A B737 CAPT MISUNDERSTANDS THE RWY ASSIGNED AND ENTERS THE WRONG RWY WHILE TAXIING.

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XA30 WAKE-UP; XB30 VAN PICK-UP FOR XD00 DEP. ATIS INDICATED RWY 27 DEP. NORMAL START-UP. GND GAVE TAXI TO RWY 22L. SLOW RECEIVING ACARS WX BRIEFING. I CONTACTED COMPANY ON #2 RADIO (MONITORING GND ON #1) WHILE CAPT REMAINED ON #1 WITH GND AND CONTINUED A SLOW TAXI; THEN TOLD TO MONITOR TWR. HEARD TWR SAY THAT WE HAD AN OFF TIME FOR PHL THAT WOULD EXPIRE IN 6 MINS. CAPT TOLD TWR THAT WE DID NOT HAVE WX BRIEFING SO WE WERE TOLD TO PULL INTO RWY 22L/27L PAD. I TOLD COMPANY ABOUT THE WHEELS UP TIME. JUST AFTER STARTING THE TURN INTO THE PAD; WE RECEIVED ACARS WX BRIEFING AND CAPT CONTINUED SLOW TAXI WHILE TELLING TWR THAT THE WX BRIEFING WAS JUST COMING IN. WHILE I WAS ENTERING WX BRIEFING DATA INTO FMC I HEARD A TKOF CLRNC WITH L TURN TO 140 DEGS. DURING DATA ENTRY; I MADE A DEP ANNOUNCEMENT. WHEN FINISHED; CAPT CALLED FOR COMPLETION OF BEFORE TKOF CHKLIST; WHICH I DID. UPON COMPLETION OF CHKLIST; I LOOKED OUT AND REALIZED THAT WE WERE ENTERING RWY 27L INSTEAD OF RWY 22L AND SAID 'WRONG RWY' TO CAPT. AT THE SAME TIME THE TWR NOTICED THE MISTAKE AND SAID THAT WE WERE NOW CLRED FOR TKOF ON RWY 27L IF WE WISHED. LATER; AS WE DISCUSSED THE INCIDENT; THE CAPT SAID THAT HE DID NOT MAKE A MISTAKE AS HE THOUGHT ALL ALONG THAT WE WERE TO TAKE OFF ON RWY 27L (POSSIBLE BECAUSE OF ATIS); AND MUST HAVE THOUGHT HE HEARD RWY 27L EVEN THOUGH GND HAD SAID TAXI TO RWY 22L. I THINK THIS WAS A FAIRLY NORMAL CASE OF SOMEONE HEARING WHAT THEY EXPECTED TO HEAR. THE EARLY MORNING TIME; DARKNESS; LACK OF WT AND BAL INFO WITH A TIME SQUEEZE ALL ADDED UP TO A MISTAKE. I HAD TO SPEND A FAIR AMOUNT OF TIME TALKING TO THE COMPANY AND HENCE HAD LITTLE TIME TO SPARE TO ASSIST THE CAPT; ALTHOUGH AT THAT TIME OF THE MORNING THINGS WERE PRETTY QUIET; WITH LIMITED MOVEMENTS GOING ON; SO I WAS NOT UNDULY CONCERNED. HAD WE NOT BEEN UP AGAINST AN EXPIRING TKOF TIME AND TRYING TO COMPLETE A NUMBER OF TASKS AT THE LAST MOMENT; I WOULD HAVE REALIZED A LOT EARLIER THAT WE WERE NOT GOING TO THE RIGHT RWY AND ALL OF THIS WOULD HAVE BEEN A NON EVENT.