Acta Chim. Slov. 2003, 50, 771-776. 771 IMPACT OF STRUCTURED PACKING ON BUBBLE COLUMN MASS TRANSFER CHARACTERISTICS EVALUATION. Part 3. Sensitivity of ADM Volumetric Mass Transfer Coefficient evaluation Ana Lakota Faculty of Chemistry and Chemical Technology, University of Ljubljana, Aškerčeva 5, SI-1000 Ljubljana, Slovenia Received 13-10-2003 Abstract Based on the available concentration profiles the present work discusses the sensitivity of volumetric mass transfer coefficient on axial dispersion coefficient. The calculations were performed for a bubble column without internals, the parameters of ADM were determined with nonlinear regression. The volumetric mass transfer coefficient shows a slight dependence on the axial dispersion coefficient which leads to the conclusion that ADM provides reasonable values for kLa whenever more or less reliable correlation for EL is available. Nevertheless, the exact concentration profile evaluation requires EL to be determined with caution. Introduction An extensive experimental study of hydrodynamic and mass transfer characteristics of bubble column, with or without internals, is described in details in Part 1 and Part 2. The experiments were performed in the Plexiglas column with a high length to diameter ratio. The column operated in the cocurrent upflow mode, tap water and oxygen were employed as the flowing phases. Both hydrodynamic regimes, the homogeneous and heterogeneous, were partly covered. The perforated plate served as the gas distributor. A significant deviation from the ideal plug flow of the liquid phase was experimentally confirmed and validated in the form of axial dispersion number, El. For the evaluation of mass transfer characteristics the measurement of oxygen concentration in the liquid phase were taken under stationary conditions at four different axial positions along the column. The data were then interpreted with the use of axial dispersion model (ADM) and plug flow model (PFM). The resulting values for the volumetric mass transfer coefficients clearly showed the more realistic response of ADM against PFM. A. Lakota: Impact of Structured Packing on Bubble Column Mass Transfer Characteristics Evaluation... 772 Acta Chim. Slov. 2003, 50, 771-776. Axial dispersion model (Part 1, equation 3 to equation 11) involves two parameters, the Stanton number, St, and the Bodenstein number, Bo. At the given operating conditions k^a and El may be explicitly expressed and used instead. The ADM concentration curves are extremely sensitive to the Stanton number, while the Bo number shows minor effect. In the present work the sensitivity of the calculated volumetric mass transfer coefficient based on the available concentration profiles, on axial dispersion coefficients is shown. The calculations were performed on the experimental data for a bubble column without internals, the parameters of the ADM were determined with nonlinear regression procedure by means of the Mathematica. Results and discussion The deviation of the calculated profile from the experimental one is expressed as the sum of the differences between the measured and calculated values of the concentration to the square, in ali cases. In Table 1 the k^a values as an average along the column were obtained from the adaptation to the measured concentration profiles. For the second parameter of the model, El, the experimental values best represented with the following equation: 7^ 0.191 hL =129.05? uG (1) were put into the model. In the above equation El is in cm s" and ug in cms" (with ey=8.89% and ?=9.37%). The calculated profiles seems to be very close the experimental ones, the sums of the squares lie betvveen 0.74 and 12. At the ul=1.81 cms" some irregularities may be observed, the kLa values are evidently too high. The examination of the measured profiles was made. Extremely high values of the concentration at the first measuring point were found what could easily corrupt the results. For comparison the ^a evaluated from the last measured concentration in the column are also presented. Except for the first set of data at the lowest liquid velocity the ^a values are very close to those from the profile adaptation, but the deviations of the calculated profiles from the measured ones are about doubled. A. Lakota: Impact of Structured Packing on Bubble Column Mass Transfer Characteristics Evaluation… Acta Chim. Slov. 2003, 50, 771-776. 773 In spite of insufficient number of the experimental data for liquid concentration along the column an attempt to optimise both parameters from the concentration profiles was also made. These results are shown in Table 2. In this čase the summations of squares are lower than 1 in ali runs. The values of the axial dispersion coefficients do not match with the measured coefficients (equation 1). Because the concentration profile is rather insensitive to El these values are very uncertain. Surprisinglv, the volumetric mass transfer coefficients are nearlv identical to those based on the one parameter concentration profile adaptations (within 5%). Table 1. Results of ADM kLa values based on the measured concentration profiles. ADM - kLa ADM – kLa adjusted to optimized from the the last measured concentratu on profile ? concentration Run Ul Ug EL* kLa kLa Z No (cm s-1) (cm s-1) (cm2 s"1) (s-1) (A cL) 2.60 ( s"1) (A cL)2 1 1.81 1.81 144.5 0.03116 0.02795 5.47 2 3.61 165.0 0.08216 9.41 0.05242 38.22 3 5.41 178.2 0.1199 10.87 0.06911 42.68 4 9.0 196.3 0.1817 11.17 0.08247 60.05 5 3.61 1.81 144.5 0.02307 0.74 0.02372 1.026 6 3.61 165.0 0.05080 1.60 0.04850 2.45 7 5.41 178.2 0.07547 4.11 0.06752 7.80 8 9.0 196.3 0.11561 9.60 0.09250 20.42 9 5.41 1.81 144.5 0.02128 1.12 0.02104 1.16 10 3.61 165.0 0.04667 0.90 0.04525 1.98 11 5.41 178.2 0.06739 1.02 0.06485 1.65 12 9.0 196.3 0.10617 4.88 0.09537 9.05 * Equation 1. For comparison the volumetric mass transfer coefficients evaluated from the PFM are also included in Table 2. These values are adjusted to the last measured concentration in the column. As one can see the coefficients are lower then those from ADM, the summations of squares are between 10 and 100. In order to test the sensitivity of kLa on the axial dispersion coefficient the experimental data points from run No. 7 were employed. In these calculations EL was varied from 1 cm2s-1 to 1500 cm2s-1. The values of the mass transfer coefficient were then optimised to the measured concentration profile (Figure 1). A. Lakota: Impact of Structured Packing on Bubble Column Mass Transfer Characteristics Evaluation… 774 Acta Chim. Slov. 2003, 50, 771-776. Table 2. Results of both ADM parameters optimized from the measured concentration profiles and kLa values from PFM. ADM – EL and kLa optimized from the concentration profile PFM – kLa adjusted to the last measured concentration Run uL ug EL kLa No (cm s-1) (cm s-1) (cm2 s-1) (s-1) (A cL)2 kLa (s-1) (A cL)2 1 1.81 1.81 200.1 0.0308 0.0735 0.01938 100.1 2 3.61 396.1 0.0848 0.969 0.02819 166.3 3 5.41 566.7 0.1217 0.276 0.0329 166.3 4 9.0 849.6 0.1730 0.640 0.03522 200.2 5 3.61 1.81 116.6 0.02377 0.089 0.0231 20.54 6 3.61 220.5 0.05125 0.391 0.0394 34.70 7 5.41 330.4 0.0797 0.009 0.0478 56.61 8 9.0 557.0 0.1311 0.162 0.0592 74.70 9 5.41 1.81 107.0 0.02224 0.539 0.0234 10.27 10 3.61 152.9 0.04676 0.872 0.04258 13.54 11 5.41 229.8 0.06801 0.651 0.05591 18.45 12 9.0 470.5 0.1168 0.046 0.07469 35.32 0,10 80 0,09 0,08 0,07 0,06 - kLa (s"1) Z (AcL)2 l l i ¦-------v 1 \ / A / \ / \ ^ 70 + 60 w 50 40 ¦¦ 30 -¦------------------------------------------------------------------ ------—^. i » - 20 0,05 0,04 ^. t X / mm ^\j ^..... - 10 0 1 10 100 1000 10 D00 EL (cmV1) Figure 1. Volumetric gas-liquid mass transfer coefficient and the summation of squares as a function of axial dispersion coefficient (experimental concentration data points from run No. 7). From Table 1 it can be seen that at these operating conditions the experimental 2-1 value of El (equation 1) is 178.2 cm s" and the k^a value adjusted to the measured profile is equal to 0.07547 s" . The sum of the squares is about 4. When El is nearly doubled (to 330.4 cm s" ) the change in the volumetric mass transfer coefficient is within A. Lakota: Impact of Structured Packing on Bubble Column Mass Transfer Characteristics Evaluation… Acta Chim. Slov. 2003, 50, 771-776. 775 -i 5% (to 0.0797 s"). These two values are taken from the two-parameter fit from Table 2. In fact for values of axial dispersion coefficient from 1 to 1000 cm s" the volumetric mass transfer coefficients lie within 0.06 s" and 0.08 s" (Figure 1). However, the deviation of the calculated concentration profile from the measured one does change significantlv, the sum of the squares is first minimised and then goes up to 50, increasing rapidlv. In Figure 2 the calculated dimensionless concentration profile at different values of El are drawn together with the experimental data points. It is obvious that the k^a determination is quite insensitive to the value of El, while the prediction of the reliable concentration profile along the column requires both parameters to be determined with caution. 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 experimental EL= 1 cmV1 EL= 100 cmV1 EL= 400 cmV1 EL=1000 cmV1 0,2 0,4 0,6 0,8 Figure 2. Calulated concentration profiles at different values of axial dispersion coefficient (experimental concentration data points from run No. 7). Conclusion The sensitivitv of the volumetric mass transfer coefficient on the axial dispersion coefficient was examined. The experimental data were taken from the previous studies. ' The use of axial dispersion model in ki,a evaluation based on the measured concentration profile, or even one single measured concentration, gives the satisfactorv result as long as more or less reliable correlations for El are available. Nevertheless, the estimation of the exact concentration profile requires also El to be determined with caution. 0 1 z A. Lakota: Impact of Structured Packing on Bubble Column Mass Transfer Characteristics Evaluation… 776 Acta Chim. Slov. 2003, 50, 771-776. Acknowledgements This work was supported by the Slovenian Ministry of Science and Technology through Grant PO-0510-0103. C c El ey kLa L N PeL St u z Nomenclature dimensionless oxygen concentration, c/c*, / oxygen concentration, mgl"1 dispersion coefflcient, m2s_1 mean relative error, 100 N 4-^ yMES(i)-ypRED(i) y ( ) % volumetric gas-liquid mass transfer coefficient, s" column length, m number of experimental data modified Peclet number in the liquid phase, uLL El^-Eg) Stanton number, k a L u superficial velocity, ms" dimensionless length of a column, / Greek letters e o phase hold-up, / standard deviation, = .00, N-l Z J PRED ( ) J MES ( ) MES (i) Subscripts G gas phase L liquid phase * in equilibrium MES measured value PRED predicted value References 1. A. Lakota, M. Jazbec, J. Leveč, Acta Chim. Slov. 2001, 48, 453-468. 2. A. Lakota, M. Jazbec, J. Leveč, Acta Chim. Slov. 2002, 49, 587-604. 3. W. D. Deckwer, Bubble Column Reactors; J. Wiley & Sons Ltd., Chicester (GB), 1992. Povzetek Dvoparametrski aksialno disperzni model je primeren za določitev volumetričnega koeficienta snovnega transporta na osnovi eksperimentalno posnetih koncentracijskih krivulj. Sama vrednost kLa kaže rahlo odvisnost od vrednosti aksialno disperznega koeficienta, tako da EL lahko ocenimo iz razpoložljivih korelacij. V primeru, ko nas zanima eksakten koncentracijski profil vzdolž kolone, nenatančnost v oceni aksilno disperznega koeficienta doprinese k znatni napaki. / 2 1 V A. Lakota: Impact of Structured Packing on Bubble Column Mass Transfer Characteristics Evaluation…