Dear Cement Viet Nam,

I attached here an Excel file (it is zipped).
This file shows how the composition of a mixture can be calculated from some analysis of this mixture and its components. This example considers a mix of clinker, slag and additives, and assumes that the quantity of additives is known. Of course, in this calculation, the roles of the three components can be interchanged.

For simplicity, let us assume that there are no additives. If you are given a certain chemical (i) analysis  for the clinker (ki), the slag (si) and the cement (ci), then the mass balance for this chemical and the total mass balance are:

ci C = ki K + si S      (1)
   C =    K +    S     (2)

where C is the quantity of cement, K the quantity of clinker and S the quantity of slag.
Assuming C=1=100%, you get the well-known 'lever rule':

K = 1 - S = (ci - si) / (ki - si)      (3)

For example, based on analysis for SiO2 you can calculate K:

cementSiO2 = 27.71
slagSiO2 = 35.30
clinkerSiO2 = 20.80
gives:  K = (27.71-35.3)/(20.8-35.3) = 52.3% 

The same calculations, based on other chemical analysis will usually lead to other evaluations of the cement composition because of the uncertainties on the chemical analysis. We can estimate the usefulness of a chemical analysis to evaluate a composition. This is measured by the so-called power of a tracer which is given by:

 Pi = (si-ki)²/ei²     (4)

where ei is the uncertainty on the mass balance for this chemical and must be calculated from equation (1) by using standard rules for variance calculations.
Formula (4) reminds us that a chemical analysis will be useful only if the difference of clinker and slag analysis is large enough compared to the balance uncertainties.

If you have the opportunity to evaluate the composition by using several different chemical analysis, like (SiO2, Al2O3, CaO, MgO) in the attached file, then you can combine the results obtained with the different analysis to get the most likely composition. The combination is simply a weighted average based on the powers of the different chemical analysis.

You will find all this calculated in the attached file. The formulas are a little bit more complicated because of the additives taken into account and of the variance calculation ei².

Be happy,

Michel

Remark: A more general approach can solve for more components. It is based on least squares, like the calculations explained above.