Mass And Heat Balances Grinding Technology Course: Complete

This article is a course module on the mass and heat balances of the grinding technology, written for the process engineers, the production personnel and the students of the cement technology who want to master the quantitative analysis of the grinding circuits. The mass and the heat balances are the fundamental tools of the process engineering: the mass balance accounts for the material flows into, within and out of the grinding system, and the heat balance accounts for the energy flows, and the two balances together provide the complete quantitative picture of the system, which is the basis of the performance evaluation, the troubleshooting, the optimization and the design. The module explains the principles of the balances, the calculation methods, the measurement requirements, the data collection and the interpretation, and it applies the methods to the ball mill circuits, the vertical roller mills, the roller press circuits and the auxiliary systems, with the worked examples, the tables and the checkpoints. The objective of the module is to give the reader the practical capability to perform the mass and the heat balances of the grinding systems, to identify the performance gaps, the losses and the improvement potentials, and to use the balances for the continuous optimization of the grinding operation, which is the core competence of the professional process engineer.

The Course Objectives and the Structure

The course module is designed to achieve the defined learning objectives. The first objective is to explain the purpose and the principles of the mass balance and the heat balance in the grinding technology, and to define the terms, the flows and the conventions. The second objective is to describe the grinding circuits and the systems that the balances are applied to: the ball mill circuits, the vertical roller mills, the roller press circuits, the separators, the fans, the dust collectors and the auxiliary systems. The third objective is to explain the measurement requirements: the flow measurements, the density and the moisture measurements, the temperature measurements, the power measurements and the sampling, and to relate the measurements to the balance accuracy. The fourth objective is to perform the mass balance of the grinding circuit: the material flows, the recirculation, the separation efficiency, the product rates and the load calculations. The fifth objective is to perform the heat balance: the heat inputs, the heat outputs, the heat losses and the heat consumption, and to interpret the heat balance for the energy optimization. The sixth objective is to apply the balances to the performance evaluation and the optimization: the identification of the gaps, the loss analysis, the sensitivity analysis and the improvement actions.

The structure of the module follows the training format: the introduction to the balances and their place in the process engineering; the grinding circuits and their flows; the measurement and the data collection; the principles and the methods of the mass balance; the mass balance of the closed-circuit mill with the worked examples; the principles and the methods of the heat balance; the heat balance of the mill with the worked examples; the interpretation and the application of the balances; the special topics, the vertical mill and the roller press balances, and the energy and the exergy analysis; the checkpoints and the assessment; and the summary. The reader progresses through the module in the sequence, and the worked examples and the checkpoints verify the understanding at each stage.

The Purpose of the Balances in the Grinding Technology

The mass and the heat balances are the quantitative accounting of the grinding system: the mass balance states that the material entering the system leaves the system or accumulates in it, and the heat balance states that the energy entering the system leaves it or is stored in it, and the balances convert the process observations into the quantified flows that the engineer can analyze. The balances serve the several purposes in the grinding technology, and each purpose is a professional application.

The first purpose is the performance evaluation: the balances quantify the performance of the mill, the separator and the system, the production rate, the recirculation, the separation efficiency, the specific energy and the heat consumption, and the quantified performance is compared with the design, the history and the best practice. The second purpose is the troubleshooting: the balances identify where the mass and the energy go, and the anomalies, the excessive recirculation, the material accumulation, the heat losses and the measurement inconsistencies, point to the causes of the problems. The third purpose is the optimization: the balances quantify the improvement potentials, the energy savings, the production gains and the quality improvements, and the optimization actions are prioritized by the quantified potentials. The fourth purpose is the design and the equipment selection: the balances are the basis of the mill and the separator sizing, the fan and the dedusting selection, and the circuit design, and the design balances define the equipment specifications. The fifth purpose is the energy management: the heat balance quantifies the energy flows and the losses, the electrical and the thermal energy, and the energy management is the systematic reduction of the losses, which the balances support with the data. The sixth purpose is the knowledge and the communication: the balances express the process in the numbers that all the disciplines, the process, the maintenance, the quality and the management, share, and the balanced process is the understood process.

The balances are performed at the different levels: the system level, the whole grinding circuit including the feed, the product, the separator and the mill, and the component level, the mill, the separator, the fan and the dedusting, and the balances at the different levels serve the different purposes, from the system performance evaluation to the component diagnosis. The balance frequency ranges from the periodic campaigns, the full balances with the measurements, to the continuous monitoring, the online balances with the instrument data, and the professional plant performs both: the periodic detailed balances for the analysis and the continuous monitoring for the trends.

The Grinding Circuits and Their Flows

The grinding circuits are the systems that the balances are applied to, and the understanding of the circuits and their flows is the prerequisite of the balance work. The main grinding systems of the cement plant are the ball mill circuits, the vertical roller mills and the roller press circuits, and each system has its characteristic flows and its balance structure.

The ball mill circuit is the classic grinding system: the closed circuit with the mill, the elevator or the air conveyor, the separator and the fans. The material flows are the fresh feed, the mill feed, the mill discharge, the separator feed, the separator reject, the coarse return, and the separator product, the finished material, and the circuit is characterized by the recirculation: the reject returns to the mill, and the circulating load, the ratio of the reject to the fresh feed, is typically 150 to 300 percent. The air flows include the mill vent air, the separator air and the dedusting air, and the mill and the separator are air-swept in the modern circuits. The ball mill circuit balance accounts for the material flows, the air flows and the power flows.

The vertical roller mill is the integrated grinding and drying system: the mill grinds, dries and classifies the material in the single machine, with the internal separator, and the material flows are the fresh feed, the mill feed, the milled material, the internal reject, the external reject, the product and the dust return. The vertical mill uses the hot gas for the drying, and the gas flows are the mill gas, the drying gas, the separator gas and the dedusting gas, and the heat balance of the vertical mill includes the drying heat, which is the significant term. The vertical mill circuit balance accounts for the material flows, the gas flows and the thermal flows, which makes the vertical mill balance the most complete of the grinding balances.

The roller press circuit is the high-pressure grinding system: the roller press is combined with the ball mill or used as the finish-grinding system, and the material flows include the fresh feed, the press feed, the cake, the de-agglomerated material, the classifier feed, the classifier reject and the product. The roller press circuit is characterized by the high recirculation of the press and the cake processing, and the circuit balance accounts for the press, the de-agglomerator, the classifier and the mill flows. The auxiliary systems of the grinding circuits, the fans, the dust collectors, the conveyors, the elevators and the air slides, are the components of the balances, with their flows, their powers and their losses.

The flows of the grinding circuits are summarized in the table below, which the module uses as the reference for the balance calculations:

System	Main material flows	Main air and gas flows	Key balance terms
Closed-circuit ball mill	Fresh feed, mill feed, mill discharge, separator feed, reject, product	Mill vent air, separator air, dedusting air	Circulating load, separation efficiency, power
Vertical roller mill	Fresh feed, mill feed, internal reject, external reject, product	Drying gas, mill gas, separator gas, dedusting gas	Drying heat, gas-to-material ratio, power
Roller press circuits	Fresh feed, press feed, cake, de-agglomerated, classifier feed, reject, product	Classifier air, dedusting air	Press recirculation, cake fineness, power
Fan and dedusting	Dust return, product entrainment	Gas flows, velocities, dust loads	Air flows, dust recirculation, power

The Measurement and the Data Collection

The quality of the balances depends on the quality of the measurements, and the measurement planning is the first activity of the balance campaign. The measurements of the grinding balance include the material flows, the moisture, the particle sizes, the temperatures, the powers, the air flows and the pressures, and each measurement is planned with the method, the location and the accuracy.

The material flow measurements include the weigh feeders for the fresh feed, the belt scales for the conveying flows, the flow measurements at the elevators and the conveyors, and the indirect measurements by the material levels and the pressures. The flows that are not measured directly, the separator feed, the reject and the internal flows, are determined by the indirect methods: the sampling and the sieving with the known separator efficiency, the material balance around the known components and the calculated flows from the measured variables. The sampling is the critical activity: the samples are taken with the defined methods at the defined points, the sample size and the frequency are defined, and the samples are analyzed for the fineness, the moisture and the composition. The sample points include the fresh feed, the mill feed, the mill discharge, the separator feed, the reject and the product, and the sampling is performed over the defined period with the representative samples.

The moisture measurements include the feed moisture, the product moisture and the material moisture at the defined points, and the moisture is measured by the drying methods or the online analyzers. The moisture is essential for the mass balance, because the material flows are reported on the dry basis or the wet basis with the moisture correction, and the moisture is essential for the heat balance, because the water evaporation is the major heat term. The temperature measurements include the material temperatures, the gas temperatures, the surface temperatures and the ambient temperature, and the temperature measurement points are defined for the heat balance: the feed temperature, the product temperature, the mill shell temperatures, the gas temperatures at the inlet and the outlet, and the ambient temperature.

The power measurements include the mill motor power, the fan powers, the auxiliary powers and the system power, and the powers are measured with the power analyzers or taken from the electrical system data. The power measurement is the basis of the specific energy calculations, and the power data must be synchronized with the material flow data for the correct specific values. The air and the gas flow measurements include the duct velocities and the flow rates, the fan duties and the damper positions, and the flows are measured with the pitot tubes, the anemometers or the instrument readings. The pressure measurements include the mill inlet and outlet pressures, the separator pressures, the fan pressures and the filter pressures, and the pressures support the flow and the performance analysis.

The data collection is organized with the balance spreadsheet or the software: the measurement data, the sample analyses and the instrument data are collected in the defined format, the data is checked for the consistency and the completeness, and the measurement uncertainty is estimated. The data quality is the balance quality, and the professional balance campaign invests in the measurement planning, the instrument verification and the data checking, which the module emphasizes as the foundation of the balance work.

The Principles and the Methods of the Mass Balance

The mass balance is the application of the conservation of mass to the grinding system: for the system at the steady state, the total mass entering equals the total mass leaving, and for each component, the material, the water and the particle size classes, the entering equals the leaving. The mass balance is written for the total flow and for the components, and the balances are solved for the unknown flows.

The total mass balance of the grinding circuit states that the fresh feed equals the product plus the dust loss and the accumulation: the fresh feed is the measured input, the product is the measured or calculated output, and the difference indicates the measurement errors or the unaccounted flows. The component balances are the balances of the moisture, the fineness classes and the chemical components: the water balance tracks the water entering with the feed and the air and leaving with the product, the evaporation and the dust, and the fineness balance tracks the particle size classes through the mill and the separator. The component balances provide the additional equations that determine the unknown flows, and the fineness balance is the basis of the circulating load and the separation efficiency calculations.

The separation efficiency of the separator is the key result of the mass balance: the separator splits the feed into the product, the fine fraction, and the reject, the coarse fraction, and the separation efficiency is the fraction of each particle size class that reports to the product. The separation curve, the Tromp curve, is the plot of the separation efficiency against the particle size, and the Tromp curve characterizes the separator: the cut size, the sharpness and the bypass, and the curve is derived from the samples of the separator feed, the product and the reject. The mass balance of the separator uses the fineness data of the three streams to calculate the split and the efficiency, and the balance check, the consistency of the feed fineness with the weighted average of the product and the reject, verifies the sampling quality.

The circulating load is the other key result: the circulating load is the ratio of the separator reject to the fresh feed, or the total mill feed to the fresh feed, and it characterizes the circuit: the low circulating load indicates the inefficient separation or the over-grinding, and the high circulating load indicates the excessive recirculation and the energy waste. The circulating load is calculated from the fineness data and the separation efficiency, and it is the parameter that the optimization adjusts with the separator settings.

The mass balance methods include the direct balance, the data reconciliation and the online balances: the direct balance solves the balances with the measured flows, the data reconciliation adjusts the measurements to satisfy the balances with the minimum adjustments, and the online balances calculate the flows continuously from the instrument data. The professional balance practice uses the reconciliation to verify the measurements and the direct method for the campaigns, and the balance software supports the calculations and the reconciliation.

The Mass Balance of the Closed-Circuit Mill: The Worked Example

The mass balance of the closed-circuit mill is demonstrated with the worked example, which the module uses to teach the calculation method. The example considers the closed-circuit ball mill with the measured fresh feed of 100 tonnes per hour, the feed moisture of 1 percent, and the fineness data of the separator feed, the product and the reject, expressed as the residues on the defined sieve.

The sample data of the example is the following: the fresh feed fineness with the residue of 60 percent on the 90-micron sieve, the separator feed with the residue of 45 percent, the separator product with the residue of 5 percent, and the separator reject with the residue of 80 percent, and the product moisture of 0.3 percent. The balance of the separator is solved with the fineness balance: the separator feed flow is the sum of the product and the reject flows, and the fineness balance states that the separator feed fineness is the weighted average of the product and the reject finenesses. The solution gives the product flow of 40 percent of the separator feed and the reject flow of 60 percent, which translates, with the fresh feed of 100 tonnes per hour and the product of 99 tonnes per hour dry (after the moisture correction), to the circulating load of about 150 percent.

The example continues with the mill balance: the mill feed is the sum of the fresh feed and the reject, about 250 tonnes per hour, the mill discharge equals the mill feed at the steady state, and the mill performance is evaluated with the specific energy: with the mill power of 3.5 megawatts, the specific energy per tonne of the product is 35 kilowatt-hours per tonne, and the specific energy per tonne of the mill feed is 14 kilowatt-hours per tonne. The balance results quantify the circuit: the separation efficiency, the circulating load and the specific energies, and the results are compared with the design and the reference ranges, which identifies the performance gaps for the optimization.

The example demonstrates the method: the sampling, the fineness analysis, the separator balance, the circulating load calculation and the specific energy evaluation, and the reader repeats the method with the own plant data, which is the objective of the worked example. The example also demonstrates the accuracy requirements: the small sampling errors propagate into the balance results, and the professional practice verifies the results with the balance checks, the redundant measurements and the consistency analysis.

The Principles and the Methods of the Heat Balance

The heat balance is the application of the conservation of energy to the grinding system: the energy entering the system equals the energy leaving plus the stored energy, and the heat balance quantifies the energy flows, the inputs, the useful outputs and the losses. The heat balance of the grinding system is performed in the steady state, with the defined boundary, and the balance terms include the heat inputs, the heat outputs and the heat losses.

The heat inputs of the grinding system include the electrical energy input, the motor power, which is converted to the heat in the mill by the grinding action, the heat of the feed material, the sensible heat of the material at its temperature, the heat of the air and the gas, the sensible heat of the inlet air, the drying gas and the seal air, and the heat of the internal sources, the recirculating material and the friction. The heat outputs include the heat of the product, the sensible heat of the product at its temperature, the heat of the exhaust gas and the air, the sensible heat of the outlet gas, the heat of the evaporation, the latent heat of the water evaporated from the feed, and the heat losses, the radiation and the convection from the mill shell, the ducts and the equipment surfaces, and the conduction to the foundations and the supports.

The heat balance of the mill is written with the enthalpy terms: the enthalpy of each flow is the product of the mass flow, the specific heat and the temperature, and the balance sums the input enthalpies and the output enthalpies, with the power input and the losses. The enthalpy calculations use the specific heat values of the materials, the water and the gases, and the latent heat of the water evaporation, and the calculations are performed with the consistent units. The heat balance is solved for the unknown term, typically the heat loss, which is the difference between the inputs and the known outputs, and the calculated heat loss is compared with the estimated losses from the surface areas and the temperatures, which verifies the balance.

The heat balance of the vertical roller mill includes the significant drying terms: the drying gas enters at the high temperature, the water evaporates from the feed, and the heat of the drying is the major term of the vertical mill balance. The drying capacity of the mill is determined by the gas flow, the gas temperature and the moisture load, and the heat balance quantifies the drying performance and the drying limitations, which are the constraints of the vertical mill operation. The heat balance of the air-swept ball mill includes the vent air and the separator air terms, and the heat balance of the roller press includes the press power and the material and the gas flows of the classifier.

The heat balance is also the basis of the energy analysis: the specific heat consumption, the kilowatt-hours per tonne of the product, is the key energy indicator, and the balance quantifies the energy distribution, the useful energy, the grinding work, the energy in the product and the exhaust, and the losses. The energy analysis identifies the loss reduction potentials: the heat loss reduction by the insulation, the exhaust heat recovery, the temperature optimization and the power efficiency improvements, and the potentials are quantified for the investment decisions.

The Heat Balance of the Mill: The Worked Example

The heat balance of the mill is demonstrated with the worked example, which the module uses to teach the calculation method. The example considers the ball mill with the power of 3.5 megawatts, the feed of 100 tonnes per hour with the moisture of 1 percent at the temperature of 20 degrees Celsius, the product of 99 tonnes per hour at the temperature of 100 degrees Celsius, the vent air of 30,000 cubic meters per hour at the temperature of 80 degrees Celsius, and the ambient temperature of 20 degrees Celsius.

The heat inputs of the example are the electrical power of 3.5 megawatts, the heat of the feed, the mass flow times the specific heat times the temperature rise, and the heat of the inlet air, and the heat outputs are the heat of the product, the heat of the exhaust air, the heat of the evaporation, the latent heat of the water evaporated, and the heat losses. The calculation uses the specific heat of the material of 0.8 kilojoules per kilogram per degree Celsius, the specific heat of the air of 1.0 kilojoule per kilogram per degree Celsius, and the latent heat of the water of 2260 kilojoules per kilogram, and the balance is solved for the heat loss.

The balance of the example shows that the power input of 3.5 megawatts dominates the inputs, the product heat and the exhaust heat are the significant outputs, the evaporation heat is small for the dry feed, and the heat loss is the remainder, typically 20 to 40 percent of the input for the uninsulated mills. The example demonstrates the calculation method, the enthalpy terms and the units, and it demonstrates the interpretation: the heat loss is the target of the insulation improvements, the exhaust heat is the target of the recovery and the temperature optimization, and the balance quantifies the improvement potentials.

The example also demonstrates the moisture effect: with the higher feed moisture, the evaporation term grows, the mill temperature falls, the grinding and the drying conflict, and the heat balance quantifies the moisture limitations of the mill. The reader repeats the calculation with the own plant data, and the module provides the balance template and the reference values, which support the practical application.

The Interpretation and the Application of the Balances

The balances produce the numbers, and the professional value is in the interpretation and the application: the balance results are compared with the references, the anomalies are analyzed, the improvement potentials are quantified and the actions are implemented. The interpretation is the analysis of the balance results against the design, the history and the best practice.

The performance comparison evaluates the mill, the separator and the system against the references: the specific energy is compared with the design and the industry ranges, the circulating load with the optimum range, the separation efficiency with the reference curves, and the heat loss with the insulated and the uninsulated references. The comparison identifies the gaps, and the gaps are the improvement potentials. The anomaly analysis investigates the deviations: the balance that does not close, the sum of the outputs different from the inputs, indicates the measurement errors or the unaccounted flows, and the reconciliation identifies the inconsistent measurements; the circulating load that drifts indicates the separator or the mill changes; and the heat balance that shows the high loss indicates the insulation, the leaks or the temperature problems.

The improvement actions are prioritized by the quantified potentials: the separator optimization with the highest efficiency gain, the mill loading and the media adjustments, the fan and the air flow optimization, the insulation of the mill and the ducts, and the moisture and the feed management. The actions are implemented with the defined responsibilities and the verification, and the balances are repeated to confirm the improvements, which closes the optimization loop.

The balances also support the daily operation: the online balances, calculated from the instrument data, provide the continuous performance indicators, the specific energy, the circulating load and the separation efficiency, and the operation monitors the indicators and responds to the deviations. The balances support the management reporting: the performance reports include the balance results, the trends and the comparisons, and the reporting communicates the process status to the management. The balances are the professional tools of the process engineering, and the module provides the capability to use them.

The Special Topics: The Vertical Mill, the Roller Press and the Energy Analysis

The special topics of the module cover the balances of the vertical roller mill and the roller press circuits, and the energy and the exergy analysis of the grinding systems. The vertical mill balance includes the material balance with the internal and the external rejects and the gas balance with the drying gas, and the balance of the vertical mill is the integrated balance of the grinding, the drying and the classification. The vertical mill mass balance determines the internal circulation, the reject flows and the product rate, and the heat balance determines the drying capacity, the gas requirements and the heat consumption. The vertical mill balance is the basis of the mill optimization: the gas flow, the temperature, the damper settings and the separator speed are the optimization variables, and the balances quantify their effects.

The roller press circuit balance includes the press material balance with the cake flows, the de-agglomeration and the classifier, and the balance determines the press recirculation, the cake fineness, the pre-grinding effect and the product rate. The roller press heat balance includes the press power and the material and the air flows, and the balances quantify the press performance and the energy distribution. The roller press balance is the basis of the circuit optimization: the press pressure, the feed quality, the classifier settings and the mill operation are the optimization variables.

The energy analysis extends the heat balance to the second-law analysis: the exergy analysis accounts for the energy quality, the available work, and it identifies the irreversibilities, the losses of the energy quality, which the energy balance does not reveal. The exergy analysis of the grinding systems shows that the electrical energy is converted to the heat at the low temperature, with the large irreversibility, and the useful exergy in the product is small, which is the thermodynamic reality of the grinding: the grinding is the inherently inefficient process, and the optimization is the reduction of the unnecessary losses, the over-grinding, the over-circulation and the heat losses. The energy and the exergy analysis provides the framework for the energy management, and the module presents the concepts with the practical applications.

The Checkpoints and the Assessment

The checkpoints of the module test the understanding of the sections, and the reader should be able to answer the following questions. The first checkpoint: explain the purpose of the mass and the heat balances in the grinding technology. The second checkpoint: describe the flows of the closed-circuit ball mill, the vertical mill and the roller press circuits. The third checkpoint: list the measurements of the balance campaign and explain the sampling requirements. The fourth checkpoint: perform the separator mass balance and calculate the circulating load from the fineness data. The fifth checkpoint: write the heat balance of the mill and identify the main terms. The sixth checkpoint: interpret the balance results, identify the gaps and propose the improvement actions. The seventh checkpoint: explain the special features of the vertical mill and the roller press balances. The assessment of the module is the completion of the checkpoints and the worked examples with the correct results, and the trainer uses the assessment for the certification, which closes the course loop.

Frequently Asked Questions

What is the circulating load of a ball mill circuit and why is it important?

The circulating load is the ratio of the separator reject to the fresh feed, typically 150 to 300 percent, and it quantifies the recirculation of the circuit: the too-low load indicates the inefficient separation and the too-high load indicates the energy waste, so the load is the key optimization parameter.

How is the separator efficiency determined from the samples?

By the fineness analysis of the separator feed, the product and the reject, the fineness balance of the separator and the calculation of the split and the efficiency per particle size class, which produces the Tromp curve with the cut size, the sharpness and the bypass.

Why does the heat balance of the vertical mill include the drying terms?

Because the vertical mill dries the feed with the hot gas, and the drying gas heat and the water evaporation heat are the major terms of the balance, which determine the drying capacity and the drying limitations of the mill.

What is the typical heat loss of an uninsulated ball mill?

The heat loss by the radiation and the convection from the shell and the ducts is typically 20 to 40 percent of the power input, and the insulation reduces the loss, which is the improvement identified by the heat balance.

How are the measurement errors handled in the balances?

By the data reconciliation, which adjusts the measurements to satisfy the balances with the minimum adjustments and identifies the inconsistent measurements, and by the redundant measurements and the balance checks, which verify the data quality.

What is the exergy analysis and why is it relevant to grinding?

The exergy analysis accounts for the energy quality and identifies the irreversibilities, and it shows that the grinding converts the high-quality electrical energy to the low-temperature heat with the large loss, which quantifies the inherent inefficiency and directs the optimization to the unnecessary losses.

Summary and Final Recommendations

This course module has covered the mass and the heat balances of the grinding technology: the purpose and the principles of the balances, the grinding circuits and their flows, the measurement and the data collection, the methods of the mass and the heat balances, the worked examples of the mill balances, the interpretation and the application, and the special topics of the vertical mill, the roller press and the energy analysis, with the checkpoints and the assessment. The recommendations for the process engineer are these: master the principles and the methods, the mass conservation and the energy conservation, because the balances are the fundamental tools of the profession; invest in the measurement quality, the sampling, the instruments and the data verification, because the balance quality is the measurement quality; perform the balances systematically, with the defined boundaries, the consistent units and the documented data, because the systematic work produces the reliable results; interpret the results against the references and the history, and quantify the gaps and the potentials, because the interpretation converts the numbers into the actions; use the balances continuously, the online balances for the trends and the periodic campaigns for the detail, because the continuous use is the continuous optimization; and extend the analysis to the energy and the exergy, because the energy management is the frontier of the grinding optimization. The mass and the heat balances are the language of the process engineering, and the engineer who speaks the language fluently evaluates, troubleshoots and optimizes the grinding systems professionally, which is the competence that this module develops and the foundation of the professional grinding technology.

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.