Date: 201901
Local time of day: 0601-1200
Location: ZZZ.ARTCC, US
Light: Dawn
Aircraft: B737-700
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Cruise
Airspace: Class A ZZZ
ATC / advisory: Center ZZZ
Aircraft component: Fuel System
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Second reporter function: Pilot Flying; First Officer
Anomaly: Aircraft Equipment Problem Critical; Inflight Event / Encounter Fuel Issue
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Diverted; Flight Crew Landed As Precaution; General Maintenance Action
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: I was the PM (Pilot Monitoring) for the beginning of this event. We departed ZZZ uneventfully and headed to ZZZ1. The planned cruise altitude this morning was FL 280; lower than typical for a two-hour flight due to forecast turbulence above FL 290. Traffic was light; and we climbed right up to FL 280. We began flying in the dark; and sunrise was just beyond the halfway mark. The ride was smooth and I made a PA and released the Fasten Seat Belt sign. Somewhere near the 40-50 minute point into the flight; I noticed that the Number 1 fuel tank was over 200 pounds lighter than the Number 2 tank. As I have done countless times in my career; I announced that I was balancing fuel and positioned the fuel pump switches and crossfeed to regain balance. When the fuel gauges were back in balance; I returned the fuel pump switches and crossfed to their original positions.After another 10 minutes or so; I noticed that our FMC was showing us landing with about 400 pounds less than our flight plan had estimated. I checked the flight plan and noted that the actual headwinds were 10-20 knots higher than had been forecast; possibly accounting for the arrival fuel difference. Again; I had seen this situation many times before; so was not too concerned at this point. After a few more minutes; I saw that the Number 1 fuel tank was again 100-200 pounds out of balance. I opened my EFB; looked at the AOM for 'fuel leak.' It says 'Significant fuel leaks; although fairly rare; are difficult to detect.' I noted the fuel flows on both engines were identical: 2.98 each. It then directed us to the QRH to run a 30 minute imbalance check.I pulled out the QRH and began discussing the possibility of a fuel leak with the FO (First Officer) and we began reading the 'Fuel Leak Engine' Checklist. We recorded the exact fuel quantities and started the clock at (time) C (slightly longer than 1 hour into the flight). While this check was running; we began discussing the ramifications of having an actual fuel leak. I directed our 'A' FA (Flight Attendant) to go back to look for any visible spray or leaks around the engine. She reported no visible leaks. We checked that the nearest suitable airport (if we ended up shutting down the engine) would be [our departure field or two other airports.] At that point; we were exactly equidistant from each.At the 24 minute mark (on the imbalance check); we had reached 500 pound imbalance; thereby confirming an actual fuel leak. Our FMC arrival fuel now indicated 900 pounds less than our flight plan. I sent an ACARS message to Dispatch at (time + 30 minutes) C letting them know we had a confirmed fuel leak and would be contacting them via ARINC patch; which we did. After conferring with Dispatch and Maintenance; we agreed that we should continue the QRH which told us to shut down the #1 engine. We made a PA to inform our passengers of the situation.We had already discussed and used the FMC for Engine Out Information. Our drift-down altitude was 28;100 feet; so FL280 was fine. We transferred control of the aircraft to me and I handed the FO the QRH to continue with the shutdown. We followed the QRH to shut down the Number 1 engine and [coordinated with ATC]; requesting direct to ZZZ1. They gave us vectors and we headed to ZZZ1. We discussed the situation regarding what to tell the FAs and decided that an evacuation was a very remote possibility. We told the FAs that it was highly likely that we would be taxiing to the gate.The landing was uneventful and we rolled down to [the gate] (as previously discussed with the Tower). We asked for Fire Rescue to scan our Number 1 engine; and they told us the engine was cold and no leaks were seen. I made a PA to our Passengers and let them know we were given a thumbs up from the Fire Team and would be taxiing to the gate; where we arrived safely. In addition; I think now that due to the fact that I had been balancing the fuel throughout the flight; after we had shut down the engine; we had (in our minds) 'resolved' the main problem and did not continue to balance the fuel load (in the opposite direction due to engine shut down). Since we were in the descent/landing phase; both throttles were at idle a great part of the time and it was only 25 minutes or so until landing; the resulting imbalance was not too great. However; by the time we had taxied to the gate; the imbalance was probably more than 1;000 pounds.Also; it seems that after years of training in the simulator; whenever we shut down an engine in training; we always remember to balance the fuel load due to the shutdown engine. However; in a slightly different context (such as ours); the shutdown engine did not cue us to balance the fuel as we should have. This seems to be a human factors/psychology type of error that could be the basis for future training emphasis.


Second narrative: [Report narrative contained no additional information].


Synopsis: B737-700 flight crew reported diverting to an alternate airport after detecting signs of a fuel leak.