Reference material - https://www.smartcockpit.com/docs/CL605-FUEL_SYSTEM.pdf
Page: 16
Fuel tanks are expected to be within 400 lbs / 181 kgs of each other on taxi / takeoff / landing OR 800 lbs / 362 kgs during flight, to avoid Fuel Imbalance EICAS message.
First, orient yourself on the overhead panel, we'll be working in the 2nd row (or middle row) of the FUEL panel area. (Fuel.PNG)
All three of these buttons should be extinguished under normal operations.
Gravity XFLOW
Press to begin the process, there's a 1 second delay after pushing the button for it to illuminate OPEN. This will allow fuel to flow freely between both main (wing-based) tanks. There is no EICAS notification that this is open/occurring. (gravity.png)
To observe what's happening in the sim. You can go to the Challenger 650 menu -> Study -> Engines -> Fuel System...
You'll notice that whatever Main Tank (either Left or Right) has more fuel that this will continue to consume, whereas the side with less fuel will not. Thus balancing the tanks.
L (R) to AUX XFLOW
Press the appropriate button to begin the process, there's a 1 second delay after pushing the button for it to illuminate ON. This will remove fuel from whatever side is select and transfer it to the auxiliary tank.
Determine which tank has more weight in fuel
Left side? Choose L to AUX (L to AUX.png)
Right side? Choose R to AUX (R to AUX.png)
There is a lock out mechanism that does not allow you to press the opposite button when one is already selected. Pressing L to AUX, for example, then pressing R to AUX, will no longer illuminate the L to AUX button. Pressing the R to AUX button again will resume the L to AUX transfer and the button will illuminate ON again.
Once you're done balancing the tank, make sure to deselect the previously selected L (R) to AUX button. The aircraft will now suspend fuel consumption from the two main tanks and pull from the AUX tank until depleted.
*Edit* Thanks! @airforce2 As long as a main tank is below 93% full, the aux tank feeds the main tank to maintain the level at 93%. Once a main drops to 93%, the main quantity will remain constant and the aux level will drop. It will appear that the engines are burning from the aux tank, but in reality the engines are burning from the mains and that fuel is being simultaneously replaced in the main tank from the aux tank ejector xfer pumps.
To observe what's happening in the sim. You can go to the Challenger 650 menu -> Study -> Engines -> Fuel System...
Note: The plane will display an EICAS warning message: FUEL XFLOW SOV OPEN if either button is ON for more than 50 seconds and the tanks are balanced within 100 lbs.