The measure would set aside about $65,000 for the state Health Department to monitor a pilot project and develop standards.
The House approved the measure 87-6 on Tuesday. The Senate endorsed the bill earlier.
Companies targeting the rich Bakken shale formation in western North Dakota drill down nearly two miles then angle the well sideways for about another two to three miles. Oil drillers are left with some two dozen semitrailer loads of drill cuttings that either have to be stored on site or dumped in a landfill.
State Environmental Health Chief Dave Glatt says the idea has promise if it can be done in "an environmentally safe manner."