Although very late, BMW makes conclusions. Today’s topic – the injector of cylinder X is leaking in the Homogenous mode, which causes misfires in other cylinders. This is a very common scenario – at least in  80 .. 90% of cases, you can expect exactly this situation.
The injector leaking problem is pronounced in engines that use piezo injectors, so: N43/53/54/63. Unfortunately, there was (and still is) zero information regarding this problem in the official BMW resources. 
What did BMW regulations suggest? If the misfires are in cylinder X, replace everything (it means the ignition coil, spark plug, and injector) in this cylinder. If the misfires are in several cylinders, replace all injectors of the exact bank. Typically, the BMW dealer replaced all injectors, not seeing other “solutions”. True, though, the partial justification of the situation should be noted that the dealer specialist cannot use INPA, accordingly – they did not and don’t have access to the injector data. 
A note on the above problem has appeared in the Misfire identification description of the B series engines: 

Isn’tit wonderful? 15+ years late,  but finally, this note has appeared! In addition – for the engines, to which this problem is not especially pronounced.
In this entry, we will take a look at all possible scenarios if any injector has suddenly started to leak. Let’s look at the situation as simplified as possible – only in idle mode. Exactly in idle, the injector dripping can be felt most (the manifestation of the problem in the load does not differ; only the numbers in the calculations differ). We will not take into account that the wideband Lambda probe indicates incorrect information if it is “flooded” with the mixture of air and unburned fuel (a typical situation if any of the injectors is leaking) and that if the injector starts to leak gradually, DME modifies Offset type LTFT, etc.

As examples, we will use:
a. N43 series engines with two wideband probes (120i/320i/520i); one wideband probe on every 2 cylinders;
b. N53 series engines (one wideband probe on every three cylinders); the identical situation for N54 and B38 series engines;
c. N43 series engines with one wideband probe on 4 cylinders (118i; 318i), identical situation N63; B48 series engines;
d. B58 series engine with one wideband probe on 6 cylinders.


In all cases, we will assume that some of the injectors have started to leak and drip a double dose of fuel. A double dose was measured over a longer time period. Why such a remark? If the injector starts to leak, it “behaves” like this:
a. in a closed position, the injector (relatively) slightly drips;
b. When it is injected, its performance is correct.


How to understand “(relatively) slightly drips)”?
The opening position time of the typical piezo injector (the situation is comparable/similar also for nozzles of other types of DI engines): around 250us (or 0.25ms: N53 series engine, Homogenous mode, idle: 600 RPM, warmed-up engine). It is not hard to calculate the interval of the closed time (“pause”): it is 200ms (the crankshaft performs 10 turns during a second; the injector injects in every second turn or 5 times in a second). 
The ratio of the injector closed/open time is 200/0.25 = 800. For 800 time units, the injector is closed, and only for one unit is it open! We can draw two conclusions from this:
a. even a very small dripping over this long period of time causes big problems (it’s enough with around 0.12% flowrate dripping to double the amount injected);
b. injector dripping actually causes less trouble in the damaged cylinder than one might imagine, as only half of the fuel dispensed participates in combustion (is dripped during inlet and compression cycles). Another half of the dripped fuel is injected (dripped) in power and exhaust cycles (does not cause problems to the cylinder performance, but it can be “seen” by the Lambda probe placed in the exhaust). 


A. Wideband probe on every 2 cylinders. Configuration current for N43 series engines (120i; 320i; 520i). 
If any of the injectors drips a double amount of fuel, the exhaust (measurements of the wideband probe) gets:
a. 2 doses (1+1) air;
b. 3 doses (2+1) fuel.
DME adjusts the fuel mixture for the average fuel amount to be 2 doses. To do this, the total injected amount should be reduced by 33%:
a. in each cylinder (average) the injection time is reduced by 50%;
b. the fuel mixture, combusted in the damaged cylinder, comes close to perfect (!);
c. The fuel mixture in the correctly working cylinder is very lean (Lambda is close to 2).
Unfortunately, the situation is unmistakable – the culprit cylinder feels perfect, the one working properly – it has group misfires!


B. Wideband probe on every 3 cylinders. Configuration is current for N53, N54, and B38 series engines.
If any of the injectors drips a double amount of fuel, the exhaust (measurements of the wideband probe) gets:
a. 3 doses (1+1+1) air;
b. 4 doses (2+1+1) fuel.
DME adjusts the fuel mixture for the average fuel amount to be 3 doses. To do this:
a. in all 3 cylinders (on average), the injection time is reduced by 33%;
b. the fuel mixture, combusted in the damaged cylinder, is slightly rich (the leftover of the combusted fuel is around 17%) ;
c. the fuel mixture of the correctly working cylinder is very lean (Lambda is close to 1.33).
Unfortunately, the situation is unmistakable – the culprit cylinder feels perfect, the ones working properly – they have misfires/group misfires!


C. Wideband probe on every 4 cylinders. Configuration current for N43 (118i; 318i), B48 and N63 series engines.
If any of the injectors drips a double amount of fuel, the exhaust (measurements of the wideband probe) gets:
a. 4 doses (1+1+1+1) air;
b. 5 doses (2+1+1+1) fuel.
DME adjusts the fuel mixture for the average fuel amount to be 4 doses. To do this:
a. in all 4 cylinders (on average), the injection time is reduced by 25%;
b. the fuel mixture, combusted in the damaged cylinder, is slightly rich (the leftover of the combusted fuel is around 25%) ;
c. the fuel mixture correctly working cylinder is lean (Lambda is close to 1.25).
Unfortunately, the situation is unpleasant – the culprit cylinder feels perfect, the ones working properly – they have misfires, even group misfires are possible!


D. Wideband probe on every 6 cylinders. Configuration current for B58 series engines.
If any of the injectors drips a double amount of fuel, the exhaust (measurements of the wideband probe) gets:
a. 6 doses (1+1+1+1+1+1) air;
b. 7 doses (2+1+1+1+1+1) fuel.
DME adjusts the fuel mixture for the average fuel amount to be 6 doses. To do this:
a. in all 6 cylinders (on average), the injection time is reduced by around 17%;
b. the fuel mixture, combusted in the damaged cylinder, is rich (the leftover of the combusted fuel is around 33%) ;
c. the fuel mixture correctly working cylinder is lean (Lambda is close to 1.17).
The situation is unpleasant – misfires can start both in the damaged cylinder and the properly performing ones. In the damaged one (with a smaller possibility), due to a fuel mixture that is too rich, the spark plug can be flooded. In the correctly performing – the fuel mixture is lean, on the threshold when it combusts unstable. 


As we see, in NONE of the scenarios the misfires did not start exactly and only in the culprit cylinder. If the Lambda probe is for every 2/3/4 cylinders – with a guarantee, the properly working cylinder is one misfiring. If there is one/common probe for 6 cylinders, the situation is unpredictable; misfires can also happen in the damaged cylinder. Here, there is an explanation of why the BMW AG suggestions in repair cases fail when/if any of the injectors are leaking. A fight with a misfiring cylinder is guaranteed to fail!