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# Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

## Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

(OP)

I am trying to calculate the needed time to transfer a certain mass of liquid butane at constant pressure (about 2bar) to another vessel at vacuum. The environment temperature is about 273K. I tried some equations but the results were wrong. Can someone indicate me which equations should I use?. My background is in aeronautical engineering (navigation) so I am not an expert but i believe in this case on of the difficulties is that the process must be stooped before reaching the equilibrium situation (same pressure both vessels).

### RE: Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

Nothing about this problem is steady state. It is rare for a flashing problem to ever be steady state, and a vessel fill rate is a function of the dP. You start out with about 3 bar dP (depending on how deep your vacuum is and what your atmospheric pressure is) and that rapidly declines, but the rate of decline varies from millisecond to millisecond. Oh yeah, and there isn't a closed form function that you can integrate. The best you can do is approximate it by calculating very small time steps and redoing your phase calcs at each step. This is probably a problem I'd use D'Arcy Wiesbach equation on each step and be very careful with my friction factor and compressibility calculations at each step. This is as nasty a bit of arithmetic as you'll come across in fluid flow.

David Simpson, PE
MuleShoe Engineering

Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat

### RE: Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

(OP)
I'll try with D'Arcy Wiesbach equation. I hope it will work.

### RE: Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

(OP)

#### Quote (zdas04)

This is probably a problem I'd use D'Arcy Wiesbach equation on each step and be very careful with my friction factor and compressibility calculations at each step
The problem is in microgravity (about 0g) so I think the D'Arcy Wiesbach equation can't be used cause is based in ΔP=ρ*hf*g
http://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation

### RE: Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

Microgravity? Like in space? Don't you think that that would be an important parameter to share from the beginning?

David Simpson, PE
MuleShoe Engineering

Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat

### RE: Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

(OP)
Sorry zdas04, I forgot to mention that. This two vessel is a subsystem of microprpulsion system for nanosatellites.
Do you know if I can simulate this system with HYSYS, at least an approximation?

### RE: Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

When you are referring to "environment temperature is about 273K" is that the temperature surrounding both vessels? are the vessels insulated, how long is and what is the dia of the piping between both tanks, I am assuming at least one valve on the piping that will probably throttle the butane.

### RE: Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

Also what do you expect for a range of mass transfer rates?

### RE: Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

(OP)

#### Quote (chicopee)

When you are referring to "environment temperature is about 273K" is that the temperature surrounding both vessels? are the vessels insulated, how long is and what is the dia of the piping between both tanks, I am assuming at least one valve on the piping that will probably throttle the butane.

#### Quote (chicopee)

Also what do you expect for a range of mass transfer rates?

I mean the environment and inside temperature would be about 273k in both vessels. The vessels do not have any relevant isolation.

I have complete freedom to design the size of the pipes but I have in mind something really small
Diameter between 1-2mm
Length of the pipe 10-20mm
I want to transfer less than 1g but this doesn't matter right now I am i just want to find a usable method to calculate this case wit acceptable accuracy.

### RE: Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

I agree with Zdas04,
you need to select a suitable method and integrate in time domain,
by the way, I would guess from your comment about pressure drop correlations that your knowledge in this field is limited, microgravity influences mainly two phases flow, see for example Measurements and correlation of two-phase pressure drop under microgravity conditions.
in my opinion it doesn't make sense to use a simulator as you'll be unable to verify the results and this is a case where a black box can produce unconsistent data,
a better approach would be to use tools as Matlab or Mathcad and write your own code, define some test cases etc.
or (perhaps a wiser solution) ask someone more competent to do the work...

### RE: Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

You might get some useful information by searching reports at NASA. http://data.nasa.gov/nasa-technical-reports-server...

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

### RE: Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

So assuming isothermal conditions, in the large vessel, you'll have compressed butane, whether "iso" or "n" is irrelevant at this point. So liquid butane is to be conveyed under pressure up the beginning of the piping where presumably you have a valve that may act as a throttling device, therefore, assume constant enthalpy before and after the valve. Past the valve the butane could start changing into a saturated vapor still under isothermal condition of 273dC. At end of piping another valve is encountered,before the small tank, and there initially butane will flash into a superheated vapor under constant enthalpy. When this small tank is being filled, its internal pressure will increase under assumed isothermal conditions; then conditions in this small tank will reach the saturated vapor line and then saturated vapor conditions will prevail inside of the small tank. The mass transfer rate of butane at saturated vapor condition will have by that time decrease substantially. When the butane quality reaches about 5% which is very close to the saturated liquid line then you will have your final condition. I think that is one scenario that you should investigate using time step analysis of Bernoulli's equations for non-compressible fluid within the large tank assumed to be infinitely large in comparison to the small tank; Bernoulli's equation for compressible fluids under isothermal condition between the discharge end of the tube and small tank; within the tube you would probably have a capillary tube such as found in small air conditioner where you could apply the Bernoulli's equations for compressible fluid under isothermal condition. Constant enthalpy reasoning can be apply at the inlet and outlet of both valves if these valves act as throttling devices.
Get a Mollier diagram for butane; The one that I found on line was for isobutane; and research the Bernoulli's equation for the conditions stated in any fluid mechanics book or Schaum's outline. You may have to assume an initial mass rate for Butane and probably have trial and error calculations in conjunction with time step analysis for which you can designate small time elements. I would also read about capillary tubes used in AC, to get an idea on pressure drops, materials used and flow rates.

(OP)

### RE: Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

This is a bit late but I know that the following link will be of help:

Numerical Study of Refrigerant Flow in Capillary Tube ...
www.iasj.net/iasj?func=fulltext&aId=67350 · PDF file

### RE: Time to transfer a certain amount of mass between to vessels (Liquid butane to gas+liquid butane)

(OP)

#### Quote (chicopee)

This is a bit late but I know that the following link will be of help:

Numerical Study of Refrigerant Flow in Capillary Tube ...
www.iasj.net/iasj?func=fulltext&aId=67350 · PDF file

Thank you. It is not to late. IT seems really interesting and useful.

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