Ahh, Sorry about that. It's unusual for someone to inquire about that level of detail on gun design.
All gas ports are a compromise because the powders and bullet weights and therefore the pressure and pressure dwell times on the barrel side of the port have some range. The gun has to run with the lowest port pressure impulse and not be damaged by the highest. So, the first thing you would need to know is what the barrel pressure at the port location is over the time between when the bullet base passes over it and when the bullet exits, and to know that for the full range of loads expected to operate the gun properly?
The next thing you would need to know is how much force needs to be applied over what period of time to do the work of running the operating mechanism through a cycle? The gas available will start out entering the port fast and wind down after the bullet exits and gas starts to bleed backward through the gas port (assuming no valve is present as the M14 cylinder creates)? In the case of gas impingement systems, how much force is needed to impart enough inertia to compress the springs and still drive the bolt back all the way? That's your starting data.
Next you need to calculate the area the gas pressure works against so you can divide it into the required force to find the pressure needed to work the mechanism. Once you know how much pressure you need, calculate the volume of gas needed to create that pressure in the volume of your gas system.
Once you know how much gas you need, you can calculate the size of the hole. Treat it as a short pipe. Calculating the gas flow through the port isn't too bad with all the on-line calculators available. This one
may help? You will have to guess at gas temperature here.
The easiest thing, if you just want to replace a barrel, is to buy a set of wire gauges and measure the existing gas port diameter. Drill something a bit smaller initially to see if it works OK with your ammo? Buy a set of number drills so you can enlarge it in small steps from there.