How can I increase my fuel rate?

You increase the fuel production rate by upgrading the Oil Wells, building new ones when you can (upgrade the base). You can station a hero at the oil well and use skills to increase the rate also.

Also you can do the appropriate research under City Development. and others to increase the production rate and give you rapid production as well.

Alliance technology research/donation can also be used to give all members improved production rates, although only at a small percentage.