COMPARTMENTAL MODELLING OF AN INDUSTRIAL BUBBLE COLUMN Christophe Wylock 1, Aurélie Larcy 1, Thierry Cartage 2, Benoît Haut 1 1 Transfers, Interfaces and Processes (TIPs) Chemical Engineering Unit, Université Libre de Bruxelles, av. F.D. Roosevelt 50, CP 165/67, 1050 Brussels, Belgium 2 Solvay SA, rue de Ransbeek 310, 1120 Brussels, Belgium Abstract: The industrial production of refined sodium bicarbonate is realized in large-scale bubble columns, called the BIR columns. Several complex phenomena exist in these columns, such as three-phase flow, gas-liquid mass transfer of CO 2, and crystallization. This work deals with the development of a BIR column model using the compartmental modelling approach. It is fed by previous works and current studies. Some simulations results are presented for typical operating conditions of an industrial column. Moreover, a parametric sensitivity study is realized to identify the more important modelling parameters. Keywords: bubble columns, compartmental modelling, multiphase reactor, hydrodynamic, mass transfer, crystallization 1. INTRODUCTION The refined sodium bicarbonate (NaHCO 3 ) production process is one of the oldest processes of the Solvay group. The NaHCO 3 has numerous applications. It is used as an environmental-friendly technology for the cleaning of a wide range of surfaces or for the neutralisation of acids in the flue gas of numerous types of industries. It also solves a lot of everyday problems (cleaning agent, toiletry, food additive...). The main step of the production process is the dispersion of a gaseous mixture of air and CO 2 in an aqueous solution of sodium carbonate (Na 2 CO 3 ) and bicarbonate. This operation is realized in large size bubble columns (20m high and 2.5m wide), called the BIR columns (Fig. 1), nearly isothermal and composed of a cylindrical core equipped with trays in its upper part and with circulation loops in its lower part. The trays aim to limit back mixing and therefore to increase the gas-liquid mass transfer. Fig. 1. Schematic representation of a BIR column. The column is fed at its top with the Na 2 CO 3 /NaHCO 3 brine and the air-co 2 mixture is injected at its bottom. It is dispersed in the liquid phase under the form of bubbles. The CO 2 is transferred from the bubbles to the liquid phase. This transfer leads to the following chemical reactions in the liquid phase : CO CO (1) 2,(g) 2,(l)
CO + OH HCO (2) - - 2,(l) 3 = - - CO3 + H2O HCO3 + OH (3) These two last reactions create a supersaturation of NaHCO 3 in the liquid, resulting in the continuous precipitation of solid NaHCO 3 in the lower part of the column. The resulting suspension leaves the column at the bottom of the circulation loop. + - Na + HCO3 NaHCO (4) 3,(s) The circulation loops create an air-lift motion in the lower part to avoid sedimentation of the solid phase (the average sedimentation speed is 2cm/s). The slurry passing in the circulation loops is degassed and the gas is reinjected in the column just below the first tray. A fraction of gas is then bypassed. In the past decades, several optimizations of the BIR columns were performed by empiric approaches. There are today some limits to this approach for applications requiring high levels of purity and a well-defined granulometry. Moreover, despite their large size (in order to increase the amount of transferred CO 2 ), the gas phase leaving the columns contains an important quantity of CO 2 (only half of the CO 2 is transferred). It causes a huge CO 2 emission to the atmosphere. Furthermore, the CO 2 is produced by lime calcination. This process requires a large amount of energy. It represents the major part of the energy consumption. Accordingly, Solvay is seeking for a more fundamental approach. This work deals with the development of a complete BIR column model, taking into account all the phenomena taking place in it, using the compartmental modelling approach. Its structure is derived from a previous work (Haut et al., 2004), based on experimental studies on industrial and pilot columns. This model is fed by several theoretical and experimental studies currently realized and will be used to understand the complex interactions between the different phenomena in order to identify the critical parameters and to optimize the NaHCO 3 crystal quality and the CO 2 transfer rate in the column. 2.1 Division into a set of compartments 2. MODEL CONSTRUCTION The column is divided into a set of compartments. Each compartment contains a perfectly mixed liquid phase and a gaseous phase divided into 2 populations of bubbles. Each bubble population is modelled by a plug flow reactor. The lowest compartment contains a perfectly mixed solid phase, which is modelled by a population balance equation. Inside these compartments and between compartments, mass exchanges occur. A schematic view of the compartmental model is presented in Fig. 2. The first compartment ranges from the bottom of the column to the first tray. The other compartments correspond to the space between each tray, until the top of the column. In the first compartment, some gas enters in the circulation loops with the liquid and therefore bypasses the central part of the column up to the first tray. The bypassed gas fractions, for each bubble population, and the liquid velocity in the circulation loops are estimated by gas-liquid Eulerian Computational Fluid Dynamics (CFD) simulations. These simulations were realized in Fluent 6.3 (Haut, 2003). The solid phase is assumed to be present only in the first compartment, from the bottom of the column until a height between the circulation loop and the first tray. This height is left as an adjustable parameter. Between each compartment, in the liquid phase, a mass transfer is induced by the global flow rate Q and a back mixing flow rate Q r, which is a modelling parameter. This structure of modelling has been validated (Haut, 2003) and the value of the Q r parameter has been determined from tracing experiments realized in an industrial column. At the level of each tray, the coalescence and break-up phenomena are assumed to be important enough to equalize the CO 2 molar fractions within the two bubbles populations. The models describing the different mass transfers inside the compartments are presented in the next sections.
Fig. 2. Compartmental modelling of a BIR column. 2.2 Gas-gas exchanges It has been shown experimentally that the gas hold-up in the columns is larger than 20%. The gaseous flow in the cylindrical core is therefore heterogeneous: small bubbles and large bubbles coexist (Ellenberger&Krhishna, 1994). An important parameter of this modelling is the volumetric fraction of the small bubbles in the liquid-small bubble mixture (ε d ), which is assumed to be constant in the cylindrical core of the column. This regime was confirmed and this volumetric fraction was determined (ε d =0.14) using a gammametric technique in a pilot scale bubble column (Haut et al., 2004). The large bubbles have the shape of a spherical cap and an equivalent diameter of 5-8 cm and the small bubbles have an ellipsoidal shape with an equivalent diameter between 2 and 5 mm. The large and small bubble equivalent diameters are supposed constant in the column and are left as adjustable parameters. The gas to liquid relative velocity for large bubbles is related to the equivalent diameter by the Davies&Taylor correlation (Clift et al., 1978) and for the small bubbles, an experimental correlation with the equivalent diameter is currently in development. The assumption of a ε d independent of the vertical coordinate leads to a net mass exchange between the two bubble populations via the break-up and coalescence phenomena. As each of these phenomena leads to an exchange of CO 2, an exchange is superimposed to the net mass flux. The CO 2 exchange coefficient between the two bubble populations induced by the break-up and coalescence phenomena is an adjustable parameter. Its value has been identified by Haut (2003). A correlation is currently in development to express it as a function of the gas hold up and the bubble diameters of each bubble population. The resulting equations describing the gas phase evolution in the two bubble populations with the vertical coordinate, based on these different assumptions, and the experimental results were presented in a previous work (Haut, 2003; Haut et al. 2004). This previous work did not take into account the influence of the solid in the slurry zone on ε d, which is lower than in the gas-liquid mixture. In this modelling, the correlation of Krishna et al. (1997) is used to calculate it in the slurry zone and the previously identified value is used in the gas-liquid zone. 2.3 Gas-liquid exchanges It is considered that only the CO 2 is transferred from the bubbles to the liquid. Its transfer rate is enhanced by the chemical reactions in the liquid phase. Moreover, only the transfer from small bubbles is considered as their interfacial area density is much larger than large bubbles.
Following Levich (1962), the transfer rate is determined by the phenomena occurring in the diffusion boundary layer on both sides of the interface of the rising bubbles. Since the diffusion in the gaseous phase is much faster than in the liquid phase, all the mass transfer resistance is supposed to be located in the liquid phase. As the reaction (3) is very fast and the ph is always around 10, a pseudo-first order reaction model is used. The Higbie approach is used to model the liquid flow around the bubbles. The liquid phase in the vicinity of the interface of a bubble can be seen as a mosaic of liquid elements continuously renewed (Coulson&Richardson, 1999). Each element is supposed to stay in contact with the bubble the same time t C. This contact time is a modelling parameter and it is calculated as the ratio of the small bubble equivalent diameter by its relative velocity. Since the depth of the diffusion boundary layer is much smaller than the bubble diameter, the gas-element interface is supposed planar. For the mass transfer, these elements can be considered as being semi-infinite (Haut, 2004; Levich, 1962). It can be demonstrated using Laplace transforms that this model leads to an analytical expression for the average CO 2 transfer rate : - D ( ) - CO 11 2-1 - k OH k 11 OH t C (5) N CO2 = CO2 CO2 k11 OH Erf k11 OH t interface C e - + + 2 k11 OH t C πt C This approach has been validated for the BIR column in a previous work (Wylock et al., 2008a) and by CFD simulation using the COMSOL Multiphysics software (Wylock et al., 2008b). The physico-chemical parameters, as the diffusion coefficient, the kinetic constant and the CO 2 solubility constant, come from a literature review (Vas Bhat et al., 2000). 2.4 Reactions in liquid phase Assuming that the chemical equilibriums are reached for reactions (2) and (3) in each compartment, the balance equations are written for all the dissolved species. The global gas-liquid CO 2 transfer rate (along the height of the considered compartment) appears in these equations and the rate of liquid-solid NaHCO 3 transfer appears in the equations of the first compartment. Taking into account the transfer induced by the global flow rate Q and the back mixing flow rate Q r, the chemical conversion rates for the reactions (2) and (3) are calculated using the chemical equilibrium constants found in the literature (Vas Bhat et al., 2000). 2.2 Liquid-solid exchanges It is assumed that the solid phase can be described by a population balance equation (PBE), following the description of Randolph and Larson (1971). Let c[l] be the crystal size distribution (CSD) of the NaHCO 3 crystals. J L c[ L] = exp (6) G Gτ where J is the nucleation rate and G is the growth rate, L is the crystal size and τ the mean residence time. The value of τ depends on the height of the slurry zone (between the circulation loop and the first tray). By now, the CSD is estimated using J and G measures provided by Solvay for an industrial bubble column. Models to correlate J and G as functions of the operating conditions (temperature, supersaturation, mixing conditions ) are currently in development. From the CSD, the total liquid-solid NaHCO 3 transfer and the mass fraction of solid in the suspension can be calculated. 3. SIMULATION RESULTS Simulations are realized with a code written using the Mathematica 5.1 software. The equation systems for each mass exchange modelling are solved for each compartment, starting from the bottom compartment to the top compartment and using a shooting method to fit the concentrations at the top. The simulations are performed for the typical operating conditions of a bubble column reactor located at Dombasle. These data are provided by Solvay.
The dimensionless mass concentration evolution of each species in the liquid phase is presented in Fig. 3 as a function of the dimensionless height of the column. As the liquid phase is perfectly mixed in each compartment, there are only changes between compartments. (a) Fig. 3. Mass concentrations of CO 2 and NaOH (a), and NaHCO 3 and Na 2 CO 3 (b) normalized by the total concentration of all the species at the liquid entrance (top of the column) versus the vertical coordinate normalized by the height of the column. The dimensionless molar flow rate and the CO 2 ratio evolutions for the two bubble populations, as a function of the ratio of the dimensionless height of the column, are presented in Fig. 4. The influence of the bypassed gas fractions by the degassing loop on the molar flow rate is observed in Fig. 4-a by a discontinuity of the curves. The equalization of the CO 2 molar fraction at the level of each tray is clearly shown in Fig. 4-b. (b) (a) Fig. 4. Fraction of initial molar gas flow rate (a) and CO 2 molar ratio (b) for the two bubble populations versus the vertical coordinate normalized by the height of the column. The dimensionless cumulative mass distribution of NaHCO 3 crystals is presented in Fig. 5 as a function of the ratio of crystal size on the maximum crystal size. (b) Fig. 5. Cumulative mass distribution of NaHCO 3 crystals normalized by the solid mass fraction in the suspension versus the crystal size normalized by the maximum crystal size. These simulation results are in good agreement with the experimental measurements of concentrations realized at different vertical positions of the BIR column of Dombasle. Moreover, a parametric sensitivity study is performed in order to identify the parameters that have the strongest influence.
It is shown that the model is very sensitive to the operating conditions, such as the inlet gas flow rate, the inlet pressure and the inlet liquid flow rate. It is moderately sensitive to the back-mixing parameter but not sensitive to the gas fractions in the degassing loops. It is also sensitive to the temperature via its influence on the gas-liquid mass transfer parameters. For the gas-gas exchange, the model is very sensitive to the volumetric fraction of small bubbles in the liquid-small bubble mixture, both in the gas-liquid zone and in the slurry zone. The other parameter of the gaseous phase, such as the CO 2 exchange coefficient by the break-up and coalescence phenomena and the characteristics of the bubbles do not have a strong influence, except for the small bubble diameter, which is correlated to the contact time (that influences the gas-liquid transfer rate). The model shows a great sensitivity to all the parameters of the gas-liquid mass transfer, especially the CO 2 solubility constant. Concerning the chemical reactions, it shows a weak sensitivity to the reaction (2) equilibrium constant of a moderate sensitivity to this of the reaction (3). Finally, for the liquid-solid exchange, the model shows a great sensitivity to the growth rate but a moderate sensitivity to the nucleation rate. 4. CONCLUSION A general model of a BIR column is developed using the compartmental approach. The structure of this model has been validated and some modelling parameters have been estimated experimentally by Haut (2003) and Solvay. Different literature surveys, numerical tools and experimental studies are used to realize this modelling. The values of several modelling parameters are estimated by literature correlations. Some parameters remain not well-know, therefore their values are those estimated by Haut (2003). Experimental works are currently realized in order to develop correlations to express these parameters as functions of operating conditions The model is computed by solving all the equation systems using the Mathematica software. Simulations are realized for typical operating conditions of an industrial column. The gaseous phase and liquid phase evolutions and the NaHCO 3 crystal size distribution are computed. These results are in good agreement with the experimental measurements on the Dombasle column and they have to be validated by comparison with other industrial column. Moreover, a sensitivity study is realized to identify the parameters that have the strongest influence on the simulation results. This model will be used by the Solvay group as a predictive tool to determine the operating conditions that have to be performed to optimize the quality of the final product and to reduce as far as possible the resource consumption. REFERENCES Clift, R., J.R. Grace and M.E. Weber (1978). Bubbles, drops and particles. Dover Publications, Mineola. Coulson, J.M. and Richardson J.F. (1999). Chemical Engineering : Fluid flow, heat transfer and mass transfer. Vol. 1, Butterworth Heinemann, Oxford. Ellenberger, J. and R. Krishna (1994). A unified approach to the scale-up of gas-solid fluidized bed and gas-liquid bubble column reactor. Chemical Engineering Science, 49, 5391-5412. Haut, B. (2003). Contribution à l étude des colonnes à bulles mettant en œuvre une réaction de précipitation. PhD thesis, Free University of Brussels Haut, B., V. Halloin, T. Cartage and A. Cockx (2004). Production of sodium bicarbonate in industrial bubble columns. Chemical Engineering Science, 59, 5687-5694. Krishna,R., J.W.A. de Swart, J. Ellenberger, G.B. Martina and C. Maretto (1997). Gas holdup in slurry bubble columns : effect of column diameter and slurry concentrations. AIChE Journal, 43(2), 311-316. Randolph, A.D., and M.A. Larson (1971). Theory of particulate processes. Academic Press, New York. Vas Bhat, R.D., J.A.M. Kuipers and G.F. Versteeg (2000). Mass transfer with complex chemical reactions in gasliquid systems: two-step reversible reactions with unit stoichiometric and kinetics orders. Chemical Engineering Journal, 76, 127 152. Wylock, C., P. Colinet, T. Cartage and B. Haut (2008a). Coupling between mass transfer and chemical reactions during the absorption of CO 2 in a NaHCO 3 -Na 2 CO 3 brine: experimental and theoretical study. International Journal of Chemical Reactor Engineering, 6(A4). Wylock, C., A. Larcy, P. Colinet, T. Cartage and B. Haut (2008b). Study of the CO 2 transfer rate in a reacting flow for the refined sodium bicarbonate production process. Proceeding of COMSOL Conference Hannover 2008.