Particle Size Distribution Effects on Gas-Particle Mass Transfer within

Environ. Sci. Technol. 2006, 40, 3929-3933

Particle Size Distribution Effects on Gas-Particle Mass Transfer within Electrostatic Precipitators HEREK L. CLACK* Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, 10 West 32nd Street, Chicago, Illinois 60616

Varying degrees of mercury capture and transformation have been reported across electrostatic precipitators (ESPs). Previous analyses have shown that the dominant mass transfer mechanism responsible for mercury capture within ESPs is gas-particle mass transfer during particulate collection. Whereas previous analyses assumed dispersions of uniform size, the present analysis reveals the effects of polydispersity on both gas-particle mass transfer and particle collection within an ESP. The analysis reveals that the idealized monodisperse particle size distribution provides the highest gas-particle mass transfer but results in the lowest particle collection efficiency (% mass). As the particle size distribution broadens, gas-particle mass transfer decreases and particle collection efficiency increases. The results suggest that more than just reporting mean particle diameter provided by the sorbent manufacturer, pilot- and field-tests of sorbent injection for mercury emissions control need to experimentally measure the particle size distribution of the sorbent as it is injected in order to facilitate interpretation of their results.

Introduction Various approaches to mercury emissions control have been considered for coal-fired power plants (CFPPs), in anticipation of the U.S. EPA’s recently released Clean Air Mercury Rule. A single control technology is not likely to meet the needs of the power industry, half of whose generating capacity came from coal combustion in 2002. It is well-known that a variety of factors influence the concentration and speciation of mercury resulting from coal combustion (see, for example, reviews by Pavlish et al. (1) and Brown et al. (2)), chief among them being the configuration and operation of the facility. Apart from differences in their original designs, more than two-thirds of U.S. coal-fired electric generating capacity is more than 25 years old (3), raising the likelihood that facilities that were originally different in configuration and operation have become even more so as a result of facility upgrades. Fixed-bed adsorption is one leading control approach. It involves forcing the flue gas through a continuously refreshed powdered sorbent bed formed on a baghouse filter retrofitted downstream of the primary particulate control. Fixed bed approaches to mercury emissions control benefit from wellestablished analysis methods developed from the use of fixed bed reactors in other industries. For an as-yet unknown subset of coal-fired boilers, however, a variety of factors may make a baghouse retrofit undesirable; there is increasing demand and interest in multi-pollutant control technologies as alternatives to stand-alone, pollutant-specific emissions * Corresponding author e-mail: [email protected]. 10.1021/es051649c CCC: $33.50 Published on Web 04/26/2006

 2006 American Chemical Society

FIGURE 1. Schematic of one-half of a channel between two plate electrodes of an ESP for turbulent conditions (not to scale.). control. Given that the majority (more than 60% (2)) of CFPPs have electrostatic precipitators (ESPs) installed for particulate control, and given the interest in multi-pollutant control technologies, the potential for mercury emissions control within ESPs is of interest. In fact, pilot- and full-scale testing have revealed the capacity of ESPs to capture mercury, both with and without upstream sorbent injection (1, 4-6). However, the mechanism for mercury capture within ESPs is much less understood than that for fixed bed adsorption using a baghouse. Previous analyses (7) showed that, contrary to widely held assumptions, relatively little of the mercury captured within an ESP is likely to be absorbed by the particulate matter collected on the plate electrodes. Rather, analyses (8) of gas-particle mass transfer during collection of particulate matter within an ESP showed that the charged, suspended aerosol presented a much larger potential for mercury capture than the bulk particulate collected on the plate electrodes. To further expand on the mass transfer mechanisms responsible for mercury capture within ESPs, the present analysis investigates the role of particle size distribution on gas-particle mass transfer within an ESP.

Theory and Numerical Method Consider a generic representation of a particle-laden channel flow between two plate electrodes of an ESP (Figure 1). Although laminar flows have been analyzed in the past (8), it is generally accepted that both Reynolds number considerations and electrohydrodynamic effects virtually guarantee that flows within industrial ESPs are turbulent (9-11). The gas phase is air that nominally enters the channel at 500 K, 1 atm, and 3 m/s containing 4 ppbv of elemental mercury (Hg0) (CHg(x ) 0) ) 4 ppbv). The ultra dilute Hg0 concentration allows thermodynamic and fluid properties of the mixture to be approximated as those of air, an ideal gas. The width H and stream-wise length L of the channel are 0.5 and 10 m, respectively, yielding a residence time in the channel of 3.3 s and a Reynolds number of 38 800 that exceeds the critical value for turbulent flow. Spherical particles of diameter dp make up the particulate phase of the particle-laden flow, particles whose size distribution is log-normal, represented by eq 1 (12):

NDp(dp) )

〈NDp〉 (2π)1/2dpln σg

[

exp -

]

(ln dp - ln dpg)2 2ln2 σg

(1)

where NDp(dp) is the particle number density per unit particle diameter (for particle of diameter dp) [1/m3-µm], 〈NDp〉 is the total particle number density over all particles [1/m3], and σ is the geometric standard deviation of the particle size distribution [unitless]. To facilitate and emphasize gasparticle mass transfer, the particles are treated as perfect Hg0 sinks at whose surface the gas-phase Hg0 concentration is zero. Although this condition is restrictive and neglects VOL. 40, NO. 12, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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mass transfer resistances associated with adsorption kinetics, intraparticle diffusion, and sorbent capacity, it allows the collection of a polydisperse aerosol within an ESP to be interpreted unambiguously in terms of impacts on gasparticle mass transfer. Requiring the model to isolate gasparticle mass transfer effects allows subsequent consideration of both Hg0 adsorption by injected powdered activated carbon (PAC) and Hg0 oxidation by native fly ash (as demonstrated in (13)), as either (or both) is collected within an ESP. Particle dynamics within the turbulent, particulate-laden channel flow are addressed in a manner similar to that used in developing the Deutsch-Anderson equation (9) for predicting particle collection within an ESP. Specifically, the flow is assumed to be sufficiently turbulent that scalar quantities such as Hg0 concentration CHg and particle number density NDp(dp) remain uniform in the cross-stream direction (y-direction, Figure 1), with the dispersive nature of the turbulent flow preventing the development of cross-stream gradients. Self and co-workers (14) have shown through detailed modeling that ESP particle collection efficiency decreases as turbulent diffusivity is reduced from the infinite value assumed in the Deutsch-Anderson equation to finite and more realistic values. Calculated transient response times for the largest particles considered here are generally less than a fraction of a millisecond, implying that on the time scale of turbulent velocity fluctuations the particles are able to maintain the equilibrium between Coulombic and drag forces. Consequently, whereas particle paths are strongly influenced by turbulent velocity fluctuations, the relative velocity between the particle and the gas (i.e., the gas-particle slip velocity) is not. It is the relative velocity between the particle and the gas that governs gas-particle mass transfer. Crowley (15) gives the terminal electrostatic drift velocity, representing the equilibrium between Coulombic and drag forces, of a particle of diameter dp as follows (eq 2):

Ues(dp) )

neECc 3πµdp

(2)

where e is the value of an elementary charge, i.e., an electron (4.8 × 10-10 stC); n is the number of elementary charges retained by the particle; E is the electric field strength, a variable in the numerical model [stV/cm]; and µ is the dynamic viscosity of air, a function of temperature in the numerical model [dyn-s/cm2]. Cc is the Cunningham slip correction factor for Stokes drag on small particles (eq 3)

[

( (-1.1 Kn ))]

Cc ) 1 + Kn 1.257 + 0.4 exp

(3)

where Kn is the Knudsen number, defined as the ratio of molecular mean free path λ to particle diameter dp. The molecular mean free path λ varies with pressure and temperature, both variables in the numerical model, as given by eq 4:

λ)

R ˆT 2 x2πdN NAP 2

9

[

n)

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 40, NO. 12, 2006

]

[ ( )

dpkT 2π ln 1 + mikT 2e2

1/2

dpe2ni∞t

(5)

]

(Diffusion charging) (6)

where n is the number of unit charges on a particle [unitless], e is the charge of an electron [stC], k is Boltzmann’s constant [ergs/K], T is temperature [K], Eo is the electric field strength in the channel [stV/cm],  is the particle dielectric constant (assumed to be very large) [unitless], mi is the mass of a gaseous ion (assumed to be O2) [g], t is time [s], and ni∞ is the ion density far from the particle [1/cm3]. As argued by Friedlander (12), field charging of particles is sufficiently rapid that compared to the time scale of the channel flow (L/U0) it is reasonable to assume the particles attain their field charging saturation charge instantaneously; thus, eq 5 represents this saturation charge due to field charging for particles of diameter dp. By comparison, diffusion charging occurs more slowly, necessitating the use of an average value over the 3.3-s residence time of the channel. The total particle charge is the sum of the saturation field charge and the average charge acquired by diffusion over the 3.3-s residence time of the channel, although it has been noted that such additive approaches are generally less accurate than results obtained by numerically modeling the charging process (12). The initial, size-specific particle number densities entering the channel decrease exponentially with time according to eq 7, a modified form of the Deutsch-Anderson equation based on the configuration in Figure 1

t NDp(dp, t) ) NDp,0 (dp)exp -2Ues(dp) H

[

]

(7)

where NDp,0(dp) and Ues(dp) are the initial number density entering the channel and the terminal electrostatic drift velocity, respectively, of particles of diameter dp. H is as defined previously. The model assumes no particle interactions, either electrical or physical. The model does not consider operational losses such as sneakage (particulateladen flow escaping the shroud through fluid leaks) or rapping reentrainment (resuspension of collected particulate matter during periodic cleaning of collection electrodes) that degrade ESP performance in practice (10). The Fro¨ssling equation (eq 8) (16) provides a correlation between the mean Sherwood number Shd about a spherical particle and the particle Reynolds number which depends on the gas-particle slip velocity induced by the particle charge and the electric field. Equating the definition of Shd to the Fro¨ssling equation (eq 8), the mean convective mass transfer coefficient hm can be found once the molecular diffusivity Dab of the Hg0-air system as determined via an expression (eq 9) developed by Fuller et al. (17):

(4)

where R ˆ is the universal gas constant (8.314 kJ/mol-K); T is temperature [K]; dN2 is the diameter of an N2 gas molecule (3.7 Å); NA is Avogadro’s number (6.02 × 1023 no./mole); and P is pressure [kPa]. In an earlier analysis of gas-particle mass transfer within ESPs (8), the number of elementary charges on a particle was uniformly set at 1% of the maximum possible charge based on particle diameter. The present model provides a more realistic representation of particle charging within an ESP by explicitly calculating both field charging (eq 5) (12) and diffusion charging (eq 6) (9) of particles: 3930

2  - 1 Edp (Field charging) n) 1+2  + 2 4e

Shd )

hmdp 1/3 ) 2 + 0.552Re1/2 d Sc Dab

(8)

Dab )

1.858e-27T3/2 1 1 + 2 M M PσabΩD a b

(

(9)

)

1/2

in which P is pressure [atmospheres], T is temperature [K], Mx is molecular weight of species x [g/gmol], σab is the average collision diameter for species a and b [m], and ΩD is the collision integral [unitless]. Values for σ and ΩD originate from the Lennard-Jones 6-12 potential, obtained by Svehla (18) and presented by Hines and Maddox (19).

FIGURE 2. Variation of residual mercury fraction with time as a function of mean particle size dp and geometric standard deviation σ. Monodisperse (σ ) 1) results denoted by bold lines. Final particle collection efficiency (% mass) noted for each value of dp and σ. Inset illustrates particle size distributions for 1.5 < σ < 2 holding particle mass loading constant. Conditions: turbulent channel flow, electric field strength E ) 200 kV/m, particle mass loading MLp ) 0.1 g/m3, pressure P ) 1 atm, and temperature T ) 500 K. For a polydisperse suspension of particles, consider a subset of particles of diameter dp whose number density is NDp(dp). Equation 10 represents the cumulative convective mass transfer rate of Hg0 to particles of diameter dp contained within a differential fluid volume ∆V of height H/2, differential length ∆x, and unit depth (see Figure 1). Because the particles are of uniform size, they exhibit identical charge (equal to the sum of eqs 5 and 6) and thus have the same chargedriven gas-particle slip velocity Ues. Note that the assumption of a uniform value of Ues yields a uniform value of hm for all particles of diameter dp:

M ˙ Hg(dp,t) ) hm(dp)NDp(dp)∆V4π(dp/2)2F(CHg(t) - 0) (10) The number density of particles of diameter dp is determined from the total particle mass loading MLp (0.1 g/m3 for the present analysis) and the particle size distribution (eq 1). For a log-normal size distribution of specified geometric mean and standard deviation (eq 1), specifying the total particle mass loading MLp and assuming a bulk particulate density of 0.45 g/cm3 (a mean value for both fly ash and powdered activated carbon) yields the size-specific particle number density NDp(dp). Integrating eq 10 over all sizes dp yields the total gas-particle mass transfer rate (eq 11):

M ˙ Hg(t) )

∫

∞

0

∫ M˙ ∞

0

Hg(dp,t)d(dp)

)

hm(dp)NDp(dp)∆V4π(dp/2)2F(CHg(t) - 0)d(dp) (11)

Finite difference integration of eq 11 for a specified particle size distribution yields the total rate of gas-particle mass transfer as a function of time, which is linked by a mass balance to the rate of change of the Hg0 concentration in a differential volume of fluid ∆V (eq 12):

F∆V

∂CHg ) -M ˙ Hg(t) ∂t

(12)

Results and Discussion Figure 2 reveals the influence of both the mean particle size and the standard deviation of the particle size distribution on gas-particle mass transfer within an ESP. The particle mass loading for all cases is 0.1 g/m3, which approximately corresponds to a powdered activated carbon (PAC) injection rate of 6 lbs/MMacf (pounds per million actual cubic feet).

This particle mass loading is consistent with the higher PAC injection rates that have been used in field tests of mercury capture within ESPs (1, 6, 20), but is significantly higher than that typically used for mercury capture within a downstream baghouse. Implicit in these comparisons is the presumption that native, entrained fly ash present in the flue gas exhibits no capacity for adsorption or oxidation of mercury; to consider native fly ash with finite reactivity or sorption capacity would involve much higher values (1-10 g/m3) of particle mass loading. For both 10- and 25-µm particles, Figure 2 shows both the temporal evolution of the normalized residual mercury concentration (CHg/CHg0) as well as the final collection efficiency of the particulate phase at the channel exit. For each particle size dp, Figure 2 presents results for one monodisperse suspension (σ ) 1 and uniform dp) and three polydisperse suspensions (σ ) 1.5, 1.75, and 2.0 with a common mean dp). The inset in Figure 2 compares the particle size distributions for 1.5 < σ < 2 holding particle mass loading constant. Comparing results for the two particle sizes reveals several effects. As expected, for the same particle mass loading, smaller particles present larger total surface area and greater potential for mercury capture. However, larger particles acquire greater charge per unit area and therefore attain higher gas-particle slip velocities, Reynolds numbers, and convective mass transfer coefficients. The enhanced mass transfer brought about by convection, however, is offset by the decrease in particle number density as a result of particle collection: Larger particles experience higher convective mass transfer but this is offset by their more rapid decrease in particle number density as compared to smaller particles. Comparing monodisperse results for the two particle sizes (represented by heavy lines in Figure 2), mass transfer to monodisperse 10-µm particles has the potential to remove 76% of the initial mercury (0.24 residual mercury fraction) as compared to 12% (0.88 residual mercury fraction) for an equal mass of monodisperse 25-µm particles. Particle collection exhibits the opposite trend, with 99% of the monodisperse 25-µm particles being collected over the 3.3 s residence time in the channel, as compared to 85% of the monodisperse 10-µm particles. As particle size distribution broadens (i.e., for increasing σ), the effect is to reduce the overall mass transfer to the particles and increase the residual mercury fraction, while also yielding greater particle collection. For a polydisperse suspension of mean particle size dp ) 25 µm, increasing σ from 1 to 2 further erodes the already poor mass transfer performance, resulting in residual mercury fractions higher than 0.9 while at the same time achieving greater than 99% particle collection efficiency. The effect of increasing polydispersity on 10-µm particles was more pronounced. Increasing σ from 1 to 2 decreases mass transfer and increases the residual mercury fraction from 0.23 to 0.70, while increasing the particle collection efficiency from 85% to 98%. For all of these effects, the disproportionate influence of increasing σ on the mass fraction of the larger particles in the size distribution (for constant particle mass loading) increases the mass mean diameter of the suspension and mean gas-particle slip velocity while decreasing the total surface area and increasing the rate at which particle number density decays due to particle collection. Figure 3 shows the effect of electric field strength E on gas-particle mass transfer and particle collection efficiency for monodisperse and polydisperse suspensions. Particle size and polydispersity trends are similar to those shown in Figure 2. Increasing the electric field strength increases the particle charge (by field charging) and results in higher Coulombic forces on the particles, inducing higher gas-particle slip and yielding higher rates of particle collection. As is apparent in Figure 3, the net result is that although the higher value of E (600 kV/m) produces initially higher rates of gas-particle VOL. 40, NO. 12, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 4. Variation of residual mercury fraction with time as a function of gas temperature and geometric standard deviation σ for suspensions of 10-µm mean particle size. Final particle collection efficiency (% mass) noted for each value of temperature and σ. Conditions: turbulent channel flow, particle mass loading MLp ) 0.1 g/m3, and pressure P ) 1 atm.

FIGURE 3. Variation of residual mercury fraction with time as a function of electric field strength E and geometric standard deviation σ for 25-µm (upper) and 10-µm (lower) mean particle sizes (scale has been expanded for 25-µm results). Monodisperse (σ ) 1) results denoted by bold lines. Final particle collection efficiency (% mass) noted for each value of dp and σ. Conditions: turbulent channel flow, particle mass loading MLp ) 0.1 g/m3, pressure P ) 1 atm, and temperature T ) 500 K. mass transfer in response to the higher gas-particle slip velocities, this enhancement is quickly offset by the rapid decay in particle mass loading and number density due to strong particle collection. This tradeoff is apparent for both 25-µm (Figure 3, upper) and 10-µm (Figure 3, lower) particles, regardless of the degree of polydispersity. The 600-kV/m results for both particle sizes indicate such effective particle collection that an asymptotic value of residual mercury fraction is reached, indicating that particle mass loading has dropped to near zero. This occurs at much earlier times than for the 200-kV/m results, which approach asymptotic CHg/CHg0 values for the 25-µm particles but still exhibit significant decay potential for the 10-µm particles. For E ) 600 kV/m, particle collection efficiencies exceed 99% for both mean particle sizes, regardless of the level of polydispersity. The effect of polydispersity is diminished for E ) 600 kV/m largely because the rapid decay in particle mass loading and particle number density foreshortens the time available for gas-particle mass transfer, thereby reducing the impact of broader particle size distributions on the ultimate residual mercury fractions attained within the channel. Figure 4 illustrates the influence of gas temperature on gas-particle mass transfer within polydisperse suspensions. As reported previously (8), fluid viscosity decreases as temperature decreases, resulting in higher electrostatic drift velocities, higher values of convective mass transfer coefficient, and higher rates of particle collection. The more rapid particle collection and decrease in particle mass loading outweigh the higher convective mass transfer coefficient, resulting in increasing residual mercury fraction (lower gasparticle mass transfer) with decreasing temperature. This contradicts the temperature-dependent behavior of adsorption, where decreasing temperatures yield improved adsorption capacity (i.e., lower residual mercury fractions). The evidence of improved mercury capture with decreasing 3932

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temperature observed in pilot- and field-tests of sorbent injection and in-flight mercury adsorption (see review by Pavlish et al. (1) and references therein) suggests that the increase in sorbent performance outweighs the decrease in gas-particle mass transfer with decreasing temperature. The additional impact of polydispersity on the temperature effect is marginal. Decreasing the gas temperature from 500 to 400 K reduced the gas-particle mass transfer for a monodisperse (σ ) 1) suspension of 10-µm particles by 23%, as compared to a 34% reduction within a polydisperse (σ ) 2) suspension of 10 µm mean particle size for the same decrease in temperature. These results suggest that polydisperse particle suspensions are not disproportionately influenced by gas temperature effects. Particle collection efficiencies, also shown in Figure 4 for each value of temperature and σ, increase with decreasing temperature, reflecting lower fluid viscosities and higher particle electrostatic drift velocities as temperature decreases.

Literature Cited (1) Pavlish, J. H.; Sondreal, E. A.; Mann, M. D.; Olson, E. S.; Galbreath, K. C.; Laudal, D. L.; Benson, S. A. Status review of mercury control options for coal-fired power plants. Fuel Process. Technol. 2003, 82, 89-165. (2) Brown, T. D.; Smith, D. N.; Hargis, R. A., Jr.; O’Dowd, W. J. Mercury Measurement and Its Control: What We Know, Have Learned, and Need to Further Investigate. J. Air Waste Manage. Assoc. 1999, 49, 1-97. (3) National Research Council. Interim Report of the Committee on Changes in New Source Review Programs for Stationary Sources of Air Pollutants; National Academies Press: Washington, DC, 2005. (4) Public Service Company of Colorado/ADA Technologies, Inc. Investigation and Demonstration of Dry Carbon-Based Injection for Mercury Control; Final Report Under Phase I DOE/FETC Mega PRDA Program (period of performance September 1995 to July 1997); 1997. (5) Broderick, T.; Haythornthwaite, S.; Bell, W.; Selegue, T.; Perry, M. Determination of Dry Carbon-Based Sorbent Injection for Mercury Control in Utility ESP and Baghouses. Presented at the 91st Air and Waste Management Association Conference and Exhibition, San Diego, CA, June, 1998. (6) Rostam-Abadi, M.; Chang, R.; Chen, S.; Lizzio, T.; Richardson, C.; Sjostrom, S. Demonstration of Sorbent Injection Process for Illinois Coal Mercury; Final Technical Report; Illinois Clean Coal Institute Project Number 00-1/2.2D-1; 2001. (7) Clack, H. L. Mass Transfer within Electrostatic Precipitators: Trace Gas Adsorption by Sorbent-covered Plate Electrodes. J. Air Waste Manage. Assoc., in press. (8) Clack, H. L. Mass Transfer within Electrostatic Precipitators: In-flight Adsorption of Mercury by Charged Suspended Particulates. Environ. Sci. Technol. 2006, 40, 3617-3622. (9) White, H. J. Industrial Electrostatic Precipitation; AddisonWesley: Reading, MA, 1963.

(10) Davis, W. T., Ed. Air Pollution Engineering Manual/Air & Waste Management Association; John Wiley & Sons: New York, 2000. (11) Calvert, S., Englund, H. M. Handbook of Air Pollution Technology; John Wiley & Sons: New York, 1984. (12) Friedlander, S. K. Smoke, Dust, and Haze, Fundamentals of Aerosol Dynamics, 2nd ed.; Oxford University Press: Oxford, 2000. (13) Dunham, G. E.; DeWall, R. A.; Senior, C. L. Fixed-Bed Studies of The Interactions Between Mercury And Coal Combustion Fly Ash. Fuel Process. Technol. 2003, 82, 197-213. (14) Leonard, G.; Mitchner, M.; Self, S. A. Particle Transport in electrostatic precipitator performance. Atmos. Environ. 1980, 14, 1289-1299. (15) Crowley, J. M. Fundamentals of Applied Electrostatics; Wiley: New York, 1986. (16) Frossling, N. Uber die Verdunstung fallender Tropfen. Beitr. Geophys. 1938, 52, 170.

(17) Fuller, E. N.; Schettler, P. D.; Giddings, J. C. A New Method for Prediction of Binary Gas-Phase Diffusion Coefficients. Ind. Eng. Chem. 1966, 58, 19. (18) Svehla, R. A. NASA Tech. Rep. R-132; Lewis Research Center, Cleveland, Ohio, 1962. (19) Hines, A. L.; Maddox, R. N. Mass Transfer: Fundamentals and Applications; Prentice-Hall: New York, 1985. (20) Senior, C.; Wang, D.; Cremer, M.; Chiodo, A.; Valentine, J. CFD Modeling of Activated Carbon Injection for Mercury Control in Coal-Fired Power Plants. Presented at the 8th Electric Utilities Environmental Conference, Tucson, AZ, January, 2005.

Received for review August 19, 2005. Revised manuscript received December 19, 2005. Accepted January 24, 2006. ES051649C

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