FLT CREW OF CITATION X CROSSED RWY 15R AT BWI WITHOUT CLRNC.

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MY COPLT AND I WERE FLYING 2 PAX FROM BWI TO ORL. WE WERE TAXIING FROM FBO TO RWY 15R. DURING THE TAXI; GND CHANGED OUR TAXI CLRNC TWICE TO HELP ACCOMMODATE OTHER ACFT MOVING ON THE GND AS WELL AS TO PROPERLY SEQUENCE US AT THE RWY. WHILE TAXIING ON RWY 22 OUR FINAL TAXI CLRNC WAS TO TURN R ON TXWY C; L ON TXWY P AND TAXI TO RWY 15R. AT THAT POINT TXWY P RUNS PARALLEL TO RWY 10; HOWEVER I BELIEVED IT TO BE RWY 15R. ABOUT 100 YARDS FROM WHERE WE ENTERED TXWY P THE TXWY MADE A 90 DEG R TURN TO PARALLEL RWY 15R. THE TXWY ON THE OPPOSITE SIDE OF RWY 15R IS LABELED 'R.' I READ IT AS P AND; AFTER CHKING FOR TFC AND CONFIRMING WITH THE COPLT THAT WE WERE CLRED ALL THE WAY TO RWY 15R I CROSSED RWY 15R BELIEVING IT TO BE A DIFFERENT RWY. AT THAT POINT; THINKING I WAS GOING TO TURN R; COPLT PUT HIS HEAD DOWN TO CHK THE CHART AND CONFIRM OUR RTE. HE DID NOT REALIZE I HAD CROSSED THE RWY UNTIL WE WERE ON THE OTHER SIDE. WE STOPPED THE ACFT AND JUST AS WE REALIZED WHAT HAD HAPPENED; WE GOT A CALL FROM THE TWR INFORMING US WE HAD CROSSED THE RWY 15R. WE ACKNOWLEDGED THAT WE REALIZED WHAT WE HAD DONE. THE TWR GAVE US NEW TAXI INSTRUCTIONS TO RWY 10 AND TOLD US TO PLAN ON RWY 10 FOR DEP. NOTHING ELSE WAS SAID. CONTRIBUTING FACTORS: DUTY DAY: STARTED DAY AT XA30 IN OAK FLEW TO PWM AND WAS BRIEFED THAT WE WOULD BE DONE FOR THE DAY AT PWM. ON ARR PWM WE WERE REASSIGNED TO FLY PWM; BWI; ORL. WE DEPARTED BWI AT XC06 AND ARRIVED IN ORL AT XM00. WE DID NOT HAVE AN OPPORTUNITY TO EAT OUR MEALS UNTIL WE REACHED THE HOTEL AT XN10. THAT'S A TOTAL OF 12 HRS AND 40 MINS WITHOUT A REAL MEAL. TAXI CLRNC: FROM THE TIME WE LEFT THE CHOCKS TO THE TIME OF THE INCIDENT; WE RECEIVED 3 TAXI CLRNCS: OUR ORIGINAL CLRNC AND 2 AMENDED CLRNCS. THE ARPT DIAGRAM SHOWS 3 RWY INCURSION HOT SPOTS. OUR INCIDENT TOOK PLACE AT HS3. THESE HOT SPOTS WERE NOT BROUGHT TO MY ATTN DURING THE TAXI. AFTER DEBRIEFING THE INCIDENT; THE COPLT SAID HE DID NOT NOTICE THE NOTE UNTIL FURTHER STUDY OF THE CHART. THE FINAL TAXI CLRNC WAS AMBIGUOUS CAUSING THE COPLT TO BRING HIS ATTN INSIDE THE ACFT AT A CRITICAL TIME. THE TXWY MARKINGS ARE NOT CLR IN THE AREA OF THE INCIDENT. A RE-LABELING OF THE TXWYS IN THIS AREA MIGHT HELP PREVENT CONFUSION AND MISUNDERSTANDING WHICH WAY TXWY R GOES. CREW COM: WHEN I ASKED THE COPLT TO CONFIRM OUR CLRNC; I DID NOT MAKE IT CLR TO HIM THAT I INTENDED TO CROSS THE RWY WE WERE APCHING. HAD I DONE SO; HE WOULD HAVE CORRECTED ME.