Drilling rig with continuous microwave particulate treatment system

A drilling rig with continuous microwavable particulate treatment system for treating fluid from a wellbore on an offshore platform. The system uses a materials handling controller, a vibrating sieve device or filtering device to separate particulate from drilling fluid, a cuttings discharge collection device for continuously moving the slurry to a cuttings processing station, a treatment system controller controlling the continuous cuttings processing station that uses a microwave generator creating microwaves that heat the slurry and a plurality of non-deforming microwave heatable polishing and grinding media in a vibrating trough. The system continuously creates water vapor with oil droplets and cleaned cuttings, and a vapor recovery system is used for removing the oil droplets from the water vapor having a vapor recovery system controller in communication with the material handling controller and treatment system controller.