LJ35 CREW HAD A RUNAWAY ENG THAT REQUIRED AN INFLT ENG SHUTDOWN IN CARIBBEAN EXTENDED OVERWATER OP.

Narrative

WHILE DSNDING FROM FL430 TO FL410; I RETARDED THE PWR LEVERS TO REDUCE AIRSPD. AT APPROX FL425 THE R ENG REVERSED COMMAND OF MY INPUT AND HEADED TOWARDS AN OVERSPD TREND. I SHUT OFF THE ENG USING THE PWR LEVER IDLE/CUTOFF DETENT AND THE PROB WAS RESOLVED. TOLD ZMA IMMEDIATELY AFTER SHUTDOWN THAT WE HAD TO SHUT DOWN THE R ENG AND NEEDED TO DSND TO FL250 IN ORDER TO MAINTAIN AN ALT WHICH PROVIDES SAFE SINGLE ENG OP SPD AS WELL AS AN ALT WHICH IS WARMER AND CAPABLE OF AIR START. AT FL250 WE ENCOUNTERED CLOUDS AND ICING SO WE IMMEDIATELY GOT APPROVAL FOR FL210 WHICH WAS VMC. WE WERE ABLE TO START THE R ENG BUT SHOWED ANOTHER TREND TOWARDS UNCTLABLE PWR LEVER INPUTS. BY NOW WE WERE 100 NM FROM OUR DEST WHICH WAS ZZZ. DECIDED WE WOULD FLY SINGLE ENG TO ZZZ WHERE I HAD OUR DISPATCHER SET UP CUSTOMS. WE WERE COMING FROM ZZZ1; DID ALL APPROPRIATE CHKLISTS; AND REHEARSED PROCS FOR OTHER EMER OCCURRENCES WHICH COULD HAPPEN WHILE FLYING SINGLE ENG. I NEVER ACTUALLY DECLARED AN EMER BUT ZMA KNEW OUR SIT AFTER SHUTDOWN AND LET US CONTINUE DSNDING. LANDED UNEVENTFULLY AND FOUND OUT THAT A FUEL COMPUTER PROBE MUST HAVE HAD MOISTURE IN IT BEFORE WE TOOK OFF AND FROZE AT THE HIGH ALT WHICH CONFUSED THE FUEL COMPUTER. WAS CLEANED OUT AND HAS BEEN FLYING FINE SINCE THE INCIDENT.