Date: 201907
Local time of day: 0001-0600
Location: ZZZ.Airport, US
Flight conditions: VMC
Aircraft: A300
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Cargo / Freight / Delivery
Flight phase: Parked
Airspace: Class D ZZZ
Aircraft component: Fuel Quantity-Pressure Indication
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Human factors: Confusion; Distraction; Communication Breakdown
Second reporter function: Pilot Not Flying; First Officer
Anomaly: Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Weight And Balance; Inflight Event / Encounter Fuel Issue
Detector: Person Flight Crew
When detected: In-flight
Result: General None Reported / Taken
Contributing factors: Aircraft; Human Factors
Primary problem: Human Factors

Narrative: We pre-flighted Aircraft X in preparation to fly Aircraft X to ZZZ1. The aircraft had MEL 28-XX-XX-XX left inner fuel tank quantity inop. Just prior to push time the fueler brought a fuel service form stating the left inner tank has 18.3 on board. Then the Maintenance Technician brought an AML with a write up stating the left inner tank is fueled to 18.3. The FO (First Officer) checked the fuel service form and initially thought it was correct. I manually added together all working tanks and then added the 18.3 to confirm we had the minimum fuel required. My calculations showed we had 53.1 on board with 52.9 the flight plan total fuel. On departure I made the comment to the FO that the plane felt bent and the left wing feels heavy. On our gauge the left inner tank showed 28.3; 10;000 above the right inner tank; but the quantity was considered inop. I confirmed the engine thrust was even; centered the turn and slip triangle then put in 2.5 degrees trim left wing up. I made the comment the aircraft feels left wing heavy. At cruise we made the decision to burn 1000 lbs out of the left inner tank. I felt this action would leave the aircraft within the 2000 inner tank to inner tank limit and lessen the aileron trim required. At our current burn it required 5 minutes of burn out of the left inner only to lighten it 1000 lbs. After this action; the aircraft required 2 degrees left wing up. The airplane was behaving normal. We thoroughly briefed what we would look for on the approach; 5 degrees nose up for the approach; we also briefed a go around if there was any indication of a heavy wing. The approach was uneventful with no indication of a heavy wing. At this point I felt confident there was nothing wrong with the fuel load. After our layover and on the way back to the ramp to fly back to ZZZ; the First Officer stated there was a 10;000 lb discrepancy in last flights fuel service form. There were several scratched out lines but when you add the metered fuel to the before fueling fuel you get 63.0; 10.0 heavy. When we landed back at ZZZ; we met with the fueler and Maintenance to see if we could determine what was correct. The fueler was certain that the uploaded gallons was correct and that the aircraft fuel load was correct for departure; but couldn't explain the 10.0 discrepancy. At this time I don't know if the fuel service form was wrong; or it is right and we dispatched with 10.0 more fuel in the left inner tank than we knew. With this question I called ZZZ Maintenance and asked them to determine the fuel on board AC XXX. Maintenance said they couldn't get to it until X local time. I then called Maintenance Control and explained the situation. If the fuel on the aircraft is between 17.0 and 18.0 there isn't a problem. If the aircraft has around 27.0; this would confirm the left inner tank was fueled to 28.3; 10.0 over. I then contacted the Duty Officer and expressed my concerns. If the aircraft has 17.0; the only problem is a fuel service form discrepancy we couldn't explain. If it is closer to 27.0; this would confirm we flew the aircraft with a 10.0 inner to inner tank imbalance with the limit being 2000. At the time of writing this report; ZZZ1 Maintenance hasn't been able to determine the fuel load and has written up a left inner tank magnetic level indicator problem. It may be there was no problem; but in the interest of safety I felt it prudent to find out if the fuel load was correct. It may be there was no event; if we were 10.0 heavy in the left inner tank; the fueler; Maintenance; and the crew of the aircraft missed. Closer scrutiny of the fuel service form would have caught the discrepancy and we could have de-fueled and re fueled that tank prior to departure.


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


Synopsis: A300 Flight crew reported aircraft had inoperative left hand inner fuel tank quantity indicator  MEL; which lead to a fuel imbalance issue.