Date: 201812
Local time of day: 1801-2400
Location: ZZZ.Airport, US
Light: Daylight
Aircraft: B737-700
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Cruise
Aircraft component: Pressurization System
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Pilot Not Flying; Captain
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Human factors: Troubleshooting
Second reporter function: Pilot Not Flying; First Officer
Anomaly: Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural MEL / CDL; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Overcame Equipment Problem; Flight Crew FLC Overrode Automation
Contributing factors: Aircraft; Procedure; MEL
Primary problem: MEL

Narrative: We arrived in ZZZ and swapped to aircraft XXX. This aircraft had two MELs; one was the number two engine anti ice cowl valve failed in the open position. The other was the number one engine bleed air shut-off valve (PRSOV) was closed. This MEL was added in ZZZ as the previous crew made a logbook entry for left engine bleed trip. The number two engine anti-ice valve was locked in the open position and high stage valve was locked closed per MEL SP #30 - Ice and Rain Protection. We were dispatched at FL250. During cruise flight we were directed by ATC to slow to 260 knots. As the throttles moved towards idle; the cabin altitude began to climb at 3000 fpm. I pushed the power up and regained control of the cabin altitude. During descent into ZZZ1; I maintained approximately 1000 fpm descent rate. This maintained control of the cabin altitude. The APU was started and at 17;000 FT; we powered the left pack with the APU. The rest of the descent was normal.


Second narrative: The aircraft we operated had two separate MELs. One was the #2 engine cowl anti-ice valve was stuck open. The other was number one engine bleed air shutoff valve was closed. The MEL for the anti-ice valve requires that the high stage valve be manually locked closed; leaving only low pressure air. We operated the aircraft in the bleed configuration specified in the MEL for the entire flight; and all was well until we started our descent into ZZZ1. Once the aircraft commenced an idle descent; the cabin started to climb at a rate of approximately 3000 fpm. The Pilot Flying decreased the rate of descent of the aircraft which added power to the engines. Once the engines came out of idle the cabin rate returned to a normal indication of approximately 500 fpm descent. It is my opinion that the combination of these two MELs does not provide sufficient bleed air maintain cabin pressurization while the engines are at idle. With the left bleed closed and the right limited to low pressure; there simply was not enough bleed pressure to keep the cabin pressurized. The flight was planned at FL 250 per the MEL; and it was leaving this altitude on our initial descent when the problem arose. Once below 17;000 FT we operated the left pack off of the APU and cabin pressurization was normal for the remainder of the flight. It is my opinion that this aircraft should have been removed from service in ZZZ instead of operating revenue flights. If the aircraft had to be flown; I believe it should have been limited to 17;000 FT and required the APU to be used to provide bleed air to the number one pack (and only to ferry it to a suitable maintenance facility).


Synopsis: B737-700 flight crew reported 2 MELs that when combined did not provide sufficient bleed air to properly pressurize the aircraft during descent.