A gaseous effluent from a biomass combustion system has a particle composition that follows a

log$-$normal distribution, and whose respective parameters are $dPLM=25\mathrm{.}0m$ and ${}_B=1\mathrm{.}5m.$

The effluent will be treated to reduce the concentration of particles using an electrostatic

precipitator $($PPEL$).$

Characteristics of the gaseous effluent to be treated in the deduster:

$>P=100$kPa

$>T=200C$

$>G^m=31\mathrm{.}0kg$ gaseous effluent $\frac{?}{S}$

$>C^0=20$ gparticles $\frac{?}{m^3}$ gaseous effluent $($under conditions $P$ and $T$ of the gaseous effluent$)$

$>$ P particles $=1400k\frac{g}{m^3}$

$>$ The molar composition of wet flue gases is $Y_{H2O}=0\mathrm{.}071$;$Y_{N2}=0\mathrm{.}748$;$Y_{O2}=0\mathrm{.}040$;$Y_{CO2}=$

$0\mathrm{.}141$

${}_{\text{w}\text{e}\text{t}\text{g}\text{a}\text{s}\text{e}\text{s}}=2\mathrm{.}5{10}^{-5}kg{m}^{-1}{s}^{-1}$

Parameters to consider when sizing the PPEL:

Dielectric constant of particles

Void permittivity

Electric field strength

$=6\mathrm{.}14$

${}_0=8\mathrm{.}85{10}^{-12}{C}^2{N}^{-1}{m}^{-2}$

$E=E_0=3\mathrm{.}15{10}^{5}N{C}^{-1}$

a$)$ Calculate the total area of the plates of an electrostatic precipitator $($flat$)$ to treat the gaseous

effluent in order to meet a particle emission value of $25k\frac{g}{h}$;

b$)$ Determine the specific particle collection efficiency model for the electrostatic precipitator;

c$)$ Carry out the mass balance of particles in the electrostatic precipitator, knowing that the overall

particle collection efficiency is $98\%,$ and check that the emission value of $50m\frac{g}{N}{m}^3(273K$ and

$101\mathrm{.}3$kPa is met.