Energy Fuels 2010, 24, 2787–2789 Published on Web 03/04/2010
: DOI:10.1021/ef100071y
Comment on “Flue Gas Desulfurization with an Electrostatic Spraying Absorber” Amitava Bandyopadhyay* Department of Chemical Engineering, University of Calcutta, 92, APC Road, Kolkata 700 009, India Received January 21, 2010. Revised Manuscript Received February 25, 2010
Dou et al.1 presented in their paper (10.1021/ef700646c) a study on the removal of SO2 from a simulated stream of SO2 diluted with N2 in an electrostatic spraying absorber using Ca(OH)2 slurry. This paper revealed some technical doubts that are pointed out in this comment with plausible suggestions to clear them. On page 1042, lines 4-5 state “According to some investigations,4,8,12,13 the rate of the above chemical reaction is rapid relative to the diffusion.” The reference cited by the authors as “13” refers to an paper by Bandyopadhyay and Biswas2 in which they did not investigate the absorption of SO2 into Ca(OH)2 slurry as well as the chemical reaction between SO2 and Ca(OH)2 slurry and, hence, nothing was mentioned regarding this chemical reaction. Thus, the reference cited as “13” should be ignored. On page 1042, equation 4 was used to determine the interfacial area of contact for spray droplets. This equation is classically used for the gas-dispersed system, such as in bubble columns, rather than the liquid-dispersed system, such as in a spray column, that the authors reported. In fact, gasphase fractional hold up or the gas fraction (εg) is determined in a bubble column from the hydrodynamic studies. It is generally determined by measuring the volumes of liquid with and without aeration as follows εg ¼ ðV -Vo Þ=V
volume to surface mean bubble diameter [Sauter mean diameter (SMD)], as given below a ¼
ð1Þ
ð2Þ
The fractional gas hold up intrinsically depends upon the physicochemical hydrodynamics of the system considered. With the increase in the hold up, the interfacial area of contact is also increased, which increases the gas-liquid mass transfer. The interfacial area of contact in such a situation is determined from its relationship with the gas hold up and
where Fi is the number of droplets in the ith group. SMD averages the diameter (first order of length) yet weighs according to its surface area (second order of length), which contributes to the total surface area of the droplet population. SMD is useful in the case of gas-droplet mass transfer because it is influenced by the droplet surface among other parameters similar to other gas-liquid mass-transfer applications. Furthermore, the PDA also measures the droplet
*To whom correspondence should be addressed. Telephone: þ91-3323508386, ext. 515. E-mail:
[email protected]. (1) Dou, B.; Byun, Y.-C.; Hwang, J. Flue gas desulfurization with an electrostatic spraying absorber. Energy Fuels 2008, 22, 1041–1045. (2) Bandyopadhyay, A.; Biswas, M. N. Prediction of the removal efficiency of a novel two-stage hybrid scrubber for flue gas desulfurization. Chem. Eng. Technol. 2006, 29, 130–145. r 2010 American Chemical Society
ð3Þ
The bubble SMD can be measured directly by any of the methods among various conventional techniques, such as the photographic method, electrical conductivity probe method, etc. Sometimes visual observation is also made in determining the average bubble size for relatively larger bubbles in the range of a few millimeters. Also, such a measurement is comparable to the values measured by measuring the interfacial area of contact and fractional gas hold up.3 Equation 4 on page 1042 presented by the authors is analogous to eq 3 above, where the bubble SMD is replaced with the droplet SMD. Interestingly, the authors had assigned a value of 0.5 for the gas fraction (εg) as reported in Table 1 (page 1044) for determining the “a” of spray droplets, which is therefore incorrect. Even if the assigned value is considered for the spray column, then the method of measurement of liquid hold up in such a liquid-dispersed system should have been elaborated. While the measurement of gas hold up in a bubble column is simpler, this elaboration is necessary from the perspective of difficulty in measuring the liquid hold up under the present circumstance. However, there are several simple techniques for determining the interfacial area of contact for spraying systems. In general, the interfacial area of contact is determined in a spraying device from the droplet size and number density of droplets. The method is briefly described below for our understanding. The droplet size is usually measured with a phase doppler analyzer (PDA). The PDA was programmed to evaluate the droplet SMD in situ while measuring the size distribution. The droplet SMD or the droplet volume to surface mean diameter is defined as X Fi di 3 ð4Þ DD, SMD ¼ Fi di 2
This expression is widely used for bubble columns, for instance, columns with varied cross-section, such as in a tapered column and in columns with uniform cross-section. Such measurement is unaffected by the cross-section of the column as long as it is uniform; e.g., hold up in a bubble column with uniform cross-section can be simply determined by measuring the height of the aerated liquid (H) and that of the clear liquid without any aeration (Ho) as εg ¼ ðH -Ho Þ=H
6εg DB, SMD
(3) Bandyopadhyay, A.; Biswas, M. N. SO2 scrubbing in a tapered bubble column scrubber. Chem. Eng. Commun. 2006, 193, 1562–1580.
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Energy Fuels 2010, 24, 2787–2789
: DOI:10.1021/ef100071y
number density along with many other hydrodynamical parameters. The interfacial area of contact per unit of volume
interfacial area of contact, a ¼
of liquid sprayed is calculated from the following relationship under homogeneous droplet flow conditions:
½single droplet surface area½droplet number density per unit time volume of liquid sprayed per unit time Equation 7 is analogous to the equation used by the authors (equation 6 on page 1042) considering a mole ratio of 1:2. Thus, developing an expression for predicting the SO2 removal efficiency as a function of various pertinent variables of the system should have incorporated the mass-transfer enhancement factor from eq 6 above instead of equation 6 described on page 1042. This consideration would have realistically developed the expression for describing the performance of the SO2 scrubbing in Ca(OH)2 slurry. The assumptions necessary for the development of the model for predicting the removal efficiency of SO2 in electrostatic sprays of Ca(OH)2 slurry should have been clearly specified. For instance, particle dissolution, spherical shape of particles and droplets, etc. should have been mentioned. In section 2, “Modeling” (pages 1041 and 1042), such assumptions were missing. In general, the chemistry of the process is described6 here for broad perspective. The rate of chemical absorption of a gas into a slurry containing fine particles is influenced by the particle dissolution. The rate of dissolution of the solid can be accelerated by the reaction between the absorbed gas and the dissolved solid near the gas-liquid interface, especially when the particle size is much smaller than the thickness of the liquid film. As a result, the rate of gas absorption is complicated by the solid dissolution coupled with the chemical reaction even when the reaction scheme is simple, such as in the case of SO2 and Ca(OH)2 described below
Thus ½πdi 2 ½N_ d ðm2 =m3 Þ a ¼ QL
ð5Þ
Although several interactions are involved in droplet flow, such a calculation gives a reasonable estimate of interfacial area of contact for spraying devices. The interfacial area can, however, be measured by the chemical method as described by Danckwerts and Sharma.4 On page 1042, equation 6 was used in the presented study under discussion for determining the mass-transfer enhancement factor following a two-film theory for instantaneous chemical reaction. We have used this equation in our paper2 referred by the authors for describing the mass-transfer enhancement for absorption of SO2 in a clear alkaline solution of NaOH. While elucidating the behavior of absorption of a gas with fast chemical reaction into a slurry following two-film theory, Ramachandran and Sharma5 had arrived at the same equation (equation 6 on page 1042) for determining the masstransfer enhancement factor for absorption in a saturated solution containing no suspended solids (i.e., solid concentration in wt % = 0). However, the authors presented in their paper the process of scrubbing of SO2 in Ca(OH)2 slurry as the scrubbing liquor. The slurry flow rate was in the range between 15 and 35 mL/min rather than using a clear solution saturated with Ca(OH)2 [i.e., with 0 wt % of Ca(OH)2 as solid]. Thus, the mathematical formulation presented by the authors is not in conformity with their experimentation. This can be further established from the fact that the removal efficiency of SO2 predicted by equation 18 on page 1042 was a function of various parameters, except Ca(OH)2 particle specifications. To eliminate this serious error, it is therefore suggested to use the mass-transfer enhancement factor following two-film theory for absorption of SO2 into Ca(OH)2 slurry represented by the expression developed by Sada et al.6 as pffiffiffiffi pffiffiffiffi N N D b Cb Db Cb pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi ð6Þ E ¼ 1þ 2Da Ci tan h NxI 2Da Ci sin h NxI
SO2ðgÞ f SO2ðaqÞ CaðOHÞ2ðsÞ f CaðOHÞ2ðaqÞ SO2ðaqÞ þ CaðOHÞ2ðaqÞ f products The process of absorption with the chemical reaction in this case can be represented by the two-reaction-plane model, in which, at one reaction plane, the following reaction takes place: SO2 þ SO3 2- þ H2 O f 2HSO3 while at the other reaction plane, the reaction taking place is as follows: HSO3 - þ OH- f SO3 2- þ H2 O
For a clear solution saturated with Ca(OH)2 (i.e., when the scrubbing solution contains no solid), Sada et al.6 showed that eq 6 reduces to the following form: D b Cb ð7Þ Eo ¼ 1 þ 2Da Ci
These considerations are detailed in the available literature5 for arriving at the enhancement factor for mass transfer described by eqs 6 and 7 earlier. The paper entitled “Flue Gas Desulfurization with an Electrostatic Spraying Absorber” was published in Energy & Fuels in 2008 containing some technical shortcomings. Importantly, two of them were (a) the use of fractional gas hold up to determine the interfacial area of contact generated by spray droplets and (b) the use of the enhancement factor of mass transfer of a saturated alkaline solution containing no solids in the case of Ca(OH)2 slurry. In the present comment, all of these shortcomings were addressed in detail and suggestions guided by technical reasons were put forward to have these shortcomings rectified for the broad interest of the readers.
(4) Danckwerts, P. V.; Sharma, M. M. The absorption of carbon dioxide into solutions of alkalis and amines (with some notes on hydrogen sulphide and carbonyl sulphide). Chem. Eng. 1966, 44, CE244–CE280. (5) Ramachandran, P. A.; Sharma, M. M. Absorption with fast reaction in a slurry containing sparingly soluble fine particles. Chem. Eng. Sci. 1969, 24, 1681–1686. (6) Sada, E.; Kumazawa, H.; Sawada, Y.; Hashizume, I. Kinetics of absorption of lean sulfur dioxide into aqueous slurries of limestone and magnesium hydroxide. Chem. Eng. Sci. 1981, 36, 49–55.
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: DOI:10.1021/ef100071y
Nomenclature
Eo = mass-transfer enhancement factor when the scrubbing liquid does not contain suspended solids Fi = number of droplets in the ith group H = height of the aerated liquid (m) Ho = height of the clear liquid without aeration (m) kS = mass-transfer coefficient for solid dissolution (m/s) N_ d = number density of droplets per unit time (s-1) N = solid dissolution parameter (ksApδ2/Db) xI = dimensionless position of one reaction plane QL = liquid flow rate (m3/s) V = volume of the aerated liquid (m) Vo = volume of the clear liquid without aeration (m) δ = liquid film thickness (for gas absorption) (m) εg = fractional gas holdup
a = interfacial area of contact (m2/m3) Ap = specific surface area of solid particles (m2/m3) Cb = concentration of limestone in water (kmol/m3) Ci = interfacial concentration of SO2 in the liquid phase (kmol/m3) Da = diffusion coefficient of SO2 in water (m2/s) Db = diffusion coefficient of limestone in water (m2/s) DB,SMD = Sauter mean diameter (SMD) of the bubble (m) DD,SMD = Sauter mean diameter (SMD) of the droplet (m) di = droplet diameter in the ith group (m) E = mass-transfer enhancement factor when the scrubbing liquid is slurry containing fine solid particles
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