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Simultaneous Computational Fluid Dynamics (CFD) Simulation of the Hydrodynamics and Mass Transfer in a Partially Aerated Bubble Column Elena M. Cachaza, M. Elena Dı´az, Francisco J. Montes,* and Miguel A. Gala´n Chemical Engineering Department, UniVersity of Salamanca, Plaza de los Caı´dos 1-5, 37008, Salamanca, Spain
In this work, simultaneous hydrodynamics and mass-transfer computational fluid dynamics (CFD) studies in a rectangular partially aerated bubble column were conducted. The proposed transient Eulerian-Eulerian model was applied to a two-phase flow composed of polydispersed air and water. Four different kl correlations were implemented in the CFD code, and the results were compared. At superficial gas velocity values ranging from 2.4 mm/s to 21.3 mm/s, the developed flow regimes were experimentally characterized by means of visual observations, global gas holdup, plume oscillation period, and Sauter mean bubble diameter measurements. Simultaneously, the transfer of oxygen from the disperse phase to the initially deoxygenized water was characterized by the measurement of the evolution of the dissolved oxygen concentration with time. Comparison between the experimental and simulated parameters previously mentioned allows for the validation of the computational model. According to the results presented in this work, experimental and simulated hydrodynamic and mass-transfer results show a remarkable agreement at all studied superficial gas velocity values. In addition, mass-transfer results reveal (1) no influence on the developed hydrodynamics, (2) the adequacy of the selected kl correlations obtained by an attentive simplification of mass-transfer equations, and (3) the enhancement of mass-transfer processes when using partially aerated bubble columns. 1. Introduction Approximately 25% of all chemical processes that involve mass transfer across an interphase, including water treatment, absorption, and aerobic fermentations, occur between a gas phase and a liquid phase. One of the equipments most commonly used for bringing gas and liquid phases into contact is, together with stirred tank reactors, bubble columns, because their inherent characteristics, such as the attainable high interphase contact area and their significant mixing capacity, enhance the masstransport process. Despite the numerous published studies dealing with bubble columns, unanswered questions that have hindered the global control of this equipment remain. The main, although still unresolved, challenges in the design and scaleup of bubble columns are the complete knowledge of the hydrodynamics, together with the reliable definition of the masstransport phenomena that occur between phases, two fields that are inexorably inseparable. Only after the resolution of these unanswered questions the prediction of the optimum conditions at which transfer processes should occur will become a reality. The evaluation of the interphase mass-transfer rate in bubble columns is usually performed in terms of the volumetric masstransfer coefficient (kla) that comprises the liquid-side masstransfer coefficient (kl) and the specific gas-liquid interfacial area (a). Keeping the operating conditions unaltered, the particular values of a become intrinsically joined to hydrodynamic variables such as the developed flow pattern and the degree of turbulence of the system. In this way, the study of the mass-transfer processes that occur in bubble columns becomes a difficult multiparameter problem1 that must consider the complexity of the interactions between hydrodynamics and mass-transport phenomena in two-phase flows. In this context, computational fluid dynamics (CFD) becomes an essential tool, because it can facilitate the calculations and improve the prediction of bubble columns performance, optimizing, this way, their efficiency. * To whom correspondence should be addressed. Tel.: +34 923 29 44 79. Fax: +34 923 29 45 74. E-mail:
[email protected].
Most of the efforts regarding the use of CFD to model bubble columns have been directed toward the hydrodynamic description of totally aerated bubble columns, considering either simple or multiple bubble size distribution, which has resulted in numerous published works.2-14 In contrast, only a few studies that additionally include mass transfer in the CFD code,15,16 are available, and there are even less that simultaneously take into account hydrodynamics, mass transfer, and a multiple bubble size distribution.17,18 Wang et al.18 reported CFD studies that involve hydrodynamics and mass transfer in totally aerated bubble columns. These authors18 developed a CFD-PBM coupled model, considering multiple mechanisms for bubble breakup and coalescence and several mass-transfer models. The simulations performed showed an acceptable prediction of the bubble size distribution at superficial gas velocities (UG) lower than ∼0.065 m/s, while at high UG values (>0.065 m/s), a great deviation from the experimental results was reported. The masstransfer coefficient obtained by means of the CFD-PBM coupled model was predicted with accuracy for the entire range of UG under study. CFD studies dealing with bubble plumes in partially aerated bubble columns are much less numerous than those in totally aerated bubble columns although, again, most of them focus on the hydrodynamic characterization.19-33 Furthermore, CFD mass-transfer studies,34-36 accounting for simple or multiple bubble size distribution, remain insufficient, as a result of the inaccuracy of the few reported studies. In this way, Darmana et al.,34 based on the Eulerian-Lagrangian approach for a partially aerated two-dimensional (2D) bubble column, combined a discrete bubble model with hydrodynamics, mass transfer, and chemical reaction, reporting good concordance between experimental and simulated hydrodynamic results, when mass transfer was not considered. However, when accounting for mass transfer, the simulated results underpredicted the experimental overall mass-transfer rate while they overpredicted the averaged bubble size experimentally obtained,
10.1021/ie900314s CCC: $40.75 2009 American Chemical Society Published on Web 08/13/2009
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leading to significant differences between simulated and experimental hydrodynamic parameters. Because of the lack of a complete and accurate computational model that combines hydrodynamics, mass transfer, and multiple bubble size distribution capable of modeling partially aerated bubble columns, a three-dimensional (3D) Eulerian-Eulerian hydrodynamic and mass-transfer model of a multiphase system in a partially aerated 2D bubble column is presented in this paper. The gas, which is composed of a mixture of oxygen and nitrogen and modeled as spherical bubbles divided in multiple groups of different sizes, is considered as the dispersed phase, whereas the liquid, which is composed of a mixture of water and dissolved oxygen, is considered as the continuous phase. Several kl correlations, including those developed in a previous paper,37 have been implemented in the CDF code to simulate mass-transfer processes in the continuous phase surrounding the bubbles. Validation of the proposed CFD model is achieved by comparing the simulated results with several experimental parameters. Comparison of visual observations of the laboratoryscale bubble column with images numerically obtained is used to validate the simulations qualitatively. For quantitative validation, the chosen experimental parameters are the global gas holdup (εG), the plume oscillation period (POP), and the Sauter mean bubble diameter (d32) for hydrodynamic validation, the dissolved oxygen (DO) concentration curves and the volumetric mass transfer coefficient (kla) for mass-transfer validation.
suggest a spherical bubble shape for low and intermediate Reynolds (Re) values, when the Eo¨tvo¨s number (Eo¨) remains 7.1 mm/s, the reproducibility of the experimental DO curves is remarkable; the resulting numerical DO concentration curves obtained by means of the AB model are slightly closer to the experimental values than those obtained by means of the CSTR model. In contrast, for UG < 7.1 mm/s, calculated DO concentration curves obtained
Figure 5. Comparison between experimental and calculated d32 values at different UG values.
using both proposed mass-transfer models clearly overpredict the experimental curves, although, in this case, the CSTR model results are more similar to the experimental ones. This tendency can be related to the empirical correlations proposed for the computation of kl values that are based on the approximately linear variation of kla with εG. According to previously reported results,37 kla, which was obtained by the application of both the CSTR and AB models, versus εG linear regressions show that the goodness of fit is significant at high UG values for both models, whereas at low UG values, a higher dispersion of the data is obtained, with the CSTR model being the one that better followed the linearity. The overall accurate prediction of experimental DO concentrations using the CFD model (accounting for the complete continuity equation) when the empirical eqs 5 and 6 in Table 1 are implemented, evidence that the simplifications introduced into the continuity equation to obtain both mass-transfer correlations were adequate. Furthermore, relative to the reproducibility of the experimental data using eq 6 in Table 1, it can be concluded that the analytical solution proposed for the AB model, developed by Klinkenberg74 for the modeling of packed columns, was correct and applicable to bubble columns. Figure 7 shows the DO concentration curves obtained by means of eqs 7 and 8 in Table 1 at three different UG values, and their comparison to experimental results. As it can be seen, experimental DO concentrations are clearly underpredicted by simulated results. Relative to the differences observed, it is evident that these prediction equations claimed to be general equations cannot be applied to the particular experimental setup considered in the present paper. Similar results were obtained with the implementation on the computational model of the correlations proposed by Calderbank and Moo-Young,43 Hughmark,44 Ranz and Marshall,46 and Schu¨gerl et al.47 The simulated DO concentration curves obtained differ considerably from the experimental results, underpredicting the experimental
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Figure 6. Comparison between experimental and simulated DO concentration curves obtained using CSTR and AB models for different UG values. Solid circles represent experimental results; dotted line represents the CSTR model (eq 18); and the dashed line represents the AB model (eq 19).
DO concentration data even more remarkably (results not shown). The inability of the previously mentioned correlations to reproduce experimental DO values can be related to the improvement on mass transfer rates observed in bubble columns when bubble plumes are present.19,72,75 The enhancement on the transport processes is directly related to the appearance of liquid circulation cells that favors them by means of two different mechanisms. First, the liquid circulation cells increase the contact time between the gas phase and the liquid phase,
retaining the bubbles in the liquid bulk by returning them down. Second, these liquid circulation cells have an upward and descending movement, which enhances the mixing processes. Quantitative validation of the mass-transfer computational model has been achieved comparing experimental and computational kla results (see Figure 8) obtained through both transfer models: CSTR (Figure 8a) and AB (Figure 8b). As shown by Figure 8, good agreement between experimental and simulated
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expected, because of the better fit of the AB numerical DO concentration curves to experimental values. In addition, Figure 8 shows the influence of UG in the resulting kla values. According to the results obtained, increasing kla values are obtained when UG is increased, following, with remarkable good adjustment, the general equation proposed by Deckwer et al.76 (eq 20): kLa ) RUGβ
(20)
The coefficients R and β in eq 20 can be determined from a regression analysis, fitting kla vs UG data to eq 20. The resulting experimental and simulated R and β values shown in Table 5 are similar and comparable to the those obtained by other authors.47,77,78 6. Summary and Conclusions
Figure 7. Comparison between experimental and simulated DO concentration curves obtained using eqs 16 and 17 for different UG values. Solid circles represent experimental results; the dashed line represents data from the Akita and Yoshida equation (eq 16); and the dotted line represents data from the Kulkarni equation (eq 17).
kla is obtained for both the CSTR and AB models, with the latter model being the one that leads to slightly lower relative errors, compared to experimental data (Table 5). This fact was
Hydrodynamics and mass transfer of a gas-liquid system in a partially aerated rectangular bubble column has been successfully simulated using a complete Eulerian-Eulerian (E-E) computational model. The model proposed accounts for the complete continuity equation, where the primary mass source term due to interphase mass transfer has been evaluated considering the two resistance models, while the secondary mass source term, taking into account the mechanisms of breakup and coalescence, has been evaluated according to the Luo and Svendsen model and the Prince and Blanch model, respectively. To study the evolution of the bubble size distribution, the computational model proposed accounts for a multiple size group model that considers the dispersed phase divided into 10 groups of bubbles of different mean diameter, ranging in size from 1 mm to 10 mm and discretized using the equal diameter method. The turbulence model considered takes into account the standard two-equation k-ε turbulence model for the liquid phase and the dispersed phase zero equation model for the gas phase. An averaged form of the momentum conservation equation has been considered, where the interphase mass transfer momentum source and the interphase momentum transfer due to drag force have been taken into account. The numerical solution of the conservation equations has been obtained using the commercial CFD code ANSYS CFX 11.0, considering a nonuniform hexahedral grid and a time step size of 25 ms. Validation of the computational model has been performed, comparing the numerical simulations with the experimental results previously obtained. The chosen experimental parameters have been visual observations of the bubble column, for qualitative validation, and the global gas holdup (εG), the plume oscillation period (POP), the Sauter mean bubble diameter (d32), the dissolved oxygen (DO) concentration curves, and the volumetric mass transfer coefficient (kla) for quantitative validation. To obtain numerical DO concentrations, two empirical equations for mass-transfer coefficient prediction, obtained using two different analytical solutions of the simplified massconservation equations (CSTR model and AB model), have been implemented in the CFD code (described by eqs 5 and 6) and the results have been compared to those obtained through the equations proposed by Akita and Yoshida (eq 7)42 and by Kulkarni (eq 8).45 Considering the good agreement between simulated and experimental εG values (relative errors, in absolute value, within 0.24%-9.69% (seeTable 2)), it can be concluded that the computational model shown in the present work is able to predict the time-averaged hydrodynamic flow regime developed inside the experimental bubble column. Further validation is
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Figure 8. Comparison between experimental and calculated kla values at different UG: (a) kla values obtained by means of the CSTR model and (b) kla values obtained by means of the AB model. Table 5. Comparison between Experimental and Simulated kla Values Obtained Using the CSTR Model and the AB Model kla (s-1) CSTR UG (m/s) 0.0024 0.0071 0.0120 0.0166 0.0213 R β
AB
Relative Error (%)
experimental
simulated
experimental
simulated
experimental - simulated (CSTR)
experimental - simulated (AB)
0.0031 0.0081 0.0118 0.0150 0.0183 0.412 0.809
0.0029 0.0075 0.0116 0.0149 0.0184 0.476 0.843
0.0034 0.0089 0.0129 0.0165 0.0201 0.454 0.809
0.0032 0.0081 0.0127 0.0165 0.0197 0.503 0.835
6.89 8.00 1.72 0.67 0.54 13.44 4.03
6.25 9.87 1.57 0.00 2.03 9.74 3.11
obtained when visual observations of the existing bubble plumes are compared to simulated gas holdup distributions and superficial water velocity profiles. The existence of three regions perfectly distinguished in the simulated images (central bubble plume region, vortical region, and descending flow region) corroborates the capacity of the computational model in simulating, also, the time-dependent flow regime developed in the partially aerated bubble column. Moreover, the evolution of the aeration of the column, from partial to total, is also reproduced. The characteristic parameter POP obtained with and without mass transfer consideration has been also presented. Both computational models have shown adequate reproducibility of the experimental results, reporting the latter greater relative errors (up to 29.34%, in absolute value) that those obtained with the former, with relative errors (in absolute value) of 0%-11.25% (see Table 3). Validation of the bubble size distribution has been settled comparing the resulting numerical and experimental d32 values. The good agreement obtained for the range of UG values under study (with relative errors in absolute value oscillating over a range of 0.15%-4.6% for the complete computational model (see Table 4)) not only demonstrates the proper selection of the multiple bubble size group model but also validates the breakup and coalescence models considered. The exposed concordance between experimental and calculated hydrodynamic parameters confirms the hydrodynamic validation of the computational model proposed. Furthermore, and attending to the comparison of the results obtained with and without mass transfer consideration, it can be concluded that the hydrodynamics of the system remains unaltered when mass transfer is included. To validate the mass-transfer model implemented into the CFD code, experimental and simulated DO concentration curves and kla values have been compared for different UG values. Attending to the CSTR and AB results, accurate reproduction of experimental DO curves and kla (with relative errors of
