If you are at the infinite stage of the game, with at least some research going into mining productivity, and are increasing the capacity of your factory at a steady rate (e.g. 100 spm per hour), then you don't need to place any more mining drills: the increase in mining productivity is exactly enough to supply the increased demand.
The proof of this is left as an exercise for the reader
. Of course, you do have to increase the capacity of the infrastructure transporting the mined ore, and you do have to move drills from exhausted patches to new ones; but no new drills are required. The faster you are expanding, and the lower the fraction of your research that is going into mining, the larger the required number of drills; but once you have enough for your chosen rate and fraction, that's it, for however long you keep going.