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Ind. Eng. Chem. Res. 2008, 47, 1310-1317
Dynamic Measurement of Carbon Dioxide Volumetric Mass Transfer Coefficient in a Well-Mixed Reactor Using a pH Probe: Analysis of the Salt and Supersaturation Effects M. Kordacˇ and V. Linek* Department of Chemical Engineering, Institute of Chemical Technology, Prague, Technicka´ 5, 166 28 Prague 6, Czech Republic
This paper presents a new method for the evaluation of volumetric mass transfer coefficients (kLa) using a pH probe response recorded during the absorption of carbon dioxide in a well-mixed reactor. For this method of evaluation, it is not necessary to know the reaction equilibrium constant, the experiment start time, or the initial and final steady-state pH probe readings. The experimental procedure is based on Hill’s recent publication (Ind. Eng. Chem. Res. 2006, 45, 5796). Hill reported a decrease in kLa following the addition of salt during carbon dioxide absorption in a well-mixed reactor and explained it as the result of ionic charge effects reducing the ability of carbon dioxide molecules to diffuse away from the surface. Generally, oxygen absorption from air is preferred because the solubility of oxygen is low and, thus, so will be the gas-phase depletion. In such experiments, the mass transfer coefficients are less affected by gas-phase residence time distribution and by bubble-size distribution. The solubility of carbon dioxide is 26 times higher than that of oxygen, which can lead to significant gas concentration changes. Thus, the kLa values, measured using absorption of diluted carbon dioxide, are more likely to be distorted by driving force errors caused by the use of an inappropriate gas-mixing model. Using a stirred cell, the interfacial area of which is known, the mass transfer coefficients of oxygen and carbon dioxide in water and in a salt solution were compared. The mass transfer coefficients obtained for oxygen agreed with, or were slightly superior to, the coefficients obtained for carbon dioxide, which corresponds with the lower molecular diffusivity of CO2. The mass transfer coefficients of carbon dioxide obtained in salt solution were not significantly lower than those obtained in pure water, which is in strong agreement with the literature but contradicts the results reported by Hill. It is shown that Hill’s findings may be the result of his use of both an inaccurate gas-mixing model (no depletion of gas) and an imprecise reaction term in his equations. Introduction The steady increase in carbon dioxide concentration in the atmosphere, and the belief that it is a significant contributing factor to global warming,1 has recently led to attempts (e.g., refs 1 and 2) to develop photobioreactors that use atmospheric carbon dioxide as a source of carbon for cell cultures. Because the solubility of carbon dioxide, compared with other substrates, is not high enough to ensure an adequate carbon supply at the start of fermentation, carbon dioxide must be continuously fed into a fermentation broth by gas absorption. The rate of carbon dioxide absorption is a limiting factor in the process, and thus, the volumetric mass transfer coefficient is an important parameter in photobioreactor design. Typically, engineers estimate the mass transfer rate of carbon dioxide using oxygen mass transfer coefficients that factor in a different diffusion coefficient of carbon dioxide. Recently, this procedure has been questioned by Hill,3 who reported notably lower carbon dioxide mass transfer coefficients compared to those of oxygen. Hill3 used a dynamic method to measure carbon dioxide mass transfer coefficients in a well-mixed reactor, with the coefficients being evaluated from pH profiles of the aqueous phase after the introduction of bubbles containing carbon dioxide. In this procedure, Hill assumed that the gas-phase concentration of carbon dioxide in the vessel was constant and equal to the inlet concentration. The aims of this paper are as follows: (i) to demonstrate that the use of an incorrect absorption driving force results in * Corresponding author e-mail:
[email protected].
serious underestimation of kLa values in the case of carbon dioxide absorption, (ii) to propose a new method that allows kLa to be calculated without knowledge of the experiment start time or of the initial and final steady-state readings of the pH probe (knowledge of which are essential to Hill’s method), and (iii) to critically reassess the effect of salt on the absorption rate of carbon dioxide presented by Hill. Theory of the Method Carbon dioxide is dissolved in the aqueous phase as four different compounds (carbon dioxide, CO2; carbonic acid, H2CO3; bicarbonate ion, HCO3-; and carbonate ion, CO3)), the equilibrium concentrations of which are pH-dependent. Assuming equilibrium reactions to be instantaneous, Hill deduced how to recalculate a pH profile into a profile of dissolved carbon dioxide and, therefore, how to evaluate the volumetric mass transfer coefficients of carbon dioxide. The dissociation of carbon dioxide in water can be described using the following relation set K0
K1
H2O + CO2 798 H2CO3 798 H+ + HCO3-
(1)
From the value of the dissociation constant K0 (7 × 10-7 M, Danckwerts4), it follows that the concentration of dissolved CO2 greatly exceeds that of H2CO3 and, thus, that the dissolved CO2 and H2CO3, the neutral compounds, may be considered as one component, which, following Hill’s notation, is called carbonic acid, H2CO3, in the following text. Danckwerts and Sharma5
10.1021/ie0711776 CCC: $40.75 © 2008 American Chemical Society Published on Web 01/08/2008
Ind. Eng. Chem. Res., Vol. 47, No. 4, 2008 1311
provided the following expression for calculation of the solubility of carbon dioxide
(cH2CO3)/ ) pCO2/H ) pCO2 × 10-(5.3-1140/T)
(2)
where H is Henry’s coefficient, pCO2 is the partial pressure of carbon dioxide above the aqueous phase, and (cH2CO3)* is the concentration of physically dissolved CO2 and H2CO3 in equilibrium with pCO2 in the gas phase. The same authors5 also provided the following expression for the equilibrium constant of the second reaction
K1 )
cH+cHCO3cH2CO3
) 10-(3404.7/T+0.03279T-14.832)
(3)
By analyzing equilibrium reactions, Hill3 deduced that the concentration of carbonate ion is insignificant and that, as the solution becomes acidic (pH < 6), the concentration of hydroxide ion may also be ignored. In this case, the principle of electroneutrality requires that the concentrations of hydrogen and bicarbonate ion be equal
cH+ ) cHCO3-
(4)
Danckwerts and Sharma5 also provided the following rate equation of the hydrolysis (eq 1)
dcH2CO3 dt
(
) -k B1 cH2CO3 -
)
cH+cHCO3K1
(5)
log B k 1 ) 329.85 - 110.54 log T - 17265/T
dcH2CO3
For absorption from gas bubbles in dispersion, the lowest value estimated for the physical mass transfer coefficient koL is 2 × 10-4 m/s (e.g., Calderbank and Moo-Young6). Using eq 5, together with the relation given in ref 4, the enhancement factor of absorption accompanied by a first-order irreversible chemical reaction (eq 1) at 27.5 °C can be estimated as
x(k ) E)
o 2 L
+B k 1DCO2 koL
x(2 × 10
the interface. Assuming both an ideal mixing of the gas phase and a negligible mass transfer resistance in the gas phase, (cH2CO3)/2 is in equilibrium with the carbon dioxide concentration in the gas leaving the vessel. The latter assumption holds for the absorption of sparingly soluble gases, such as oxygen and carbon dioxide, but the former assumption is questionable at some situations when absorption takes place in a mechanically agitated gas-liquid contactor. A detailed study7 on the correct use of the dynamic method for the determination of kLa in aerated agitated vessels has shown that these assumptions hold for the measurement of low values of kLa ( 0) develops in the liquid phase, and, where supersaturation is followed by spontaneous bubble nucleation, this can increase the mass transfer coefficients for these processes in comparison with the reverse ones. Bubble creation enhances mass transfer but depends on conditions that are not irreproducible, such as the presence of trace contaminants that act as nuclei for new bubbles. This explains why we found a more pronounced enhancement in electrolyte solutions than in pure water (see Table 1), a finding also reported in the literature.14,15 Therefore, in what follows, we only consider the mass transfer coefficients of oxygen and carbon dioxide for responses obtained from gas interchanges unhampered by this almost irreproducible supersaturation effect, namely, (O2 f N2) and (N2 f CO2). A number of conclusions can be drawn from the results presented in Table 1. The mass transfer coefficients obtained for oxygen agree with, or are slightly superior to, the coefficients obtained for carbon dioxide, which corresponds with the lower molecular diffusivity of CO2. The mass transfer coefficients of carbon dioxide obtained in salt solution were not significantly lower than those obtained in pure water, thereby contradicting Hill’s statement that the ionic charge effect of NaCl at the bubble surface reduces the ability of
Relation 13, derived by Hill3 for the rate of carbon dioxide absorption in water in a well-mixed reactor, gives substantially lower kLa values than those evaluated using relation 11 in this paper. We have shown that this is due to Hill’s use of an incorrect absorption driving force in the model (eq 13), which itself is a result of the omission of the concentration changes induced by the absorption of highly soluble gases, such as carbon dioxide. A new method for the evaluation of kLa, based on pH probe responses to the absorption of carbon dioxide, was presented. The advantage of this method is that it is not necessary to know the reaction equilibrium constant, the experiment start time, or the initial and final steady-state pH probe readings. By comparing the mass transfer coefficients of carbon dioxide in water and in a salt solution in a stirred cell, we have shown that Hill’s finding that the addition of salt (NaCl) reduces kLa values compared to those in pure water is not caused by ionic charge effects at the bubble surface reducing the ability of carbon dioxide molecules to diffuse away from the surface but by the incorrect absorption driving force used by Hill to evaluate kLa. Our experiments have shown that volumetric mass transfer coefficients evaluated from responses occurring after CO2 f N2 interchanges are enhanced by the effect of liquid supersaturation. Acknowledgment Support from the Ministry of Education (MSM 6046137306) and from the Grant Agency of Czech Republic through Project No. 104/05/P203 is gratefully acknowledged. Nomenclature A ) QGH/(kLaVLRT) c ) concentration (mol/L) D ) coefficient of molecular diffusivity (m2/s) E ) enhancement factor of absorption G ) reading of oxygen probe (volt) H ) Henry’s coefficient ((atm L)/mol) Hu ) steady-state gas holdup, volumetric fraction of gas K0,1 ) equilibrium constant (mol/L) k1 ) first-order kinetic constant (s-1) koL ) mass transfer coefficient for physical absorption (m/s) kLa ) volumetric mass transfer coefficient (h-1 or s-1) pt ) barometric pressure (atm) pCO2 ) partial pressure of carbon dioxide (atm) pLj ) equilibrium partial pressure of gas component j (atm) QG ) aeration rate (L/s) R ) gas constant ((atm L)/(mol K)) S ) salinity (g/kg) s ) supersturation criterion defined by eq 24 T ) temperature (K) t ) time (s) VL ) liquid volume in reactor (L) y ) molar fraction
Ind. Eng. Chem. Res., Vol. 47, No. 4, 2008 1317
R ) saturation of liquid phase with carbon dioxide [)cH2CO3/ (cH2CO3)/1] θ ) start-up period [)VLHu/{QG(1 - Hu)}] (s) Literature Cited (1) Sik, S. H.; Ryong, C. S. Continuous photo bioreactor for carbon dioxide removal to inhibit global warming and mass-production of microalgae. Korean Patent No. KR 2005-081766. Korean Patent Appl. KR 2004-10141, 2004.02.16. (2) Chae, S. R.; Hwang, E. J.; Shin, H. S. Single cell protein production of Euglena gracilis and carbon dioxide fixation in an innovative photobioreactor. Biores. Technol. 2006, 97, 322. (3) Hill, G. A. Measurement of Overall Volumetric Mass Transfer Coefficients for Carbon Dioxide in a Well-Mixed Reactor Using a pH Probe. Ind. Eng. Chem. Res. 2006, 45, 5796. (4) Danckwerts, P.V. Gas Liquid Reactions; Harvard University Press: Cambridge, MA, 2003. (5) Danckwerts, P. V.; Sharma, M. M. The Absorption of Carbon Dioxide into Solutions of Alkali and Amines. Chem. Eng. 1966, 202, CE244. (6) Calderbank, P. H.; Moo-Young, M. B. The Continuous Phase Heat and Mass Transfer Properties of Dispersions. Chem. Eng. Sci. 1961, 16, 39. (7) Linek, V.; Vacek, V.; Benesˇ, P. A. Critical Review and Experimental Verification of the Correct Use of the Dynamic Method for the Determination of Oxygen Transfer in Aerated Agitated Vessels to Water, Electrolyte Solutions and Viscous Liquids. Chem. Eng. J. 1987, 34, 11. (8) Linek, V.; Vacek, V. Chemical engineering use of catalyzed sulfite oxidation kinetics for the determination of mass transfer characteristics of gas-liquid contactors. Chem. Eng. Sci. 1981, 36, 1747. (9) Mook, W.G.; deVries, J.J. EnVironmental isotopes in the hydrological cycle: Principles and applications. Volume 1: Introduction, theory, methods, reView; IAEA Publication: Vienna, Austria, 2005; pp 143-166. (10) Robinson, C. W.; Wilke, C. R. Oxygen Absorption in Stirred Tanks: A Correlation for Ionic Strength Effects. Biotechnol. Bioeng. 1973, 15, 755. (11) Van’t Riet, K. Review of measuring methods and results on nonviscous gas-liquid mass transfer in stirred tank. Ind. Eng. Chem. Process Des. DeV. 1979, 18, 357. (12) Fujasova, M.; Linek, V.; Moucha, T. Mass transfer correlations for multiple-impeller gas-liquid contactors. Analysis of the effect of axial dispersion in gas and liquid phase on “local” kLa values measured by the
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ReceiVed for reView August 30, 2007 ReVised manuscript receiVed October 26, 2007 Accepted October 30, 2007 IE0711776
