Can you swap the injector to see if the problem moves?

Also, I just looked at the graph and noticed the different axes. Which bank is up around .83 volts (senses too rich mixture)?

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Prost!

Moving the injector is the most work so Im going to move the coil first and replace the plug, just looking for a source of compressed air first to clean out the plug cavity.

Referring to image 3:
Range 0.785 to 0.840 is the yellow line, Bank1 Lambda(colour not visible on the axis)
Range 0.1 to 0.9 is the blue line, Bank 2 Lambda
Range 680 to 725 is the red line, Engine RPM

The colours stay the same for all the graphs but the ranges on the axes differ. Bank2(blue) is the problematic one. Both of the banks are running rich because the fuel system is running open loop due to insufficient temperature.

Just exchanged Coil 5 with coil 1 and recorded the attached data.
Coulours refer to the same sensors as described above.
Misfires are still present although the data looks better than yesterday. Yesterday I tested over a 15min period but couldn't today due to rain.

Attached Thumbnails

     

how are the plugs? are they factory original to the engine?

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2012 BMW X5 (Beef + Granite suspension model)

1995 E300D - The original humming machine (consumed by Flood 2017)
2000 E320 - The evolution (consumed by flood 2017)

Don't know yet, going to try and remove them today to take a look.
I will only replace ignition components with OEM.
The coil packs are OEM, I noticed coil5 has already been replaced by the previous owner as it has a newer part number.
The previous mechanic that worked on the car also spilled a lot of oil on the second bank. I found a lot of thick oil inside the electrical connections to the coils, have started cleaning that out too.

I took the car for a drive to go buy a compressor. This time with coil 1 and 5 swapped. Recorded data during the trip there and during the return trip. Bank1 O2 levels were still very consistent and bank 2 still showed misfires although not as sever as before. I attached the graph of the return trip, recording started just after starting the car in it was still in high idle. Bank 2 is running leaner than bank 1 and fluctuates too much.

I cleaned out the engine with compressed air and removed all the coils for cleaning and inspection as well as the plugs on cylinder 5. All the coils looked good except for the one originally on cylinder 5. This one's low voltage connector as well as the plug connector were covered in thick oil. Upon removing the wires leading from the coil to one of the plugs I saw that in stead of a nice copper pin there is only blue dust inside. The copper pins has completely disintegrated on the wire, see pictures in the attached links.

The plugs on cylinder 5 are also still very good, see attached pictures.
I also removed a plug from cylinder 1 for comparison with one the of cylinder 5 plugs.

I am going to replace coil5 and the corroded cable on monday and test again. I still suspect the injector as the car did drive better today and from the data I could see the dips in bank 2 O2 levels were less severe than before.

Coil pack connection corroded:
https://www.dropbox.com/s/xts9ev8twbruwi0/20140201_155114.jpg
https://www.dropbox.com/s/mjte9ntrrypm0kt/20140201_154958.jpg
https://www.dropbox.com/s/ll2eysjzn0ysxx6/20140201_154939.jpg
https://www.dropbox.com/s/tau29qe5p8tt20b/20140201_154846.jpg

Plug a and b from cylinder 5:
https://www.dropbox.com/s/jrqplbmsq0sku21/20140201_162201.jpg

Cylinder 1 plug(top) compared to cylinder 5 pulg(bottom)
https://www.dropbox.com/s/ry2a6yxq1r3in8z/20140201_162606.jpg

Attached Thumbnails

 

I removed the fuel rail this morning, it came out quite easily. The most work went into removing the portion of the engine harness that was in the way.

After removing the rail I noticed that injector 5 was missing the bottom O-ring and retaining clip. I found the O-ring stuck in the cavity but the clip is nowhere to be found. I attached a thin pipe to my vacuum cleaner with a stocking as filter and after about 15mins I only extracted little bits of hard crud. I assume this is whats left of the clip as the bottom of the O-ring is burnt hard and the top is still a bit soft. This might be the cause of the funny sound emanating from this cylinder, it sounds like piston slap, yet doesn't sound like piston slap.

Fuel rail:
https://www.dropbox.com/s/1sixds1cn0xbtf2/20140202_150132.jpg

Injector 5:
https://www.dropbox.com/s/c6q9wbvw98cjxvn/20140202_150244.jpg

Im going to have to remove the head on bank 2 to see whats going on in there, something I was avoiding. Im also building an injector cleaner to properly clean the injectors and test them afterward.

This simple job just turned very big....