Johnstone Method Of Calculating Particle Efficiency

Since 1 psf=0.1922in. H20,

The Calvert equation significantly underpredicts the pressure drop at low values of R. Note that this equation fails when R is zero.


A consulting firm has been requested to calculate the throat area of a venturi scrubber to operate at a specified collection efficiency.

To achieve high collection efficiency of particulates by impaction, a small droplet diameter and high relative velocity between the particle and droplet are required. In a venturi scrubber this is often accomplished by introducing the scrubbing liquid at right angles to a high-velocity gas flow in the venturi throat (vena contracta). Very small water droplets are formed, and high relative velocities are maintained until the droplets are accelerated to their terminal velocity. Gas velocities through the venturi throat typically range from 12,000 to 24,000 ft/min. The velocity of the gases alone causes the atomization of the liquid.

Perhaps the most popular and widely used venturi scrubber collection efficiency equation is that originally suggested by Johnstone:

where E = fractional collection efficiency k = correlation coefficient whose value depends on the system geometry and operating conditions, typically 0.1-0.2, lOOOacf/gal R = qL/qG — liquid-to-gas ratio, gal/1000 acf \j/ = C'ppvdp /1&d0p, the inertial impaction parameter pp = particle density, lb/ft3

v = gas velocity at venturi throat, ft/s dp = particle diameter, ft d0 = droplet diameter, ft p = gas viscosity, (lb/ft • s) C = Cunningham correction factor

Note: Some engineers define i// as

CPpvtf 9 d0p

This change is reflected in the correlation coefficient, k. Pertinent data are given below.

Volumetric flowrate of process gas stream =11,040 acfm (at 68°F)

Density of dust = 187 lb/ft Liquid-to-gas ratio = 2 gal/1000 ft3 Average particle size = 3.2 pm (1.05 x 10"5 ft) Water droplet size = 48 pm (1.575 x 10"4 ft) Johnstone scrubber coefficient, ¿ = 0.14 Required collection efficiency = 98% Viscosity of gas = 1.23 x 10 "5 lb/(ft • s) Cunningham correction factor = 1.0


Calculate the inertial impaction parameter, >[/, from Johnstone's equation:

From the calculated value of t¡/ above, back calculate the gas velocity at the venturi throat, v:


_ 18i¡/don _ (18)(195.2)(1.575 x 10~4)(1.23 x 10~5) V~ ppdj ~~ (187)(1.05 x 10~5)2

Calculate the throat area, S, using gas velocity at the venturi throat, v: S = q/v — (11,040)/[(60)(330.2>] = 0.557 ft2


Three identical venturi scrubbers are connected in series. If each operates at the same efficiency and liquid-to-gas ratio, qL/qG, calculate the liquid-to-gas ratio, assuming the Johnstone equation to apply. Data are provided below.

E0 (overall) = 99% Inlet loading = 200 gr/ft3 Johnstone scrubber coefficient, k — 0.14 Inertial impaction parameter, i// = 105


First calculate the outlet loading (OL) from the last unit:

Express the individual and overall efficiencies in terms of the penetration P:

Calculate the individual efficiency for each venturi scrubber, noting that the efficiencies (or penetrations) are equal:


Using the Johnstone equation, solve for the liquid-to-gas ratio, qL/qG:

_ ln(l — E) _ ln(l- 0.785) W ~ k4>°-5 ~ (0.14)(105)° 5 = 1.07 gal/1000 acf = 1.07 gpm/1000 acfm


Contact power theory is an empirical approach relating particulate collection efficiency and pressure drop in wet scrubber systems. The concept is an outgrowth of the observation that particulate collection efficiency in spray-type scrubbers is mainly determined by pressure drop for the gas plus any power expended in atomizing the liquid. Contact power theory assumes that the particulate collection efficiency in a scrubber is solely a function of the total power loss for the unit. The total power loss, SPT, is assumed to be composed of two parts: the power loss of the gas passing through the scrubber, SPG, and the power loss of the spray liquid during atomization, 0>L. The gas term can be estimated by

where SfG is the contacting power based on gas stream energy input in hp/1000 acfm and AP is the pressure drop across the scrubber in inches of water. In addition,

where SPL is the contacting power based on liquid stream energy input in hp/1000 acfm, PL is the liquid inlet pressure in psi, qL is the liquid feed rate in gal/min, and qG is the gas flowrate in ft3/min. Then

To correlate contacting power with scrubber collecting efficiency, the latter is best expressed as the number of transfer units. The number of transfer units is defined by analogy to mass transfer and given by where Nt is the number of transfer units, dimensionless, and E is the fractional collection efficiency, dimensionless. The relationship between the number of transfer units and collection efficiency is by no means unique. The number of transfer units for a given value of contacting power (hp/1000 acfin) or vice versa varies over nearly an order of magnitude. For example, at 2.5 transfer units (E = 0.918), the contacting power ranges from approximately 0.8 to 10.0 hp/1000 acfm, depending on the scrubber and the particulate.

For a given scrubber and particulate properties, there will usually be a very distinct relationship between the number of transfer units and the contacting power. The number of transfer units for a series of scrubbers and particulates is plotted against total power consumption; a linear relation, independent of the type of scrubber, is obtained on a log-log plot. The relationship could be expressed by where a and ft are the parameters for the type of particulates being collected and the scrubber unit.

A vendor proposes to use a spray tower on a lime kiln operation to reduce the discharge of solids to the atmosphere. The inlet loading is to be reduced to meet state regulations. The vendor's design calls for a certain water pressure drop and gas pressure drop across the tower. You are requested to determine whether this spray tower will meet state regulations. If the spray tower does not meet state regulations, propose a set of operating conditions that will meet the regulations. The state regulations require a maximum outlet loading of 0.05 gr/ft3. Assume that contact power theory applies. Operating and design data are provided:

Gas flowrate = 10,000 acfm Water rate = 50 gal/min Inlet loading = 5.0gr/ft3

Maximum gas pressure drop across the unit= 15 in. HzO Maximum water pressure drop across the unit= lOOpsi

The vendor's design and operating data are also available:

Water pressure drop = 80 psi

Gas pressure drop across the tower = 5.0 in. HzO


Calculate the contacting power based on the gas stream energy input, in hp/1000 acfm:

Calculate the contacting power based on the liquid stream energy input, 0>L, in hp/1000 acfm:

The total power loss, SPT, in hp/1000 acfm is then

The number of transfer units, Nt, is

The collection efficiency can be calculated based on the design data given by the vendor:

SPQ =(0.157) AP = (0.157)(5.0) = 0.785 hp/1000 acfm

= 0.5S3PL(qJqG) = (0.583)(80)(50/l 0,000) = 0.233 hp/1000 acfm


The collection efficiency required by state regulations, Es, is

Inlet loading — Outlet loading /jqqx s ~~ Inlet loading

Since Es > E, the spray tower does not meet the regulations.

One may now propose a set of operating conditions that will meet the regulations:

The total power loss, SPT, in hp/1000acfm is

Solving for 2/>T

Calculate the contacting power based on the gas stream energy input, SPG, using a AP of 15 in. H20:

The liquid stream energy input, is then

Calculate qL/qa, in gal/acf, using PL in psi:

The new water flow rate, q'L in gal/min, is therefore qi = (?l/9g)(10, 000 acfm) = (0.0104)(10,000 acfm) = 104 gal/min

The new set of operating conditions that will meet the regulations are

Unlike the Johnstone equation approach, this method requires specifying two coefficients. The validity and accuracy of the coefficients available from the literature for the contact power theory equations have been questioned. Some numerical values of a and fi for specific particulates and scrubber devices are provided below.


Scrubber Type



Raw gas (lime dust and soda fume)

Venturi and cyclonic spray



Prewashed gas (soda fume)

Venturi, pipe line, and cyclonic spray



Talc dust




Black liquor recovery furnace fume

Venturi and cyclonic spray



Phosphoric acid mist




Foundry cupola dust




Open-hearth steel furnace fume




Talc dust




Ferrosilicon furnace fume

Venturi and cyclonic spray



Odorous mist





A venturi scrubber is being designed to remove particulates from a gas stream. The maximum gas flowrate of 30,000 acfm has a loading of 4.8 gr/ft3. The average particle size is 1.2 |.im and the particle density is 200 lb/ft3. Neglect the Cunningham correction factor. The Johnstone coefficient, k, for this system is 0.15. The proposed


flowrate is 180gal/min and the gas velocity is 250 ft/s.


What is the efficiency of the proposed system?


What would the efficiency be if the gas velocity were increased to 300 ft/s?


Determine the pressure drop for both gas velocities. Assume


equation to apply.


Determine the daily mass of dust collected and discharged for

each gas



What is the discharge loading in each case?



The ratio of liquid-to-gas flowrates is given by

R = ( 180)( 1000)/(30,000)

= 6.0 gal/1000 acf = 6.0gpm/acfm


vG = 250 ft/s dv = 1.2 nm = 3.937 x 10~6 ft pp = 200 lb/ft3 p= 1.23 x 10~5 lb/(ft • s) Assume the Nukiyama-Tanasawa (NT) equation to apply: </„ = OM00/I>)+1.45 R1-5 = (16,400/250) + 1.45 (6.0)15 = 86.91 |rm

(3.937 x 10~6)2(200)(250) ~(9)(1.23 x 10~5)(2.85 x 10"4) = 24.56

2. If v were increased to 300 ft/s, d0 = (16,400/300) + 1.45(6.0)1'5 = 75.98 pm

(3.937 x 10~6)2(200)(300) 1 — (9)(1.23 x 10"5)(2.85 x 10"4)

3. The pressure drops are given by (see Problem VEN. 5)

APa = (5 x 10~5)(250)2(6) = 18.75 in. H20 APb = (5 x 10~5)(300)2(6) = 27 in. H20

4. The total mean loading, TML, is

TML = (4.8 gr/ft3)(30,000)(60)(24)/7000 = 29,600 lb/day = 14.81 tons/day

Dust discharged = 3441b/day

Dust discharged = 225 lb/day

VEN.10 OPEN-HEARTH FURNACE APPLICATION 357 5. The discharge loading (DL) for v = 250ft/s is


The installation of a venturi scrubber is proposed to reduce the discharge of particulates from an open-hearth steel furnace operation. Preliminary design information suggests water and gas pressure drops across the rubber of 5.0psia and 36.0 in. of H20, respectively. A liquid-to-gas ratio of 6.0gpm/1000acfm is usually employed with this industry. Estimate the collection efficiency of the proposed venturi scrubber. Assume contact power theory to apply with a and ft given by 1.26 and 0.57, respectively. Recalculate the collection efficiency if the power requirement on the liquid side is neglected.


Due to the low water pressure drop, it can be assumed that

Solving for gives

The number of transfer units is calculated from

The collection efficiency can now be calculated:

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