The only respirators which would work are the bottled air type, if you haven't got a gas detector you won't know when the air is safe or not so you'll have to do the full drain in one if you want to be safe!
That's when the logistics then get interesting as you'll have to ensure you have enough air to do the drain and extra just in case the shit hits the fan. I carry a 15 minute escape set when working in confined spaces at work, it's heavy and bulky and would only be worn to escape a location due to the gas meter alerting, to do a drain with this you will need multiple bottles.
The next thing would be a hose fed respirator, you have the freedom of no bottle, but you are then attached to a hose meaning you have to come out the way you went in and are limited to how far you can go by the amount of hose you have, you will also need an extra person to change the air bottles over outside the culvert and possibly a 2 man rescue team on stand by, both with breathing apparatus too, after all safety is paramount
I tend to use common sense, if it's a culvert with open ends no issues, and concerns bail and better still if going anywhere that may be dodgy like a sewer use a 4gas or better still get a friend who owns one, but check he has it calibrated correctly by reviewing the certificate of calibration, last resorts buy a canary
Hope that helps a little?