FLT CREW OF B737-700 EXPERIENCE UNEVEN SPOOL-UP OF ENGS ON TKOF FROM MDW. NEARLY RESULTS IN A RWY EXCURSION.

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MDW; REJECTED TKOF RWY 31C. AFTER BEING CLRED FOR TKOF; TAXIED ONTO RWY 31C. WHILE TURNING R TO CTRLINE; PUSHED UP THROTTLES AT 1 INCH. ALIGNED WITH CTRLINE; ROLLING DOWN RWY AND STABILIZED; PUSHED THROTTLES UP FOR TKOF. ACFT IMMEDIATELY TURNED R. XCHKED N1'S AND NOTICED LARGE SPLIT --#1 NEAR TKOF SETTING AND #2 AT 40-50%. TRIED TO CORRECT TO CTRLINE (WHILE #2 CONTINUED TO SLOWLY SPOOL) USING RUDDER THEN YOKE/NOSEWHEEL STEERING. ACFT DID NOT RESPOND AND CONTINUED R TOWARD EDGE OF RWY. PULLED THROTTLES TO IDLE AND USED DIFFERENTIAL BRAKING TO CORRECT ACFT TO RWY CTRLINE. COMPLETED REJECTED TKOF PROCS; INFORMED TWR; AND WAS ABLE TO EASILY CLR RWY; USING NOSEWHEEL STEERING; AT TXWY K. OBTAINED CLRNC FROM GND CTL TO RETURN TO GATE. COMMUNICATED PROB/SIT TO FLT ATTENDANTS; OPS; MAINT AND PAX. MAINT MET ACFT AT GATE AND DEBRIEFED. IN COORD WITH DISPATCH; MDW MAINT AND MAINT CTL; ELECTED TO PULL ACFT 'OFF LINE' TO INSPECT NOSEWHEEL AND RUN #2 ENG. OFFLOADED PAX. DISPATCH ASSIGNED NEW ACFT NUMBER AND DEPARTED 2 HRS LATE. I BELIEVE #1 ENG SPOOLED MUCH FASTER THAN #2. NOT SURE WHY NOSEWHEEL STEERING WOULD NOT CORRECT BACK TO CTRLINE. MAYBE MOMENTUM? I'VE NOTICED AN INCREASED NUMBER OF ENGS NOT SPOOLING EVENLY; ESPECIALLY -300'S AND EARLY -700'S. IN THE FUTURE; I PLAN TO MORE CAUTIOUSLY PUSH THROTTLES FOR TKOF THRUST AND HOPEFULLY AVOID ANOTHER ABOVE SIT. SUPPLEMENTAL INFO FROM ACN 668565: I WOULD LIKE TO RECOMMEND THAT THIS TYPE OF SIT BE INCLUDED IN SIMULATOR TRAINING.