A B737-700 DEVELOPED A FUEL LEAK NEAR THE #1 ENG INFLT. AN EMER WAS DECLARED AND FLT DIVERTED TO NEARBY ARPT.

Narrative

AT FL380 APPROX 15 MINS AFTER DEPLETING CTR TANK FUEL AND SWITCHING OFF CTR TANK PUMPS; WE DISCOVERED A RAPIDLY PROGRESSING IMBAL OF THE #1 TANK. WE ALSO NOTICED OUR ARR DEST FUEL WAS ABOUT 3000 LBS LESS THAN PLANNED. WE ALSO DISCOVERED OUR XING FUEL AT ZZZ WAS APPROX 3000 LBS LESS THAN PLANNED. AT THAT TIME WE CALCULATED THAT OUR PER MIN BURN RATE ON THE #1 ENG WAS SEVERAL HUNDRED LBS GREATER THAN THE #2 ENG. I ALERTED THE FLT ATTENDANTS AND ASKED THEM TO LOOK FOR EVIDENCE OF A LEAK BY LOOKING OUT THE OBSERVATION WINDOW IN THE BACK OF THE ACFT. THEY RPTED A MIST OF SOME KIND FOLLOWING THE CONTOUR OF THE ACFT ON THE #1 SIDE AND NOT PRESENT ON THE #2 SIDE. AT THAT TIME I DECLARED AN EMER AND ASKED FOR VECTORS TO LAND AT ZZZ. WE FOLLOWED THE QRH FOR AN ENG LEAK. AT APPROX FL180 I ELECTED TO SHUT DOWN THE #1 ENG AS PER THE QRH AND TO PREVENT A POSSIBLE FIRE. I CHOSE TO WAIT TO SHUT DOWN THE ENG AT FL180 SO AS TO HAVE THE OPTION TO LEVEL OFF IN CASE OF A TFC CONFLICT. I NOTIFIED DISPATCH. WE WERE VECTORED FOR THE VISUAL TO RWY 16R AND LANDED WITHOUT INCIDENT.