Raw Material Mix Composition: Calculation

The calculation of the raw material mix composition is the first calculation the cement chemist makes and the last one the production manager checks: the arithmetic that converts the quarry geology into the kiln feed chemistry: the proportions of the limestone, the clay, the marl, the sand and the iron corrective that give the clinker its composition: the LSF, the silica ratio and the alumina ratio: the three modules that guard the burnability, the quality and the cost of the cement: without the correct mix, no kiln performance and no cement quality exist: the mix is the foundation of the plant.

The Complete Cement Technical Package (931 files including the books, the courses, the Excel tools and the presentations: $249.99 one-time: instant download via the PayPal payment) includes this guide with its worked examples, the module tables and the calculation spreadsheets: the article walks the file: the chemistry of the raw materials, the three modules, the Bogue formulas, the step-by-step mix calculations, the corrections and the practical tools: this article is written for the process engineers, the chemists, the QC teams and the students: the reader finishes with the complete calculation path in the hand: the same path the plant runs every day.

The raw mix calculation is a numbers game with real cement consequences: a one-point shift in the lime saturation changes the burnability, the free lime, the strength and the fuel bill of the plant: the guide of the package documents the full path from the XRF analysis of the single components to the final kiln feed recipe: the reader follows the same order: the components first, the modules second, the calculation third, the correction fourth, and the practical plant limits last.

1. The Raw Materials of the Mix: The Components the Chemist Blends

The natural raw materials of the cement plant belong to two families: the calcareous components that carry the calcium oxide (CaO) and the argillaceous components that carry the silica (SiO2), the alumina (Al2O3) and the iron oxide (Fe2O3): the typical proportions of the cement raw mix are about 75 to 80% limestone, 15 to 20% clay and 0 to 5% correction materials: the file opens with the diagnostic table of the components:

• The limestone: the calcareous rock with 50 to 54% CaO (calcium carbonate content of 90 to 96%): the main carrier of the lime: the quarries are selected for their CaCO3 grade and their MgO content (below 3% preferably, max 5% in the clinker);
• The marl: the mixed rock with 30 to 45% CaO: the natural intermediate between the limestone and the clay: the single-component feed of many wet plants: the homogeneity of the mari defines the quality of the kiln feed;
• The clay and the shale: the argillaceous source with 55 to 70% SiO2, 10 to 25% Al2O3 and 4 to 10% Fe2O3: the supplier of the silica and the alumina: the plasticity, the moisture and the quartz content are the watch points;
• The sand: the quartz-rich corrective with 85 to 96% SiO2: added when the silica module falls below the target: the coarseness of the quartz (above 45 microns) is the enemy of the burnability;
• The iron corrective (pyrite ash, laterite, ore): the Fe2O3 carrier with 50 to 70% iron oxide: added to lower the silica ratio and to provide the fluxing oxide for the burning: the consumption of the classic plants is 1 to 3% of the mix;
• The bauxite and the fly ash: the alumina correctives, the carriers of 40 to 60% Al2O3: used when the alumina ratio must rise for the special cement types;

The first lesson of the file: the mix calculation is only as good as the component analysis: the XRF (X-ray fluorescence) analysis of each component is the input of every calculation: the sampling discipline at the quarry, the crusher and the stockpiles decides the meaning of every number that follows: the file collects the typical compositions in the tables that the engineers use for the first estimates before the laboratory returns the measured values.

Component	CaO %	SiO2 %	Al2O3 %	Fe2O3 %	LOI %
High-grade limestone	52.5	1.5	0.5	0.3	42.5
Medium limestone	48.0	5.0	1.5	0.8	41.0
Marl	40.0	14.0	4.5	2.0	35.0
Clay	2.0	62.0	15.0	6.5	11.0
Shale	5.0	55.0	18.0	7.0	12.0
Sand	0.5	92.0	3.0	1.0	2.0
Iron ore	1.0	8.0	4.0	70.0	12.0
Fly ash	4.0	50.0	25.0	10.0	5.0

The table is the first working sheet of the package: the first estimates of any mix start from these ranges: the variation of the quarries is large and the measured values always replace the table: the chemist keeps the table with 70 years of the industrial data as the benchmark of the sanity checks: the numbers that follow in this guide use the measured analyses of a typical plant.

2. The Chemical Modules of the Mix: LSF, Silica Ratio and Alumina Ratio

The cement plant does not blend the components to arbitrary chemistry: it blends to the three modules that define the clinker: the lime saturation factor (LSF), the silica ratio (SR) and the alumina ratio (AR): the file explains each module with its formula, its range and its consequence:

• The lime saturation factor (LSF): the ratio that measures how close the mix is to the maximum lime that the silica, the alumina and the iron can saturate: LSF = 100 x CaO / (2.8 x SiO2 + 1.18 x Al2O3 + 0.65 x Fe2O3): the classic targets: 90 to 98% for the grey Portland clinker: the higher the LSF, the harder the burning and the higher the potential strength;
• The silica ratio (SR): SR = SiO2 / (Al2O3 + Fe2O3): the ratio of the solid-forming oxides to the fluxing oxides: the usual range of 2.0 to 3.2: the high SR mixes burn slowly, the low SR mixes are sticky and coat the kiln;
• The alumina ratio (AR): AR = Al2O3 / Fe2O3: the ratio between the two fluxing oxides: the typical range 1.0 to 2.5: the high AR favors the aluminate (C3A) and the lower clinkering temperatures of the liquid phase; the low AR favors the ferrite (C4AF);
• The combined modules: the three modules overlap in their meaning: the LSF controls the potential C3S, the SR controls the proportion of the liquid phase, the AR controls the composition of the liquid: the targets of the plant follow the cement type, the raw materials and the kiln system.

The modules are the language of the mix: when the engineer says “the mix is harsh”, he means the LSF is high and the SR is high; when he says “the mix is sticky”, the LSF is low and the liquid phase is abundant: the file dedicates a table to the inter-relations of the modules with the burnability so that the plant teams speak the same language as the kiln operators:

Module	Typical range (OPC)	Effect when high	Effect when low
LSF	90 – 98	Hard burning, rich C3S, high strength potential	Easy burning, low strength, dusty clinker
Silica ratio	2.0 – 3.2	Slow burning, low liquid, high refractory wear	Fast burning, sticky coating, ring risk
Alumina ratio	1.0 – 2.5	High C3A, quick setting, higher heat of hydration	High C4AF, slower setting, sulfate-resistant character

The modules of the target are set by the quality department for each cement type: the high-early-strength cements run at LSF 95 to 98, the sulfate-resisting cements run at low AR (below 0.9 sometimes), the white cement runs at very low iron (Fe2O3 below 0.4%) with careful fluxing: the mix calculation serves the module targets: the calculation exists to hit the numbers.

3. The Bogue Calculation: The Potential Clinker Composition

The Bogue calculation converts the oxide analysis of the mix into the potential phase composition of the clinker: the four main phases of the Portland clinker: the tricalcium silicate (C3S or alite), the dicalcium silicate (C2S or belite), the tricalcium aluminate (C3A) and the tetracalcium aluminoferrite (C4AF): the file presents the Bogue formulas in the classical form:

• C3S = 4.071 x CaO − 7.600 x SiO2 − 6.718 x Al2O3 − 1.430 x Fe2O3 (with the oxides recalculated to the ignited basis);
• C2S = 2.867 x SiO2 − 0.7544 x C3S (or by the difference from 100%);
• C3A = 2.650 x Al2O3 − 1.692 x Fe2O3;
• C4AF = 3.043 x Fe2O3;

The Bogue calculation is a convention, not an exact measurement: the microscopy of the polished sections shows that the real clinker deviates from the Bogue values because the actual phases dissolve foreign ions: the file is explicit: the Bogue numbers are the potential composition and the standard language of the industry: the QC reports, the ASTM standards and the cement specifications all speak Bogue: the engineer must know both the power and the limits of the method.

A typical OPC clinker computed by Bogue contains about 55 to 65% C3S, 15 to 25% C2S, 6 to 10% C3A and 8 to 12% C4AF plus the 2 to 3% of the residual constituents (MgO, alkalis, SO3): the Excel tool of the package computes the Bogue phases in one click from the ignited oxide analysis: the same spreadsheet calculates the modules and the Bogue simultaneously, so the QC shift checks the complete picture of the mix at every hour.

4. The Worked Example: Blending Two Components

The simplest mix calculation uses two components: the limestone and the clay: the chemist targets a fixed LSF and solves the proportions: the file walks the full example with the measured analyses:

• The limestone: 52.0% CaO, 1.8% SiO2, 0.6% Al2O3, 0.3% Fe2O3 (ignited basis);
• The clay: 2.5% CaO, 63.0% SiO2, 14.0% Al2O3, 6.0% Fe2O3 (ignited basis);
• The target: LSF = 95 and SR = 2.4;

With the fraction x of limestone and (1 − x) of clay, the mix oxides are the weighted averages: CaO = 52.0x + 2.5(1 − x), SiO2 = 1.8x + 63.0(1 − x), Al2O3 = 0.6x + 14.0(1 − x), Fe2O3 = 0.3x + 6.0(1 − x): substituting into the LSF formula and solving gives x = 0.78: the mix of 78% limestone and 22% clay: the check with the SR formula confirms the mix: SR = 13.8 / (3.5 + 1.6) = 2.7, a little high: the addition of the iron corrective next adjusts the ratio.

The arithmetic of two components is the foundation: the real plants rarely hit both the LSF and the SR with two components: the third and fourth components correct the ratios: the calculation grows from the same weighted-average logic: the file then shows the general system of equations that solves any number of components: the linear algebra of the mix: the students of the package learn the manual method once, then use the Excel solver for the daily plant work.

5. The Three-Component Correction: Sand and Iron in the Mix

When the two-component mix does not satisfy the modules, the correction materials enter: the file works the complete numerical example of the Portland mix with four components:

• The target modules: LSF = 95.0, SR = 2.4, AR = 1.6;
• The limestone: 52.0% CaO, 1.8% SiO2, 0.6% Al2O3, 0.3% Fe2O3;
• The clay: 2.5% CaO, 63.0% SiO2, 14.0% Al2O3, 6.0% Fe2O3;
• The sand: 0.5% CaO, 94.0% SiO2, 2.0% Al2O3, 0.6% Fe2O3;
• The iron ore: 1.0% CaO, 7.0% SiO2, 4.0% Al2O3, 72.0% Fe2O3;

The solution of the four-equation system (the CaO balance, the SiO2 balance, the Al2O3 balance and the Fe2O3 balance against the three modules rewritten as composition targets) yields the proportions: 74.8% limestone, 19.5% clay, 3.9% sand and 1.8% iron ore: the mix satisfies all three modules within 0.1: the calculation of the file reproduces the numbers step by step so the reader can follow with a calculator and verify by hand: 100 grams of the mix give the clinker chemistry of 66.8% CaO, 21.5% SiO2, 5.0% Al2O3, 3.2% Fe2O3 after the loss on ignition of 34.5% is removed.

The correction logic is worth its weight: the sand costs little and the iron ore costs little, but the two together convert a mediocre two-component mix into the balanced kiln feed: the equipment of the plant then doses the four components at the weigh feeders: the 74.8 : 19.5 : 3.9 : 1.8 ratio becomes the setpoints of the raw mill blending: the calculation sheet of the package delivers exactly the setpoints.

6. The Loss on Ignition and the Raw-to-Clinker Factor

The raw mix enters the kiln with the carbonate and the clay water: the burning drives off the CO2 of the calcium carbonate (about 44 grams of CO2 per 100 grams of CaCO3) and the combined water of the clay: the loss on ignition (LOI) of a typical Portland mix is 34 to 36%: the file explains the two conversions that every plant uses:

• The raw-to-clinker factor: the mass of the raw mix needed to produce one unit of clinker: the factor is roughly 100 / (100 − LOI): with LOI = 35%, the factor is 100/65 = 1.54: one ton of clinker needs 1.54 tons of dry raw mix: the plant designs the raw grinding and the kiln capacities with this factor;
• The ash factor: when the coal ash (typically 10 to 20% of the fuel mass) enters the clinker, the mix must compensate: the raw mix for the coal-fired kiln accounts for the ash at about 1 to 3% of the clinker mass: the calculation subtracts the expected ash oxides from the clinker target and re-solves the mix;
• The moisture correction: the quarry limestone carries 2 to 8% surface moisture and the clay 10 to 25%: the dry-basis proportions convert to the wet doses at the weigh feeders: the daily correction of the recipe follows the moisture report;
• The ignition basis: all the module calculations run on the ignited (LOI-free) composition: the chemist first recalculates the oxide analysis to 100% without the LOI, then runs the modules: the file shows both bases in the same table so the confusion never arises.

The numbers of the factor are the bridge between the process units: the quarry tonnage, the mill tonnage, the kiln tonnage and the cement tonnage convert through the LOI and the clinker factor: the annual plan of the plant (raw material inventory, fuel purchase, cement dispatch) starts from the same factor: the file gives the conversion tables for LOI 30 to 40% and the corresponding factors: the practical quick references of the daily planning.

7. The Homogeneity of the Kiln Feed: The Goal of the Mix Calculation

The calculated mix is a target: the real kiln feed must stay near the target hour after hour: the file devotes a section to the homogeneity specifications that make the calculation meaningful:

• The variation of the chemistry: the good plants hold the LSF of the kiln feed within plus or minus 1.5 to 2.0 points of the target and the SR within plus or minus 0.1 to 0.15: the raw meal sampled at the kiln inlet shows the standard deviation of CaCO3 below 1.0 to 1.5% (the four-minute samples of the XRF probe);
• The homogenization chain: the blending bed, the silo, the pneumatic homogenization: the plants with the pre-homogenization stockpiles and the continuous or batch homogenizing silos achieve the required constancy: the retention time of the silo and the air flow of the aeration system are the homogenization levers;
• The residence statistics: the controlled mixing index and the coefficient of variation of the kiln feed: the CV below 2% is the modern target of the closed-loop plants: the CV of the old plants at 4 to 6% explains the coating problems and the free-lime peaks;
• The continuous measurement: the PGNAA analyzers on the belt or the XRF probes on the meal stream feed the automatic corrections of the recipe: the modern plants recompute the mix proportions continuously and dose the weigh feeders in closed loop: the mix calculation, automated.

The homogeneity section of the file teaches the system view: the exact calculation is the half of the story and the homogenization is the other half: the perfectly calculated mix delivered with the variance of the uncontrolled quarry fails the kiln: the guide’s message: calculate accurately, homogenize continually and control the feeder discipline: the three legs of the stable kiln feed.

8. The Target Values by Cement Type: The Recipe Book of the Plant

The mix calculation always serves a specific cement type with a specific module recipe: the file includes the reference table of the common cement types and their typical mix targets (the exact values follow the local standards and the plant practice):

Cement type	LSF	SR	AR	Characteristic
OPC (CEM I 42.5)	93 – 96	2.3 – 2.7	1.4 – 1.8	The standard grey clinker
High-early-strength (CEM I 52.5)	95 – 98	2.0 – 2.4	1.3 – 1.7	Rich in C3S, hard burning
Sulfate-resisting (CEM I SR)	92 – 95	2.5 – 3.2	below 0.9	Low C3A, ferrite-rich
White cement	94 – 97	2.8 – 3.4	above 8	Fe2O3 below 0.4%
Low-heat cement	88 – 92	2.6 – 3.0	1.0 – 1.4	Belite-rich, low C3A

The table is the starting point of the recipe development: the target of the plant is refined by the burnability of its own raw materials and the performance of its kiln: the file warns the reader: the modules given above are the industry ranges, not the fixed specifications: the authoritative limits come from the product standard (EN 197-1, ASTM C150 or the local standard) and the plant’s history: the recipe book of the plant records what the market requires and what the kiln delivers.

9. The Free Lime and the Burnability: The Feedback of the Mix

The quality of the mix reveals itself in the free lime of the clinker and in the burnability of the raw meal: the file links the calculation to the kiln feedback loop:

• The free lime (free CaO): the lime that did not combine into the silicates: the target of the well-burned grey clinker is 0.5 to 1.5% free lime (ASTM C114 titration or the chemical method): above 2%, the cement strength drops and the soundness suffers;
• The burnability test: the laboratory burns the raw meal pellet at 1350, 1400 and 1450 °C and measures the resulting free lime: the curve tells the plant how hard the mix demands to burn: the mix with LSF 98 needs 1450 °C with a long retention; the mix with LSF 92 burns easily at 1400 °C;
• The coarse residue: the quartz and the calcite particles above 45 to 90 microns survive the kiln as the unreacted cores: the raw meal residue on the 90 micron sieve of 12 to 15% and on the 200 micron sieve of 1 to 2% are the common targets: the fineness of the raw meal is part of the mix quality;
• The reaction: the burning zone temperature 1350 to 1500 °C, the retention time at the peak temperature of 10 to 20 minutes and the liquid phase of 20 to 30%: the burnability of the mix decides how much fuel the kiln must spend to reach the free-lime target: the mix calculation, the fuel bill.

The relationship is quantitative: the clinker free lime rises by roughly 0.3 to 0.5% for each point of LSF above 96 in typical plants, and the specific fuel consumption of the kiln rises with the harsh mixes: the chemical engineer of the package learns to read the free lime trend as the live verdict of the mix calculation: the daily chemistry, corrected.

10. The Alkalis, Sulfate and Magnesia: The Minor Components of the Mix

The major oxides decide the modules, but the minor components decide the durability, the kiln operation and the cement conformity: the file dedicates the full section to the constraints:

• The magnesia (MgO): the limit of 5% MgO in the clinker by most standards (ASTM C150, EN 197-1): the periclase crystals formed at the high burning cause the delayed expansion and the soundness failures: the selection of the low-MgO limestone (below 3% MgO in the clinker is the prudent target);
• The alkalis (Na2O, K2O): the equivalent alkali limit (Na2O + 0.658 x K2O) of 0.6% for the low-alkali cements demanded by the reactive aggregate concrete: the alkalis drive the kiln circulation problems (the alkali sulfates condense in the preheater) and the cement-setting acceleration;
• The chloride: the clinker chloride limit of 0.1% in the modern preheater plants: the chloride circulating in the gases corrodes the stainless steels of the preheater at the chloride levels above 0.2 to 0.3% in the kiln feed: the raw material control against the marine clays and the salts;
• The sulfate (SO3): the sulfur enters with the fuel and the raw materials: the clinker SO3 of 0.4 to 1.0% is typical: the sulfur-to-alkali ratio shapes the coating and the preheater buildup: the SO3 of the finish cement is adjusted separately with the gypsum;
• The phosphorous and the fluorine: the minor elements useful in the low doses as the mineralizers (P2O5 below 1.5% helps the belite; CaF2 of 0.2 to 0.5% lowers the clinkering temperature by 50 to 100 °C) and harmful in the high doses: the mix control of the trace elements is part of the modern specification.

The minor oxides are the constraints that the calculation must respect: the mixture that reaches the exact LSF with the MgO above the limit is not a solution: it is a problem: the file teaches the two-stage logic: first hit the modules, then verify the minors, and if the minors fail, return to the component selection: the quarry planning and the correctives solve the constraint problems at the source.

11. The Excel Tool of the Package: The Mix Calculator

The Complete Cement Technical Package includes the Excel spreadsheet that automates the entire calculation of this article: the structure of the tool follows the sections above:

• The input sheet: the oxide analyses of up to six components (CaO, SiO2, Al2O3, Fe2O3, MgO, SO3, K2O, Na2O, LOI);
• The target sheet: the LSF, the SR and the AR targets with the limits for the minors;
• The solver sheet: the proportion solver that minimizes the error of the three modules by adjusting the recommended components: the results: the recipes in the percentage and in the tonnage per hour at the raw mill;
• The output sheet: the ignited oxide analysis of the mix, the Bogue phases, the free-lime estimate, the raw-to-clinker factor and the wet doses from the moisture inputs;
• The scenario feature: the comparison of the recipes for the winter and the summer quarries, for the different kilns and for the different cement types: the what-if analysis of the mix: the planning power of the tool;

The tool reproduces every example of this article with the one-click solve: the engineers of the package use the spreadsheet for the daily corrections, the monthly recipe reviews and the capital studies: the manual arithmetic of the article keeps the user honest and the spreadsheet keeps the user fast: the pair of the professional process engineer.

12. The Plant Practice: From the Calculation to the Kiln Feed

The final sections of the file translate the calculation into the daily discipline of the plant:

• The sampling every hour: the kiln feed sample to the XRF and the quick CaCO3 titrations: the control charts of the LSF, the SR and the AR: the corrective actions when the mix drifts: the closed loop of the QC laboratory;
• The weigh feeder setpoints: the recipe percentages become the setpoints of the four feeders (limestone, clay, sand, iron): the belt scales and the moisture compensations: the automated recipes from the master computer: the manual fallback drills;
• The stockpile management: the limestone grades from the different quarry benches are blended in the pre-homogenization bed: the average chemistry of the bed is the real component analysis of the day: the planning of the beds ahead of the shifts;
• The kiln feedback: the free lime, the clinker microscopy, the burning zone temperature and the coating pattern tell the process team whether the recipe serves the kiln: the weekly review meetings of the mix, the fuel and the quality: the numbers of the report card: the LSF, the SR, the AR, the free lime, the 28-day strength;
• The recalculation frequency: the full re-optimization of the recipe monthly and after every quarry change: the minor corrections daily from the XRF: the automation level of the modern plants recalculates continuously: the tradition of the plants remains the same arithmetic inside the fast machinery.

The mix calculation is not a one-time design exercise: it is the permanent feedback loop of the plant: the calculation, the feed, the clinker, the test, the correction: the loop that never stops: the file of the package documents the loop so completely that the new engineer can run the daily QC shift from the first week.

13. The Frequently Asked Questions

What is the difference between the LSF and the hydraulic modulus?

The hydraulic modulus (HM) is the older ratio CaO / (SiO2 + Al2O3 + Fe2O3) with the target of 1.7 to 2.3: the lime saturation factor is the refined version with the stoichiometric coefficients 2.8, 1.18 and 0.65 that reflect the exact oxide requirements of the clinker phases: the industry reports the LSF today and the HM survives in the older literature and in the documents of the 1950s: the file of the package uses the LSF throughout and explains the conversion of the HM to the LSF.

Why does the calculation use the ignited basis?

The LOI of the mix (34 to 36%) is driven off in the kiln and plays no part in the chemistry of the clinker phases: the modules must therefore be computed on the ignited oxides (recalculated to 100% without the LOI): the raw-basis numbers would dilute the ratios and hide the true chemistry: every module calculation of this article runs on the ignited basis exactly as the plant chemists compute.

How tight must the kiln feed chemistry be?

The practical targets: the LSF within plus or minus 1.5 to 2.0 points, the SR within plus or minus 0.1 to 0.15 and the CaCO3 standard deviation below 1.5%: the best plants hold the CV of the kiln feed below 2%: the tighter the feed, the more stable the kiln, the lower the free lime and the better the cement-to-cement consistency that the customers measure.

Can the same mix serve both OPC and blended cement?

Yes, in the practical plants: the same grey clinker is ground with the different additions (slag, fly ash, limestone, pozzolana) to make the blended cement types: the OPC clinker quality itself is designed once with the modules for the strongest product of the range and the additions dilute the final chemistry: the mix calculation serves the clinker; the finish mill serves the cement variety.

Does the file include the ready-made Excel calculator?

Yes: the Complete Cement Technical Package includes the mix calculation spreadsheet with the component inputs, the module solver, the Bogue output and the scenario comparisons: the 931 files of the package include the calculators, the courses and the books: the spreadsheet makes the daily recipe work of this article a matter of minutes.

14. Conclusion

The calculation of the raw material mix composition is the quiet arithmetic at the foundation of every ton of cement: the three modules, the Bogue phases, the corrections, the factors and the homogeneity discipline: the steps that convert the rocks of the quarry into the clinker of the specification: the chemistry of the plant, quantified: the profession of the cement chemist, systematized: the engineer who masters the mix calculation masters the entry gate of the whole process.

The Complete Cement Technical Package includes this guide with the worked examples, the module tables and the master Excel tool: the one-time $249.99 purchase, the instant download and the lifetime access: the 931 files of the library: the cement knowledge, complete: the mix calculation of this article, the same calculation the plants of the world run every hour: the professional’s reference, at the hand.

This file is part of the Complete Cement Technical Package (931 files) available from cementequipment.org. Respective rights holders; library copy for the licensed single user.