A B737-700 FLT LOSES OIL IN ITS #2 ENG. AFTER CONFERRING WITH DISPATCH; PIC ELECTS TO CONTINUE FLT TO DEST ARPT AT MSY; LA.

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WE HAD LEVELED OFF AT FL390 AT CRUISE FOR ABOUT 40 MINS. APPROX 125 MI FROM MSY; THE FO AND I NOTICED A RAPID DROP IN OIL QUANTITY FOLLOWED BY A DROP IN OIL PRESSURE. I ASKED FOR THE LOW OIL PRESSURE CHKLIST. IT WAS ACCOMPLISHED FORTHWITH. WE ADVISED CTR THAT WE WOULD BE NEEDING A LOWER AND DECLARED AN EMER. WE ASKED FOR DIRECT TO MSY. AS WE PULLED THE THROTTLES BACK TO IDLE TO START THE DSCNT; WE SHUT DOWN THE R ENG AS PER THE CHKLIST. FROM THE TIME WE NOTICED THE OIL PRESSURE DROPPING TILL WE HAD THE ENG SECURE WAS APPROX 30 SECONDS. WE CALLED DISPATCH AND CONFERRED THAT MSY WAS THE CLOSEST SUITABLE ARPT. THE FLT ATTENDANTS WERE ADVISED OF THE SIT WHEN WE FIRST STARTED THE DSCNT. THE PAX WERE ADVISED IN THE DSCNT AFTER ALL CHKLISTS AND ATC AND DISPATCH CALLS WERE COMPLETE. THE OPC WAS USED FOR DRIFTDOWN AND SINGLE ENG LNDG PERFORMANCE. AN UNEVENTFUL LNDG WAS MADE AT MSY. SENT THE FIRE TRUCKS HOME AND ARRIVED AT THE GATE. MADE LOGBOOK ENTRY FOR ENG SHUTDOWN AND APU NOT STARTING INFLT. TRIED THE FIRST APU START AT FL220. THIS WAS THE FO'S FLT LEG; BUT AFTER THE ENG SHUT DOWN; I ASSUMED THE CTLS.