These devices called ESP’s, enjoy a relatively low payback period – often 3 - 5 years – especially those that are able to recover valuable solids for sale / reuse.
Calculating collection efficiency:
ESP’s are used to treat particulate laden gases at high flow rate alone or together with Bag house Filters, Cyclones, Hydro-cyclones and Wet scrubbers and have following advantages.
- Low pressure drop (about 2.5 cm H2O compared to 5-10 cm H2O for other methods)
- High removal efficiency (> 97+%) even for flows with particles < 2m.
- Handling gases with high moisture content (even 30%).
- Easy separation and recovery of collected material when it is reused.
During ESP operation, first the airborne particles are electrically charged. The charged particles then migrate to the collector (negatively changed electrode) where they are neutralized and collected in a hopper. The high voltage system works at 25-100 KV, and a corona type discharge occurs at the negatively charged electrode.
The theoretical efficiency of an ESP can be determined by equation-1, known as Deutsch equation given as under:
Eff = 1- exp(- 2VL/RU) (1)
Where L = collector length, m
V = Particle velocity towards the electrode, usually 0.03-0.21m/s
R = Collector radius, m
U = Net gas velocity, m/s
Collector area : A = 2 Pi RL - (1a)
Volumetric flow rate Q = U R^2 - (1b)
Substituting 1a & 1b in eqaution (1), it can be re-written as:
Eff = 1- exp(- AVL/Q) - (2)
Higher collection efficiencies can be obtained by increasing the throughput velocity (V), collector area (A) or by reducing the gas flow rate (Q). However, increasing collector area is not always feasible.
To increase efficiency from 90 to 99%, the area needs to be doubled; while from 90 – 99.9%, three times area corresponding to 90% efficiency, is required.
Increase in flow rate will increase the particle loading at the outlet. In a typical ESP, reduction in the collection efficiency from 99 to 97% will triple the particle loading in the exhaust.
The Deutsch equation was later modified (equation 3) and now widely used to calculate collection efficiency with varying operating parameters.
Eff = 1- exp(- AVK/Q) - (3)
Where VK is the effective migration velocity and given by equation (4).
VK = v ln (1/1-Eff) … (4)
Where v is the effective migration velocity of particles areas across the inter electrode space, as computed by equation (5). Accordingly to electrostatic field theory,
v = [PDE^2 (1 + J L/D)]/ 36x10^7 Pi Mu (5)
Where D = Particle diameter, m
E = Electrostatic force field, V/m
J = Average free distance run by the gas molecules, as given by equation (6), m
L = Length between electrodes, cm
Mu= Absolute gas viscosity, Poise
P = A unit less parameters, given by equation (7), where C is the di-electric constant, coulombs/gm
J = 1.764 + 0.562 e-0.785 D/L - (6)
P = 3C/(C+2) - (7)
Equation (5), used for calculating effective migration velocity for particles, is based on three assumptions:
- Particles rapidly reach to their final velocity while moving towards the negatively charged electrode.
- For particles with a diameter similar to, or lower than, the average free distance run by gas molecules, the hydrodynamic buoyancy can be calculated using ‘Stokes law’ with ‘Cunnighum Correction’ factor.
- The accumulated electrostatic charge nearly instantaneously reaches its maximum, limit value.
Theoretical determination of ESP efficiency though straight forward, but involves theoretical formulations for variables like V, VK and J, which is often difficult to get in industrial situations.
“Practical” efficiency can be determined by equation (8) involving volumetric flow rate and particulate content, which can be determined using an Isokinetic method.
Eff = (Cpi.Qi – Cpo.Qo)/ Cpi.Qi - (8)
Where Cp = Particulate content of the gas, mg/m3
Q = Volumetric flow rate, m3/hr
i = inlet
o = outlet.
Isokinetism correlates gas velocity with sampling velocity. 100% isokinetism means gas velocity equals sampling velocity. For practical purpose (stack sampling), 90-110% isokinetism gives fairly good value.