The Effects of Pulsed Corona Discharge on SO - American

The absorption of SO2 from the gas mixtures of SO2/N2 into deionized water was measured under corona discharge at 22 °C and 1 atm. A model based on f...
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Ind. Eng. Chem. Res. 2001, 40, 5822-5830

The Effects of Pulsed Corona Discharge on SO2 Absorption into Water Joo-Youp Lee,† Soon-Jai Khang,*,† Chao-Heng Tseng,‡ and Tim C. Keener‡ Departments of Chemical Engineering and Civil and Environmental Engineering, University of Cincinnati, Cincinnati, Ohio 45221

The absorption of SO2 from the gas mixtures of SO2/N2 into deionized water was measured under corona discharge at 22 °C and 1 atm. A model based on film theory was developed to evaluate the effects of mass-transfer enhancement in the liquid phase by chemical dissociations and corona discharge current. It has previously been reported that mass transfer in the gas phase is enhanced by corona discharge. In this study, it was also found that corona discharge enhances mass transfer in the liquid phase through liquid-side boundary-layer thinning caused by corona-induced surface vibrations. The liquid boundary layer decreases as the corona power is increased. For our experimental conditions, mass transfer was enhanced by about 5.5 times in the gas phase and about 2.3 times in the liquid phase. Introduction Research on SO2 absorption into aqueous solutions has been focused on the chemical reactions taking place in the liquid phase as liquid-phase mass-transfer resistance frequently dominates the absorption rate. One of the characteristics of the absorption of SO2 is that it dissociates instantaneously and reversibly to form H+ and HSO3- in an aqueous phase, and this dissociation reaction makes the absorption rate much faster than the physical absorption rate. Hikita et al.1 studied pure SO2 absorption into water with penetration theory by considering the single SO2 dissociation reaction as instantaneous and reversible. They showed that absorption accompanied by chemical reaction could be predicted well by an approximate analytical expression. It was assumed that the concentrations of H+ and HSO3were equal by the condition of electroneutrality in the absence of the water hydrolysis reaction. Teramoto et al.2 also used penetration theory to model dilute SO2 absorption into water, as well as aqueous solutions of H2SO4, NaHSO4, and Fe(II)-EDTA. It was found that the presence of H2SO4 or NaHSO4 prevented SO2 dissociation, resulting in a lower absorption rate than found in pure water. For the case of Fe(II)-EDTA solution, the absorption rate was found to increase because of its buffer capacity. Chang and Rochelle3 showed that an approximate solution to the surface renewal theory could be obtained by using the square root of the diffusivity ratios in the film. They pointed out that the SO2 hydrolysis reaction with pure H2O is highly suppressed in pure gaseous SO2 and can only enhance the physical absorption rate by about 10% because of the high SO2 concentration at the interface. On the other hand, the absorption of a dilute SO2/N2 mixture in pure H2O showed a greater effect of mass-transfer enhancement due to the hydrolysis reaction. The system of a single dissociation reaction was * To whom correspondence should be addressed. Department of Chemical Engineering, University of Cincinnati, Cincinnati, OH 45221-0171 ([email protected]). † Department of Chemical Engineering. ‡ Department of Civil and Environmental Engineering.

also extended to that of three instantaneous reversible reactions.4 The reversible SO2 hydrolysis reaction was found to have a significant effect on the absorption rate when the partial pressure of SO2 is low. The enhancement factor increases with decreasing gas partial pressure of SO2. The effect of organic acid additives on SO2/ N2 absorption into CaO/CaCO3 slurries was also investigated by the same authors.5 It was pointed out that SO2 absorption is more gas-phase-controlled for low SO2 partial pressures and that adipic acid enhances the absorption of SO2 more effectively at high SO2 partial pressures. Another SO2 absorption model was developed on the basis of the film theory of gas absorption with chemical reaction in aqueous solutions containing CaSO3 and Ca(OH)2.6 The SO2 absorption rate and the enhancement factors were found to be governed by chemical equilibrium at the gas-liquid interface and in the bulk liquid. If the diffusivities of the chemical species were equal, then the rate of absorption depended on the composition of the bulk phase rather than on chemical equilibrium. Recently, the simultaneous absorption of SO2 and dissolution of CaSO3 have been taken into account using the Nernst theory to consider the effect of diffusion on the electric potential gradient.7 The dissolution of limestone particles in aqueous solutions containing SO2, H2SO4, and HCl has also been studied using a diffusive model based on film theory.8,9 Although the models employed the solid dissolution rate and the electric potential gradient, the mass-transfer enhancement turned out to be mostly influenced by the SO2 hydrolysis reactions and the acidity of the solution. No detailed study can be found in the literature on the effect of gas-phase discharge plasma on the liquid phase. However, the absorption of SO2 into distilled water under DC corona discharge was experimentally investigated for varying discharge density, polarity, and O2 content in a batch system.10 A significant increase in the rate of SO2 removal was observed as the intensity of the corona discharge increased. For similar current densities, both positive and negative discharge showed similar results in a humid air mixture, and a high O2 content resulted in a high SO2 removal rate.

10.1021/ie001039f CCC: $20.00 © 2001 American Chemical Society Published on Web 10/24/2001

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Figure 2. High-voltage pulsing module.

Figure 1. Schematic of the batch system.

In the present work, the effect of corona discharge on SO2 absorption into deionized water is studied in a batch system. The experimental results with corona discharge are compared to those without corona. A diffusion model based on film theory is used to determine the masstransfer enhancement due to the corona discharge as well as the mass-transfer enhancement due to the SO2 hydrolysis reactions. The ultimate goal of this study is to apply the results to a wet electrostatic precipitator (wESP). Wet electrostatic precipitators are traditionally used to control tacky particulates or in situations where high ash resistivity causes severe collection problems. They have typically been applied with tubular collector surfaces although any other configuration such as flat plates can be used as long as the collector surfaces are wet. The major advantages of wESPs include (a) no dust layer formation especially for the aerosol liquid, tars, and oil mists contained in flue gases; (b) no problems with back corona, spark-over, or dust re-entrainment; (c) low pressure drops; and (d) removal of acid gases and heavy metal vapors. Furthermore, wESPs have been experimentally shown to be better than dry ESPs for removal of NOx11 because the chemical reactions associated with water and its radicals help remove NOx gases.12 Experimental Apparatus and Procedure A schematic diagram of the experimental apparatus designed by Tseng et al.13 is shown in Figure 1. The batch experimental system was constructed to study SO2 absorption into the liquid phase under corona and noncorona conditions. The system was made of aluminosilicate nonconductive glass with a 0.6-cm thickness. A mixing fan, a discharge wire, a pressure manometer, and a septum for injecting pure SO2 with a syringe were installed in the upper box (gas phase) with a volume of

29 740 cm3. A fan was enclosed in the upper box to agitate the gas. The SO2 concentration in the upper box was measured by circulating a small stream of gas from the upper box through a nondispersive infrared SO2 analyzer (Horiba PIR-2000, Horiba Instruments Inc., Irvine, CA). The loop-shaped corona discharge wire was located 10.2 cm above the gas-liquid interface, and the wire was wrapped in stainless steel mesh with short, pointed stubs to enhance the corona generation. The wire tip for the needle electrode was installed so that it vertically faced the water surface. The corona discharge was generated with a commercial high-voltage transformer (PS/WR 100 R2.5-11 series WR, Glassman High Voltage Inc., Whitehouse Station, NJ) with the capability of producing both positive and negative DC voltages up to 100 kV. The maximum voltage for the system was around 60-65 kV because of the limitation of sparkover, which was close to a typical sparking potential (59kV peak potentials) for the case of a wire in a 4-in. pipe at atmospheric pressure.14 The corona power was calculated by taking an average of the measurements of voltage and current from the high-voltage transformer for every 2 s. A pulsing module shown in Figure 2 was constructed and added between the high-voltage power supply and the corona discharge electrodes. This module was capable of pulsing the voltage with a frequency range of 10-90 Hz and was operated at the highest frequency of 90 Hz for all experiments. Pulsing allows the power level to be increased without undue sparking, and these high power values are believed to be effective in generating radicals and ions. A mixer; a grounded, chemically inert gold-plated plate in water; and a stainless steel mesh to act as a ground were installed in the lower box. The hydrogen ion concentration in the bulk liquid phase was measured by circulating a liquid stream through an on-line pH meter (Fisher Scientific Accumet 825 MP, Pittsburgh, PA). An ion chromatograph unit (IC, Dionex DX-120, Dionex Corp., Sunnyvale, CA) was used to analyze the background concentrations of deionized water and the total sulfite concentration in water. A mixture of SO2/N2 in the gas phase was used for all experiments. Initially, a small amount of SO2 was injected through a syringe so that the initial SO2 concentration was between 3150 and 3400 ppmv in the upper box. This initial condition was used for all experiments as it has been reported that SO2 absorption under corona discharge mostly depends on the initial concentration of SO2, the corona voltage, the electrostatic polarity, the acidity of the absorbing liquid, and the system temperature.15 All of the experiments were conducted under batch operating conditions with respect to both the gas and the liquid phases. The gas chamber was evacuated and then purged with N2. As soon as the total pressure reached atmospheric pressure, the nitrogen purge was

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shut off, and the system was closed. Agitation was started in both the liquid and gas phases, and a stable unbroken interface was maintained between the gas and liquid phases. Then, the circulating gas and liquid streams were started through the SO2 analyzer and pH meter, respectively. At the same time, the data acquisition system started to record the SO2 concentration, pH, voltage, and current every 2 s. Pure SO2 was taken from a gas cylinder using a 100-mL glass syringe and injected through a septum that was located near the air mixer. At this point, the high-voltage power supply and the pulsing module were turned on. Each experiment was conducted for 30 min, but the SO2 absorption rate was measured only during the first 10 min as it was observed that water vapor began to condense on the inner wall after about 10 min. This results in an overestimation of the SO2 absorption rate because of the absorption of SO2 into the water droplets. After each trial, the SO2 analyzer was recalibrated, and a water sample was taken for sulfur ion analysis. Enhancement Factor for the SO2 Absorption into the Liquid Phase When SO2 is absorbed into deionized water, the following reactions take place in the liquid phase

SO2 + H2O ) HSO3- + H +

(1)

HSO3- ) SO32- + H +

(2)

H2O ) H++ OH -

(3)

The model used to describe SO2 absorption was developed with the commonly used hypothesis that the above dissociation reactions are considered to be always in equilibrium compared with the relatively slow diffusion rates of the species involved.1-9 Reaction 1 is considered to be a very fast reaction, with a forward rate constant of 3.4 × 106 s-1 at 20 °C, and reactions 2 and 3 are considered to be even faster as they are proton-transfer reactions.3-5,16,17 Therefore, chemical equilibrium is assumed at every point in the liquid phase. In addition, it is assumed that only SO2 can diffuse through the interface. (No ionic transfer is assumed except for the corona-generated ions.) The values of the equilibrium constants for reactions 1-3 were extracted from the data used by Kawazuish and Prausnitz.18 The film theory and a pseudo-steady-state assumption are used to describe the transport of SO2 in the liquid. The total molar balances of diffusing and reacting components are expressed in terms of the total sulfite, S(IV), and the electroneutrality condition within the liquid film. The proper diffusive flux expression should include both the concentration gradient and the electric potential gradient

dcj F dψ - Djozjcj Nj ) -Djo dx RT dx

(4)

For the purpose of numerical calculation, the term of the electric potential gradient successfully has been lumped together with ionic diffusivities when a high concentration of nondiffusing ions is present.7,19 Using effective ionic diffusivities, the governing differential equations in the film become similar to those reported in the literature4,5

DSO2

d2[SO2] dx2

+ DHSO3-

d2[HSO3-] dx2

+

DSO32-

D H+

d2[H+] dx2

- DHSO3-

2DSO32-

d2[HSO3-]

dx2 2 d [SO32-] dx2

d2[SO32-] dx2

) 0 (5)

-

- DOH-

d2[OH-] dx2

) 0 (6)

The first boundary conditions at the gas-liquid interface are as follows

At x ) 0 [SO2] ) [SO2]i, [HSO3-] ) [HSO3-]i, [SO32-] ) [SO32-]i d[HSO3-] d[SO32-] d[H+] DH + - DHSO3- 2DSO32dx dx dx d[OH ] + NH+ ) 0 (7) DOHdx where NH+ is the flux of positive ions formed from the corona discharge entering the gas-liquid interface and was estimated from the average electric currents supplied by the high-voltage power source. It has been reported from plasma physics and chemistry that positive ions generated in the presence of water vapor are predominantly of the type H+(H2O)n (n ) 0, 1, 2, ...)20 or H3O+.21 The next boundary conditions are derived from the assumption that the concentrations of every species become equal to those of the bulk solution at a film depth of δ

At x ) δ [species] ) [species]δ for all species

(8)

The two equations 5 and 6 with boundary conditions 7 and 8 give the set of general solutions 9 and 10

DSO2[SO2] + DHSO3-[HSO3-] + DSO32-[SO32-] ) f(0) - f(δ) x + f(0) δ where

f(0) ) DSO2[SO2]i + DHSO3-[HSO3-]i + DSO32-[SO32-]i f(δ) ) DSO2[SO2]δ + DHSO3-[HSO3-]δ + DSO32-[SO32-]δ (9) δ)

DSO2 kl°

DH+([H+]i - [H+]δ) - DHSO3- ([HSO3-]i [HSO3-]δ) - 2DSO32-([SO32-]i - [SO32-]δ) DOH- ([OH-]i - [OH-]δ) - NH+δ ) 0 (10)

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The liquid-phase mass-transfer coefficient, kl, is defined by the following equation based on the total flux of S(IV) in the liquid phase

NSO2 ) kl([SO2]i - [SO2]δ) where kl ) φlkl°

DHSO3- ([HSO3-]i - [HSO3-]δ) + DSO2 ([SO2]i - [SO2]δ)

Physical Properties The model described above requires equilibrium- and transport-related physical properties. The solubility of SO2 in water was estimated using the Henry’s law constant for SO2 in pure water reported by Rabe and Harris22

PSO2* ) H[SO2]δ where 103 exp(9.3795 - 2851.1/T) 1.01325 (atm cm3/mol) (13)

Because the equilibrium constants, Ka, for reactions 1-3 are defined in terms of activities, an activity coefficient must be evaluated for each component to calculate the effective equilibrium constants, Kc, in concentration units. The activity coefficient of uncharged SO2 in water, γSO2, was estimated from an expression by Harned and Owens23

log γSO2 ) 0.076I

(14)

n where I ) 1/2∑j)1 cjzj2 is the ionic strength, j is an ionic component, n is the number of ionic components, cj is the concentration of the jth ion, and zj is the charge of the jth ion in the solution. The activity coefficients for individual ions were calculated using the modified Debye-Hu¨ckel equation

log γj ) A(T)zj2

[

- I1/2 + C4j 1 + B(T)C3jI1/2

]

(15)

where A(T) and B(T) are Debye-Hu¨ckel parameters reported by Bradley and Pitzer,24 zj is the charge on the jth ion, I refers to the ionic strength, and C3j and C4j are specific parameters for each ionic component used by Lowell et al.25 whose values are listed in Table 1. The ionic concentrations of other species in deionized water were analyzed using an ion chromatograph and are listed in Table 2. These data were used to estimate the ionic strength. The liquid-phase diffusivities of SO2 and other ionic species in water at 22 °C were taken from the data used

C3j

C4j

6.0 3.0 4.5 4.5 0.508 0.328

0.4 0.3 0.0 0.0

Table 2. Deionized Water Quality

a

DSO32- ([SO32-]i - [SO32-]δ) (12) DSO2 ([SO2]i - [SO2]δ)

H)

H+ OHHSO3SO32A(T) B(T)

(11)

The term φl is the mass-transfer enhancement factor due to the combined effect of chemical reaction and corona current in the liquid phase (when NH+ is extracted from eq 7 for calculation, this needs to be changed to “due to the effect of chemical reaction in the liquid phase”), and kl° is the liquid-phase mass-transfer coefficient without corona discharge. Combined with the general solutions, the factor φl can be expressed in terms of the interface and bulk concentrations as

φl ) 1 +

Table 1. Parameters Used in Modified Debye-Hu 1 ckel Equation at 22 °C

species

content (mg/L)

Na+ Ca2+ Clsulfite sulfate nitrite nitrate

7.55-13.28 1.8 4.0-4.2 NDa NDa NDa NDa

ND ) not detectable.

Table 3. Diffusivities in Water at 22 °C species

D × 105 (cm2/s)

H+ OHSO2 HSO3SO32-

8.54 4.82 1.62 1.22 0.879

by Chang et al.4 at 25 °C and corrected for the temperature and viscosity of water by the Stokes-Einstein equation. The diffusivity data used in this study are summarized in Table 3. Determination of Mass-Transfer Coefficients from Batch Experiments To investigate the effect of corona discharge on SO2 absorption into water, the mass-transfer coefficients, kg and kl , for the gas and liquid phase, respectively, and the overall mass-transfer coefficient, KOG, are defined by using the following molar balance equation

NSO2(t) )

VG dPSO2(t) ) ART dt -KOG(PSO2(t) - H[SO2]δ(t)) (16)

) -kg(PSO2(t) - H[SO2]i(t))

(17)

) -kl([SO2]i(t) - [SO2]δ(t))

(18)

where NSO2 is the SO2 absorption flux [mol/(cm2 s)]; VG is the gas-phase volume, 29 247 cm3; A is the gas-liquid interfacial area, 87.7 cm2; R is the gas constant, 82.056 atm cm3/(mol K); T is the temperature, 295.15 K; PSO2 is the SO2 partial pressure (atm); H is the Henry’s law constant for SO2 in water (atm cm3/mol); Pt is the total pressure (atm); ySO2 is the mole fraction of SO2 in the gas phase; kg is the gas-phase mass-transfer coefficient [mol/(atm cm2 s)]; and kl is the liquid-phase masstransfer coefficient (cm/s). All mass-transfer coefficients were assumed to be constant with respect to time as the mass-transfer rate of SO2 is relatively low. (The initial concentrations were between 3150 and 3400 ppmv.) The total sulfite concentration in the liquid phase, [S(IV)], was determined from the mass balance of SO2 assuming that the amount of SO2 disappearing from the gas was added to the total

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Table 4. Experimental Results for SO2/N2 Absorption run

power (W)

KOG × 106 a

1 2 3

0 6.1 18.7

11.12 61.63 58.04

4 5 6 7 8 9 10

0 0 2.7 4.0 6.3 14.1 20.5

pH

φl,avg

k1 (cm/s)

φE,l measured

kg × 105 a

φg

1/KOGb

1.112 6.163 5.804

1.00 5.54 5.22

89 909 16 225 17 230

1.112 1.112 3.348 4.424 6.163 6.163 6.163

1.00 1.00 3.01 3.98 5.54 5.54 5.54

442 451 472 191 325 587 340 495 300 018 217 491 177 587

H/k1b

1/kgb

352 543 382 282 295 717 317 893 283 793 201 266 161 362

89 909 89 909 29 869 22 602 16 225 16 225 16 225

NaOH solution

a

13.41 13.51 13.51

2.260 2.118 3.071 2.937 3.333 4.598 5.631

5.85-3.60 5.50-3.47 7.50-3.75 5.70-3.50 5.40-3.44 6.10-3.40 6.60-3.30

5.28 5.21 5.07 5.03 4.98 4.93 5.01

deionized water 0.002 12 1.00 0.001 95 1.00 0.002 52 1.24 0.002 35 1.15 0.002 63 1.29 0.003 70 1.81 0.004 62 2.26

Units of mol/(atm cm2 s). b Units of atm cm2 s/mol.

sulfite concentration in the bulk liquid phase. Then, eq 19 was used with the measured pH values to calculate the SO2 concentration in the bulk liquid phase, [SO2]δ, from the total sulfite concentration

kg from run 3 in Table 4 was not used because of its abnormal behavior: it became smaller as the corona power was increased.)

1 1 H 1 H ) + ) + KOG kg kl φ k o φlkl° g g

[S(IV)] ) [SO2] + [HSO3-] + [SO32-] [SO2] [HSO3-] ) Kc1 + [H ]

(19)

The SO2 concentration at the interface, [SO2]i, can subsequently be evaluated using eq 23, which is derived from eqs 17 and 18

[SO2]

[SO32-] ) Kc1Kc2

[H+]2

[SO2]i )

The overall mass-transfer coefficient, KOG, in eq 16 was determined by minimizing the objective function f of eq 20 tf

f)

(PSO cal(t) - PSO exp(t))2 ∑ t)t 2

2

(20)

(22)

PSO2 - NSO2/kg H

)

kgPSO2 + kl[SO2]δ kgH + kl

(23)

The value of [H+]i was obtained by solving eq 10 combined with [SO2]i from eq 23 and the equilibrium relations for bisulfite, sulfite and hydroxyl ions. The values of [HSO3-]i and [SO32-]i were then calculated by the equilibrium relations of eq 19.

i

where ti and tf indicate the initial and final sampling times. Aqueous NaOH solutions (0.33-0.4 M) were used to measure the gas-phase mass-transfer coefficient, kg. Because dissolved SO2 reacts instantaneously and irreversibly with a strong alkali reactant, the liquid-phase mass-transfer resistance becomes negligible for this case. The absorption rates of SO2 from SO2/N2 mixtures into the solution were measured at different corona power levels from 0 to 18.7 W with positive polarity. Positive pulsed streamer corona was used for all of the experiments because it showed a better performance on SO2 removal than negative pulsed corona at the same corona power level in previous work.13,26,27 This effect of SO2 removal on polarity was not reported by other researchers for pulsed corona discharge28 and DC corona discharge.10 Linear interpolation was used to correlate the relation between kg and power. An enhancement factor due to the corona discharge in the gas phase, φg, was introduced to quantify the mass-transfer enhancement in the gas phase. It was determined by dividing kg of the corona-applied case by that of noncorona case

kg ) φgkg°

(21)

where kg° refers to the gas-phase mass-transfer coefficient in the absence of corona discharge. The liquid-phase mass-transfer coefficient, kl, was determined by eq 22 using the experimentally determined KOG and kg values. (The experimental value of

Results and Discussion Experimental results for the absorption of SO2/N2 into NaOH solution and deionized water are listed in Table 4. As the corona discharge interfered with the measurement of the SO2 concentration in the gas phase, a moving average method was applied to the raw data by implementing a Fourier impulse response low-pass filter called a Savitzky-Golay smoothing filter.29 The lowpass filter coefficients were calculated by taking (1 min of data at every sampling time of 2 s. After the moving average was obtained, a sampling period of between 3 and 10 min was used to analyze the experimental measurements. Although SO2 gas was injected almost instantaneously through a septum, it took about 3 min for the gas mixture to be completely mixed and for the SO2 analyzer to read steady concentrations. The mass-transfer enhancements for SO2 absorption into water under corona discharge can be attributed to three different effects: (a) mass-transfer enhancement in the gas phase due to the direct corona effect, (b) masstransfer enhancement in the liquid phase due to the effect of boundary-layer thinning on the liquid film, and (c) sorption capacity increase due to chemical reactions in the liquid phase. These effects are discussed in more detail below. SO2/N2 Absorption into Aqueous NaOH Solution: Gas-Phase Mass-Transfer Enhancement by Corona. The gas-phase mass-transfer coefficient with respect to corona power was determined by evaluating the overall mass-transfer coefficient for SO2/N2 absorp-

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Figure 4. KOG vs input corona power for SO2/N2 absorption into NaOH solution (runs 1-3).

Figure 5. KOG vs input corona power for SO2/N2 absorption into deionized water (runs 4-10).

Figure 3. Comparison of calculated PSO2 (-) with measured PSO2 (•) for SO2/N2 absorption into NaOH solution at different corona powers.

tion into aqueous NaOH solutions (0.33-0.4 M). As discussed earlier, it was assumed that there was no mass-transfer resistance in the liquid phase. Because aqueous NaOH solutions for the three runs shown in Figure 3 were highly alkaline (pH ) 13.41 and 13.51), the amount of SO2 absorption for the first 10 min did not change the acidity of the solutions. Equation 16 was used to determine the best fit of the experimental data. Figure 3 shows measured PSO2(t) along with the bestfit curves taken 20 s for experimental runs 1-3. It was observed that the absolute slope of the SO2 concentration in the gas phase increased dramatically as corona discharge was applied to the system, which indicates a faster rate of SO2 absorption into the liquid phase. The effect of corona discharge on gas-phase mass transfer is shown in Figure 4. Despite the small number of experimental data points, the enhancement effect of the corona power is clearly shown to reach an asymptotic value as the power increases. Considering experimental errors, a linear interpolation function was used to estimate the values of kg between 0 and 6.1 W, and

a constant value of kg at 6.1 W was applied thereafter. The mass-transfer enhancement factor due to electrostatics in the gas phase, φg listed in Table 4, was determined by taking the ratio of kg for the coronaapplied case to that of the noncorona case. SO2/N2 Absorption into Deionized Water: LiquidPhase Mass-Transfer Enhancement by Corona. The overall mass-transfer coefficient, KOG, was evaluated for the absorption of SO2 into deionized water and is plotted as a function of corona power for runs 4-10 in Figure 5. As the power increases to 20.5 W, KOG seems to linearly increase, and its value at 20.5 W is about 2.5 times larger than that of the noncorona case. The liquid-phase mass-transfer coefficient, kl, was calculated with eq 22 using these values of KOG and the previously determined values of kg. The enhancement factor, φl(t), was subsequently estimated from eq 12 using concentrations of all of the ionized species in the bulk liquid phase as well as those at the interface. The interfacial concentrations, [SO2]i and [H+]i, were calculated using eqs 23 and 10, respectively. When the flux of positively charged ions to the gas-liquid interface, NH+, is included in eq 7 to obtain [H+]i, it results in a very slight increase in [H+]i. Thus it attenuates the effect of mass-transfer enhancement due to chemical reactions in the liquid phase although its effect is small: NH+ was estimated to be about 2-3 orders of magnitude lower than the diffusive flux of hydrogen ions generated by dissociation reactions in the liquid because the corona power supplied to the gas-

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Figure 6. φE,l vs input corona power for SO2/N2 absorption into deionized water (runs 4-10).

Figure 8. Effect of liquid boundary-layer thinning in terms of corona power input.

It has been reported that SO2 is not oxidized in a DC corona field and that enhancement of its removal is due to the corona wind and vibrations that reduce the thickness of the boundary layer.27 To estimate this effect, the film thicknesses for the cases of corona discharge were determined from eq 25 by combining the expression for δ in eq 9 with that for kl° in eq 11

Figure 7. φl,avg vs input corona power for SO2/N2 absorption into deionized water (runs 4-10).

liquid interface is relatively so small. The term of NH+ in eq 7 could have safely been ignored in obtaining [H+]i. The enhancement factor due to corona discharge in the liquid was calculated by taking the ratio of measured kl values for corona-applied cases to the arithmetic average of the kl values for the noncorona cases (runs 4 and 5). These ratios of measured values are plotted in Figure 6. The measured enhancement factor, φE,l, reaches 2.3 at the highest corona power. Because φl(t) is a function of time, an average value, φl,avg, was calculated within a sampling period according to eq 24

∫tt φl(t) dt f

φl,avg )

i

tf - ti

(24)

The results are plotted in Figure 7, along with the results obtained by neglecting NH+ in eq 7. The two cases show almost the same values, but the results when NH+ was applied to eq 7 show slightly lower values as the power increases. This results from the fact that small values of NH+ bring about slight increases in [H+]i and decreases in φl,avg. Even if the effect of NH+ on φl,avg is considered, the average enhancement factor, φl,avg, does not seem to show any relationship with corona power and has an almost constant value. Thus, chemical reactions and charge transfer from corona discharge cannot adequately describe the liquid-side mass-transfer enhancement.

δ ) φl,avg

DSO2 kl

(25)

The liquid-phase mass-transfer coefficient in the absence of corona discharge, kl°, was determined from the kl and φl,avg values for the noncorona cases, runs 4 and 5. A value of 3.88 × 10-4 cm/s, which is an arithmetic average of the values of 4.02 × 10-4 cm/s of run 4 and 3.74 × 10-4 cm/s of run 5, was taken as kl°. The liquid film thickness in the absence of corona discharge, δ°, was estimated as 0.0418 cm from eq 9. φl,avg was determined by excluding NH+ in eq 7 to obtain [H+]i so that the effect of boundary-layer thinning is entirely included in the liquid film thickness, δ. Because NH+ was eliminated from eq 7, φl,avg indicates only the effect of mass-transfer enhancement due to chemical reactions in the liquid. The effect of boundary-layer thinning is plotted as a function of corona power in Figure 8 and increases as power increases. It shows more than 50% reduction of the boundary layer at 20.5 W of input corona power. Even though the mass-transfer enhancement in the liquid phase is inexplicable with the electric current transfer to the liquid, it is certain that corona power can reduce not only the gas-phase mass-transfer resistance but also the liquid-phase mass-transfer resistance for the absorption of SO2/N2 into deionized water. As power increases, the gas-phase mass-transfer resistance decreases dramatically to about one-fifth of its value in the noncorona case. On the other hand, the liquid-phase and overall mass-transfer resistances reduce to between one-half and one-third of their values in the noncorona case.

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Conclusions

Subscripts

SO2 absorption into water under corona discharge was measured to investigate the effects of corona discharge and chemical dissociation on mass transfer. Experiments were carried out with a gas mixture of SO2/N2 absorbing into distilled deionized water in a batch system. The overall, gas-phase, and liquid-phase masstransfer coefficients were evaluated using the regression method. A model was developed on the basis of film theory to take into account mass-transfer enhancement due to chemical reactions and charge transfer of positive ions. Small amounts of charge transfer of positive ions did not adequately explain the mass-transfer enhancement in the liquid. Boundary-layer thinning caused by corona-induced vibrations is thought to play a major role in the mass-transfer enhancement in the liquid phase. The corona discharge increased the mass transfer in the liquid phase as well as in the gas phase. The effect of corona discharge in the liquid phase was greater than the effect of chemical reactions in the liquid.

f ) final g ) gas i ) gas-liquid interface or initial j ) species j l ) liquid

Nomenclature A ) gas-liquid interfacial area ) 87.7 cm2 c ) concentration, mol/L D ) effective diffusion coefficient, cm2/s D° ) true diffusion coefficient, cm2/s H ) Henry’s law constant, atm cm3/mol I ) ionic strength, mol/L [j] ) concentration of species j, mol/cm3 Ka ) thermodynamic equilibrium constant Kc ) effective equilibrium constant in concentration units KOG ) overall mass-transfer coefficient, mol/(atm cm2 s) kg° ) gas-phase mass-transfer coefficient in the absence of corona discharge, mol/(atm cm2 s) kg ) gas-phase mass-transfer coefficient, mol/(atm cm2 s) kl° ) liquid-phase mass-transfer coefficient in the absence of corona discharge, cm/s kl ) liquid-phase mass-transfer coefficient, cm/s M ) molarity, mol/L N ) absorption flux, mol/(cm2 s) Pt ) total pressure, atm PSO2 ) SO2 partial pressure in the gas phase, atm PSO2* ) equilibrium partial pressure of SO2 in the gas phase, atm R ) gas constant ) 82.056 atm cm3/(mol K) T ) temperature, K t ) time, s VG ) gas-phase volume ) 29 247 cm3 x ) distance from gas-liquid interface, cm ySO2 ) SO2 mole fraction in the gas phase z ) charge Greek Letters δ° ) liquid film thickness in the absence of corona discharge, cm δ ) liquid film thickness in the presence of corona discharge, cm φg ) mass-transfer enhancement factor due to corona discharge in the gas phase φl ) mass-transfer enhancement factor due to chemical reactions and corona discharge (or just chemical reactions) in the liquid phase φl,avg ) average mass-transfer enhancement factor over time due to chemical reactions and corona discharge (or just chemical reactions) in the liquid phase φE,l ) mass-transfer enhancement factor due to corona discharge in the liquid phase γ ) activity coefficient ψ ) electric potential, V

Superscripts * ) equilibrium ° ) no corona discharge

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Received for review December 4, 2000 Revised manuscript received August 30, 2001 Accepted September 13, 2001 IE001039F