Reaching altitude 10.000ft after a rapid descent from fl200
Cabin altitude at starting point let say 18.000ft
At this starting situation, dP= -2.7 PSI
Where did you get -2.7PSI from? If the cabin is at 18000 feet and the airplane is at FL200, the differential pressure will be about 0.6~-0.7psi (cabin pressure greater than ambient).
(I have a pressure/altitude graph showing an ambient pressure of 6.75psi for 20,000' and 10.11psi for 10,000', so 18000' is around 7.1psi.)
Assuming no leaks (outflow valves closed), the aircraft would have to descend to an altitude equivalent to 7.1 plus 1.0 (8.1 psi) before the negative pressure relief valve opened. 17,000'? The aircraft has to descend 7000 feet from this point.
I'll let the experts take it from here. I'd be guessing the rest. I don't know the size of the outflow valve so I can't compare it with the relief valve for pressure equalisation properties. The outflow valves on a
747-400, for example, can dump pressure on landing at (at least) 2000fpm
with the packs running in high flow.
I know Boeing's credibility has been stretched of late, but I'm sure they've crunched the numbers and come up with the required size and spring strength of the negative pressure relief valve.