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.
You 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 control parameters:
- Silica ratio
- Alumina-iron ratio
- Lime factor
The 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 analysis.
• 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 original work
1. “Chemical Control of Portland Cement Clinker,” Ceramic Bulletin, Vol. 61, No. 4, 1982, pages 511 to 515.
|Silica ratio = SR or SM = SiO2/Al2O3 + Fe2O3 |
|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) + (0.65Fe2O3) |
For MgO below 2%
|Lime saturation factor = LSF = 100(CaO + 1.5Mg) / (2.85SiO2) + (1.18Al2O3) + (0.65Fe2O3) |
For MgO above 2%
Bogue Equations for Potential Composition
|C3S = 4.071C – 7.6S – 6.718a – 1.43F |
|C2S = -3.071C + 8.6S + 5.068A + 1.079F |
|C3A = 2.65A – 1.692F |
|C4AF = 3.043F |