re How to calculate C3S?
It will depend on your SO3/Alkali molar ratio. If this ratio is less than or equal to 1, then all of the SO3 is likely to be present as alkali sulphates and therefore you simply use the regular Bogue equation for C3S i.e.;-
4.07 * CaO - 7.6 * SiO2 - 6.718 * Al2O3 - 1.43 * Fe2O3
However, if the molar SO3/Alkali ratio is greater than 1.0, it becomes quite difficult to know exactly what form the excess SO3 takes in the clinker and how much SO3 is in each particular state.
For SO3/Alkali ratios between about 1 and 2, the excess SO3 reacts with K2SO4 and CaO to form calcium langbeinite (2CaSO4.K2SO4), preventing the equivalent amount of CaO from reacting to form C3S.
For SO3/Alkali ratios from about 2 to 4, it is likely that the excess SO3 is present in solid solution within the silicate minerals, particularly C2S.
For SO3/Alkali ratios above 4, there is likely to be enough SO3, in excess of the alkali sulphates, plus that dissolved in the silicate minerals, to form CaSO4. If the amount of CaSO4 formed is significant (>~0.3%) then the C3S should ideally be calculated by allowing for the CaO combined as CaSO4. i.e.
4.07 * CaO - 7.6 * SiO2 - 6.718 * Al2O3 - 1.43 * Fe2O3 - 2.85 * SO3a (Where SO3a is the SO3 contributed by the amount of CaSO4 present.)
However, it is not easy to determine how much CaSO4 is actually present in your clinker. Also, SO3 in solid solution inhibits C2S from reacting further with CaO to form C3S, so your actual C3S and C2S content will probably be very different from any of the Bogue calculations anyway.
Another problem in high SO3 clinkers arises with C3A. Increasing amounts of SO3 in solid solution also cause high incorporation of Al2O3 into the silicate minerals as well. This lowers the actual amount of C3A that can be formed.
Unfortunately, at this stage, there is no simple formula that allows the calculation of C3S in high SO3 clinkers.
As a matter of interest, what is your molar SO3/(K2O+Na2O) ratio?