B737-700
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 140; Flight Crew Type 2850
Aircraft Equipment Problem Less Severe; Inflight Event / Encounter Fuel Issue
Air Traffic Control Provided Assistance; Flight Crew Landed As Precaution; Flight Crew Diverted
Aircraft
Climbing out of ZZZ; both fuel pump low pressure lights illuminated on the Number 2 tank. The FWD low pressure light would go on and off. The AFT low pressure light illuminated constantly. We stopped the climb at FL330 to troubleshoot. While troubleshooting the issue; the Number 2 engine rolled back quite a bit; and then returned to normal operation.The Captain sent an ACARS message to Dispatch to advise them. We all agreed that the QRH said we could continue. The Captain decided to talk to Dispatch over AIRINC. While on the radio with Dispatch; the number 2 engine had another minor loss of power and surge. We were pretty much right over ZZZ1; and we all decided to divert to ZZZ1 in the interest of safety. We changed our destination with ATC to ZZZ1. We did not request priority handling and landed in ZZZ1 without further incident.
On climb out from ZZZ; passing 15;000 feet; the Number 2 Aft Fuel Pump low pressure light illuminated. We performed the appropriate QRH procedure; turning off the Number 2 Aft Fuel Pump and continued to climb. Passing FL300; the Number 2 FWD Fuel Pump low pressure light illuminated. We leveled at FL330 knowing at high altitude we could lose power. Per the QRH; we were still okay to continue the flight to ZZZ1. When testing the fuel pumps power draw per Maintenance Control; the number two engine momentarily lost power when the FWD Fuel Pump was selected off. I immediately turned it back on noting when the switch was turned off the AMPS dropped from 47 to 42 AMPS.While talking to Dispatch and Maintenance Control over ARINC; the FWD low pressure light went out then cycled on and off. While the low pressure light was cycling; the Number 2 engine began to surge between 82-89% N1. At that time we elected to divert to ZZZ2 to have the aircraft inspected and repaired. We did not [request priority handling] at that time. We were met by Contract Maintenance and I initiated a call to Dispatch and Maintenance Control. The Operations Center Chief joined the call and I answered several questions for him. We were given another aircraft and we continued to ZZZ1 without incident.
B737 flight crew reported low fuel pump pressure indication for the Number 2 engine and surges in power output that resulted in a diversion.