B737 Undifferentiated or Other Model
Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 130; Flight Crew Total 4000; Flight Crew Type 150
Situational Awareness; Time Pressure; Troubleshooting
Aircraft Equipment Problem Less Severe
Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Inflight Shutdown; Flight Crew Diverted
Aircraft
While in cruise at FL370; we noticed that that the right fuel valve closed light was illuminated bright. We began to discuss the possible risks and contingency plans as we pulled out the QRH. We contacted the Company. The right engine began to roll back and then shortly after; came back to full power. We advised ATC of our situation and began to plan a divert then shortly after the right engine rolled back to idle again. We again advised ATC. We decided that ZZZ was the best option to land as soon as practical. We followed the QRH checklist for engine failure through to the Single Engine Landing Checklist. On the ground; we were met by the emergency vehicles that followed us to the FBO. The Captain was calm and professional through the whole flight and all procedures were followed in accordance with the company and manufactures recommendations. Great coordination was maintained between all parties involved including the crew; the company and ATC.
B737 pilot reported an indication of a fuel valve anomaly; followed by erratic engine operation on the associated engine.