Compression of a gas results in an increase in its temperature. The compressed gas is very hot and the goal is to get it very cold. One is able to reduces the size of the cooling tower by getting the hot, compressed as cold as possible before it enters the tower. One could build a small refrigeration units or use dry ice. The simplest I found was using an ice bath. If the ambient temperature is low enough one can just use the outside air as a heat sink.
One needs a device that will allow for an effective heat transfer. Below is a simple precooler that I used. I made temperature measurements with and without the precooler in order to determine how rate of temperature drop at the throttle. There was a significant increase in dT/dt with the use of the precooler.
Basically, the precooler is a long coil of tubing. I used 20 feet of 1/4" 304 seamless stainless steel with a 0.035" wall thickness. Again, one could go to 0.027" wall, but this got too thin for me. I did not want a wall rupture at 3500 PSI. I added 0.016" thick aluminum fins which increased dT/dt even further. I carefully drilled a hole 1/64" smaller than the tubing. I then cut the square and snapped the fin in place. I can then submerse the cooler in an ice bath or expose it to sub-freezing outdoor temperatures if possible.
Coil of tubing
Coil with 0.016" thickness aluminum fins.
Below is a ring-roller that I used to fabricate the coils. I mounted this onto a work-bench and was able to shape the coil by hand. You can refer to the video and see me using this.