A B737 CREW; WHILE TAXIING UNDER LIMITED VISIBILITY CONDITIONS AT IND; TURNED THE WRONG WAY ONTO THE ACTIVE RWY REQUIRING AN EXPEDITED EXIT TO MAKE ROOM FOR LNDG TFC.

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HELD AT THE GATE UNTIL XA45 (1 HR 15 MINS LATE). WX IMPROVING; PUSHED; AND INSTRUCTED TO TAXI TO HOLD SHORT OF A4 ON TXWY A FOR RWY 5L DEP. WE WERE INFORMED THAT WE WERE #5 FOR DEP BUT THE RVR WAS STILL BELOW MINIMUMS. WX WAS IMPROVING ON RWY 5R QUICKER THAN RWY 5L; SO ACFT IN FRONT OF US ON TXWY A WERE REQUESTING TAXI INSTRUCTIONS TO RWY 5R. FIGURING THAT THERE WAS ONLY 1 ACFT AHEAD OF US; AND THAT THE RVR WAS NOW 1200/500/600 FT; WE AGREED THAT WE WOULD JUST WAIT IT OUT FOR RWY 5L. I TOLD THE FO TO ASK GND THAT WHEN IT BECOMES AVAILABLE; WE'D LIKE TO CONTINUE TAXI FOR RWY 5L. TO THE BEST OF OUR RECOLLECTION; WE HEARD GND IMMEDIATELY ASK ACR Y AT A5 (IN FRONT OF US) SOMETHING TO THE EFFECT IF THEY WERE READY FOR THEIR INTENTIONS. THEY REPLIED THEY WERE NOT READY. GND THEN TOLD US TO TURN L ONTO A4 THEN RPT TURNING ONTO RWY 5L. WE ASSUMED THESE INSTRUCTIONS WERE TO TAXI AROUND ACR Y AT A5 THEN EITHER TAXI TO THE END AND 180 DEGS FOR DEP OR TAKE A7 AND CONTINUE ON TXWY A TO THE DEP END OF RWY 5L. UPON TURNING ONTO RWY 5L; THE FO XMITTED; 'ACR X; ON RWY 5L; HEADING SW.' GND THEN INSTRUCTED US TO RPT CLR OF THE RWY. A MIN OR SO LATER; GND ASKED US IF WE WERE CLR OF THE RWY SINCE THERE WAS AN ACFT ON AN 8 NM FINAL. WE TOLD THEM NO. GND INSTRUCTED US TO EXPEDITE. WE THEN RPTED WE WERE PASSING A7 JUST TO GIVE BETTER S/A TO GND IN A LOW VISIBILITY ENVIRONMENT. GND THEN STATED TO US THAT WE WERE GOING THE WRONG WAY AND TO EXIT ON A11 AND HOLD ON TXWY A. THE RVR CAME UP WITHIN APPROX 10 MINS AND WE DEPARTED RWY 5L UNEVENTFULLY. THERE WAS NO FURTHER DISCUSSION FROM GND OR TWR REGARDING A CONFLICT WITH THE TAXI INSTRUCTIONS. AT NO TIME DID WE EVER REQUEST OR INTEND TO CHANGE RWYS AND DEPART RWY 5R. THE FACT THAT 3 OF THE 4 PRECEDING ACFT REQUESTED A CHANGE IN DEP RWYS MAY HAVE LED THE GND CTLR TO ASSUME WE ALSO WANTED RWY 5R INSTEAD OF OUR ORIGINALLY ASSIGNED RWY 5L. WE THOUGHT WE WERE BEING EXTRA VIGILANT GIVING ADDITIONAL S/A CALLS TO GND TO INDICATE OUR POS AT CRITICAL AREAS OF OUR TAXIING; BUT THERE STILL EXISTED A BREAKDOWN IN COM. IT WAS OUR UNDERSTANDING THAT GND CTL UNDERSTOOD OUR REQUEST TO CONTINUE THE TAXI TO RWY 5L. WE ASSUMED HE WAS GOING TO MANEUVER US AROUND THE OTHER ACFT FOR RWY 5L SINCE THEY WERE NOT READY. GND UNINTENTIONALLY ASSUMED WE WANTED RWY 5R INSTEAD OF RWY 5L. WE DID NOT. HAD WE BEEN GIVEN A L OR R DIRECTIVE ONTO RWY 5L; THAT WOULD HAVE BEEN A RED FLAG TO US THAT GND ASSUMED WE WANTED RWY 5R AND WE COULD HAVE CLARIFIED THE MISUNDERSTANDING MUCH EARLIER. IN A LOW VISIBILITY AREA; WE NEED TO BE AS DESCRIPTIVE AS POSSIBLE. THIS COULD HAVE BEEN A VERY SERIOUS SIT. WE THOUGHT WE WERE BEING EXTREMELY VIGILANT IN THE LOW VISIBILITY CONDITIONS; BUT FROM OUR END; WE POSSIBLY COULD HAVE BETTER CLARIFIED TO GND TO THE EXTENT THAT WE WERE TURNING R FOR RWY 5L INSTEAD OF HEADING SW ON RWY 5L.