Air volumes 1

[maxh]

Hi - can anyone help on this

I have a water tank 10m o/heads by 2.6m diameter operating at 8 to 10 BarG.

The water tank is situated outside, is uninsulated, and the water temperature is generally 5C throughout the year, to prevent freezing in winter extremes the tank has immersion heaters. The water is clean and treated.

If I want to keep the water level at 50% in the tank with steady state conditions in the attached system do I need to worry about the external temperature heating / cooling the air volume which might then cause the water level to rise / fall. My thermodynamics from many years ago suggests P1V1=constant and PV=mRT to me, but I don't know if they apply in this situation because I guess there will be 100% humidity in the tank and the latent heat of the water in the air may change how the system behaves.

I expect the local ambient extremes to be -20C to +35C, with the surface temperature of the vessel in the direct sunlight up to 50C, although this upper temp may be conservative as I am not sure of what would be an appropriate estimate with the outside temp of 35C.

Any suggestions on how to tackle this one would be appreciated.

 

[IRstuff]

see columns on density and specific volume:

http://www.engineeringtoolbox.com/water-thermal-properties-d_162.html

Density of water decreases slightly as a function of temperature, so specific volume increases, but is a rather small amount

TTFN

Eng-Tips Policies FAQ731-376

 

[maxh]

Thanks IRstuff
but I am concerned about expansion / contraction of the air volume.

Would the air above the water be at 10% humidity ?

If the air is at 100% humidity does it still act like a perfect gas when heated / cooled or does the water vapour change its behaviour ?

maxh

 

[IRstuff]

What "behavior" are you specifically talking about? There are tables for water properties:

http://www.thermexcel.com/english/tables/eau_atm.htm

Your original posting said something about the water levels rising/falling, but you have an apparently sealed system.

see:

http://www.engineeringtoolbox.com/water-vapor-air-d_854.html

but the amount of condensible water in air even at 100% RH is pitifully small:

http://www.engineeringtoolbox.com/humidity-ratio-air-d_686.html

TTFN

Eng-Tips Policies FAQ731-376

 

[25362]

[•] How do you maintain the pressure ?
[•] Water is practically incompressible at the given conditions.
[•] Any expected change in air pressure shouldn't appreciably affect the water volume.
[•] Just look for tabulated liquid water specific volumes at various conditions to get an idea. For example

http://webbook.nist.gov/cgi/fluid.cgi?ID=C7732185&Action=Page

[•] Kindly note also that higher air pressures would also involve greater air-in-water solubilities.

 

[maxh]

Hi Guys - methinks I have enabled you to get hold of the wrong end of the stick.

If the air expands or contracts the water level in the tank will fall / rise as the tank is connected at the bottom to a pipeline which terminates in an open ended discharge some 90 metres above the level of the tank.

The air in the tank acts as a cushion to prevent pulsation and we need to keep a constant air volume, so I am concerned that changes in temperature or the air will cause a change in the volume of the air in the tank.

I am not concerned about the water, how it contracts or expands as this will be a small factor compared to what happens to the air.

Hope this clarifies the question.

Thanks

 

[quark]

You can neglect humidity of air. If you have 90 meters height pipe connected to the bottom and if you maintain 50% volume of water in the tank, the equilibrium pressure in the tank vapor space will be 90-5 = 85 meters, which is approximately 8.5 bar g.

Suppose, you maintain 8.5 bar g during 35⁰C ambient condition. When the temperature drops to -20⁰C, the pressure decreases to (8.5+1)*(273-20)/(273+35) = 7.8 bar a (assume constant volume - see note below).

Half of the tank volume is 26.55 m³. To raise the pressure to 9.5 bar a, you have to pump in 9.5x26.55/7.8 = 32.33 ³ (standard) of air into the tank.

Note: Now doing some back calculation, if the pressure at lower temeprature is 7.8 bara (or 6.8 barg), water may be pushed into the vessel. If you consider 100mm pipe, then the water level may decrease by 85-68 = 17 meters. By doing volume balance, the level in the tank may increase by (0.1/2.6)*17 = 0.65 meters. This should reduce the volume to 22.42 meters. Now, applying universal gas law, the pressure should be (9.5*26.55*253)/(308*22.42) = 9.24 bar a, which is an impossible case. So, the pressure should be less. If you do some trial and errors, you will come close to constant volume process, and it can be a good approximation.

 

[maxh]

Thanks for the advice quark

What if the pipe were connected to a large reservoir whereby when the temperature falls, the volume reduces but the head on the tank remains the same as the reservoir only falls a fraction of not very much at all.

I guess I would have to put air in to compensate for the level increase in the tank and vice versa when the temperature rises ?

Do you say ignore humidity because the amount of water actually in the air is so small as not to make any difference at all - can this be calculated to show our client ?

 

[quark]

1. Yes, you should increase the diameter of the reservoir and decrease its height.

2. Yes, the quantity of water in the air is negligible, in our case. The humidity ratio at 35⁰C and 100% RH is about 0.0036. The density of air at 9.5 bar(a) pressure can be calculated from universal gas law and is approximately 10.88kg/m³. If the air volume in the tank is 26.55 m³, then total quantity of air is 10.88x26.55 = 288.86 kgs. So, moisture content will be 0.0036*288.86 = 1.04 kgs or 1.04 liters.

Even if you consider the air to be 100% dry at -25⁰C, i.e entire water vapor condenses, the water level may raise by 0.19mm.

I am sure 25362 jumps in, to help me, if my numericals are not accurate. I am too lazy this monday morning.

 

[25362]

Maxh

[•] For a constant pressure (water column) of 10 bar, and at ~ 300 K, air would show a volumetric expansion (or contraction) coefficient (1/V)([∂] V/[∂] T)_p of about 0.0034/^oC.

[•] To show your client the small contribution of air moisture to the total pressure use the ideal gas law (again quark's advice) as follows:

Vapor pressure of water as function of temperature from tables, p_w
Air pressure, given by you, p_a

Dalton's law teaches us that each gas occupies the full volume and exerts pressure independently:

p_w = n_wRT/V; p_a = n_aRT/V; and p_w+ p_a= p_total, therefore:

n_w/(n_a+ n_w) = p_w/p_total​

and

n_w/n_a = p_w/p_a​

where n is the number of moles. Use molecular weights (water:18, air:29) to convert to mass ratios.

Quark, forgive me for not trying to correct your estimate. I'm also too lazy to start looking for steam tables.

 

[quark]

maxh,

I forgot to ask you, how do you prevent the water from freezing during -25⁰C? If you heat the water then extra air may not be required.

Et tu 25362

 

[maxh]

The water is heated using immersion heaters and the tank is to be uninsulated.

I know this means that we will have to work out heat input from the heaters and heat lost from the tank to the external environment - time for head in a book to refresh those calcs I have not done for a good few years, or I guess I could lean on the supplier of the immersion heaters, its amazing what you can get out of good suppliers as long as you don't try to compete with what they do.

At the lower temperatures I can see that humidity will not present a problem as the air in the tank will be near to freezing and the air will not be able to hold much water.

I can also see there is a discussion point around how you set up the heaters, do you set them using their thermostat and try to account for the temperature gradient between the bottom of the tank where they are positioned and the top of the water level where the water may freeze if you don't put in enough heat, or do you use a local temperature sensor near to top water level to get it right - I don't know what is common practice, but I do see that a lot of people will probably just set the heater thermostat to somewhere between 5 and 7 deg C and hope that everything turns out OK !!

Quark - As to the discussion on humidity I think the help from yourself and 25362 has given me the right ammo to fire off a response to my client - so thank you for that.

 

[25362]

I don't know what is the purpose of the exercise, but if allowed, additions either of Propylene Glycol, CaCl₂, methanol or ethanol, for example, wouldn't allow the water solutions to solidify at the envisaged low temperatures.

 

[IRstuff]

I still don't understand your comments regarding "air will not be able to hold much water." Why is this a concern? Saturated air at 30ºC holds about 26 gm of condensable water per kilogram of air, which is about 0.8 m^3 volume, which means that even if your tank had ONLY wet air, there would still only be 1.7 kg of water total.

You don't say what your tank is made of, but the heaters should probably be at the bottom and the sides, since the air blanket is probably a much better insulator than the tank walls, and warm water will rise.

TTFN

Eng-Tips Policies FAQ731-376

 

[MintJulep]

This description of your system

If the air expands or contracts the water level in the tank will fall / rise as the tank is connected at the bottom to a pipeline which terminates in an open ended discharge some 90 metres above the level of the tank.

describes a giant barometer.

But then you go on to state

The air in the tank acts as a cushion to prevent pulsation

Which makes me think that you have not yet given us the whole picture. A tank connected to a pipe seems unlikely to experience pulsations, unless there is some other force acting on the system.

 

[maxh]

To answer your questions

The tank is steel and the heaters are inserted sideways at the bottom of the tank as close to bottom dead center as the construction code permits for hillside nozzles of the diameter used.

The tank is connected to a pumped main, pumped mains have valves, pumps and other equipment attached that can create pulses.

The weight of water in the air was a client question for which we didn't really know the best approach to give a suitable answer as we had always previously ignored the issue as being irrelevant to our equipment. The client didn't accept that as an argument and so we have to show some calculations.

You know how it is when you have to prove something to your client that you know isn't a big issue, but you don't know quite how to show it properly.

I guess its a received wisdom thing, something has always been so, is accepted by everyone, is never questioned, you never have to prove it, then someone asks for proof. To me it was like someone saying "show what 1+1 equals", you know the answer but can you do the mathematical proof !