Sounds like a fuel pump on the way out. Diesel have two, one to move the fuel to the engine compartment and one to pressurize to high pressure for injection into the cylinders. Could be either but hope and pray it's the low pressure pump it's a lot less expensive.

How many estimate hours (divide odometer by average speed)

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)