Aeroderivative gas turbines have been used in industrial power generation and offshore / onshore pipeline gas compression for decades. They use diesel (DF2) or natural gas. Some of the more common gas turbine (or more accurately, as someone mentioned above, gas generator) equivalents are:
Aircraft Model = Industrial Model and MW output
Allison T56 = Allison 501/517/601 3-10MW
GE CF6-6 = GELM2500/+ 25-30MW
GE CF6-50 = GE LM5000 38MW
GE CF6-80 = GE LM6000 45MW
Pratt & Whitney J75/JT4 = FT/GG 4 15MW
Pratt & Whitney JT8 = FT/GG 8 30MW
Rolls Royce Avon = RR Avon 10MW
Rolls Royce Olympus = RR Olympus 20MW
Rolls Royce RB21 = RR RB211 25-30MW
Rolls Royce Trent = RR Trent 50MW
Roughly speaking, 1MW is enough to power a city of 1000 people. 40MW, 40,000 people, etc.
Aeroderivatives have many advantages, such as high efficiency, high power v. weight/footprint which is important for offshore and marine applications, and quick start/stop with no maintenance penalty for power grid peak shaving applications.
Disadvantages over more conventional "heavy frame" type turbines are relatively expensive capital costs (offset by lower fuel burn), stricter fuel quality (contrary to previous post, they can't just burn "anything", and the specs are pretty tight due to the cooling hole technology in the hot section).
Aeroderivatives consist of essentially the "core" gas generator, without the high bypass fan. For example, a GE LM2500 is about 90% common with its aircraft cousin.
In the late 1970's, the UK oil & gas offshore sector tended to use the Rolls Royce technology, while the Norwegian sector chose mostly the GE LM2500. Today more than 100 GE gas turbines are used offshore Norway for power production and gas compression.