I actually managed to do this the other day. Two zones are too close, and their areas kind of connect (in that place between two rocks that kind of make a canyon and a little further north), and I believe the minerals that happen to be in that "shared" area register for both mining zones. So you have to be really careful and finish one zone and then another. And yes, they are of normal size, not small, but because of the glitch with computer it may show that you are out of range.
So, I started with the southern one and went from left to right, from border to border (including mountains on the left and behind it), moving from South to North and mining everything I found. Thus I moved toward those rocks/cliffs/canyon thing (tops of the cliffs included) and I believe the last mineral for this zone was exactly in that "shared" area (and there was a lot of something). I mined it and SAM said that the zone was depleted, but the computer still showed "fair". I checked the map - the southern icon was blue.
Then I started working on the northern one. I explored the area behind mountains on the left and that camp with bad guys further north (it happen to be in the area of mining zone as well). And then finally I found that one mineral I was looking for somewhere on the road in the middle between the northern mining zone icon and that camp with exiles (it is not on the map). There was a lot, like full scale or whatever, of copper (Cuprum). After mining it that zone was depleted as well.
The minerals are probably placed randomly each time you reload though, so I'm not sure if my locations will help you or anyone. But maybe :3
And I hope my description is not terrible and you will be able to understand what I meant ^_^"
