Fluent offers a pdf-equilibrium model using two mixture fractions, I'm sure other CFD codes do as well. There might be some publications in the documentation. Be advised though that such a simulation can be rather time-consuming, especially of you use a beta-pdf for turbulence-chemistry interaction. A double-delta pdf is much quicker here.

I'm not sure though if your idea to define one mixture fraction as a perfectly mixed mixture of a fuel and an oxidizer will work as intended. I think you would see immediate ignition in the inlet of that mixture fraction which would be unphysical.

Would it maybe help you to define your mass_B as a flue gas solution from the combustion of fuel B and air? I've done that before and it yielded reasonable results.

Dear Mr. Leicher,

Thank you for the idea, to define the mass_B differently. I will look into this.

Hi;

if you are talking about the simple way of calculating it then you are right. But the problem is in the phases you are dealing with ..... if it is a two phase flow system than it will be completely different. if all the phases you are using are homogeneous then it is ok 

Mr. Bari is right. I've assumed that you talk about gas combustion. If your problem is a multi-phase flow, things are quite different... and more difficult.