What was found
LOSS OF CABIN PRESSURE AT 16,000¿ AND CABIN ALTITUDE AMBER CAS MESSAGE. AFTER DEPARTING FROM NASSAU TO MIAMI AT APPROXIMATELY 16,000 FEET, WE HEARD A LOUD BANG IN THE AIRPLANE FOLLOWED BY A LOSS OF CABIN PRESSURE SLOWLY RISING AT 500 FOOT A MINUTE AND WE STOPPED THE CLIMB. WE INFORMED ATC OF OUR SITUATION AND REQUESTED A DESCENT BACK TO 10,000 FEET AND GIVING US THE CABIN ALTITUDE AMBER CAS MESSAGE. WHILE DESCENDING WE OBSERVE THE CABIN CONTINUE CLIMBING UNTIL IT EVENTUALLY MET OUR ALTITUDE AT 10,000 FEET. APPROACHING MIAMI WE HEARD FURTHER NOISES ACCOMPANIED WITH LOUD RUSHING AIR SOUNDS. WE WEREN¿T SURE IF WE HAD A WINDOW STARTING TO GO OR SOMETHING ELSE STRUCTURAL HAPPENING TO THE AIRPLANE SO WE DECLARED AN EMERGENCY AND ASKED FOR PRIORITY HANDLING INTO MIAMI. UPON REACHING MIAMI DURING POST FLIGHT INSPECTION WE FOUND THE DUCT GOING INTO THE COOLING TURBINE HAD BLOWN OFF AND COME DISLODGED FOUND DUCTING FROM AIR CYCLE MACHINE TURBINE DETACHED. TECHS REINSTALLED DUCTING TO AIR CYCLE MACHINE IAW AMM 21-21-00. ACCOMPLISHED PRESSURIZED OPS CHECK WITH APU. OPS CHECK GOOD.