What was found
LEFT ENGINE ENGINE COMPRESSOR STALL: AFTER DEPARTURE AND DURING THE INITIAL CLIMB THROUGH APPROXIMATELY 5000 FEET. THE LEFT ENGINE HAD A SUDDEN LOUD BANG, FOLLOWED BY HEAVY VIBRATION IN THE LEFT ENGINE. NO INDICATION OF FIRE OR OTHER TYPE OF MALFUNCTION WAS PRESENT ON THE CAS SYSTEM. AT THE TIME OF THE LOUD BANG AND VIBRATION I NOTED THE LEFT ITT EXCEEDED 950° BOTH THE INDICATOR AND TEMPERATURE INDICATION TURNED RED. THE VIBRATION WAS STILL PRESENT EVEN AFTER A FEW SECONDS I.E. ELECTED TO REDUCE THE THROTTLE TO SEE IF WE COULD LESSEN THE VIBRATION. THE VIBRATION WAS STILL PRESENT AND THE ENGINE DID ROLL BACK TO 30% N1. HOWEVER, SHORTLY AFTER WE NOTED, THE LEFT ENGINE WAS IDLING AT 60% N2. THE VIBRATION WAS STILL PRESENT, EVEN AT FLIGHT IDLE. WE ELECTED TO DO AN IN-FLIGHT ENGINE SHUT DOWN. WE DID SHUT DOWN THE LEFT ENGINE. AFTER THE ENGINE WAS SHUT DOWN, WE RETURNED UNEVENTFULLY TO WEST PALM BEACH. UPON EXITING THE AIRCRAFT LATER, NO DAMAGE OR DISCOLORATION OR ANY OTHER DAMAGE WAS NOTED ON THE ENGINE COWLING NO FLUIDS WERE LEAKING OR STAINING THE EXTERIOR OF THE COWLING. REPLACED LH ENGINE. OPS CHECK GOOD. IAW CE-680A AMM 71-00-05 AND PW306D1 EMM 71-00-00.