Cooler Calculation Excel: Calculations & Excel Sheet

The clinker cooler calculation is the engineering workbook of the clinker cooler: the air flows, the heat recovery, the grate loading, the cooling curves, the pressure drops and the fan requirements that together determine how much of the clinker heat is recovered into the process and how much is lost to the stack. The cooler is the machine between the kiln and the cement mill: it receives the clinker at 1,300–1,450°C from the kiln discharge and it must cool the clinker to 80–150°C for the storage, the grinding and the dispatch, while returning the maximum possible heat to the kiln and the calciner as the hot secondary and tertiary air. The cooler calculation spreadsheet carries the entire design and verification procedure in structured sheets: the input data, the air requirements, the heat balance, the efficiency, the fan duties, the pressure drops and the operating parameters.

The Complete Cement Technical Package (931 files including the Cooler calculation Excel workbook, engineering tools, books, courses and presentations, $249.99 one-time, instant download) includes the cooler calculation spreadsheet with its sheets for the fuel type, the clinker data, the air flows, the pressure drops and the current operating parameters, exactly as used in the plant engineering practice. This article walks through the cooler calculation in complete technical detail: the role of the cooler in the process, the types of coolers, the input data, the cooling air requirement, the heat balance and the recovery, the cooler efficiency, the grate loading and the bed depth, the air distribution and the fan duties, the pressure drops, the worked example, the interpretation of the results, the common mistakes and the link to the rest of the pyro system.

1. The Role of the Clinker Cooler in the Process

The clinker cooler performs three duties in the cement plant. The first is the process duty: the rapid cooling of the clinker to lock in the quality, because the rate of the cooling determines the crystal structure of the clinker phases, the grindability of the clinker and the strength development of the cement. The second is the heat recovery duty: the cooling air becomes the hot secondary air of the kiln and the tertiary air of the calciner, and the recovery of this heat is worth 100–150 kcal/kg clinker to the specific heat consumption of the system. The third is the logistics duty: the cooled clinker can be conveyed, stored and ground without damaging the belts, the silos and the mills.

• The quality duty: the fast cooling of the clinker below 1,200°C fixes the alite and the belite in their hydraulic forms, prevents the alite reversion and improves the grindability and the reactivity;
• The recovery duty: the secondary air returns to the kiln at 850–1,100°C and the tertiary air to the calciner at 750–950°C, and together they carry 500–700 kJ/kg clinker of the recovered heat;
• The logistics duty: the clinker leaves the cooler at 80–150°C, a temperature that the belt conveyors, the bucket elevators, the storage halls and the mill feed systems accept;
• The exhaust duty: the surplus cooling air leaves the cooler as the vent air at 250–400°C, available to the raw mill drying, the waste heat recovery or the dedusting;

The cooler therefore sits at the heart of the pyro system’s efficiency: a poorly performing cooler raises the specific heat consumption, lowers the secondary air temperature, damages the clinker quality and burdens the kiln, while a well-performing cooler returns its capital cost many times over through the fuel savings over the plant life. The cooler calculation workbook is the instrument that sizes, verifies and operates this machine.

2. The Types of Clinker Coolers

The cooler calculation must know its subject, and the workbook supports the main cooler types of the industry. The reciprocating grate cooler is the standard of the modern plants, with the clinker forming a bed on the inclined grates and the air blowing up through the bed from the compartments below. The cross-bar cooler and the shaft cooler are the recent developments of the same principle, with the clinker transported by the cross bars through the fixed grate and the air supplied by the separate shafts. The planetary cooler and the rotary cooler belong to the older designs, mounted on the kiln itself, and the rotary cooler is found on the smaller and the older plants.

The modern grate coolers dominate the calculation practice because they equip the majority of the world’s new and retrofitted lines. Their operation is characterized by the three-zone air supply: the first compartment under the hottest clinker receives the highest specific air flow to quench the clinker surface, the middle compartments continue the cooling with the moderate air, and the last compartments receive the low air that simply stabilizes the bed and the clinker discharge temperature. The calculation workbook mirrors this three-zone structure in the air distribution sheet.

3. The Input Data of the Cooler Calculation

The cooler calculation begins with the input sheet, the same sheet that the example workbook carries with the fuel type and the operating parameters. The inputs fall into four groups: the clinker data, the kiln data, the air data and the operating data.

• The clinker production: the tonnes per day of the clinker at the cooler inlet, the anchor of every calculation line;
• The clinker temperature at the inlet: 1,300–1,450°C from the kiln discharge, measured at the hood or taken from the kiln balance;
• The clinker temperature at the discharge: the target of the design, 80–150°C for the modern plants, plus the ambient temperature;
• The clinker specific heat: about 0.19–0.21 kcal/kg°C or 0.80–0.88 kJ/kg°C, with the small variation by the clinker composition;
• The kiln fuel and the secondary air: the fuel type (pet coke, coal, alternative fuel), the fuel rate and the theoretical air of the kiln, because the secondary air demand is set by the kiln combustion;
• The calciner fuel and the tertiary air: the calciner fuel rate and its air demand, which set the tertiary air requirement;
• The ambient conditions: the temperature, the pressure and the altitude, which correct the air densities and the fan duties;
• The operating parameters: the grate speed, the bed depth, the compartment pressures and the air flows, the data that the plant records in the daily operation;

The workbook carries the input cells in the shaded format and the calculated cells in the protected format, so the user enters the plant’s data and reads the complete calculation: the same discipline as the kiln pyro balance and the material balance workbooks of the package. The fuel type line of the example workbook, pet coke, determines the combustion air demand that the cooler must supply as the secondary and the tertiary air, which is why the fuel data is the first input of the sheet.

4. The Cooling Air Requirement: The Basis of the Design

The cooling air requirement of the cooler has two components: the air that the process demands and the air that the cooling demands, and the larger of the two at each point of the cooler governs the design. The process demand is the secondary and the tertiary air of the kiln and the calciner, computed from the fuel rates and the excess air of each burner. The cooling demand is the air that the clinker needs to shed its heat, and it is computed from the heat balance of the cooler.

The specific cooling air of a modern grate cooler runs at 1.8–2.4 Nm3 per kg of clinker, of which the secondary and the tertiary air take roughly 0.7–1.0 Nm3/kg and the vent air the balance. The cooling air total is the product of the clinker rate and the specific air flow:

Q air = M clinker x q air

where Q air is the total cooling air in Nm3/h, M clinker the clinker rate in kg/h and q air the specific air flow in Nm3/kg. For a 5,000 t/d line at 2.1 Nm3/kg, the total cooling air is about 437,000 Nm3/h, a figure that the fan sheet of the workbook converts into the fan duties with the pressure and the temperature corrections.

• The secondary air demand: the kiln fuel rate multiplied by the theoretical air per kg of fuel and the excess air factor, corrected for the primary air share;
• The tertiary air demand: the calciner fuel rate multiplied by its theoretical air and the excess air factor;
• The vent air: the total cooling air minus the secondary and the tertiary air, the flow that leaves the cooler to the stack, the dedusting or the heat recovery;
• The balance check: the air mass balance of the cooler: the inlet air equals the secondary plus the tertiary plus the vent plus the seal leakage and the false air;

The distribution of the air between the compartments follows the clinker temperature profile: the hottest first compartments receive 40–60% of the total air in the quench zone, because the heat transfer rate is highest where the temperature difference between the clinker and the air is highest, and the air that passes the hot clinker returns as the hot secondary air. The workbook distributes the air by the compartment zones and computes the air velocity in the bed, the governing parameter of the heat transfer and the clinker elutriation.

5. The Heat Balance of the Cooler

The heat balance of the cooler is the account of the heat flows across its boundary, and it is the verification of the whole calculation. The heat in is the heat of the hot clinker from the kiln; the heat out is the heat of the cooled clinker, the heat of the secondary and the tertiary air, the heat of the vent air, and the radiation and convection losses of the cooler shell.

Q clinker in = Q clinker out + Q secondary air + Q tertiary air + Q vent air + Q shell losses

The heat of the clinker at any temperature is the product of the clinker mass, its specific heat and the temperature above the reference:

Q = M x cp x (T – T reference)

For the example of the 5,000 t/d line, the clinker enters at 1,400°C and leaves at 120°C: the heat available for the recovery is the clinker mass of 208 t/h times the specific heat of 0.20 kcal/kg°C times the drop of 1,280°C, which is about 53.3 million kcal/h. Of this heat, the secondary and the tertiary air recover about 60–70%, the vent air carries 20–30% to the stack, the cooled clinker carries about 8%, and the shell and the radiation losses take the small remainder. The balance sheet of the workbook holds each term and closes the account to within the measurement tolerance, and the closure is the check of the input data.

6. The Cooler Efficiency: The Recovery and the Cooling Efficiencies

The performance of the cooler is expressed in two efficiencies, and the calculation workbook computes both. The heat recovery efficiency measures the share of the clinker heat that returns to the process:

Heat recovery efficiency = (Q secondary air + Q tertiary air) / (Q clinker in – Q clinker at reference)

The cooling efficiency measures the share of the heat that the cooler actually removes from the clinker:

Cooling efficiency = (Q clinker in – Q clinker out) / (Q clinker in – Q clinker at reference)

For a modern grate cooler, the heat recovery efficiency is typically 60–75% and the cooling efficiency is typically 90–96%, because the discharge temperature of 80–150°C leaves little heat in the clinker while the vent air inevitably carries a share of the recovered heat away. The difference between the two efficiencies is the definitional trap that the workbook labels explicitly: the recovery efficiency includes the vent air in the loss column, while the cooling efficiency counts only the heat that the clinker keeps.

The improvement of the recovery efficiency is the central optimization of the cooler operation: a deeper clinker bed, a uniform bed profile, the correct grate speed and the proper air distribution raise the secondary air temperature and reduce the specific heat consumption by 30–80 kJ/kg clinker, which is 5,000–12,000 tonnes of coal per year on a large line. The workbook computes the recovery at the current parameters and at the target parameters, and the difference is the value of the cooler improvement project.

7. The Grate Loading and the Bed Depth

The grate loading is the clinker rate per unit of the grate area, and it is the principal sizing parameter of the cooler. The modern grate coolers run at 35–55 t/m2/day of the grate area, with the larger lines at the higher loadings, and the bed depth runs at 600–900 mm in the quench zone, falling toward the discharge as the clinker volume shrinks with the cooling. The grate speed is the operating variable that the operator controls to hold the bed depth: the speed rises when the clinker is fine or the rate is high, and falls when the bed grows too deep.

Grate loading = Clinker rate / Grate area

The bed depth and the clinker size distribution determine the pressure drop across the bed, which is the resistance that the fans must overcome: a typical grate cooler bed drops 600–1,200 mm WG (millimeters of water gauge) across the full bed, and the air distribution between the compartments is controlled by the compartment pressures to hold the uniform aeration. The pressure drop sheet of the example workbook carries the current compartment pressures, the basis of the fan adjustment and the diagnosis of the blocked or the dead compartments.

• The quench zone: the first one to two compartments, the deepest bed at 700–900 mm, the highest specific air and the most aggressive cooling of the clinker surface;
• The recovery zone: the middle compartments, where the secondary and the tertiary air ducts draw their hot air and the bed begins to thin;
• The final cooling zone: the last compartments, the thin bed at 300–600 mm, the low air flow and the stabilization of the discharge temperature;
• The clinker size distribution: the fine clinker packs the bed and raises the pressure drop; the coarse and the open clinker leaks the air and reduces the recovery;

The operation of the bed is the daily art of the cooler: the uniform feed distribution across the grate width, the stable bed depth, the balanced compartment pressures and the hot-spot control are the four variables that the operator watches, and the calculation workbook provides the design basis against which the current operation is compared.

8. The Air Distribution and the Fan Duties

The cooling air is supplied by the cooler fans, one or two fans per compartment, and the fan sheet of the workbook computes each fan duty from the air flow, the pressure and the temperature. The fan duty follows the fan laws: the flow is set by the compartment air requirement, the pressure by the bed resistance plus the duct losses, and the power by the flow, the pressure and the efficiency.

P fan = Q x delta p / (eta fan x eta drive)

where P fan is the fan shaft power in kilowatts, Q the air flow in m3/s, delta p the total pressure in pascals, and eta the fan and the drive efficiencies. For the example cooler, the total air of 437,000 Nm3/h at an average pressure of 900 mm WG with a fan efficiency of 75% demands about 14,000–16,000 kW of installed fan power, a figure that appears in the plant-wide power budget and in the financial model’s OPEX sheet. The workbook converts the air flows to the actual cubic meters at each fan’s temperature, because the hot air of the recovery zone draws more fan power per kilogram than the cold air of the final zone, and the density correction is the difference between the correct and the under-sized fan.

• The quench fans: the highest pressure fans, 1,000–1,400 mm WG, serving the deep bed of the hottest clinker;
• The recovery zone fans: 700–1,000 mm WG, serving the middle compartments and the hot air ducts;
• The final zone fans: 400–700 mm WG, serving the thin bed and the low air of the discharge end;
• The vent air fan: the induced draft of the cooler exhaust, sized for the vent air at its temperature and the bag filter pressure;
• The fan control: the variable speed drives on the modern coolers, saving 20–40% of the fan power against the damper control at the part load;

The fan sheet of the workbook also records the current fan currents and the pressures, exactly as the example workbook carries the pressure drop sheet with the current values dated at the plant visit: the comparison of the designed and the current fan duties reveals the worn fans, the blocked ducts, the leaking compartments and the false air entries that degrade the cooler performance over the years.

9. The Pressure Drop and the False Air of the Cooler

The pressure drop of the cooler system is the sum of the bed resistance, the grate and the plate resistance, the duct losses and the seal leakages, and it is measured compartment by compartment. The pressure drop across the bed is the dominant term, and it follows the bed depth, the clinker size distribution and the air flow: the deeper the bed and the finer the clinker, the higher the drop. The compartment pressures are the operator’s window into the bed condition, because a pressure drop that falls while the air flow holds means the bed has thinned or the clinker has coarsened, and a rising drop means the bed has grown or the fines have packed the voidage.

• The bed resistance: the friction of the air through the clinker voids, the dominant term, 60–75% of the total drop;
• The grate and the plate resistance: the fixed resistance of the grate elements and the clinker support, typically 10–15% of the total;
• The duct and the damper losses: the resistance of the air ducts, the dampers and the flow meters to the compartments;
• The false air: the air that enters the cooler housing through the seals, the inspection doors and the joints, bypassing the bed and lowering the air temperature and the recovery;
• The seal leakage: the air that leaks past the grate seals and the side seals into the compartments, redistributing the aeration and the pressures;

The false air of the cooler is a silent thief: it dilutes the secondary and the tertiary air with the cold leakage, it lowers the temperature of the recovered heat, and it increases the vent air flow and the fan power. The measurement of the false air follows the same oxygen balance method as the preheater: the gas analysis at the duct and the housing points reveals the air that entered between the points, and the workbook carries the calculation sheet that converts the oxygen differences into the false air flow.

10. The Worked Example: The Calculation of the 5,000 t/d Cooler

To make the calculation concrete, run the complete example through the workbook. The line produces 5,000 t/d of clinker at 208 t/h, the clinker enters the cooler at 1,400°C and leaves at 120°C, the fuel is pet coke with an LCV of 7,800 kcal/kg burned at a specific rate of 100 kg/t clinker, and the excess air of the kiln and the calciner combustion runs at 2.5% oxygen in the exit gas. The ambient air enters at 30°C.

The cooling air: the total air at 2.1 Nm3/kg clinker is 437,000 Nm3/h. The secondary air demand of the kiln is the pet coke rate of 20.8 t/h times the theoretical air of about 9.3 Nm3/kg of coke times the excess air factor, about 200,000 Nm3/h. The tertiary air demand of the calciner, at 60% of the total fuel, is about 150,000 Nm3/h. The vent air is the balance, about 87,000 Nm3/h, which is 0.42 Nm3/kg, a low figure that reflects the modern low-vent design with the high recovery.

The heat balance: the clinker heat available is 53.3 million kcal/h. The secondary air recovers about 22 million kcal/h, the tertiary air about 16 million kcal/h, the total recovery of 38 million kcal/h is 71% of the available heat. The vent air carries about 8 million kcal/h, the cooled clinker about 4.5 million kcal/h and the shell losses and the unaccounted the remaining 2.8 million kcal/h. The cooler’s heat recovery efficiency is 71%, the cooling efficiency is about 92%, and the secondary air temperature of about 1,000°C supports the kiln flame with a stable heat input. The fan power of the example computes to about 14,800 kW installed, and the comparison of the current compartment pressures with the design values closes the operating picture.

11. The Interpretation of the Cooler Calculation Results

The results of the cooler calculation are interpreted against the design intent and the industry benchmarks. A recovery efficiency below 60% with a discharge temperature above 150°C points to the classic operating problems: the shallow bed with the air short-circuiting through the clinker, the high vent air with the low secondary temperature, the blocked compartments, the worn grate plates or the false air. A recovery above 70% with a discharge below 120°C indicates the healthy cooler, and the remaining opportunity is the fine tuning of the air distribution and the bed profile.

• The recovery below target: check the bed depth and its uniformity, the clinker size distribution, the grate speed and the compartment pressures, in that order;
• The discharge temperature above target: check the final zone air, the vent extraction and the clinker size: the coarse clinker cools slowly and the fines pack and channel;
• The high vent air with low temperature: check the false air and the seal conditions, the classic dilution of the recovered heat;
• The fan power above design: check the fan efficiencies, the inlet conditions, the damper positions and the worn impellers;
• The pressure drop anomalies: a rising drop with a falling flow points to the bed packing or the clinker coarsening; a falling drop with a rising flow to the bed thinning;

The interpretation sheet of the workbook lists these symptoms and their causes in a table, so the plant engineer uses the calculation as the diagnostic instrument of the daily operation: the numbers that the cooler records each shift are compared with the design basis, and the deviations direct the operator’s attention to the compartment that needs the adjustment.

12. The Cooler Retrofits and the Upgrades: The Calculation in the Investment Case

The cooler calculation is also the basis of the retrofit decisions: the replacement of the grate, the addition of the static aeration, the redesign of the air distribution, the installation of the variable speed drives or the full replacement of the cooler. Each option has its cost and its measured benefit, and the workbook computes the benefit from the recovery difference.

The classic retrofit ladder of the industry: the first rung is the replacement of the worn grate plates and the seals, a low-cost measure that restores the design air distribution and typically recovers 10–30 kJ/kg clinker. The second rung is the optimization of the compartment air and the fan control with the variable speed drives, recovering 20–40 kJ/kg at a moderate cost. The third rung is the static aeration and the modernization of the quench zone, and the top rung is the full cooler replacement, which raises the recovery to the 70–75% level and saves 50–100 kJ/kg clinker at a capital cost of tens of millions of dollars.

• The benefit calculation: the recovery difference in kJ/kg multiplied by the clinker production and the fuel price is the annual saving of each option;
• The payback: the capital cost divided by the annual saving gives the payback of the project, typically 2–5 years for the good retrofits;
• The secondary benefits: the better clinker quality, the lower discharge temperature, the lower fan power and the higher kiln stability add to the fuel saving;
• The interaction with the kiln: the higher secondary air temperature reduces the kiln fuel rate, and the calculation must be re-run with the kiln balance to capture the loop;

The cooler retrofit is one of the best economic projects in the cement industry, and the calculation workbook provides the evidence: the current balance and the target balance, the recovery difference, the fuel saving and the payback, presented in the format that the investment committee expects. The same numbers feed the financial model of the company, closing the loop between the cooler engineering and the corporate value.

13. The Link Between the Cooler and the Rest of the Pyro System

The cooler does not stand alone: its calculation is linked to the kiln pyro balance, the preheater balance, the fan systems and the waste heat recovery. The secondary air temperature appears in the kiln balance as the sensible heat input term, and the tertiary air in the calciner balance; the vent air is the inlet of the raw mill drying system or the waste heat recovery boiler; and the cooler fans appear in the plant-wide power budget and the electrical load of the substation.

The integrated analysis is the strength of the package: the cooler calculation workbook feeds its air flows and temperatures into the kiln pyro balance workbook, which computes the specific heat consumption of the whole system; the same numbers feed the fan calculation for the power demand; and the vent air parameters feed the waste heat recovery assessment. The engineer who runs the coolers through the package ends with the full picture: the fuel rate, the power demand, the recovery efficiency and the CO2 intensity of the pyro section, all consistent with each other because they share the same data.

14. The Common Mistakes in the Cooler Calculation

The classic errors of the cooler calculation are the ones that the workbook prevents by structure. The first is the density confusion: the air flows quoted at the standard conditions are used without the temperature correction, and the fan duties and the duct sizes come out wrong; the hot air at 1,000°C occupies nearly four times the volume of the same mass at the ambient, and the fans must be sized on the actual volumes. The second is the fuel rate error: the secondary and the tertiary air demands are computed from the as-received fuel rate without the moisture and the ash corrections, and the combustion air comes out short or long.

• The specific heat drift: using the clinker specific heat of 0.19 kcal/kg°C for the cold clinker and the hot clinker alike, while the value rises with the temperature;
• The reference confusion: the heat terms computed against the different reference temperatures, corrupting the recovery efficiency;
• The vent air double count: counting the vent air heat both as the cooler loss and as the raw mill input, distorting the cooler and the mill balances;
• The pressure drop at the wrong point: the compartment pressure read at the fan instead of the plenum, including the duct losses in the bed drop;
• The steady state illusion: the calculation run on the data of an unstable kiln period, representing the disturbance rather than the operation;

The checks of the workbook are the air mass balance, the heat balance closure and the consistency between the cooler, the kiln and the preheater sheets, and the engineer who respects the discipline produces the calculation that the design office, the investment committee and the operation all trust.

15. Frequently Asked Questions

What is the normal cooling air requirement of a grate cooler?

A modern grate cooler operates with 1.8–2.4 Nm3 of cooling air per kg of clinker. Of this, roughly 0.7–1.0 Nm3/kg returns to the process as the secondary and the tertiary air, and the balance leaves as the vent air at 250–400°C.

How is the cooler efficiency calculated?

The heat recovery efficiency is the heat of the secondary and the tertiary air divided by the heat available in the hot clinker, typically 60–75% for a modern cooler. The cooling efficiency is the heat actually removed from the clinker divided by the available heat, typically 90–96%.

What is the normal clinker discharge temperature?

A well-operated modern cooler discharges the clinker at 80–150°C. The discharge temperature above 150°C points to the insufficient final cooling, the coarse clinker or the shallow bed in the last compartments.

Why is the secondary air temperature important?

The secondary air returns to the kiln at 850–1,100°C and carries a large share of the recovered heat. Every 50°C of the secondary air temperature is worth roughly 10–20 kJ/kg clinker of the specific heat consumption, which is why the cooler performance is a kiln fuel lever.

How much fan power does the cooler need?

The cooler fans of a 5,000 t/d line typically install 14,000–16,000 kW at the design air flows and pressures. The variable speed drives and the correct air distribution reduce the power at the part load by 20–40%.

How can the cooler calculation reduce the fuel consumption?

The calculation identifies the recovery gap: the difference between the current and the target recovery efficiency, converted into the fuel saving at the clinker rate and the fuel price. The classic measures recover 30–100 kJ/kg clinker, worth millions of dollars per year on a large line.

16. Conclusion and Summary

The clinker cooler calculation is the complete engineering account of the machine that recovers the heat of the clinker: the air requirements, the heat balance, the efficiencies, the grate loading, the fan duties, the pressure drops and the operating parameters, computed from the clinker data, the fuel data and the air data that the plant measures every day. The workbook of the package carries the calculation in the structured sheets, exactly as the example workbook with its fuel type, its pressure drop sheet and its current operating parameters.

The cooler is the hinge of the pyro system’s efficiency: a recovery gain of 50 kJ/kg clinker is worth thousands of tonnes of fuel per year, and the same gain appears in the kiln balance, the financial model and the CO2 account. The engineer who runs the cooler calculation with the discipline of the heat balance and the air mass balance produces the numbers that the operation, the design and the investment all trust, and the Complete Cement Technical Package provides the full set of the linked tools: the cooler calculation, the kiln pyro balance, the fan calculations and the material balances that together describe the entire pyro section.

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.