Heat vegetable oil in a frying pan over medium heat then brown the pork chops on both sides, 5 to 8 minutes per side. Place the chops into an oblong baking dish. In a saucepan, whisk together the cream of chicken soup, cream of mushroom soup and milk until smooth. Stir in the rice then add the butter; bring the mixture to a boil over medium heat then stir until the butter has melted. Pour the rice mixture over the chops; cover the dish with foil.
Bake in the preheated oven until tender, about 2 hours.