Clinker: the Bogue calculationThe standard Bogue calculation refers to cement clinker, rather than cement, although it can be adjusted for use with cement. This is a very commonly-used calculation in the cement industry. The calculation assumes that the four main clinker minerals are pure minerals with compositions: Alite: C3S, or tricalcium silicate Belite: C2S, or dicalcium silicate Aluminate phase: C3A, or tricalcium aluminate Ferrite phase: C4AF, or tetracalcium aluminoferrite These assumed compositions are only approximations to the actual compositions of the minerals. Clinker is made by combining lime and silica and also lime with alumina and iron. If some of the lime remains uncombined, (which it almost certainly will) we need to subtract this from the total lime content before we do the calculation. For this reason, a clinker analysis normally gives a figure for uncombined free lime. Firstly, according to the assumed mineral compositions, ferrite phase is the only mineral to contain iron. The iron content of the clinker therefore fixes the ferrite content. Secondly, the aluminate content is fixed by the total alumina content of the clinker, minus the alumina in the ferrite phase. This can now be calculated, since the amount of ferrite phase has been calculated. Thirdly, it is assumed that all the silica is present as belite and the next calculation determines how much lime is needed to form belite from the total silica content of the clinker. There will be a surplus of lime. Fourthly, the lime surplus is allocated to the belite, converting some of it to alite. In practice, the above process of allocating the oxides can be reduced to the following equations, in which the oxides represent the weight percentages of the oxides in the clinker: BOGUE CALCULATION C3S = 4.0710CaO-7.6024SiO2-1.4297Fe2O3-6.7187Al2O3 C2S = 8.6024SiO2+1.0785Fe2O3+5.0683Al2O3-3.0710CaO C3A = 2.6504Al2O3-1.6920Fe2O3 C4AF = 3.0432Fe2O3
Using the above analysis, the calculation is as follows:
Worked example of a Bogue calculation: Combined CaO = (66.6% - 1.0% free lime) = 65.6% This is the figure we use for CaO in the calculation. From the analysis, we have: CaO=65.6%; SiO2=21.5%; Al2O3=5.2% and Fe2O3=2.8% The Bogue calculation is: C3S = 4.0710CaO-7.6024SiO2-1.4297Fe2O3-6.7187Al2O3 C2S = 8.6024SiO2+1.1Fe2O3+5.0683Al2O3-3.0710CaO C3A = 2.6504Al2O3-1.6920Fe2O3 C4AF = 3.0432Fe2O3 Therefore: C3S = (4.0710 x 65.6)-(7.6024 x 21.5)-(1.4297 x 2.8)-(6.718 x 5.2) C2S = (8.6024 x 21.5)+(1.0785 x 2.8)+(5.0683 x 5.2)-(3.0710 x 65.6) C3A = (2.6504 x 5.2)-(1.6920 x 2.8) C4AF = 3.0432 x 2.8 So: C3S = 64.7% C2S = 12.9% C3A = 9.0% C4AF = 8.5% It should be stressed that the Bogue calculation does not give the 'true' amounts of the four main clinker phases present, although this is sometimes forgotten. The results of the Bogue calculation differ from the 'true' amounts (often called the phase proportions) principally because the actual mineral compositions differ - often only slightly, but occasionally more so, aprticularly in the case of the ferrite phase - from those assumed in the calculation. Next / Home
You are in Clinker: the Bogue calculation The following pages have more details on clinker composition, reactions in the kiln and cement milling: Cement notation / Clinker compositional parameters / Combinability / Reactions in the kiln / Cement milling
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