Mass Transfer Coefficients in Batch and Continuous Regime in a Bubble Column

The physical absorption has been experimentally investigated in a bubble column for to determination of volumetric mass transfer coefficients referred to the liquid phase, kLa, and quantify the effect of the viscosity of the absorbent solution on the same, operating in continuous and batch regime with respect to the liquid phase. The variables studied in the process have been the physical properties of the liquid phase (density and viscosity) and the physical properties of the gas phase (diffusivity and solubility), the gas flow rate and the pore diameter as well as the liquid flow rate. The experimental results have been correlated through two equations, depending on the flow regim. Both equations reproduce the experimental data with an average deviation of 10%. INTRODUCTION Mass transfer process in gas-liquid systems is an elemental field in chemical engineering, both on industrial and laboratory level. In the former case, this process was carried out using specific apparatus, but it is very difficult to predict its behaviour only with theoretical models [1, 2, 3]. Due to it, it is necessary to evaluate the volumetric mass transfer coefficients or the specific interfacial areas at the laboratory level. Many authors had developed different models in order to simulate industrial absorbers, i.e. apparatus with the wall-wetted column [4, 5, 6, 7], the rotator tambour [8], the mobile band absorbed [9], the laminar jet apparatus [10] and the bubble column [11]. The behaviour of an industrial column is similar to the laboratory model when for a same solution and equal operation conditions, the volumetric volumetric mass transfer coefficient (kLa) remains constant. When we perform absorption studies with pure gas, i.e. without resistance to mass transfer in gas phase, it is not possible to determine the liquid side mass transfer coefficient (kL) and the specific interfacial area (a) independiently. Then the volumetric mass transfer coefficient (kLa) is obtained through absorption experiments that have a character purely physical (physical method). Bubble columns are important among the different gas-liquid contactors because they present some advantages respect other contactors, like minor cost of maintenance, effective interfacial areas and very high mass transfer coefficients, big versatility of operation and high residence times. This type of contactors is widely used in the chemical industry as absorbers, fermenters and anaerobic and aerobic biology reactors. The design parameters of these apparatus [4, 5, 12, 13, 14], are: flow regime, coalescence and bubble size, hold-up, mass transfer coefficient and interfacial gas-liquid area. Further, there are some factors which influence the hydrodynamic of the system, like the physical properties of the contact phases, the operation parameters (gas flow, liquid flow and liquid volume) and geometric parameters (diameter and height of the column, height of the liquid in the column) Different authors show that the volumetric mass transfer coefficient (kLa) is a parameter related directly with superficial velocity and physical properties of liquid phase. However, the relation between these parameters is distinct from some authors to others (Table 1). This fact can be attributed to the different plates and the different range of variables [12, 17, 18, 19]. Most part of authors reproduce the experimental results using equations with the physical properties of the solutions, with the physical properties of the gases, and other characteristics of the systems. Other authors use correlations with dimensionless numbers [12, 13, 18, 20]. It is possible to classify both types of equations in two big groups: equations that depend on hold-up [12, 14, 17] and equations that are non-dependent on this parameter [20, 21, 22]. Some authors [23, 24] correlated the kLa values with the superficial gas velocity. In these equations the influence of the physical properties is reflected in the constant of the correlation. Taking into account the diversity of correlations that exist in the bibliography, we have opted for the experimental determination of the volumentric mass transfer coefficient, as well as the obtainment of the empirical equations that reproduce the behavior of our system. In this work we will present the results obtained upon accomplishing physical absorption experiments in batch and continuous regime. We have correlated kLa with the superficial gas velocity, with the physical properties of the liquid phase, with the liquid flow rate and with the bubble size. We have employed as liquid phase aqueous sucrose solutions (0-135 g/l), and as gas phase pure CO2 in the different experiments. MATERIALS AND METHODS Mass transfer measurements Mass transfer measurements were carried out using the apparatus shown in Fig.1. Except for the contact device, this set-up has been described in detail elsewhere [25]. The bubble column used as contact device in this work, 1, was made from two metacrylate cylinders. The internal diameter of the column is 11.3 cm, the external diameter is 12.1 cm and the height is 108.6 cm. In order to make all absorption experiments to the same temperature, a thermostated liquid pass between the two cylinders of the column. The top plate is flat and has three orifices, a central orifice for a thermometer, 2, two off-centre orifices for inflow of liquid, 3, and outflow of gas, 4. Table 1. Previous correlations for volumetric mass transfer coefficient in a bubble column Author System Operating Variables Equation Akita (1973) H2O, glycol, methanol Na2SO2, CCl4, NaCl, O2, Air, Helium, CO2 uG=5.3·10-4.2·10 m/s dc=15-60 cm T=40-10 oC Single-orificie sparged 10 . 1 g 93 . 0 17 . 0 62 . 0 L 12 . 0 L 50 . 0 L 2 L g D D c a k ε       ρ σ θ = − − 10 . 1 g 31 . 0 62 . 0 50 . 0 2 Ga Bo Sc c Sh ε = Akita (1974) H2O, glycol, methanol, CCl4, Sodium sulphite Air, O2 uG=3·10-4·10 m/s dc=7.7-15 cm T=5-40oC Single-orifice sparged 50 . 0 vs 37 . 0 37 . 0 L 50 . 0 L 60 . 0 L d D g 5 . 0 k − σ ρ = 25 . 0 37 . 0 50 . 0 Ga Bo Sc 5 . 0 Sh= Hikita (1981) H2O, Sucrose, butanol, methanol, Na2SO4, KCl, K2SO4, K3PO4, KNO3, AlCl3, CaCl2 Air, O2, H2, CH4, CO2 uG=4.2·10-3.8·10 m/s dc=10-150 cm, T=10-30oC Contin.-semicont Reg. Single-orificie sparged 76 . 0 G 75 . 0 85 . 0 L 24 . 0 g 08 . 0 L 02 . 1 0.60 L L u g D 9 . 14 a k ρ μ μ σ = − − Hughmark (1967) Water, glycerine Air, O2 uG=4·10-4.5·10 m/s Multiple-orifice sparged dc>10 cm 779 . 0 L 78 . 0 g 06 . 0 68 . 1 L 04 . 0 L 6 . 0 2 . 0 L L L U D 051 . 0 D 65 . 0 k ε σ ρ + σ ρ = 779 . 0 L 78 . 0 g 06 . 0 88 . 0 L 04 . 0 31 . 0 g U g U ε σ μ Kawase (1987) Water, carbopol 1, 2, Sodium carboxymethylcellulose, CO2 uG=1·10-1 10 m/s Multiple-orifice sparged dc=14-762 cm 01 . 1 a 44 . 0 g 4 L U 10 35 . 8 a k − − μ ⋅ = 62 . 0 057 . 0 62 . 0 5 . 0 Re Fr Bo Sc 646 . 0 Sh= Kawase (1996) Water, glycerine, Sodium carboxymethylcellulose Air uG=1·10-1 10 m/s Multiple-orifice sparged dc=23 cm 89 . 0 a 52 . 0 G 3 L u a k 10 14 . 2 − − μ = ⋅ 87 . 0 07 . 0 60 . 0 50 . 0 Re Fr Bo Sc 2 S 14 . 0 h= Nakanoh (1980) Water, Sucrose, Sodium carboxymethylcellulose, O2 uG<1 10 m/s Multiple-orifice sparged dc=14.55 cm, T=30 oC 39 . 0 0 . 1 75 . 0 5 . 0 Ga Fr Bo Sc 09 . 0 Sh= Sada (1985) NaCl, NaOH, Ca(OH)2 CO2, O2 uG=1·10-1 10 m/s Multiple-orifice sparged dc=5 cm, T=35 oC 86 . 0 G L u c a k = c= f (solution) Sotelo (1988) Sucrose Glycerine, Water, Ethanol Air, CO2 Multiple-orifice sparged T=25 oC uG=6.4·10-4.9 10 m/s n G L u b a k = b, n= f (solution) Zhao (1994) Sucrose, CMC, oil, water, SAE CO2 Multiple-orifice sparged dc=14 cm uG=0.8.10-6.5 10 m/s 50 . 0 37 . 0 80 . 0 G L H u b a k − − μ = The baseplate has three orifices, a central orifice, 5, for inflow of gas through a porous plate 4 cm in diameter, 10, (plate 1: equivalent pore diameter 150-200 10 m; plate 2: equivalent pore diameter 90-150 10 m; plate 3: equivalent pore diameter 40-90 10 m) and two off-centre orifices for a thermometer, 6, and outflow of the liquid phase, 7. Figure 1. Experimental set-up for measuring absorption of gas. The gas to be absorbed, pure CO2, was passed through a humidifier at 25 °C, 8, into a thermostated, 9, and entered the contact device at a constant flow rate measured with a bubble flow-meter, 10. Gas outflow was measured with another bubble flowmeter, 11, before its release into the atmosphere. The gas absorption rate was calculated as the difference between inflow and outflow rates. We had employed different gas flow oscillating between 3 10 and 9 10 mol/s. The liquid phases used in this work (water and aqueous solutions of sucrose of concentrations up to 135 g/L) were thermostated to room temperature (25°C) before entering the contact device. For batch runs the liquid load was 12 L. The contact between the liquid phase and gas phase was in counter current flow. Physical properties Interpretation of the mass transfer data obtained as described above required knowledge of the densities, viscosities and surface tensions of the liquid phases used, and the diffusivities and solubilities of the gas in these phases. The densities and viscosities of the sucrose solutions were measured, at 25°C, by a pycnometric method and a Schott capillary viscometer (model VAS 350), respectively. The surface tensions were measured by means a Prolabo tensiometer, which uses the Wilhelmy plate method. The diffusivity was calculated from the Joosteen and Danckwerts equation [26] obtained different values with sucrose concentration, and the solubility of CO2 was calculated from the equation proposed by Linke [27]. The obtained values were shown in the Table 2. Table 2. Values of physical properties. ρ (kg/m3 ) μ·103 (Pa·s) σ·103 (N/m) D·109 (m2/s) Ce·102 (mol/L) WaterCO2 997.00 0.896 72.00 1.897 3.36 Sucrose (16 g/L)-CO2 1003.14 0.923 72.09 1.768 3.33 Sucrose (50 g/L)-CO2 1016.19 1.015 72.29 1.664 3.28 Sucrose (85.7 g/L)-CO2 1029.90 1.135 72.49 1.549 3.23 Sucrose (135 g/L)-CO2 1048.83 1.327 72.78 1.401 3.15 THEORY The calculation procedure followed for the two operation regimes is the one which is shown below. Batch processing The amount of gas absorbed per unit time per unit of liquid phase volume (N) is given by ) ( C C a k dt dC N e L − = = (1) where the driving force for the transfer process (C C) is calculated as the difference between the concentration of the gas in the interface, C*, in equilibrium with pure gas (solubility) and the concentration of the gas in bulk liquid. This concentration was evaluated through a mass balance of the experimental absorption rates with the time. Dependence of N with the time for different gas flow rates is shown in Fig. 2, as an example. The volumetric mass transfer coefficient is calculated as the amount of gas absorbed in function of the time, if the volume of the column and the concentrations of the gas at the interface and in the bulk liquid are known. Continuous processing The absorption rate is defined by Eq. (1). As the concentration in the liquid bulk varies throughout the column its value is calculated through a logarithmic average. The volumetric mass transfer coefficient is then: