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      3   Bag filters (Suite 3)        
       3.10   Elements of sizing (suite):        
       3.10.7 Case of the pulse jet filter:        
        - During the online cleaning process of the bags of the pulsed air filter, only a small fraction of the dust coating the
          filter bag falls into the recovery hopper.        
        - The rest of the dislodged dust is redeposited on the bags by following the gas flow in the filter.
        - It is clear that the redeposited dust has different characteristics of pressure drop than the dust previously deposited.
        - A modelization of the online cleaning was developed by Dennis and Klemm and this has resulted in the following
          S is the resistance of the filter        
          Se is the resistance of the just cleaned filter      
          (K2)c is the specific resistance of the recycled dust      
          Wc is the areal density of the recycled dust        
          K2 is the specific resistance of the freshly deposited dust      
          Wo is the areal density of the dust deposited later      
        - This model has the advantage that it can easily report the three filtration regimes of a pulse jet filter, ie:
          clean filter, new dust deposited and redeposited dust.      
        - Considering the operating conditions, the values of Se, (K2)c and Wc can be assumed to be constant,
          so that they can be grouped into the following relationship:      
          ΔP is the total pressure drop        
          V is the filtration velocity        
        - This equation describes the behavior of the pressure drop for a single filter bag but also determines the pressure
          drop of the baghouse due to the parallel arrangement of the bags.      
        - The disadvantage of the model represented by the last two equations is that the constants, Se, (K2)c, andt Wc, are
          are difficult to know.        
        - The solution is to develop other empirical equations for special cases.    
        - For example, for the combination of Dacron felt with fly ash, the proposed formula is:  
          V in ft/min        
          Pj is the pressure of the pulsed air, normally between 60 and 100 psig    
        - Of course, the above equation can not be applied to other cases.      
        - The formula calculating the total pressure drop becomes:      
          ΔP in mmH2O        
          V in ft/min        
          Pj in psig (psi)        
          K2 in inH2O/(ft/min).(lb/ft2) and generally between 1,2 and 40      
          C in g/ft3        
          tf in min        
       3.10.8 Example calculation for pulsed air filter:        
        - Data:        
          * Quantity of Gas: 110 000 m3/h        
          * V equals 7 ft/min        
          * Pj equals 100 psi        
          * K2 equals 10        
          * C equals 1,4 g/ft3        
          * tf equals 40 min        
        - Solution:        
          By applying the above formula, we have:        
        - There is also an empirical formula to calculate K2.      
        - The formula, developed in the 70s by Dennis and David, shows that K2 depends on the average particle diameter
          and the speed of filtration.        
        - By adding the particle density and viscosity of gas, we have:      
          D is the mean diameter by mass of the particles in m      
          μT is the gas viscosity at the operating temperature in kg/m.s      
          μ20°C is the viscosity of the gas at the temperature of 20°C (1,81.10ˉ⁵ kg/m.s)    
          ρ is the material density in kg/m3        
          V is filtration velocity in m/s        
        - K2 is in mmH2O/(m/s).(kg/m2) or in inH2O/(ft/min).(lb/ft2)      
       3.10.8 Filtration efficiency:        
        - The efficiency is given by the following formula:      
          η is the efficiency        
          C is the concentration of dust at the inlet in kg/m3 or g/m3      
          Co is the concentration of dust at the output in kg/m3 or g/m3      
        - The efficiency is usually above 99%.        
       3.11   Calculators:        
        - Two calculators are available for:        
          * Filter cleaning by reverse air        
          * Filter cleaning by pulsed air        
          Note: These calculators are based on empirical formulas.      
          We must also be careful with units which are Anglo-Saxon or in the international system (SI).  
        - For the link to the calculator, see below.   
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