roker:
As you have stated, there can be multiple passes (above 2) in a U-tube heat exchanger. However, not all the partitions need be in the conventional horizontal-vertical orientation. Heck, I've had channels partitioned in a "Z" pattern. The partitioning all depends on the original design, scope, and mechanical requirements. And it is this difference in partitioning and nozzle locations that largely determine how many vents you need and where they should best be located.
For example, in a conventional 2-pass, U-tube unit you have one normal horizontal partition in the channel (or bonnet). Here, it is easy to visualize and determine that if you have liquid phases on both tube and shell side, then the smartest thing to do is introduce both the liquids at the bottom, respective nozzles: in this manner, the fluid flow induces self-venting and purging of any gases or non-condensables; these exit the unit with the product streams.
You have failed to state the phases of your fluids. I have to assume something, so I'll assume you are dealing with liquid-liquid heat transfer. In that case, you don't necessarily have an efficient vent if you install it "at the highest point of the channel". You still have inherent gas pockets in the multiple channel partitions! In fact, if you don't take care and ensure that your U-tubes are positioned without sag and with a slight upward tilt, you may create gas pockets within the U-tube (or hairpin) assemblies. This is a weak point in the normal U-tube design.
The best way to vent your channel of gases is to follow the indications above and study the mechanical assembly of your U-tube bundle. Incorporate positive flow methods (i.e. always try to use up-ward liquid flow on both shell and tube side; this works every time) and vent any and all internal channel air pockets created by the partition plates' design -- on every tube pass.
I hope this experience helps.
Art Montemayor
Spring, TX