A B767-300 DIVERTED TO A DOMESTIC ARPT WITH A SOUTH AMERICAN DEST BECAUSE OF DECREASING OIL QUANTITY.

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LEFT ZZZ2 WITH 16 QUARTS OIL IN R ENG. AS WE PROCEEDED S THE OIL CONTINUED TO DROP. BY ABC WE HAD DROPPED TO 9 QUARTS. I CALLED DISPATCH AND INFORMED THEM OF THE BURN RATE (ABOUT 1 QUART/HR) AND TOLD THEM I DID NOT THINK WE HAD ENOUGH OIL TO MAKE IT TO ZZZ3 (ANOTHER 7 HRS). HE CONFERENCED US WITH MAINT WHERE WE LEARNED THE ENG WAS ON 'OIL WATCH' AND THAT THE PREVIOUS RATE OF CONSUMPTION WAS .6 QUARTS/HR AND THEY WERE TRACKING IT. THE ENG HAD BEEN ON THE WING FOR 8 YRS! ALL THIS WOULD HAVE BEEN NICE TO KNOW BEFORE WE LEFT ZZZ2. THERE WAS A DISCUSSION OF STOPPING TO ADD OIL (WE HAD JUST PASSED OVER PANAMA) AND GO. THAT WAS NOT GOING TO WORK BECAUSE THE ENG WAS GOING OVER THE CONSUMPTION LIMIT (QUART/HR) AND WE WOULD NOT TAKE OFF WITH A SICK ENG. WE WERE GETTING READY TO GET ON THE OTHER SIDE OF THE ANDES AND OUR OPTIONS (SINGLE ENG) WERE GOING TO BE EXTREMELY LIMITED WITH SANTA CRUZ (THE NEAREST FACILITY WITH ANY TYPE OF ACFT; CREW AND PAX SUPPORT) STILL 3 HRS DOWN RANGE; IN THE MIDDLE OF NOWHERE. MAINT; DISPATCH AND I ALL AGREED ZZZ WOULD GET THE PLANE; PAX AND THE CREW BACK TO CIVILIZATION WHERE EVERYTHING COULD BE TAKEN CARE OF FROM PLANE TO PAX; WE HAD THE OIL TO GET THERE AND DIVERTED TO ZZZ UNEVENTFULLY.