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Ideal Gas Law - domain of validity
3

Ideal Gas Law - domain of validity

Ideal Gas Law - domain of validity

(OP)
Hi,

I need a reliable mathematical model (P, V, T) of compressed air.  The pressure ranges from 1 to 160Bar, and the temperature is bound by -30 and +70°C.

Is the Ideal Gas Law "accurate" in the present case?  An error of about 10-20% is probably acceptable.

/hpon  

RE: Ideal Gas Law - domain of validity

Air is pretty special stuff.  I plotted deviation from ideal (i.e., compressibility) from absolute zero (Z=1.0) to 151 bar(a) (Z=1.0) and found that at about 76 bar(a) it reached a minimum at Z=0.985.  At the rate of change that the curve shows as it passes Z=1.0 at 151 bar(a) I would guess that unless it has another inflection at higher pressures (which is very possible) it should reach 1.015 around 200 bar(a).  I would say that that meets your +/-10-20% criteria at 160 bar(a).

David Simpson, PE
MuleShoe Engineering
www.muleshoe-eng.com

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

RE: Ideal Gas Law - domain of validity

How fast are you changing the pressure?   If you change the pressure quickly you should consider the process to be adiabatic.
http://en.wikipedia.org/wiki/Adiabatic_process

When charging accumulators I recommend using the ideal gas law because there is plenty of time for heat transfer but during actual operation the cycles times are short and there isn't much time for heat transfer so I recommend using the adiabatic gas laws.

http://en.wikipedia.org/wiki/Adiabatic_process

A lot depends on how fast the air is being compressed and decompressed.  If you can nail down the values for specific heat for constant volume and pressure you have a better approximation than simply using the ideal gas law.

  

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com

 

RE: Ideal Gas Law - domain of validity

(OP)
Thank you for your valuable replies!

The pressure changes are slow in the sence that the process will be approximatelly isothermal.

I just realized something else that might cause a bias from the Ideal Gas Law.  The air is in fact small bubbles in a hydraulic media; and as the pressure increases the bubbles may become super-small.  I wonder if the surface tension (around each bubble) could become noticable in such conditions.  What do you think?

/hpon

RE: Ideal Gas Law - domain of validity

You will get a massive departure from the ideal gas laws because as you increase the pressure the gases will dissolve into the hydraulic fluid. For example, at atmospheric pressure and typical ambient temperatures, a mineral oil based hydraulic fluid will contain about 9% by volume of dissolved air. As the pressure increases the amount of air dissolved in the fluid increases. When you decrease the pressure the fluid becomes super-saturated with air and the air will come out of solution - this usually happens in the hydraulic reservoir.

DOL

RE: Ideal Gas Law - domain of validity

(OP)
Thank you DOL!

That was a very valuable piece of information.  Do you have more data points?

In the current problem, a vesil of a variable volume V will initially be filled with N parts of oil and M parts of air (at 1 bar).  Subsequentially, more oil will be added until the pressure reaches about 10-25 bar.  After that the pressure will vary between about 10 to 160 bar, as a function of the total volume V of the vesil.  Should I expect the ratio between the pressure and the volume V, to be affected by the initial M parts of air?  Or, will the air be completelly disolved throughout the entire presure interval?  Currently there is more air than oil at the initial state (M > N, maybe M/N = 2).     

Does the disolved air influence the physical properties of the oil in any significant way (viscosity, compressability etc.)?

/hpon

RE: Ideal Gas Law - domain of validity

hpon, do you also account for the dissolved air introduced with the added oil?  You will be adding enough oil to compress the air 10:1 to 25:1 pressure ratios.

Once dissolved I don't believe the air will behave as a gas.

Ted

RE: Ideal Gas Law - domain of validity

Good Evening All

I believe Ted is spot on when he says that the air will not behave as a gas once it has dissolved. In practice, when commissioning hydraulic systems, you try to bleed out all the air as you fill with oil but you just know that there's some pockets of air that you can't bleed out. So you operate the system gently and slowly at first to both push the air out (as a froth) and to allow it to dissolve into the oil and be "transported" out.

The dissolving and subsequent release of air doesn't take place instantaneously. So if you can gradually build up and hold the oil pressure high for a few minutes then gently depressurise and let that supersaturated oil rest in the tank for a few minutes more so that the dissolved air will come out in the tank.

What you do find is that, after a while, the hydraulic system starts to behave properly/consistently and you then know the air has been transported away. Even though you left in pockets of air during the filling process you don't find any pockets of air when you take the system apart at a later date. We don't notice the system behaving like a sponge when all the gaseous air has gone.

The problem you will have in calculating what you're trying to calculate is that it is very hard to know just how fast the air will dissolve and how fast it will release. And we keep saying AIR as if that was the gas - forgetting that air is a mixture of gases and the Nitrogen will behave differently from the Oxygen which is different to the Carbon Dioxide etc. etc.

I've added a file which gives a little more explanation (see section 2.1.4) but I believe what you're trying to calculate will be very very hard to do. Is there any way you could keep the air in a bladder so you could prevent the solution problem. BUT - you should be aware that there have been instances of hydraulic accumulators exploding because of the mixing of the oxygen and the flammable oil at high pressures. For this reason accumulators are now charged with dry nitrogen not compressed air. If you have to charge with compressed air (such as some huge drilling rig heave compensators) then you can't use mineral oil as your fluid.

But, I'm sure you're thinking, compressed air gets mixed with pressurised mineral oil when you first start up the system. You're right but it's a tricky process getting it out and it can be dangerous if you don't know what you're doing. If you rapidly compress a hydraulic [mineral] oil with entrained (rather than dissolved) air there is a risk of triggering a destructive and irritating process called "micro-dieseling". The rapid compression of the air bubble before it has had chance to go into solution causes a huge rise in its temperature. Think about it for a second ... we have: a mineral oil (the vapour of which is inside the bubble), oxygen (from the air), rapid compression and very high temperatures - remind you of anything?

Here's an interesting article: http://www.machinerylubrication.com/Read/373/entrained-air-oil-hydraulic

Good luck.

DOL

RE: Ideal Gas Law - domain of validity

(OP)
Ted and DOL, thanks for your replies!

DOL, in respons to your ending paragraph.  Wow!  I did not anticipate that...

An adiabatic idealization suggests a peak temperature of nearly 1200°C in an otherwise non-conservative case.  In other more extreem senarios the temperature could probably reach >1600°C.  These findings are discerning and of upmost importance.    

Once again, your input has been most valuable!

/hpon   

RE: Ideal Gas Law - domain of validity

In a "micro dieseling" scenario, the key word is "micro".  The process that DOL is describing has a low probability of creating an explosion that could level your building.  It is "just" a very large number of very small explosions that happen more or less independently and are generally damped by the surrounding fluids.  Temperature goes up.  Apparent turbulence increases.  The world doesn't end.
 

David Simpson, PE
MuleShoe Engineering
www.muleshoe-eng.com

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

RE: Ideal Gas Law - domain of validity

Micro dieseling degrades the oil by burning additives and small amounts of oil creating comtamination/deposits which can collect in system comonents, that is why it is to be avoided.

Ted

RE: Ideal Gas Law - domain of validity

(OP)
OK, that good and feels kind of right.  

However, it seems natural to think that if one bubble goes of, it will elivate the pressure in the surrounding fluid which in turn truggers other bubbles to combust in an escalating sequence, and so on.  I take it, this does not happen very often in practice.  

Surelly there is a range from true micro-dieseling to a large scale explotion.  I know there may be quite a bit of air in the system.  If I really wanted to, I could probably use the system as is and create a fairly potent poof.  At this point, I need to make absolute certain that no such thing can happen ever.

Are there suitable oils that are particularly difficult to combust?  Is there a reliable criteria that I can apply to ensure that the system is safe with respect to Diesel-combustion?

/hpon  

RE: Ideal Gas Law - domain of validity

You say your process is slow an ~isothermal.  There should be no dieseling since the temperature does not reach combustion temperature.  Rapid pressure rise with resulting rapid temperature rise could result in combustion temperature.  Think of diesel engine operation.

Ted

RE: Ideal Gas Law - domain of validity

I was involved in a diagnosis where a 500 gallon hydraulic tank, ISO 68 petroleum oil, blew the lid off shearing all the bolts and tossing the lid, plus about 300 lbs of stuff mounted on it, about 50 feet away into the weeds. It was eventually believed to be combustion but the oil was severely aerated from an internal problem. It was not simply air in system but foaming up to the point of maybe 10x original volume, combined with a point source of ignition, go boom. There was a huge amount of air in contact with the minimal fluid.

In the micro dieseling scenario the mass of the surrounding fluid is such a thermal sink that the combustion is quenched and not propagated. Also, the amount of air/O2 available in the micro bubble isn't enough to support continuing combustion. Not to say it couldn't happen, this is the extent of my knowledge on the topic, but I would not worry about your system blowing up from the small air bubbles. There are plenty of other ways a system can hurt you though.

An accumulator charged with O2 or air instead of nitrogen might be a different story, if the gas was not separated from the oil with a bladder. I can't comment there.

kcj

RE: Ideal Gas Law - domain of validity

(OP)

Thank you Ted and kcj,

Ted, yes my description has been contradictory. The system will be subjected to both slow and rapid pressure changes.

kcj, I cannot exclude the posibility of foaming. And the vesel could be mostly depleated from oil. My gut is dubious.

/hpon

RE: Ideal Gas Law - domain of validity

Hi hpon

In answer to your question about choosing a suitable fluid - you could do worse than select one of the fluids specially designed for use with offshore drilling-rig crown compensators and tensioners.

These devices generally consist of multiple, huge, long stroke and fast moving hydraulic cylinders which act as the suspension for the drill string. A suspension is needed because the the rig goes up and down with the wave action but the drill bit is in the hole in the ground so mustn't go up and down in the same way. The "spring" in the suspension system comes the compressed gas in a bank of "accumulators" and if the systems were smaller these would be standard bladder or piston accumulators. But the systems are too big for these standard components so simple "gas over liquid" pressure vessels are used, i.e., with no separator between the gas and the liquid. To further complicate the issues, the gas pre-charge has to be rapidly and continually adjusted continually to cater for changes in the suspended weight. If the standard choice of Nitrogen were to be used then the system would consume/waste a lot of gas. To keep the scheme running this gas supply would have to be replenished: either generated on site and compressed into storage vessels (a cumbersome and expensive solution) or delivered regularly by the support ships (also unrealistic). Or use compressed air - which is only a possibility if the liquid is changed from mineral oil to a special non-explosive hydraulic fluid.

There seem to be a lot of similarities between this established technology and your particular requirements so you don't need to re-invent the wheel. The link below will take you to one manufacturer's website (there are others) and the site leads on to some technical datasheets for the fluids.

http://offshore.macdermid.com/cms/products-services/motion-compensator-tensioner-fluids/index.shtml

DOL

RE: Ideal Gas Law - domain of validity

(OP)
Thank you, DOL!

Very interesting. I shall keep that alternative in mind.

/hpon

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