5 replies to this topic

Hi all,

I am trying to estimate the time to empty a pipe filled with high pressure, dense phase CO2 (~100 barg, 25 degrees celcius) which suddenly guillotine fractures at one end (assume the other is blocked).

Ignoring solid dry ice formation effects, can I use Rasouli Williams formula (on Milton Beychok's website) as a first approximation model for this situation?

What would be the best framework to use for quickly modelling this problem?

Best regards,
Matt

[Art Montemayor]

Matt:

I don’t know specifically what you are trying to model – a real life case or a theoretical case. Nor do I know for what purpose. But I happen to know a lot about what is really going to happen when you have a pipe filled with pure CO₂ at 100 barg & 25 ^oC. I’ve seen what happens and I’ve operated systems where we did this every day – making dry ice.

And that is exactly what will happen when you expose the pressurized liquid CO₂ to atmospheric pressure – a percentage of it will convert almost immediately to solid, CO₂ “snow”. You infer you want to ignore this conversion. I don’t know why you would want to do that; I believe you can’t do that safely – but then, it is your decision and, as I say, you don’t tell us very much about what you are doing.

Before I close, I must give you the recommendation that you do a heat and mass balance around the system and, upon doing that, you will find that you created a considerable amount of dry ice snow that you must account for – phase wise and thermally. You see, you will have a pipe at -109 ^oF, & partially filled with solid snow. Unless you have special steel or material of construction, you will have a useless and ruined pipe for starters. And you will continue to generate sublimation vapors until ALL of the solid snow sublimes.

Another hint: when you make the heat and mass balance to find the amount of solid snow generated by the isenthalpic expansion, note that you will go through the Triple Point before getting to atmospheric pressure. You can’t use the NIST Thermo data base because it unfortunately doesn’t go down beyond the Triple Point, so you will need a more detailed database for your enthalpy values.

Good Luck.

Hi Art,

thanks for the swift reply. Hmmmm! I knew I'd make a lot of snow! Problem I have is that I need to put a health and safety case forward to show how much gas is released and what the plume concentration vs distance would be from a 5.5 km, section of 18'' diameter (very good) steel pipe.

On top of that I need to make a good first estimate of the release rate (kg/s) of the fluid. Which I was hoping to use rasouli williams (cheesy I know for this app) and then factor out the solid afterwards assuming a certain mass was converted.

Just assuming JT cooling is not enough (apparently) for this app since other heat loss mechanisms potentially dominate (given the largeness of the flow - 3000 kg/s approximately).

I'm a physicist rather then a chem engineer and some of this is quite new to me! Am I talking nonsense or am I on the right lines? (having read a number of your previous posts I know you know what you are talking about!)

Best regards,
Matt

[Art Montemayor]

Matt:

You need to know the basic fact that is all around us: CO₂ fire extinguishers. These apparatii are at almost the same conditions that you are stating.

If you have ever handled or seen a CO₂ fire extinguisher activated, you will know that it generates snow (plus some very cold vapor) at -109 ^oF. It is not the vapor that is effective in fighting the fire, but rather the snow that settles into the fire itself and is sublimed into an inert cloud of CO₂ gas that eventually "snuffs" out the flames by keeping out the oxygen it needs.

Your failed pipe line will behave in exactly the same way. You will instantly create a 3-phase system that quickly converts itself into a 2-phase system of very cold snow and vapor. Unless your pipeline is rated to withstand the -109 ^oF ultimate temperature, it itself will be effectively ruined and can't be used again (probably). Very few carbon steel pipe lines can undergo this type of thermal abuse and survive without any future brittle failure effects.

There is no Joules-Thomsom Coefficient involved in this type of cooling. Mr. Joules did his famous research on the expansion of real gases through porous plugs - not liquids. Lord Kelvin (Mr. Thomson) later joined him in putting together the total picture and results, thereby profiting in fame and fortune from Joule's original findings. What you have is an instantaneous, adiabatic, isenthalpic expansion that will generate approximately 30 to 50% solids - I forget just exactly how much because it's been a long time when I did the original calculations. I can do the calcs again, but it's going to take some time because I'm in the middle of remodeling my house for my wife (my real boss) and all my library is disorganized in that the contents are stacked in our Family room while all the 1st floor is being tiled from wall-to-wall. It may take a couple of days next week to get the exact figure, but rest assured I'll do it for you to help you get a handle on what is really happening.

I will be working at home all weekend, so I can't promise any work output during that time. You need the correct evaporation rate of the initial vapors and then a calculation of the remaining vapors that are generated due to the subsequent sublimation of the snow that remains inside the pipe. Believe me, that is the scenario - unless I'm terribly wrong in interpreting your problem.

Any additional information you can add would be a help.

[Art Montemayor]

Matt:

I just got home and found one file where I did some of the work I remember. Attached find a copy of this file and in it you will find the calculations I described.

As you can see, approximately 25% of the pipeline liquid content will revert to Dry Ice.

Perhaps this can help you and assist in setting up the model you are seeking.


 CarbonDioxide.xls   116KB   95 downloads

Hi Art,

thanks for the file really really useful. Hope you're real boss is treating you fairly this week! You and Milton Beychok have been really helpful. Thanks so much. I'm starting to get somewhere

> You need to know the basic fact that is all around us: CO2 fire extinguishers. These apparatii are at > almost the same conditions that you are stating.

yes but the volumes they release are much much smaller. My feeling is that this doesn't matter but others think differently. What do you think? Does ramping up the volume of CO2 make a difference?

> What you have is an instantaneous, adiabatic, isenthalpic expansion

yes I agree (in fact when I said JT cooling before this is what I really meant! Sorry!!). However, is the process really adiabatic? Others here are saying that because the volume of CO2 flowing through is large and the pipe cools rapidly then heat transfer through pipe walls causes alternative paths to 1 atmosphere to be taken so that the process is not adiabatic and so you get a different amount of solid to that predicted via the isenthalpic path

> As you can see, approximately 25% of the pipeline liquid content will revert to Dry Ice.

Hmmm! I was close with my estimate - I reckoned it would be 30%!! Thanks for this.

One problem still springs to mind - that of the mass flow rate out of the pipe vs time (as the pressure decreases). Correcting for the loss of solid CO2 out of the pipe, does rasouli williams still give approximately the correct answer for dP/dt? I'm awaiting a copy of Milton Beychok's book with a derivation of rasouli williams which hopefully will help me in my thinking.

Another question of interest is what happens when the fluid starts life in a supercritical state (but don't have specifics at the moment)

Best Regards,
Matt