ACR SMT ENCOUNTERS INFLT WX DELAY CAUSING LOW FUEL STATE REQUIRING LNDG BELOW WX MINIMUMS.

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MY F/O AND I ARRIVED AT TCL OPS AT XA00 AM; LCL TIME. AT APPROX XB15 LCL TIME I REVIEWED THE BNA XA48 WX. CONDITIONS AT BNA WERE RPTED AS CLR; VISIBILITY 7 MI; WITH A FORECAST OF CLR; VISIBILITY 5 MI AND FOG; WITH AN EXTENDED FORECAST OF CLR AND VFR. I THEN ASKED THE GATE AGENT WHAT OUR PAX LOAD WAS; AND SHE INFORMED ME THAT WE HAD 14 PAX BOOKED. I THEN ADVISED HER THAT OUR FUEL LOAD WOULD BE 1100 LBS; WHICH WAS AN APPROPRIATE FUEL LOAD FOR AN IFR FLT; IN VMC CONDITIONS; WITH NO ALTERNATE ARPT REQUIRED. I THEN TOLD MY F/O TO PUT 1200 LBS OF FUEL ON THE ACFT; THE EXTRA 100 LBS OF FUEL WAS TO START THE ACFT EARLY TO WARM THE CABIN. AT DEP TIME; 12 PAX BOARDED THE ACFT. ALL PREFLT CHKS AND COCKPIT CHKS WERE NORMAL. AFTER DEP WE WERE TOLD TO CONTACT BHM APCH. ALL PHASES OF DEP WERE NORMAL. UPON CONTACTING ZME I REQUESTED PRESENT POS DIRECT TO SHB DIRECT BNA; THE REQUEST WAS GRANTED. THE ENRTE PHASE OF THE FLT WAS NORMAL AND ROUTINE. AT APPROX 60 MI FROM BNA; BNA ATIS RPTED SKY CLR VISIBILITY 7 MI. UPON ARRIVING IN THE BNA AREA; WE CONTACTED BNA APCH. WE THEN NOTICED A LARGE AREA OF FOG OVER THE J PERCY PRIEST LAKE. WE ALSO NOTICED THAT THE SMYRNA ARPT APPEARED TO BE FOGGED IN; BECAUSE WE COULD NOT SEE IT SE OF BNA. AT APPROX 15 MI OUT WE MADE VISUAL CONTACT WITH THE BNA ARPT. APCH CTL ADVISED US THAT WE COULD EXPECT ILS RWY 2L. WE ACKNOWLEDGED. WE WERE VECTORED SW OF THE ARPT; THEN WE WERE INSTRUCTED TO CONTACT THE FINAL APCH CTLR ON FREQ 133.9. WE ESTABLISHED CONTACT AND THE CTLR ADVISED US TO EXPECT RWY 2L. WE RPTED THAT WE HAD THE ARPT IN SIGHT; AND THAT WE COULD USE RWY 2R. THE CTLR THEN INSTRUCTED US TO FLY HDG 340 DEGS; CLRED VISUAL APCH TO RWY 2R. AT APPROX 3-3 1/2 MI OUT WE WERE INSTRUCTED TO CONTACT BNA TWR. UPON CONTACTING BNA TWR; WE ADVISED THEM THAT WE WERE ON A VISUAL TO RWY 2R. THE TWR CTLR IMMEDIATELY CAME BACK INFORMING US THAT THE ARPT IS IFR; AND TO FLY HDG 020 DEGS MAINTAIN 3000' CONTACT APCH ON 124.0. WE ACKNOWLEDGED; AND BROKE OFF THE APCH. THE NEXT CTLR ADVISED US THAT WE WOULD BE USING ILS 2L; RVR 6000'. I THEN ASKED WHAT OUR SEQUENCE WOULD BE; THE CTLR ANSWERED #5. I THEN ADVISED HIM THAT WE WOULD HAVE TO MAKE IT QUICK. WHEN BEING VECTORED TO THE FINAL APCH TO RWY 2L ILS; THE CTLR RPTED RWY 2L RVR 700' T/D; 0 ROLLOUT. I ADVISED THE CTLR THAT WE MAY HAVE A FUEL PROB. HE THEN ACKNOWLEDGED. ANOTHER ACFT RPTED THAT HE MAY HAVE A FUEL PROB ALSO. I REQUESTED CLRNC AND CURRENT WX FOR BWG. THE CTLR INSTRUCTED US TO FLY HDG 360 DEGS; MAINTAIN 3000'; AND TO STANDBY FOR CLRNC. I THEN CALCULATED THAT OUR FUEL UPON ARR AT BWG WOULD BE UNACCEPTABLE; 100 LBS OR LESS. I TOLD THE CTLR THAT BGW WOULD BE UNACCEPTABLE. THE CTLR ADVISED US THAT JOHN C TUNE ARPT WAS AT OUR 3 O'CLOCK POS AND APPROX 3-5 MI. I TOLD THE CTLR WE WOULD ACCEPT JC TUNE ARPT FOR AN APCH. WE WERE FLYING AT A NE DIRECTION; AT APPROX XC50 AND DUE TO THE MORNING SUNLIGHT CONDITIONS WE LOST VISUAL CONTACT WITH THE ARPT. AFTER ADVISING APCH THEY VECTORED US FOR A LOCALIZED DME APCH TO THE ARPT; THEN GAVE US LOC FREQ; INBND COURSE AND STEP DOWN FIXES. MEANWHILE FOG ROLLED OFF THE CUMBERLAND RIVER AND OBSCURED THE ARPT. AT APPROX 2.5 DME WE WERE UNABLE TO MAKE VISUAL CONTACT; SO I INFORMED BNA APCH THAT WE WOULD BE UNABLE TO CONTINUE THE APCH. WE WERE THEN TOLD TO CLB AND MAINTAIN 3000'. AT THIS POINT WE HAD APPROX 400-450# OF FUEL REMAINING; AND I ADVISED BNA APCH THAT WE WERE GOING TO HAVE TO LAND AT BNA. THE CTLR ASKED IF WE WERE 'DECLARING MINIMUM FUEL.' I REPLIED; 'AFFIRMATIVE.' BNA APCH THEN VECTORED US TO ILS 2L. AT APPROX 4 MI OUT WE HAD THE APCH LIGHTS AND FIRST 200' OF RWY 2L IN SIGHT. WHILE TURNING ONTO THE RWY 2L LOC THE FINAL APCH CTLR RPTED TO ALL ACFT THAT SMYRNA ARPT WAS VFR. BY THIS TIME I HAD COMMITTED TO LAND AT BNA AND I COULD STILL SEE THE APCH LIGHTS AND PART OF THE APCH END OF THE RWY. I ALSO COULD SEE AN MLG HOLDING SHORT ON THE E SIDE OF RWY 2L. I DECIDED NOT TO RISK THE CHANCE OF GOING TO SMYRNA AND HAVING THE POSSIBILITY OF THE FOG MOVING IN AS IT HAD OVER BNA AND JOHN C. TUNE. IF THAT HAPPENED; I WOULD HAVE TO RETURN TO BNA WITH A CRITICAL FUEL SITUATION. APCH CTL TOLD US TO CONTACT BNA TWR; WE ACKNOWLEDGED AND BNA TWR CLRED US TO LAND. THE ENTIRE APCH TO BNA RWY 2L WAS FLOWN IN CLEAR AIR. I TOUCHED THE MAIN WHEELS DOWN AT THE THRESHOLD OF RWY 2L. WHEN I DID ENTER THE FOG; THE VIS WAS APPROX 1000'. T/D AND ROLLOUT WERE UNEVENTFUL. BNA TWR ASKED US TO RPT CLR OF THE RWY. WE ACKNOWLEDGED WHEN WE WERE CLR AND WERE INSTRUCTED TO CONTACT GND CTL. THE TAXI TO THE GATE WAS UNEVENTFUL. ARR TIME WAS APPROX XD20.