A little history; I bought my car from a dealer who told me he had replaced the flywheel. After about a year a ticking developed under the hood which progressed into a loud metallic grinding sound during acceleration and finally to a constant loud tapping.
I took it in for repair and they told me three bolts had snapped off the transmission and another had never been put in. The flexplate was cracked and only attached by one bolt, and the exhaust was assembled incorrectly. Basically, the "dealer" wasn't qualified to repair a jigsaw puzzle.
Once repaired, the engine ran so quiet I had to step out of the car to hear it running, but after driving out a full tank of gas in a day a 'patting' sound developed similar to a pushmower. The sound goes away after several minutes of driving, but returns briefly if I turn off the car and start it back up. I can hear a bit of lifter ticking if I pop the hood, but this sound is different and a little louder. I haven't been able to trace the origin.