# How to approach a vertical gas flow situation - vapor into condenser

I am trying to understand how best to analyze the following situation:

I have solvent vapor rising from a vessel into a condenser, condensing, and then flowing out as a liquid back into the vessel. I’m interested in understanding what type of analysis I should do to determine if a given pipe size is sufficient for the vapor leg. One point of confusion I have is how buoyancy factors into this situation.

My initial thought is, using operating temperatures, calculate the vapor pressure of the solvent at the vessel and condenser (T_vessel > T_condenser) and use that difference in temperature as the driving force, assume some pipe size, and work back to a flowrate and see if that flowrate makes sense. I’d have to make some other assumptions like laminar flow and what Fanning friction factor I wanted to use. I’m also ignoring any effects from height change and I don’t know if that’s plausible; I’m thinking the height change is in the 10’s of feet type of range and my pressures will be relatively low.

The pressure in the condenser is usually fixed by there being a vent to atmosphere on the cold end, or a line to a vacuum/pressure control system. A flow velocity of 20 to 50 ft/s up the vapor leg generally requires only an inch or two of water gauge pressure drop. This very slightly higher pressure in the column or kettle is all that is needed to get the vapor to flow to the condenser and I have never seen buoyancy taken into account.

In a typical industrial condenser you are very unlikely to find laminar flow in the vapor leg. It is usual to ignore height change effects.

Is there a liquid seal on the wet end so the vapor pressure difference ( @ T_vessel - @ T_condenser ) can be utilized for fluid flow?

I’m not certain I understand what you mean by liquid seal. Do you mean if I am keeping the liquid end of the condenser at some liquid full height so that the liquid leg always runs full? If yes, then that is my current thought. Since I don’t have process specifics, I am assuming I will have enough vapor coming up that I could keep a couple inches of level in the condenser with a control valve or orifice.

Thanks for the response. I was assuming laminar flow because I was assuming a relatively low volumetric flow rate (yet enough that I could maintain some level inside the condenser). I don’t think the situation I am designing for is something abnormal, so I will try the velocities you mentioned to see what results I get.

I typically assume height changes are negligible in the types of gas flow problems I normally encounter (high pressure, moderate to high flows) but this being a low pressure situation, I was thinking that assumption may not hold.

If the vapor is not separated from the circuitous loop from the vessel to the condenser (dry leg) and back to the vessel again (wet leg) with a liquid seal, the bulk fluid flow cannot be established because everything is at the same pressure and all you have working for you is diffusion, which is a much slower process.

The important section where you need to keep a liquid seal is where the liquid return re-enters the vessel. The reason for this is that you do not want vapor trying to go up the liquid return leg (which can cause flow and vapor hammer problems). This seal can be achieved either with a U-trap outside the vessel, or by entering below the liquid level in the vessel - whichever is more convenient. Putting valves and controllers in the return leg is usually an unnecessary expense and complication. Gravity is all you need to get this liquid to flow because the pressure difference between the condenser and vessel will be a matter of inches of water column.

I always size the liquid return leg for self-venting flow. Some may regard that as overly conservative, but it works.

The only instance I have found for gas flow where it is necessary to take the change in height into account is for low pressure gas mains in highrise buildings. The low density of the gas (inside the pipe) compared with air (outside the pipe) means that the gauge pressure in the gas pipe increases as you go up the building and some appliances are sensitive to this.

Ok, I get what you two are saying about the liquid level. I was thinking if the level was built up in the condenser via a flow restriction on the outlet that would be enough; having a small U-trap should be doable. I’ll have to do some math for the self venting line and see if the lead would be okay with that - some of the possible vessel sizes that are being thrown around are kind of small so there may be some conflict.

@katmar - I never thought about that situation before, thankfully it does happen so you don’t fill the gas main with air from your apartment!

I installed some instruments on a boiler for a lumber kiln.
The steam coils were at a higher elevation than the boiler.
One large pipe connected to steam drum to the steam coils.
The steam filled the coils and condensed. The water drained back into the boiler through the same pipe.
With the difference in specific gravity between water and steam, gravity was the driving force.
There was little need for makeup water and no condensate pumps were needed.
No control valves were needed.
The temperature in a lumber kiln is fairly forgiving.
The temperature was controlled by turning down the boiler firing rate.