Date: 201911
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: VMC
Light: Daylight
Aircraft: B757-200
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Climb
Airspace: Class B ZZZ
Aircraft component: Air Conditioning Distribution System
Component problem: Failed
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Second reporter function: Pilot Flying; First Officer
Anomaly: Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural MEL / CDL
Detector: Person Flight Crew
When detected: In-flight
Result: Aircraft Aircraft Damaged; Flight Crew Diverted; General Flight Cancelled / Delayed; General Maintenance Action
Contributing factors: MEL; Aircraft; Procedure
Primary problem: Aircraft

Narrative: Our aircraft was dispatched with a pitot probe heater system inoperative. (MEL 30-XX). The aircraft also had an Eng Bleed Air PRSOV write up (MEL 36-XX) which was placarded. We taxied out and took off as normal. Climbing through ~17;000 ft. we turned off the APU and shut down the left pack system as per MEL and utilizing only the right pack for pressure. We received an intercom call from the rear of the aircraft from a deadheading pilot telling us she heard something beneath her feet near the exit row mid aircraft shortly thereafter. Climbing through the mid 20 thousands; the First Officer feels pressure in his ears. We ask for a lower flight level (I think 31;000 ft.) than previously cleared (35;000 ft.) to work the problem. This is when we realized the cabin was climbing the same rate as the aircraft. We asked ATC for a lower altitude and received it. The oxygen mask was put on as we did an emergency descent to 10;000 ft. We asked for direct ZZZ and landed. Mechanical failure of pressurization ducting. Although the pitot probe heater had nothing to do with the event it is my opinion aircraft should not be dispatched without this being fixed first. Flying a transport aircraft with people on board and expecting to not fly through a cloud (icing conditions) is preposterous.


Second narrative: Aircraft was dispatched with two MEL's; AUX pitot tube inoperative and left engine Bleed Valve PRSOV INOP. The second MEL required a single pack operation using the right pack only.While in the climb through mid-FL20's to FL350 we heard an unusual noise seeming to originate from the aft of the cockpit. This was shortly followed up by a call from the cabin. A deadheading pilot related her concern about the noise.As we continued to climb we noticed the cabin rate of climb was equaling the aircraft's rate of climb and began to believe that there was a pressurization issue. While evaluating to issue we decided to level off at FL310.The cabin pressure altitude seemed to be holding around 8;000 ft. with duct pressure still showing normal from the right pack but the cabin rate continued to climb. At this time we decided to descend and was given an ATC descent to FL240.As we began to level off we noticed the cabin pressure altitude was now climbing above 8;000 ft. and asked for a descent to 10;000 ft. We expedited the decent and was given clearance to proceed directly to ZZZ2.While in the decent the cabin altitude reached the set value where the passenger oxygen masks deployed. The Captain; as the Pilot Monitoring; directed all communications with the cabin; passengers; ATC and company Dispatch. I; as the Pilot Flying put on my oxygen mask and aviated. We ran the loss of pressurization checklist and landed in ZZZ2 without further incident.


Synopsis: Captain reported that a pressurization problem resulted in a diversion.