A B737-800 FLT CREW EXPERIENCED SEVERE ENGINE DAMAGE IN CRUISE FLIGHT. THEY SHUT DOWN THE ENGINE; DECLARED AN EMERGENCY; COORDINATED WITH DISPATCH AND MAINT; AND DIVERTED TO THE NEAREST SUITABLE AIRPORT.

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TKOF AND DEP WERE UNEVENTFUL. ABOUT 2.5 HRS AFTER TKOF; CRUISING AT FL370 APPROX 100 MI N OF ZZZ WE HEARD A LOUD BANG FROM THE L ENG. IMMEDIATELY FOLLOWING; THE ACFT YAWED TO THE L AND BOTH THE AUTOPLT AND AUTOTHROTTLES DISENGAGED. WE CROSS CHKED THE INSTRUMENTS AND NOTED THE L ENG N1 AND N2 INDICATED 0. OIL QUANTITY WAS AT 15 QUARTS WITH ZERO OIL PRESSURE INDICATED. THERE WERE NO INDICATIONS OF FIRE BUT THE ENG HAD EXPERIENCED A SEVERE DAMAGE EVENT. THE CAPT IMMEDIATELY TOOK CTL OF THE ACFT AND I COORDINATED A DSCNT WITH ATC AND DECLARED AN EMER. NEXT; WE WORKED THE QRH PROCS FOR 'ENG FIRE; SEVERE DAMAGE OR SEPARATION.' AFTER THAT WE RAN THE 1 ENG INOP LNDG QRH PROC AS WELL. ATC; COMPANY; AND FLT ATTENDANT COORD WERE ALL ACCOMPLISHED AS WELL. WE DIVERTED TO ZZZ FOR AN ILS RWY X SINGLE-ENG APCH TO A FULL STOP ON THE RWY. AFTER CRASH AND FIRE GAVE US THE ALL CLR; WE OPTED TO BE TOWED TO THE GATE FOR DEPLANING OF THE PAX. NO INJURIES WERE RPTED; SO NO MEDICAL ATTN WAS REQUIRED. THE PAX RPTED A MOMENTARY FIRE FROM THE ENG AT THE SEIZING MOMENT BUT NO FIRE INDICATIONS WERE RECEIVED IN THE COCKPIT. WHILE BEING TUGGED TO THE GATE; WE REVIEWED THE FOM POST-INCIDENT CHKLIST AND COMPLETED A LOGBOOK ENTRY. POSTFLT EXAM REVEALED THE N1 FAN WOULD ONLY TURN ABOUT 4 INCHES. NO EXTERNAL DAMAGE WAS READILY APPARENT.