Putting Bogue Back in Vogue
Today the Bogue equations are most often cited for their
shortcomings rather than their usefulness, but their contribution
to cement chemistry and especially raw mix design are invaluable.
The Bogue equations provide a simple and convenient method
to find out the final composition of a clinker, which tells
us a lot about its likely behavior. Technically, they indicate
the potential composition since not all of the reactions that
occur in the kiln will go to completion and since the cement
phases are not ideal compounds. Plant chemists have used these
equations for years, sometimes adjusting them based on their
own raw materials and their own experience.
can’t make cement if you don’t know all about
your raw materials. An oxide analysis of the raw materials
is the first step, which provides input for a wide variety
of ratios and moduli that relate oxide compositions to one
another. These include: LSF (lime saturation factor), SM (silica
modulus or ratio), AR (alumina-to-iron ratio), and other lesser-used
formulas like the hydraulic modulus.
So just how do you come up with a raw mix proportions from
an oxide analysis? That’s the basic principle behind
raw mix design and one of the pioneers that put Bogue back
in vogue was Clyde Moore. His important contribution to raw
mix design was made in a landmark paper titled, Chemical
Control of Portland Cement Clinker1.
Moore selected what he considered were the three most critical
- Silica ratio
- Alumina-iron ratio
- Lime factor
silica ratio represents the burnability of a raw mix. The
burnability impacts how much energy is put into the system.
As the ratio of silica to alumina plus iron increases, it
becomes harder to “burn” — harder to combine
the raw materials into the phases we want. As the ratio decreases,
the tendency for fluxing (the ability of the solid materials
to become liquid) increases, and the combining reactions become
easier. Another consideration is that silica present as quartz
is generally more difficult to combine than silica present
as silicates. The alumina-to-iron ratio is important because
it controls the potential C3A/C4AF ratio
in the finished cement, which is important because of sulfate
resistance, heat generation, and admixture compatibility issues.
The lime saturation factor controls the potential C3S
to C2S ratio in the finished cement. C3S
governs the early age strength development while C2S governs
the later age strength.
Moore discovered that Kind’s formula (which defines
a modulus based upon the lime, alumina, iron, and silica amounts)
can be further refined into what he defined as the lime factor.
The importance of the lime factor is that it includes all
four of the ingredients necessary for clinker production.
But Moore went a step further. He used this new lime factor
along with the silica ratio and alumina-iron ratio to come
up with a simple resource for raw mix design. By substituting
the three moduli (lime factor, silica ratio, and alumina-iron
ratio) into the Bogue equations and performing some basic
algebra, Moore was able to define the four clinker phases
by specifying just three control parameters.
The key to Moore’s method lies in recognizing that
most plants obtain their raw materials from just one source.
Even if there is some variation, any difference can be distributed
proportionally among the four clinker phases. The advantages
to Moore’s method are impressive:
• The four clinker phases (C3S, C2S, C3A, C4AF) are
defined by just three parameters.
• Equations can be derived directly for each of the
phase compositions in terms of the control parameters.
• The ratios of oxides can be used either on a clinker
basis or on a raw-feed basis since the ratios are independent
of loss on ignition.
• There’s no need to think in terms of potential
clinker phases in the kiln feed where the clinker phases
do not yet even exist.
• The relative error in the lime factor is less than
the relative error calculated in C3S content from the oxide
• There’s an easy check on the “real”
lime factor through the use of XRD.
Moore developed a variety of examples to illustrate his method,
including the design of a raw mix when three materials are
available by using two parameters, such as the lime factor
and silica ratio.
Today’s manufacturing environment uses rapid, in-stream
sampling and analysis coupled with computerized proportioning
to make almost continuous process improvements. It is a far
cry from the matrix methods that helped Moore develop his
quantitative relations between chemical control parameters
and clinker phases. Moore’s method may indeed seem simplistic.
But the real benefit is that Moore’s method makes raw
mix design intuitively obvious for the new process engineer
or plant chemist. It’s a great teaching tool because
it incorporates the basics.
The information in this newsletter was obtained primarily
from PCA’s Control
of Portland Cement Quality by Clyde Moore and his
1. “Chemical Control of Portland Cement Clinker,”
Ceramic Bulletin, Vol. 61, No. 4, 1982, pages 511
|Silica ratio = SR or SM = SiO2/Al2O3
|Alumina-iron ratio = AR = Al2O3/Fe2O3
|Lime factor = C – (1.65A + 0.315F)/S
|Lime saturation factor = LSF = 100(CaO
+ 0.75Mg) / (2.85SiO2) + (1.18Al2O3)
For MgO below 2%
|Lime saturation factor = LSF = 100(CaO
+ 1.5Mg) / (2.85SiO2) + (1.18Al2O3)
For MgO above 2%
Bogue Equations for Potential
|C3S = 4.071C – 7.6S – 6.718a
|C2S = -3.071C + 8.6S + 5.068A + 1.079F
|C3A = 2.65A – 1.692F
|C4AF = 3.043F