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      Filters          
                   
      2   Electrofilters (suite)        
       2.6   Migration velocity of a particle:        
        - The speed of migration (migration velocity) is an important factor in the calculation of an electrostatic precipitator.
        - The migration velocity of the charged particles is approximately proportional to the voltage of the precipitator.
        - The electric field in the collecting area produces a force on a particle proportional to the magnitude of the field
          and the charge of the particle.         
        - This is represented by the following formula:      
         
     
           
                 
          where:        
          Fe is the force in newtons (N)        
          qp is the charge of the particle in coulombs (C)      
          Ec is the force of the electric field in the collecting area in volt per meter (V/m)    
        - The movement of the particles under the influence of the electric field is opposed to the viscous drag force of the gas.
        - When the drag force exactly balances the electrostatic force, the particle reaches its maximum speed, also known as
          migration speed, ω.        
        - Assuming that the particle follows the Stokes law, we will have:      
         
     
           
                 
                 
          where:        
          ω is the migration velocity of the particles in m/sec      
          qp is the charge of the particle in coulombs (C)      
          (*) Coulomb = ampere-second        
          Ec is the force of the electric field in the collecting area in volt per meter (V/m)    
          μ is the dynamic viscosity of the particle (N.s/m2)      
          dp is the dimension of the particle in m        
        - When the particle is less or equal to 1μ, one multiplies by a coefficient called Cunningham factor Cc. 
         
     
           
                 
                 
        - Cc values ​​for air at atmospheric pressure are given in the diagram below.    
        - The Cunningham correction factor can be calculated with the approximate formula (for air):  
         
     
           
                 
                 
         
     
         
        - Some typical values according to the origin of the particles:      
         
     
         
        - Some typical migration speeds in the cement industry for wire-plate type filters and based on efficiency:
         
     
           
        - The speed of the table above can drop drastically if the resistivity of the particles is very high (back corona effect).
       2.7   Phenomena influencing the efficiency of filtration:      
        - The efficiency of electrostatic precipitators can often decrease due to various phenomena occurring during the
          filtration process.        
        - Consequently, these factors should be taken into account when designing an electrostatic precipitator in order to
          avoid potential problems.        
        - Here is a list of possible causes of poor performance:      
          * Effect of apparent resistivity of the particles      
          * Reentrainment of the particles        
          * Back corona effect        
          * Extinction of the discharge by the load zone      
       2.7.1   Effect of apparent resistivity of the particles:      
        - The efficiency of an electrostatic precipitator depends on the apparent resistivity of the treated particles.
        - The measurement of the resistivity is important for a good estimation of the efficiency of filtration.
        - The resistivity of the particles is dependent of the gas temperature, their moisture content and composition.
        - Here is a diagram showing the variation of resistivity of the cement in function of temperature and moisture:
         
     
         
        - The dust particles form a layer on the collection plates of an electrostatic precipitator.  
        - To reach the mass (earth), the ionic current must pass through this layer of accumulated particles.
        - This dust layer having a high resistance causes a decrease of the field strength.    
        - For resistivity values between 10² and 5 ×10 Ω·cm, a dry type electrofilter is in optimal operating conditions.
        - We will see later what happens when the resistivity of the particles is outside this range.  
       2.7.2   Reentrainment of the particles:        
        - The phenomenon of reentrainment of the particles consists in the re-introduction of the particles collected in the
          interelectrode space.        
        - In an electrostatic precipitator in normal operation, the reentrainment of the particles appears during the operation
          of rapping of the collecting electrode or due to the high velocity of the gas around it.  
        - When the resistivity the particles becomes less than 10² Ω·cm, adhesion is low and a significant back effect occurs.
        - This can also be caused by a poor distribution of the gas flow and in particular the effects of the turbulence.
       2.7.3   Back corona effect:        
        - The deposit of particles on the collecting electrode acts like a dielectric layer when the resistivity exceeds a certain
          value.        
        - The voltage across the particle layer becomes sufficiently high to cause local breakdowns.  
        - Breakdown points emit ions of opposite sign to the discharge electrode, which affects the filtration efficiency.
        - For high resistivities, a voltage drop of several kilovolts occurs when the thickness of the layer reaches a
          few millimeters.        
        - In this case, it may be that the corona effect doesn't start because the potential difference is no longer ensured.
        - This phenomenon is called back corona.        
        - The back corona effect may occur when the resistivity is greater than 5 × 10 Ω·cm  
       2.7.4   Extinction of the discharge by the load zone:      
        - When the size of the dust particles is very low and their density is high, the load zone is formed by charged particles.
        - This reduces the field intensity at the extremity of the discharge electrode, resulting in the extinction of the
          corona discharge.        
        - Sometimes the load zone increases the intensity of the field at the collecting electrode and causes flashover.
       2.7.5   Summary chart of these phenomena:        
        - Here below is a diagram summarizing these phenomena in terms of the resistivity of the particles:
         
     
       
       2.7   Sizing of the ESP:        
       2.7.1   Fields of application of electrostatic precipitators:      
        - The table below provides useful indications to know if the choice of an electrostatic precipitator is the right one:
         
     
       
       2.7.2   Design parameters of electrostatic precipitators:      
        - The table below gives the rules for sizing:        
         
     
         
       2.7.3   Power according to the resistivity:        
        - The table below show the power per area for a given resistivity of particles:    
         
     
         
       2.7.4   Specificities for cement kilns:        
        - Some interesting data encountered for cement kilns before sizing an ESP:    
         
     
           
       2.7.5   Elements of design:        
        - Calculating the number of channels required:      
         
     
           
                 
                 
          where:        
          Nd is the number of channels        
          Q is the quantity of gas in m3/h        
          W is the distance between plates and electrodes (wires) in m      
          Va is the speed of gas in m/sec        
          H is the height of the collecting plates in m        
        - The total collection surface is calculated by the following formula:      
         
     
           
                 
          where:        
          Sc is the total collecting area        
          Nd is the number of channels        
          R is the aspect ratio (L/H)        
          Considering that each plate has two sides for collecting      
        - And the plate height is found by combining the above two equations:    
         
     
           
                 
                 
          where:        
          H is the height of the collecting plates in m        
          (SCA) is equal to Ac/Q in sec/m        
          Va is the speed of gas in m/sec        
          W is the distance between plates and electrodes (wires) in m      
          R is the aspect ratio (L/H)        
        - The specific collecting area (SCA) is a parameter used to compare ESP's and roughly estimate their effectiveness.
        - Here are some typical values for SCA:        
         
     
         
       2.7.6   Energy consumption:        
        - The two main sources of energy of an electrostatic precipitator are the corona effect and the pressure drop.
        - The total pressure drop for an ESP filter and pipes is generally in the range of 30-100mmH2O.  
        - This obviously does not include the pressure drop from other connected equipments in series as the mill, the
          cyclone or the static separator.        
        - Regarding the power requirements of the filter itself (to produce the ionization of the particles), we can use the
          following correlation which is based on real operational data submitted by HJ White (1984):  
         
     
           
                 
                 
          where:        
          Wc is the power of the corona effect in Watts (W)      
          Q is the quantity of gas in m3/h        
          Pt is a penetration factor (1 - efficiency)        
       2.8   Advantages of the ESP:        
          * Reasonable investment cost for high capacity      
          * Reduced operating costs        
          * High efficiency for fine particles (<1μ)        
          * Ability for high flow rates        
          * Low pressure drop        
          * Adapted for polydisperse aerosols        
          * Much lower fire risk        
          * Adapted to changes of charge        
          * Inactivation of microorganisms        
          * Well adapted for high temperatures        
          * Ability to remove both dry or wet particles      
       2.9   Disadvantages of ESP:        
          * Efficiency depends on the electrical resistivity of the particles      
          * Takes more space when lower speeds        
          * No flexibility when installed        
          * Difficult to operate with particles at high electrical resistivity      
          * Noise pollution        
          The general trend is to replace ESP's by bag filters.      
       2.10   Calculator:        
        - A calculator is available to calculate the following:      
          * Estimate the terminal velocity of the particles      
          * Estimate the corona onset voltage        
          * Calculate the total collector plate area for an ESP      
          * Estimate the dimensions of a plate-wire ESP      
          * Estimate the overall efficiency of an ESP        
          * Estimate the power required        
        - For the link to the calculator, see below.        
                   
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