Pressure rise when filling sealed tanks

[stoppit]

Hello

I hope someone can help me with this. It's a simple question but I'm not from a classical Chem. Eng. background so could do with a pointer. If you have a sealed tank of volume V and you fill it to some proportion x (0-1) at a rate Q L/min, how can I determine the final pressure in the tank as a function of time (or fill level)? It seems like it should be easy but I've not done this before and I don't know where to start. Can I take pV^n = constant and substitute the time-dependent vessel volume V(t) for the volume term?

The pressures are low by process engineering standards and the fluid is water based to let's assume compressibility is zero.

In an extension to this, if the contents are reacting and undergo a small volume change on reaction, how can I build this in to the calculation?

Many thanks.

 

[LittleInch]

As a basic start point you can use the ideal gas law (P1 V1)/T1 = (P2 V2)/T2. You know start pressure and start volume and end volume. If you assume T remains constant there you are. Remember to use absolute pressure and degrees Kelvin.

That is pretty basic, but will give you a start point. If the gas and liquid combine to create more gas or less gas then just add or subtract that from V2 to find your new pressure.

The gas compressibility won't be ideal, but as a first order number you wont be far off. If you know the compressibility factor then you can add this in as well.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[chicopee]

Something is lacking in the description of the OP because I sense that there is a process other than just compressing a vapor. First what are you filling the tank with, a liquid or gas?; secondly what is in the tank, another word, is it s a similar liquid with a vapor space of the same material and you are trying to develop pressure in that vapor space? thirdly, is the tank insulated or is it exposed to some ambient condition? What pressure and temperature is the entering medium at?.

 

[stoppit]

Thanks for your replies. I've tried to keep the description simple because of commercial sensitivies, there is more going on in the tank but I'd like to keep that part off line.

The tank is isothermal. It is not lagged but there is a temperature control system associated with it. The headspace as the tank fills will be a water/organic mixture.

I think in thje first case the p-V-T relatinship will be adequate, and if I want to account for density changes I can modify the volume expression, I think.

 

[racookpe1978]

Get somebody (who you CAN trust with the process information) to check your work.

 

[stoppit]

I'd like to re-open this query with an update. I have a good estimate of the total pressure including accounting for the volume change. My problem now is to calculate the vapour phase composition.
I'm using Aspen+ software. I can't run this as a tank or CSTR because the dyanmics of the process are too complex to simulate in Aspen. All I want is a single point VLE calculation for times of interest in the process. i.e., Here is the liquid phase composition, here is the temperature, here is the pressure: what is the vapour phase composition?

 

[StoneCold]

Just chose the conditions you want to model and do a steady state flash for those conditions. Realizing of course that this is a dynamic situation and you won't be at equilibrium unless you filled the tank very slowly, but the flash will be "close". There will also be some error in the actual vs the model because of the way you prepare the cylinder before you fill it. If you don't pull a hard vacuum on the cylinder first and then backfill with your fluid there will be air in the cylinder which will throw your ideal model calculations off.


Regards
StoneCold

 

[stoppit]

No, this doesn't work but thanks for the suggestion. The flash needs 2 of the 4 variables specified, T, P, vapour fraction, duty. Duty is presumably the heat of vaporization. I want to fix T and calculate P and the vapour composition. I have to specify duty but have no idea what this is. The output P is very sensitive to duty so this isn't ideal.

For example, the heat of vaporization would be calculable but I don't know how much of the liquid I'm vaporizing, and this heat is lost in the overall heat balance anyway in a real application, were it to exist. The duty isn't much - 1-5 kW - but it does shift the pressure quite a bit.

 

[racookpe1978]

???

"Duty" in specifications or operations is almost always a term to specify "what percent of time is the system operating (at some specific percent of output)?"

thus, a welder may be rated at 300A, but at a 20% duty cycle (one for 1 minute, off for 4 minutes), but be rated at 200A for 100% duty cycle.

You need to look again at the specifications or problem statement: The duty cycle is likely to be "what percent of time the tank is filling?" or "What percent of time the tank is NOT being filled" - thus, the tank vapor is going back to equilibrium and not pressurizing.

 

[stoppit]

It definitely has units of kW!

 

[StoneCold]

stoppit.
You know the temperature. You know the range of pressures that the tank will go through as it is filled. So use that information to get your vapor compositions. There is no heat duty, unless you have a reaction going on. Then you have a heat duty related to the reaction kinetics.

Regards
StoneCold

 

[MortenA]

You write that "you are not from a classical Chem.background". This makes it very hard for me (with a classic chem background) to assess if you can use any advice i may provide. Is the aspen tool pure "black box" to you - or do you understand how the thermodynamics work?

The initial problem you described was mush simpler that your second desription. IF you are filling the vessel with a liquid that do flash (e.i. have a vapour pressure above the pressure of the vessel at initial condition) then its more complicated than if not.

I think you should call in aconsultant.

Best regards, Morten

 

[GHartmann]

I'm no Aspen expert, so I will start from a basics viewpoint.

At the starting point there is a liquid in the tank in equilibrium with vapor in the tank. The fluid VLE data specifies the gas composition.

At the end point it is unclear if the fluid in the tank is still at the same composition. In any case the VLE can be specified for this condition also.

One thing could have changed is that one of vapor components could have exceeded it's vapor pressure relative to the fluid and would then condense from the vapor mixture. In this case you have a lot more going on than filling a tank with water.

Without disclosing more of what you're really trying to calculate it will be hard to provide relevant help.

 

[Mutt]

You want the vapour composition at a fixed P and T. Use a flash vessel with a feed stream of the composition of the total mixture in your reactor at the T and P of the vessel. Say at a feed rate of 1 kg/s. Specify the flash vessel at the same T and P with a vapour and liquid stream offtake. Duty can then be set as zero. Duty is amount of heat to be added or removed to the feed stream to meet the conditions specified in the flash vessel. As you will have specified the feed at the same conditions no duty is required. The vapour stream composition is then what your are looking for and will represent the vapour in you reactor. Check the P and T of the 'product' streams to make sure you have entered the T and P correctly on the flash vessel. Should be the same as the feed!

Beware however that you must choose the right thermo method. The answer can change significantly and is totally dependent on the components in the reactor as well as the T and P.