A300
Flight Crew Air Transport Pilot (ATP)
Human-Machine Interface
Aircraft Equipment Problem Less Severe; Inflight Event / Encounter Fuel Issue
General Maintenance Action
Aircraft
Landed aircraft with fuel out of balance due to a fuel pump malfunction.  Near the top of climb we noticed the left outer fuel tank was about 2;500 lbs less than the right outer and the left inner was about 2;500 lbs greater than the right inner tank.  At some point in the climb one of the left inner tank pumps had failed but we received no warning.  No fault lights illuminated and no ECAM message.  We were busy with thunderstorms or we likely would have discovered it sooner.  Our Crossfeed checklist would not fix the problem because the line from that tank to its isolation valve becomes depressurized in this scenario (one pump failed but selected on and the other selected on and operating normally; both showing green with the output bar on the failed tank symbol horizontal) thus no green line to the isolation valve on the side that is to feed the manifold.  We calculated sufficient fuel to continue to destination and land with 8;000 to 9;000 lbs of usable fuel.  We ended up with about 3;000 lbs trapped in the left inner (total fuel 11;500). Aircraft flew normally all the way to landing with no ill effects resulting from the out of balance condition.  Verbally debriefed Maintenance about the out of balance condition for landing and made AML entry for what we observed on the fuel panel in flight. Subtle fuel tank pump failure.  No significant indication.  I was not aware a fuel pump could stop output and not give an amber light or warning so perhaps better systems knowledge would have helped.
A300 Captain reports a left inner fuel tank pump failure during climb that results in a fuel imbalance without any indications of pump failure. Attempts to transfer fuel are not successful but flight is able to continue to destination.