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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 = amperesecond








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 wireplate 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 ×10⁸ 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 reintroduction
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 × 10⁸ 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 30100mmH2O.






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 platewire ESP







* Estimate the overall efficiency of an ESP








* Estimate the power required









For the link to the calculator, see below.













www.thecementgrindingoffice.com

All rights reserved © 20122015 The Cement Grinding Office
