I am replacing my shower/bath, including removing the wall that houses the vent pipe (the new unit is free-standing). To make the repiping easier, I want to redirect the tub vent pipe to merge with the vent stack for the double sink, which is about 7 feet away. My plan is for the tub vent pipe to start vertical, then almost immediately turn to run horizontal for that 7 feet, then vertical again (with some maneuvering) to merge into the vent stack for the sinks. I know vent pipes can be run horizontal as long as there is a slope, but is there a rule about minimum rise distance of a vent pipe before it can run horizontal?
Yes. The vent can't run horizontal until you've reached the overflow height of the attached fixtures. The idea is you don't want the water to backup into a horizontal section of venting and deposit debris in the event that the waste pipe clogs. If the waste pipe clogs then the fixture should overflow before water runs into a horizontal section of vent pipe.