The Bogue equations widely used in cement quality control are mathematically based estimates of the quantities of the four main clinker minerals under equilibrium conditions. It is assumed that these four clinker minerals are pure minerals and have the following chemical formulae.
It is assumed that all of the Fe2O3 is present as C4AF. Each of these pure minerals contains fixed amounts of the major clinker oxides. Therefore, the total SiO2 ,Al2O3 ,Fe2O3 and CaO content in any mixture of the four minerals can be calculated as;-
Solving equation of SiO2
Solving equation of Fe2O3
Solving equation of Al2O3
Solving equation of CaO
Explanations on Bogue’s equations
An explanation for the A/F ≤ 0.64
The Bogue equations derived above are only valid for values of SiO2, Al2O3, CaO and Fe2O3 which gives positive and non-zero values for the mineral being calculated.
It is shown that these equations are valid if
It can be verified from the equation for C3A
In other words, Bogue’s equations as previously derived are only valid when the Alumina Ratio (A/F) is greater than 0.64
In the case where (A/F)≤ 0.64, theoretically, no C3A can be present. However, because of the excess of Fe2O3 a new mineral, C2F, exists. This means that in this situation, all of the Al2O3 has been converted to C4AF and the Fe2O3 exists in a solid solution composed of (C4AF + C2F).
An explanation for the SO3 in C3S calculation:
SO3 is taken into account in the Bogue equation for C3S. The assumption in this case is that all of the SO3 is present as CaSO4.
In clinker the SO3 first forms alkali sulphates and when the available alkalis are used up, SO3 then preferably dissolves in the silicate minerals particularly C2S in the proportion of around 2%. It is only then that any SO3 that finally remains can possibly form CaSO4.
In addition, CaSO4 generally decomposes to SO3 and CaO at sintering temperatures anyway. Therefore, in industrial clinkers it is rare to find much CaSO4 at all, even in clinkers with SO3 levels of several percent.
The modified Bogue formula for C3S
The Coefficient of SO3 as 2.85 is derived by the calculation of molecular weight of CaSO4, CaO and SO3.
(56.1 = Molecular weight of CaO and 80.1 = Molecular weight of SO3)
