FLC DEPARTS FROM WRONG INTXN.

Narrative

AFTER A LONG AND FRUSTRATING DAY; WE TAXIED OUT FOR THE LAST LEG OF OUR DAY. RWY IN USE WAS RWY 9L. TAXIING W ON TXWY K; BEFORE K5; WE WERE CLRED INTO POS AND HOLD. LOOKING TOWARDS THE END OF THE RWY; I SAW THE LIGHTS OF K6. KNOWING THAT THERE'S A TXWY Y THAT GOES AROUND THE END OF RWY 9L; I MISTOOK K6 FOR THAT TXWY AND ENTERED THE RWY FROM K5; THINKING IT WAS K6. I DIDN'T REALIZE THE MISTAKE UNTIL AFTER BEING CLRED FOR TKOF AND INITIATING THE TKOF ROLL. AT SOME POINT DURING TKOF; I REALIZED THAT I HAD DONE THIS AND WAS NOW TAKING OFF ON A RWY LENGTH OF 9000 FT INSTEAD OF 9500 FT. I KNEW THIS WOULD NOT BE A PERFORMANCE PROB; AND IT WAS NOT. THE REAL CAUSE OF THIS MISTAKE WAS MY FATIGUE. I GUESS THE FO WAS FATIGUED TOO; BECAUSE HE DIDN'T REALIZE WHAT I WAS DOING EITHER. PART OF THE FATIGUE WAS CAUSED BY A LONG DAY OF FLYING. ALSO CONTRIBUTING WAS THE FACT THAT MORALE IN MY AIRLINE IS VERY LOW; AND THIS SHOWS UP IN ENCOUNTERS WITH OTHER EMPLOYEE GROUPS DURING A DAY'S OP. I DON'T REMEMBER THE SIGNAGE; BUT IT CERTAINLY DIDN'T JUMP OUT AT ME. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR SAID THE ACFT WAS A DC9-30. THE SIGNS WERE STANDARD BUT THE ARPT DESIGN IS UNUSUAL IN THIS AREA. THE TXWY AFTER PASSING K6 LEADS AROUND THE END OF RWY 9L TO RWY 9R. AN 'END RUN' SO TO SPEAK. IF THE PLT PASSES K6; THE TXWY COMMITS THE PLT TO RWY 9R. SOME WORDING THAT WOULD INDICATE 'LAST CHANCE FOR RWY 9L' OR 'IF YOU PASS THIS TXWY YOU ARE ON YOUR WAY TO RWY 9R' WOULD PERHAPS BE HELPFUL.