B777 Captain reported an increasing fuel Imbalance in cruise. The flight crew monitored the observed fuel imbalance and elected to continue to the destination airport.

Narrative

Inbound aircraft had the Fuel Imbalance EICAS written up and Maintenance cleared the write with no fault codes found. We briefed the threat as I experienced the same EICAS four months ago. We briefed to monitor the Fuel Synoptic after we got the Fuel Low Center EICAS to monitor the Fuel Balance. In cruise once we got that EICAS we monitored the Fuel Synoptic at XA29. The Fuel Values were (63.4/1.8/64.0) (L/C/R) for an Imbalance of 600 pounds. The Left Engine had a fuel flow of 300 pounds higher per hour. At XB13 it was (58.2/2.0/59.3) for an imbalance of 1;100 pounds. At XB42 it was (54.5/1.7/56.0) for an imbalance of 1;500 pounds. At XC19 it was (49.0/0.2/52.2) for an imbalance of 3;300 pounds. We discussed why the Center Tank Fuel was at 0.2 when the fuel scavenge was not supposed to operate yet; due to the main tank fuel being above the onset value per the FM system section. Fuel Imbalance EICAS annunciated; and we accomplished the checklist; made an ELB write up. Contacted Dispatch and Maintenance Control to discuss the issue; they advised to keep monitoring and we gave Maintenance Control all the data above. During re-balancing we reviewed the Fuel Leak checklist and started monitoring the progress pages for totalizer fuel and calculated fuel as well as fuel remaining at ZZZ. After re-balancing we saw the imbalance numbers start to rise again. At XD12 the fuel was (42.4/0.0/44.8) for an imbalance of 2;400 pounds. At XD42 the fuel was (38.5/0.0/41.8) for an imbalance of 3;300 pounds. The :30 rate of difference was 900 pounds for XD42 and then at XE12 was 1;000 pounds. All other indications were normal the fuel totalizer and calculated fuel difference started at 1;300 pounds and went down to 400 pounds over this time period. The fuel remaining at touchdown remained consistent with our flight conditions. The HOWGOZIT fuel and the time reflected our flight. The Relief Pilot came up; and I went back to view door 3L and 4L for any sign of a Fuel Leak Spray from the Left Engine. No Spray was observed. We accomplished the checklist for Fuel Imbalance again and notified Dispatch and Maintenance Control and gave them more data and discussed diverting into ZZZZ if the :30 fuel rate of difference exceeded 1;000 pounds. After the second re balancing the imbalance only increased to 1;100 pounds for the remainder of the flight. All other values and indications were consistent with the flight (totalizer/calculated/fuel reaming at touchdown/HOWGOZIT). We decided to not blindly follow the Fuel Leak checklist and shut down the engine for just the 1;000-pound limit; as all other values and indications were within tolerances and fuel remaining and the HOWGOZIT numbers were reflective of our flight plan. The fuel imbalance; fuel totalizer calculated values did not increase after the second re balancing. Flight landed uneventful at ZZZ. Gave Maintenance Control our thoughts on the fuel scavenge system as well as the fuel imbalance issue stopped after the main tank fuel dropped below 25;000 pounds.