[Diy_efi] WBO2 and AFR

[Bruce A Bowling]

At 02:36 PM 7/6/2005, you wrote:
>OK.  how about a 10% ethanol blend gas vs the good non ethanol stuff?
>does running ethanol blend result in a richer or leaner reading on WB
>and why?  talking EFI here with NB02 sensor input to ECU.

I have recently been working on ethanol-blend fuels so this is still 
(kinda) fresh in my mind.

The Nernst cell indicates excess oxygen (both for NB and WB), the stoich 
point is defined lambda of one. Different blend fuels just change the
point of where lambda occurs (in terms of AFR).

To generate the AFR point of a blended fuel like 10% ethanol, do the following:

Mass of Carbon = 12.011
Mass of Hydrogen = 1.008
Mass of Oxygen=16

Ethanol: C1 H3 O0.5 (divided to make carbon=1, this is a common trick used 
in a lot of the literature)
Total mass = 1 * 12.011 + 3 * 1.008 + 0.5 * 16 = 23.035

Super Unleaded: C1 H1.65 O0
Total Mass = 13.674

For 10% alcohol (meaning 90% of unleaded makes up the remainder of the fuel)

Ethanol Mass Carbon = 10% * (1 * 12.011)/23.035 = 5.214
Ethanol Mass Hydrogen = 10% * (3 * 1.008)/23.035 = 1.313
Ethanol Mass Oxygen = 10% * (0.5 * 16)/23.035 = 3.473

For 90% unleaded:

Unleaded Mass Carbon = 90% * (1 * 12.011)/13.674 = 79.053
Unleaded Mass Hydrogen = 90% * (1.65 * 1.008)/13.674 = 10.947
Unleaded Mass Oxygen = 90% * (0 * 16)/13.674 = 0

Sum of Carbon = 5.214 + 79.053 = 84.267
Sum of Hydrogen = 1.313 + 10.947 = 12.260
Sum of Oxygen = 3.473 + 0 = 3.473

(note that these three numbers must add up to 100%)

H/C ratio = (12.260/1.008)/(84.267/12.011) = 1.734
O/C ratio = (3.473/16)/(84.267/12.011) = 0.031

Phi = 0.21 / ( 1 + 0.25 * H/C - 0.5 * O/C)

Lambda(stoich) = 28.85 / (Phi * (12.011 + 1.008 * H/C + 16 * O/C)) = 13.667

Note that the stoich value is a little lower than those often published, 
this is due to the use of super unleaded fuel in this example which changes
the molecular composition a bit (stoich for this one is 14.191, run the 
calculation above in the Phi and Lambda equations for C1 H1.65 - to get the
familiar 14.7 point use C1 H2, or H/C=2, O/C=0).

The point of this is that if you use Lambda to tune then the fuel 
composition is of no consequence. But if the meter is reading in AFR units 
then it
is assuming a fuel composition and you had better be running this exact 
composition, or the meter needs to allow you to adjust the conversion by
specifying direct H/C or O/C values to get the AFR values in whack based on 
the fuel really being burned. Note that if one injects water, nitrous,
etc, then the H/C and O/C ratios change as well.

But here is the wrinkle - this only works for recalibrating the stoich 
point. Move off of stoich the whole wideband curve moves based on fuel
composition, both lean and rich directions. A lot of this info is on the 
PWC web site - look in particular the Brettschneider equation and the fact
that the WB sensor is sensitive to not only excess oxygen (on the lean 
side) but also to CO and H2 (and also unburnt HC) on the rich side. So to do
this right one needs the sensor sensitivities to O2, CO, H2, and HC of a 
particular sensor (obtained from flowbench data, verified by gas analyzer)
and then use the chemical balance equation to determine lambda (in essense 
a reverse Brettschneider). The rich side is the interesting case, in
that there are multiple solutions (lambda is dependent on CO and H2 and HC) 
so one has to use tricks like invoking the water-gas equilibrium,
which now requires the knowledge of the exhaust gas temperature at the 
sensor head (or at least a good guess). Note that the LA-3 meter (and
the PWC when I finally get time to finish it) use this method, you have to 
specify H/C, O/C and water-gas equilibrium temperature, as well as
calibration factors. Not mentioned is correction for pump current offset, a 
big effect right near stoich.

If people want to get a gut feeling on how much things can change based on 
fuel composition, I made up a quick VCPP application, grab it here:

http://www.bgsoflex.com/pwb/combal.zip

In this app, set lambda to 0.9 and then set the O/C ratio to 2, observe the 
percent of CO and H2, then set the O/C ratio to 1.65 and run again. There
is a small change. Next, set Lambda to 0.8 and re-do the above and observe 
that the change is more pronounced.

Now, do the above but this time change the water-gas reaction temperature 
to something like 1500 and re-do all of the above.  Much more
pronounced change.

And I have not even discussed partial pressure effects of the sensor - to 
play with real numbers (and to correctly calibrate your WB at free-air)
grab this:

http://www.bgsoflex.com/partialp/partialp.zip

This should keep people busy for a while....

- Bruce