AU-AKN Lag: Troubleshooting & Solutions

Hi, something new again: The engine started successfully with low levels of misfire, but it takes a long time to reach operating temperature. However, it's running very unevenly at 4900 RPM, and it sounds like it's misfiring.
"Of course, the error memory is clear. I haven't taken it for a test drive yet, and I want to avoid revving the engine until I know what's causing it. If this is somehow related to air in the fuel, I risk damaging the ESP system."
It's possible that the engine was stalling due to a lack of fuel in the fuel pump, perhaps caused by air bubbles from the return line. Otherwise, there were no other issues, and the fuel tank was still more than half full.
Please provide the text you would like me to translate from German to English. I will only provide the translation, without any explanations.
Normally, air is not visible in the system. I've installed transparent tubes in the oil return lines, and occasionally, air bubbles are coming from the right bank. I can't tell whether air is entering the system when it's stationary or if the pump is pumping air in.

It would definitely be interesting to know if other vehicles with the VP44 pump have also experienced issues running at idle speed and at full throttle.

My (A4, also AKN engine) failed the emissions test. It would shut off near the maximum RPM. It wasn't a limp-home mode or anything like that, it just turned off. While driving, I only noticed that it was slowly reaching the higher speed ranges, and since I'm not a speed demon, I didn't even realize it. In any case, it consistently shuts off at 3800 rpm.
The cause of this was the pre-lift pump, which is located in the tank. The ESP (electric fuel pump) alone cannot draw in the required amount of fuel, so it reduces or shuts off the fuel supply.
Best regards,

Until just over 4000, mine usually climbs quite well .
I haven't looked into that further yet.