RPTR EXPERIENCES R ENG SURGING DUE TO FUEL SOURCE EMPTY. GAUGES INDICATED THERE WAS STILL FUEL IN THE TANKS.

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WHILE BEING VECTORED FOR THE APCH TO MEMPHIS WE LOST PWR ON THE R ENG AND ELECTED TO SHUT IT DOWN. THE PRIMARY CAUSE OF THIS WAS ERRONEOUS FUEL GAUGE READINGS; CONTRIBUTING FACTORS WERE A SLOWER THAN EXPECTED GND SPD RESULTING IN A LONGER BLOCK TIME AND A FLT TO NEAR THE MAX RANGE OF THE ACFT. DURING FUELING; THE TANKS WERE FILLED UNTIL THE FIRST WAS FULL; THEN THE AFT WAS FILLED UNTIL THE GAUGE ALSO INDICATED JUST UNDER 2000 LBS. WE LATER DISCOVERED THAT SEVERAL HUNDRED MORE LBS WOULD FIT IN THE AFT TANK. ENRTE WE NOTICED THAT THE GAUGES WERE SHOWING A FUEL IMBALANCE IN FAVOR OF THE AFT TANK. WE SELECTED XFEED UNTIL THE TANKS WERE BALANCED AT 1100 LBS EACH. WE NOW IN REALITY HAD SEVERAL HUNDRED LBS LESS FUEL IN THE AFT TANK. DURING OUR DSCNT CHKS WE NOTICED THAT WE HAD A FUEL IMBALANCE WITH 200 LBS MORE FUEL IN THE FRONT TANK; NOT A PROB AS WE THOUGHT THAT WE HAD PLENTY OF FUEL PLUS RESERVE. A FEW MINS LATER THE XFEED LIGHT CAME ON. WE VERIFIED THAT THE XFEED WAS CLOSED. A FEW SECONDS LATER THE R ENG BEGAN TO SURGE WITH NO ADDITIONAL CAUTION OR WARNING LIGHTS AND BOTH TANKS INDICATING SUFFICIENT FUEL. WE WERE ON A VECTOR TO THE LOC IN VMC WITH MODERATE TURB AT THIS TIME AND FELT THAT A PRECAUTIONARY SHUTDOWN WAS OUR BEST COURSE OF ACTION. WE NOTIFIED THE TWR THAT WE WERE SINGLE ENG; EVERYTHING WAS UNDER CTL AND THERE WAS NOT AN EMER. ON THE GND WE STARTED AND RAN THE R ENG OFF THE AFT FUEL TANKS AND TESTED THE XFEED; BOOST PUMPS; ETC. EVERYTHING WITH THE ENG APPEARED NORMAL; BUT UPON STARTING THE AFT FUEL GAUGE READ ABOUT 250 LBS THEN SLOWLY ROSE TO INDICATE NEARLY 500 LBS; REMAINING THERE UNTIL SHUTDOWN. I WENT AND STUCK THE TANKS TO VERIFY THE FUEL LEVELS; AND FOUND THAT THE AFT TANKS WERE NEARLY EMPTY WHILE THE FORWARD TANKS WERE INDICATING CORRECTLY. WE FOUND THAT WHEN WE FILLED THE AFT TANK FULL IT INDICATED SEVERAL HUNDRED LBS HIGH. I THINK THAT THIS PROB CAN BE AVOIDED BY PERIODICALLY MATCHING GAUGE READINGS TO STICK READINGS. WE SHOULD ALSO STICK THE TANKS WHEN SWITCHING TO A NEW AIRPLANE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED HE WAS FLYING A SHORTS 330. THERE ARE 2 FORWARD CELLS THAT NORMALLY FEED THE L ENG AND 2 AFT FUEL CELLS THAT NORMALLY FEED THE R ENG. THE COMPANY HAS A NEW PROC SINCE THIS EXPERIENCE WHEREIN THE PLTS WILL STICK THE TANKS PRIOR TO FUELING AND COMPARE THE FUEL PUMPED IN WITH THE RESULTS OF STICKING THE TANKS. THE WX WAS VMC. THE AIRPLANE WAS ON FINAL APCH. THE FUEL GAUGE INDICATED THERE WAS FUEL IN THE TANK. SO; THE FLC ELECTED TO SHUT THE ENG DOWN AND LAND RATHER THAN TROUBLESHOOT THE SURGING ENG.