It will have as much to do with the airfield surface as the tyres. Airfield surfaces are usually very abrasive - the better to help plane tyres grip. And they do tend to shred tyres. I've done a couple of events organised by Chelmsford Motor club at West Raynham airfield. It's run as a series of short tests around the airfield, most quite tight. A typical event mileage might be only 20 miles. I've gone from 5mm to illegal doing that (lots of power understeer, handbrake turns - generally hooning around like the topgear people, but at lower speeds). Most people take at least 1 set of spare tyres. This year the event is running again, but I'm not competing as I don't want to risk an illegal drive home (I haven't got any spare wheels for my current car) If you're planning on lots of powersliding, donuts etc, then you may well get through a set of rear tyres.
If you can find out the wheel sizes (as in wheel bolts pattern), get hold of some wheels and tyres from a scrappy. Who cares if they are illegal if you're only using them on an airfield. Most wheels are 4 or 5 stud, with something called the PCD describing the diameter of the circle the bolts are on. Common sizes might be 4x100 (ie 4 holes 100mm PCD) or 5x114.
Other tricks - swap the front and rears halfway round as the driven wheels will wear faster. And if you can't get hold of any spares, keep a close eye on the tread and stop when you get down to 2mm!
Have fun!