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      Cement mill heat balance                
                             
      1 Introduction:                  
        - It is well known that the biggest part of the energy introduced in a ball mill is converted into heat.    
        - Only around 5% of this energy is used to grind the material at the required fineness.      
        - As a consequence, this heat can induce very high temperatures inside the cement mill.       
        - These temperatures can affect the grinding process if they reach a certain limit.      
        - Therefore, it is important to make the heat balance of the installation in order to solve possible problems.  
                             
      2 Principle:                  
        - For all heat balances, there must be an equilibrium between what goes in and what goes out of the system.  
        - Of course, it is also the case for the cement mill heat balance.          
        - This principle is illustrated below:              
         
     
               
                     
                     
                     
                     
                     
                     
                     
                     
                             
      3 The three basic parameters:              
        - Regardless to the characteristics and production data of the installation that we have to know,     
          the heat balance turns principally around 3 values:            
      3.1 Temperature of the product at mill outlet:            
        - It is generally accepted that beyond 105-110 degrees centigrade, adverse reactions to the grinding process can take place.
          This can also affect the quality of the cement.            
        - These reactions are:                
          Trouble of gypsum dehydration which may cause cement "false set".        
          Particles agglomeration due to electrostatic charges which causes coating phenomenon on balls and linings.  
        - The exact temperature which must not be exceeded varies from case to another.      
          It depends of the kind of circuit, the material properties, the ambient temperature, the required fineness,  
          the separator efficiency, the ball charge...etc            
        - We consider that 105°C is a good reference.            
      3.2 Ventilation of the mill:                
        The ventilation has 3 objectives:              
        - to insure the cooling of the mill and the material            
        - to dedust the mill                
        - to remove the fine particles from the mill            
        Cooling of the mill:                
        - A good cooling of the mill and the material inside the mill is necessary to maintain a proper working temperature.  
        - The temperature of reference is the one of the material at the mill outlet (see above).      
        Problem of coating:                
        - The coating is an agglomeration of material on the lining and/or grinding media. It is due to the superficial cohesion  
          forces and the forces generated by the static electricity.          
        - Coating is an agent of efficiency loss which can be very important (up to 30%) because:      
          - coating is disturbing the segregation of the ball charge in case of classifying lining.      
          - coating is also reducing the attrition's efficiency of the small balls which are not more in contact with the material.  
        Dedusting of the mill:                
        - This function seems to be evident if we want to avoid the accumulation of dust in the whole system.    
        Ventilation usual values:                
        - When we want to define the necessary ventilation in a grinding installation, it is calculated in terms of air velocity   
          in the free section of the mill, i.e: air speed in m/sec.          
        - The reference values which are generally admitted are divided in two cases and are the following:    
          Open circuit: air speed between 0,8 m/sec and 1,2 m/sec.          
          Closed circuit: air speed between 1 m/sec and 1,5 m/sec.          
        - Remark: we can also define the ventilation in term of Nm3/kg of finished product.      
        - Normally, generally accepted values are from 0.3 to 0.45 Nm3/kg.         
        - But this method is less usual.              
      3.3 Water to inject:                
        - Water is the solution in order to keep the right temperature inside the cement mill.      
        - Generally, water is injected in the second chamber from the outlet diaphragm (in case of two compartments ball mill).
        - In some cases, it is also required to inject water in the first chamber when the temperature of the feed (clinker)  
          is very high (higher than 120°C).              
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      4 Definitions of the parameters:              
        - M = grinding heat in kcal                
        - F  = heat in total mill feed in kcal              
        - A = heat in the air in kcal                
        - W = heat in the water in kcal              
        - S = heat loss by radiation and convection in kcal            
        - C = heat loss in the material at mill discharge in kcal            
        - Ao = heat loss in the air at mill discharge in kcal            
        - Wv = heat loss by water vapor in kcal              
        - N = absorbed power at motor terminals in kW            
        - f = fresh feed in kg/h                
        - CF = circulating factor (A/F)              
        - tF = average temperature of the new feed in °C            
        - tR = temperature of the rejects in °C              
        - tA = temperature of air at mill inlet in °C            
        - tC = temperature of material at mill discharge in °C            
        - tW = temperature of water in °C              
        - V = volume of dry air in Nm3/h              
        - Ww = weight of water (injection + moisture of fresh feed) in liters        
        - Ss = mill shell surface in m2              
      5 Equations of the heat balance:              
        - Solutions of all these equations are in: kcal            
        - IN:                  
         
     
           
        - OUT:                  
         
     
         
      6 Hyphothesis:                  
        - Efficiency of energy = 85%            
        - Specific heat of cement  = 0,19 Kcal/kg °C          
        - Specific heat of water = 0,44 Kcal/kg °C          
        - Specific heat of air = 0,31 Kcal/Nm3 °C          
        - Dissipation shell = 760 Kcal/m2            
        - Vapor / Kg H2O at 100°C = 537 Kcal            
        - 1 KWh = 3600 KJ = 860 Kcal            
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      7 Practical example:                 
        - We know the ventilation of the mill, we want a temperature of the cement at mill outlet of 105°C.  
        - The mill heat balance will help us to know the quantity of water to inject in order to respect
          these conditions.                
      7.1 Data of the ball mill:                
        - Mill diameter (*) 4 m            
          (*) shell diameter              
        - Inside mill diameter 3,847 m (considering lining average thickness: 76,5 mm)    
        - Total length of the shell 12,5 m            
        - Usefull length 1st chamber 4 m            
        - Ball charge in chamber 1 74 tons or 32,7% volume load        
        - Usefull length 2nd chamber 8 m            
        - Ball charge in chamber 2 152 tons or 32,5% volume load        
        - Speed of rotation 16 rpm            
        - Absorbed power 2 765 kW            
        - Shell area calculation
     
               
      7.2 Production data:                
        - Output 90 t/h            
        - Circulating factor 2 A/F            
        - Temperature of ambient air 20°C            
        - % false air after mill 15%            
        - Temperature of water 20°C            
        - Components % total % H2O Temp.°C            
          clinker 85 0 120            
          gypsum 5 2 20            
          limestone 10 5 20            
          Total 100 0,6 105            
          corresponding to 540 l/h            
        - Ventilation 40000 m3/h            
        - Actual ventilation inside mill (*)
     
         
          (*) ventilation less false air              
        - corresponding to an air speed of (*)
     
       
          (*) check if the air speed is OK              
        - Actual ventilation in Nm3/h
     
         
        - Cement temperature (*) 105°C            
          (*) it is the temperature we want              
        - Air temperature at mill outlet 102°C (temperature of cement minus 3)      
        - Separator tails temperature (*) 100°C            
          (*) Warning with separators of the third generation where the cooling can be important!      
      7.3 Calculation:                  
        - IN:                  
         
     
       
          (*) Ww is the unknown data                
        - OUT:                  
         
     
         
          (*) Ww is the unknown data                
        - Now, we have to solve:
     
           
          with Ww as unknown data              
      7.4 Solution:                  
        - We find we need 1992 l/h of water.              
        - As we already have 540 l/h of moisture in the fresh feed, we need to inject: 1452 l/h in the second chamber   
          of the mill.                  
        - The clinker temperature is 120°C but the total feed temperature (105°C) is lower than 120°C. The Grinding   
          Engineer will choose if it is necessary to inject (or not) water in the 1st chamber.      
                             
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