Bilal:
Pilesar, in my opinion, has hit the nail on the head. The important negative points coming out from the HTRI results (assuming that the data inputs were correct) show that this application is getting very expensive due to the large energy loss imposed by the large pressure drop between your 1st and 2nd stage. Losing essentially one atmosphere of pressure is causing the compressor driver to consume more energy. I recommend that you expand your project Scope of Work to include the negative effect this application can impose on your compressor and driver if you design for a high pressure drop between stages. What I normally would expect as an acceptable pressure drop between stages would be 3-5 psi. 12.5 psi, in my opinion, is not acceptable and the price to pay is expensive in driver horsepower and operating energy consumption.
In setting the physical dimensions of the cooler, did you consider the pressure drop? The HTRI printout shows a "standard" tube length of 20 feet (6 m). For fabrication economy, the longer tube length gives lower fabrication cost - but it starts to create tradeoffs such as the pressure drop and the higher velocity in the shell side (with the related entrainment). Practical engineering, as Pilesar has suggested, may call for use of finned tubes as one means to decrease the pressure drop while contributing more heat transfer area on the most difficult side (the humid air). I would follow this suggestion and try to find out if this technique works to reduce the pressure drop and ensure complete condensation of the water moisture. Here, be mindful of the clue that I gave in my previous post: "You certainly can't justify a BEW because of the need to clean the shell side." In other words, your scope of work should recognize that the compressed air, by common sense, is not a fouling or troublesome fluid. It comes from a compressor stage that is designed to handle only clean, filtered air and as such will not need any means for future cleanout. The shellside of this unit does not need any means for access or cleanout - with the exception of inspection ports. Therefore, you are free to make this large exchanger as compact as you can. The use of finned tubes should not be a source of maintenance concern or complaints.
Another way to reduce the pressure drop and related velocity might be to increase the shell diameter (your sketch does not identify this) and reduce the tube length. This will probably force you into multiple tube passes - which shouldn't be a problem, other than increasing the partitions employed in each head. Here, the available space for the unit might be affected, but you can add a lot of tube heat transfer area with relatively small diameter increases. Further HTRI runs are called for to investigate these potential options and their results.
Accept the outlet velocity that satisfies the required total heat transfer and the complete condensation or the associated water without any entrainment. I would not use outlet velocity as an HTRI input, but would let the program calculate it. I stress the need for a 2nd stage inlet separator as an additional vessel that should be included in your scope. This is normal practice and serves to protect the compressor and the integrity of intercooler. It is at this separator that you attach such items as PSVs, surge protection connections, added streams, purge facilities, drains, pressure and temperature indicators, etc. This vessel adds to the design and operability of the compressor unit.
I have used the type of condensate drain facility that you show in your cooler-condenser sketch. I have applied this design in about 10 cases in the past. But be very careful in applying this type of condensate collection and drainage because it's final physical design is subject to the operating pressure drop across the cooler-condenser. This is where Pilesar's experienced concern for the large pressure drop comes into play on a practical basis. You cannot expect to make the drain connections you show without detailed hydraulic calculations that show that the vertical legs of each drop will remain sealed during operation. Common, practical sense should tell you that if you are expecting a pressure drop of an atmosphere between the first condensate drain leg and the last one, then the difference in condensate height between both legs will equate to the pressure drop. This could be quite considerable and call for a cooler-condenser installation height that is ridiculously too high for economic, safety, and practical reasons. Pilesar's advice calling for attention to reducing the pressure drop is more than warranted for this additional reason. The ten cases where I have used this type of design all were as cooler-condensers for the overheads streams from stripper towers - most of which were using MEA solution for CO2 removal. The units were quite large - approx 16 ft long x 30-36 ft diameter, done using a slide rule and no HTRI. The average pressure drop I allowed in these units was approx. 1-2 psi and I allowed for sufficient elevation to allow multiple drains on the shell while maintaining a water seal in each. If you don't maintain a positive seal on each drain, you will obviously create a convenient gas bypass from the high pressure shell side to the low pressure side, and not have any cooling of this bypass, humid gas. You can't tolerate this type of operation.
Again, follow Pilesar's recommendations closely and I am crossing my fingers, hoping that we also hear from SrFish (Dale Gulley) on this thread. Keep us posted with your return comments and missing data - like the diameter and additional related equipment you need like the 2nd stage suction drum.