rough estimate of bubble velocity

[gmorin]

I have an interesting problem.

I have a tank with oxidation air injected at the bottom. I need to make a rough estimate of the change in the level of the tank when the blower trips offline.

I know the flow rate of air entering the tank, but I do not have how much time that an average air bubble remains in the fluid before rising to the surface. That would directly affect the fluid level upon a trip.

On the surface, it's a simple buoyancy problem - gravity versus friction. I have the level, density, temperature, viscosity etc. of the fluid. If the bubble were a ping-pong ball with a defined diameter, no problem. Of course, the bubble is expanding and presumably breaking up as it rises

I've found bubble formulas I could use, except that I have no way to estimate the diameter of a typical bubble & how it might break up.

Does anyone out there have a way to estimate either bubble velocity or diameter???

Thanks

Greg

 

[25362]

You may find some help "googleing" around, if you better define your situation, including the type of sparging used, tank dimensions, and whether there is any kind of mechanical agitation to reduce the air bubble sizes to improve oxygen transfer. Data are generally given in m²/m³ of bubble surface per unit volume of tank.

 

[m777182]

Bubble size depends on equipment you are using to distribute gas in a liquid. As far as I remember the highest bubbles surface area per volume can be achieved by gas injector and an agitator for macro mixing.
m777182

 

[btrueblood]

gmorin,

As a first approximation, assume that the injection velocity of the air is low (i.e. on the order of the terminal rise velocity of the bubble), and assume that the bubble diameter is equal to 1 or 2 times the injection orifice diameter.

I have seen some data or analysis somewhere that related the breakup of bubbles to the ratio of viscous shear forces (caused by friction b/n bubble and liquid) to surface tension forces. Surface tension forces decrease with increasing bubble size, and shear forces increase with increasing bubble size, so there is an upper limit...wish I could recall the paper, but it's been awhile.

One other caveat to your analysis - as the volume fraction of air increases, the downwards flow velocity of the liquid near the bubble increases. Imagine a 1" diameter vertical tube, with a 0.1" diameter bubble rising through it; then imagine a 0.9" diameter bubble rising through it. "Wall effects" become significant at some point is my point.

 

[saxon]

gmorin, volume flow is volume flow (cfm). Cut off the flow, volume goes to zero. Convert gas volume to liquid volume and this is the volume you lose.

Hope this helps.
saxon

 

[gmorin]

Thanks for the input.

I think a little better problem definition is in order.

This is a power plant with a forced oxidation SO2 scrubbing system.

My vessel is large (infinite wrt bubble size) - 63 ft in diameter. My liquid level is 50ft or so. Bubble expansion as it rises may be a significant effect.

The scenario I'm trying to get a handle on is just before I have a black plant outage. The air from the oxidation system is injected at the bottom. There are side agitators which will turn off when I lose power. Pre-outage, I should have small, evenly distributed bubbles.

Comparing the condition pre-trip and say 20 minutes after a trip, the amount of liquid should be the same, but my bubbles will have risen to the surface and exited, dropping my liquid level accordingly.

Stating my problem a different way, I need to estimate the typical residence time of the air in my vessel.

 

[Cockroach]

I had a problem like this once, needed to know leakage by a seat on a Grove 4.0 diameter Model B-4C valve. In valving there is an acceptable leak rate after usage provided the valve is factory bubble tight during inital inspection.

Using an inverted tube from the downstream blind flange, I collected a volume of gas in a graduated cylinder inverted in water. Given a specified amount of time, I deduced the leak rate as volume per time, as well as volume. I sat there to count the number of bubbles in that amount of time, also giving me the "average" bubble volume. Assuming the bubble is a perfect sphere, the diameter can be easily found.

It is crude, but statistically speaking, I found errors such as variation in bubble size, number of bubbles per given time, volume of gas collected, etc, to average out quite well over a large number of runs. One thing you need to watch is the hydrostatic head introduced by your collection method and try to keep temperatures as constant as possible since gas expansion plays a key role.

Hope this helps to give you some insight. Good luck!

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[btrueblood]

Greg,

Okay, can you estimate the bubble size at the injection site? I.e. what size of hole does the air go through?

There is an upper limit to bubble velocity, check out

http://www.bubbleology.com

-- I'd forgotten this, but have heard of the same information from a WWII-era source.

So, make some assumptions - air injected at depth x, bubble size d, rises under Stokes' law (as you hinted at in first post) until the bubble diameter reaches the critical size of (from website) about 0.1" diameter, at which point the velocity won't change (even if the diamter continues to increase). You should be able to "bound" your problem with a few educated guesses at initial bubble size.

This assumes that you can't just directly experiment to find your answer -- which I assume you can't otherwise why try to calculate it? If you can, let us know, and we can all give you lots of advice for that too!

Ben T.