Volume of gas required to pressurize a container? 1

[dmackle]

Hi, Can someone please assist me with the following thermodynamics calculation;

It's been about 15years since I've done any Thermodynamics so it feels like I'm starting from scratch again.

I want to calculate the volume of argon gas required to pressurize a sealed vessel to a specific pressure with a given temperature and volume.
I have tried using the combined gas law, actually a slightly modified version but am not sure if this is the correct thing to do?

Here are the details;
I have a cylinder of gas with;
Spatial volume = 11 cubic metres
Gas volume = 47 litres
Room temperature = 288K
Pressure = 23Mpa (230bar)

I want to calculate the amount of gas required to pressurize a part in a Hot Isostatic Pressure vessel with the following conditions;
Spatial Volume = 64 cubic metres
Gas volume = ?
Vessel temperature = 1473K (1200degC)
Pressure = 100Mpa (1000bar)

I tried using the combined gas law i.e. P1*V1/T1 = P2*V2/T2. I used the spatial volume (cubic metres) in this calculation but this does not allow me to take into account the volume of gas in litres to be used.
If i use the value in litres for V1 then the calculation doesnt take into account the change in size from the pressure cylinder to the HIP vessel.

So I thought that workign both volumes into the equation could be a way forward i.e.;
P1 * Gas Volume1 * Spatial Volume1 / T1 = P2 *Gas Volume2 *Spatial Volume2 /T2

Is this a valid assumption to make or is there a more suitable approach I should take?

David

 

[Latexman]

What's the difference between spatial volume and gas volume of a cylinder/part/vessel?

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

 

[racookpe1978]

You actually want to pressure test "a part" placed inside the pressure vessel though, correct?
(Not the entire pressure vessel itself?)
Or do you need to pressure "a part" OF the pressure vessel assembly (valve, pipe, test fitting, gage, PV head, PV weld, or whatever) that includes the PV?

Second: Why are you doing ANY "testing" at 1200 deg C (1473 K)?
Will the final assembly be required to hold gas pressure at 1200 deg C? Even if so, you DO NOT test at 1200 deg to verify fabrication and welds and material, but you do run "system operational tests" using an inert gas and reactants BEFORE operation. Then an operational or capacity check with live reagents at operating temperatures.

 

[dmackle]

Thanks for the replies.
@latexman, the spatial volume is the volumetric space inside the cylinder at atmospheric pressure. The gas volume (argon) is the pressurized argon in the cylinder i.e. 47litres at 230bar.
Am i missing something here? e.g. the 11 litres of air at atm pressure would equate to 47 litres of argon if compressed to 230bar?
If i assume the both to be the same im still confused as to how i can get the argon gas volume required in litres when the vessel dimensions are known in cubic metres?


@racookpe1978,sorry for the confusion, a part is going through a heat cycle inside the vessel. It is held at that 1200degC for about 2hrs. The hold temperature and duration are variable depending on material and part geometry e.g. wall thickness. Cast parts will become 100% dense with improved mechanical properties.
I will need to subtract part volume from vessel volume in my calculation.

 

[IRstuff]

Yeah, I think you're confusing things. The cylinder water volume is 47 liters and the pressurized gas is 11 m^3, which comes out pretty close to 24 MPa, even if I don't use the correct STP.



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[LittleInch]

You're confusing me with this "spatial" thing.

Lets go back to basics - with compressible fluids when you talk about volume you also need to refer to it's pressure. Because the volume is so flexible for the same mass of gas, the use of volume at standard conditions is used, e.g. SCF or SCM. If that's what you mean then use terms every one understands, i.e. the volume of gas at standard conditions would be 11 m^3

I think that when you say "spatial" you mean SCM.

Now it may be a co-incidence but 11 SCM of gas when compressed into a volume of only 47 litres is pretty close to 230 bar.

So in order to even start to find out how much gas at standard conditions you need to achieve a pressure of 1000 bar at 1473 K you need to know what volume your container is. currently this is shown as ???

A pressure vessel of 64 m^3 at 1000 bar would just be HUGE so I'm struggling on that front.

A diagram or sketch might improve our understanding of your question.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[dmackle]

Thanks for the feedback.
@LittleInch, it's been a long time since I've used any such calculation so I'm not familiar with the standard terminologies as I once may have been, apologies for this it is not laziness it's just non-familiarity. So, yes you are correct in that when I use spatial volume I am referring to the volume of gas at standard conditions (SCM). This makes more sense to me now!

Here are the details again with all the info I have;
Cylinder of Argon gas with;
Gas Volume at SCM = 11 cubic metres
Gas Volume at 230 bar = 47 litres
Room temperature = 288K
Pressure = 23Mpa (230bar)
Gas price per cylinder = £117

I want to calculate the amount of gas required to pressurize a part in a Hot Isostatic Pressure vessel and ultimately work out the gas price. The relevant info for the vessel is below;
Vessel Volume = 64 cubic metres based off diameter 3metre diameter and 9metre height.
Vessel temperature = 1473K (1200degC)
Pressure = 100Mpa (1000bar)
I am trying to figure out how much gas would be required to fill the vessel at 100Mpa pressure and 1473K.

The process I am looking at is Hot Isostatic Pressing were an average pressure of 100MPa and the particular vessel (64m^3) is the one of the largest on the market. We could be using smaller vessels at similar temperatures and pressure. Smaller vessels can be as small as 95mm diameter and 150mm height.

I had tried another approach whereby I worked out ratios between;
1) required vessel pressure / cylinder pressure @23Mpa
2) cylinder temperature / required vessel temperature
3) vessel volume / cylinder volume @23Mpa
I then multiplied these ratios to calculate the volume if gas required (see below)

1) 100Mpa / 23Mpa = 4.34
2) 288K / 1473K = 0.195
3) 64cubic metres / 0.047cubic metres = 1361.7

Multiplying the ratios gives;
4.34 * 0.195 * 1361.7 = 1152.41
Conceptually, I see this as factoring up the conditions of the pressure cylinder to the large HIP vessel with changing temperature, volume and pressure.

Gas Volume Required = 0.047cubic metres * 1152.41 = 54.16 cubic metres

Cost per cubic metre = £117 / 11 cubic metres (volume of gas at SCM) = £10.64

So factoring in the cost;
Argon cost = £10.64 * 54.16 = £576.26

But 95% of this can be reused so actual cost is;
5% of £576.26 = £28.81

Is this a reasonable approach?

 

[LittleInch]

No problem - that's why we're here to a certain extent.

It would help if you could edit your post above and put some units against your figures as I don't understand what it is. Your error is in line 3 where you need to use the volume of the cylinder ( 0.047 m3). Makes a BIG difference.

So a 3m diameter vessel 9 m long at 1000 bar. WOW. That is some lump of metal. (any photos?)

So you have a volume of 64m3 minus your part volume. Don't know what it is but you can deduct from the volume Vv

Using gas at standard conditions and very basic gas law stuff which may not apply at these sorts of pressures, you're looking at 64,000 scm of gas assuming no temperature increase.

Now there is a temperature element here so lets iterate a bit.
Say its 200 bar at std temp then you increase temp by a ratio of 1473/ 287 = 5.13 to get to your 1000 bar at 1473 K.
So your gas requirement is now 12,800 SCM ( 200 x 64) or 1,163 of your 47 litre bottles. so a cost of £171,000 assuming zero part volume (!!)

Part of the issue though is that you really need a compressor or a whole set of compressors to go from virtually atmospheric pressure to 1000 bar. Otherwise as the pressure increases in the vessel the cylinders will only pressurise to the pressure in the vessel e.g. at 150 bar there will be 150/230 (65%) of the gas mass still in the cylinder unless you can compress the gas to your required pressure and draw down the pressure in the cylinder. Either way it will be difficult to extract all the mass of argon from the cylinder.

Large volumes of gas like this tend to come in liquid form which is then reheated / gassified and pressurized to whatever you want. At least that's how Nitrogen comes when you need it in large volumes. But 1000 bar will need a large compressor packages made up of a number of compressors and intercoolers.

Have I understood this right?

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Also: If you get a response it's polite to respond to it.

 

[LittleInch]

your line 3 - 64 m3 / 0.047 m3 is 1361, not 5.81(!)

Also how are you going to re-use 95%

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[dmackle]

No probs-I've edited the post above so hopefully that measier to follow. And thanks for the correction.
I'm doing the calculation on behalf of a customer so don't have a photo. I've a call with the machine manufacturer next week so will try and get a pic if possible. (It's not available online)

I'm struggling to follow your calculations though, here's where i've gotten to;

We get the 64,000scm by using;
P(vessel)*V(Vessel) = P(cylinder) * V(cylinder)
1000bar * 64scm = 1bar * V(cylinder)
Hence, V(cylinder) = 64,000scm
So this bit makes sense.

You mention..."Say its 200 bar at std temp"
Q1)Are we not assuming 1 bar pressure at room temperature, as in the pressure in the previous calculation?
Q2)You calculated the ratio..."1473/ 287 = 5.13 ". So should the 64,000scm not be divided by 5.13 instead of 5?

 

[dmackle]

I missed that one when updating, but have corrected it now. Thanks!
I'm not familiar with the method of recycling gas but some research has shown between 90-95% of the gas is commonly recovered with this process.

 

[dmackle]

@LittleInch, I've revised the calculation in my post '28 Nov 18 11:54'.
Can you please review to see does this method seem logical?
And yes the Hot Isostatic Pressure (HIP) Vessels rely on a set of compressors to reach the required pressure.

 

[LittleInch]

Your line 3 is mixing up volume of gas at 200 bar with scm.

Your 54.16 m3 is 54 m3 AT 230 barg, not 1 bara (standard conditions)

So the cost per STANDARD cm is approx. £10.64. You will need approx. 12,400 SCM to pressurize a 64 m3 space to 200 bar from atmospheric pressure so the cost is in the hundreds of thousands of pounds (approx. £130,000). This could be reduced a lot if your item is large and hence the space left for the gas is reduced. We have no idea how big your item is....

What I did was just change one parameter at a time to make the steps easier.

So you pressurize your (empty) large 64 m3 vessel with argon to 200 bar first at room temp to get your argon mass / volume.

Then you as you heat it up from room temp to 1473 K, it will increase in pressure approx. 5 times using the gas laws as the volume doesn't change so the pressure must increase to match the inverse of the temperature increase = approx. 1000 bar.

I can only guess with the recycling that if the argon is still pure then you can re-fill your cylinders via a compressor down to probably 10 barg in the big vessel and then just vent the rest off safely (it's inert so it can kill people if you do it in an enclosed space.)

I'm just working in round numbers here as the gas law isn't perfect either so don't get hung up on the odd fraction.



Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[dmackle]

Thanks for all the clarification LittleInch.
I think this all makes sense to me.
So I could calculate the gas volume required by using the vessel parameters of volume(64m3), pressure(1000bar) and temperature(1473K) with a choice of two inputs.
Inputs 1
Pressure = 1.01bar
Volume = 11m3
Temperature = 287K

Inputs 2
Pressure = 230bar
Volume = 0.047m3
Temperature = 287K

Inputs 1 gives a cost of £135,614
Inputs 2 gives a cost of £133,151

These costs are high but the vessel is empty and we can recover 90+% of the gas. Also the cost will be amortized across the number of parts that can fit in the vessel.

 

[MintJulep]

Do you or don't you evacuate the air before you start?

 

[LittleInch]

Don't forget the calculations don't allow for the volume of your parts. I can only assume these are quite big if you want to use such a big vessel, but I think you've got the gist of it.

That's still a mighty pressure and temperature you're working at and you would need over a 1000 gas bottles!!

Let us know how it goes.

LI

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[EdStainless]

Usually vacuum purged, these units often go through an elaborate warm up, vacuum, partial fill, vacuum process to assure complete outgassing.
And the Ar is always supplied from large cryo tanks.
They often use liquid Ar pumps and high pressure vaporizers in order to reduce the compressor work needed to get from the 15 bar source to 200Bar or so needed prior to heat up. This system also allows for some high pressure gas storage that is part of the recovery system.

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[Latexman]

PV=nRT

n=PV/RT

number of gas cylinders needed = n_vessel/n_{1 cylinder} = (PV/T)_vessel / (PV/T)_{1 cylinder}

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.