What was found
ON DEPARTURE WE EXPEREIENCED A RED CABIN RATE OF OF CLIMB OF 1000 FPM ON THE CAS. AT 13000 MSL, CABIN CONTINUED TO CLIMB TO 5600 BEFORE WE DECLARED EMERGENCY AND DIVERTED TO TJSJ. WE WENT TO MANUAL MODE PER THE QRH AND IT DID NOT WORK. THE CABIN CONTIUED TO CLIMB IN MAN MODE. AT 3000 MSL THE CABIN BEGAN TO OVERPRESSURIZE TO -500 CABIN ALT WHICH LED TO US DUMPING THE CABIN, PER THE QRH BEFORE IT GOT WORSE. WE ALSO HEARD A VIBRATING NOISE AT THE CABIN DOOR. NO EICAS INDICATIONS SHOWING DOOR WAS UNSECURE. REMOVED OUTFLOW VALVE P/N 103922-1; S/N 103922-00225. REPLACED IT WITH A "REPAIRED" OUTFLOW VALVE P/N 103922-1; S/N 103922-00596, IAW PHENOM 300 AMM 21-31-02-000-801-A/400-801-A14. COMPLETED PRESSURIZATION CHECKS, IAW PHENOM 300 AMM 21-31-00. ALL OPERATIONAL WERE GOOD NO DEFECTS NOTED.