall in PVC pipes. Based on this, I estimate that the freeze times with PVC pipe will be on the order of about 5X those of steel. Is this what is observed experimentally?

Summarily…it’s possible if 3/4” steel froze in 5-mins as for 3/4” CPVC I use 25-mins.

I’ve never frozen steel pipe in either location, but I have frozen both copper and CPVC in Colorado. Field results suggest 12-minutes for 3/4” copper with water (guessing) between 10º-16ºC and 25 minutes for 3/4” CPVC. For 1/2” copper, 8-minutes seems to work. I’ve never frozen 1/2” CPVC, so I have no observations.

For the Detroit location, we’ve only frozen 1” copper and smaller, so no observations for steel or plastic. Freeze times follow the CS table; however, the number of freezes per 20-lb bottle are fewer than indicated on CS table.

Going forward I’m going to collect quality measurements including documenting supply water temp, pipe size, type, LCO2 used, tank temp and time. Always I have run a stop watch or countdown on my phone, yet actual freeze time is a bit fuzzy.

For example, when it was super cold outside at -14ºC and I was freezing 3/4” CPVC, the water was probably closer to 4ºC in the pipe. Still I used 25-mins freeze time and actually gave it 28-mins just to be sure (basically used all but 3-4 lbs of 20-lb cylinder). This was also the first time I had to warm the tank and no idea how warm it got. So on this day did the plug freeze at or earlier than 23-mins? At 25 or 28? Who knows.

Honestly, you never really know if the plug is good until you test it. The problem is if you test it and it’s too early, you really have no choice but to start again. Another example: I’ve tried 15-minutes on 3/4“ CPVC (assuming water circa 10ºC), and 100% it’s been a bust every time. So I just use 25-mins as minimum for 3/4” CPVC and really you don’t get much more than one freeze from a 20-lb cylinder. You have some residual, so you can start a freeze next time with it, but it doesn’t last long before you’re swapping to tank #2.

 

[Chestermiller]

To get a more refined calculation of the freeze time, we are going to need a more refined picture of the CO2 flow distribution (velocity vs spatial position) within the freeze head. This would probably require the use of computational fluid dynamics (CFD).

 

[MrFreezeMiser]

CFD is beyond my expertise. However, I could run some controlled tests on steel/GIP, copper and CPVC in my shop to gather better measurements. Do you think more refined measurements would help? I was thinking of even doing some partial freezes and cutting open the pipes to observe and measure plug formations and quality.