I think the pump is in the tank and if it is when your fuel level gets really low the pump is not fully submersed in fuel so it sounds noisy. When you have plenty of fuel the sound isn't bad because the tank is not empty. I doubt the chevron fuel has anything to do with the noise.
Also it is good practice to never let your tank level to go less than 1/4. The fuel also acts as a coolant to cool the pump if you always drive near empty the pump has a tendency to always run hot and will eventually overheat and go out.
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