Mixing in a gas/liquid flow countercurrent bubble column

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1 Computational Methods in Multiphase Flow III 35 Mixing in a gas/liquid flow countercurrent bubble column T. A. Bartrand, B. Farouk & C. N. Haas Drexel University, Philadelphia, USA Abstract This paper presents results of experimental and numerical investigations into the hydrodynamics of a bench scale bubble column reactor. Countercurrent bubble column reactors are the reactors most commonly used in water treatment for effecting the mass transfer of ozone to the aqueous phase. The experimental reactor is a glass cylinder with an internal diameter of 17 cm and height of 1.8 m. Gas is introduced at the bottom of the column via a 2.5 cm spherical diffuser and water is introduced to the top of the column through a manifold packed with glass spheres. Residence time distribution (RTD) studies were conducted for a range of gas flow rates chosen to span the dispersed flow bubble regime. A computational fluid dynamics computer code was used to model flow in the bubble column. Numerical studies were performed to refine and validate the CFD model and to gain insights into the fluid dynamics of countercurrent flow bubble columns. Investigations identified a gas flow rate within the ideal bubbly flow regime at which large-scale hydrodynamics and phase distribution were significantly different from those encountered at lower gas flow rates. These results will be used in subsequent studies in which ozone mass transfer and chemistry are included. Keywords: countercurrent, bubble column, dispersion, CFD. 1 Introduction In water and wastewater treatment, bubble contactors are used frequently for dissolution of gaseous ozone into the aqueous phase because of their simple design, low energy requirements (excluding the energy required in ozone generation) and familiarity to the industry and regulatory agencies (Langlais et al. [1]). Full-scale contactors typically employ baffled chambers in which

2 36 Computational Methods in Multiphase Flow III ozonated gas is contacted with untreated water in both countercurrent and cocurrent fashion. Reducing operating costs and minimization of deleterious byproducts associated with reaction of ozone with bromide and natural organic matter (NOM) require the minimization of ozone dose and the optimization of ozone transfer and contact with untreated water. This study investigates the use of computational fluid dynamics (CFD) for detailed study of countercurrent bubble column flow. Despite a rich literature on bubble column reactors, few studies have explored the details of countercurrent flow and fewer studies applied CFD to countercurrent flow. 1.1 Dispersion in bubble column reactors Rising bubbles promote liquid-phase hydrodynamic dispersion and influence mixing of the phases and mass transfer rates. To date, most analyses have characterized liquid dispersion in bubble columns via a single Peclet number, though dispersion varies axially in bubble columns (Bischoff and Phillips [2]). Among the many relations developed for predicting axial dispersion in bubble columns, only three (Table 1) were developed explicitly for countercurrent operation. Table 1: Relation E L u g 2 d c v b Summary of countercurrent bubble column dispersion relations. Study Bischoff and Phillips [2] a ( P e = 2u + v g b)d c = 3.0 ± 0.3 Reith et al. [3] b E L P 1 e = 4.88 H u g ν L 53 Kim et al. [4] c u L d b a Based on analysis of data from numerous small diameter cocurrent, countercurrent and nonflowing liquid phase bubble columns. Only valid in the ideal bubbly flow regime. b Based on experimental data taken in 5 cm and 14 cm cocurrent and countercurrent bubble columns (air/tap water). The term 2u g + v b is the relative velocity between phases. c Developed for co- and countercurrent flow in a 15 cm circular bubble column. Units of H must be m and all other units must be dimensionally consistent. In the relations shown in Table 1, P e is the Peclet number, defined as P e = u L, (1) E L E L, is axial dispersion, u g and u L are superficial gas and liquid velocities, v b is bubble terminal rise speed, d c is column diameter, and H is column height. In pilot studies of bubble columns of differing diameter and with a nonflowing liquid phase, the column diameter influences mixing due to the dependence of large-scale fluid structure (circulation) on column diameter but did not influence gas phase holdup (Forret et al.[5], Krishna et al. [6], Ruzicka d c

3 Computational Methods in Multiphase Flow III 37 et al [7]). Column height can also influence transition from homogeneous to heterogeneous bubbly flow and dispersion in columns with non-flowing liquid phase, with transition occurring earlier as column height is increased (Ruzicka, et al. [8]). Minor vertical misalignment of tall cylindrical bubble columns can drastically change column hydrodynamics; a reactor tilt of only 0.5 resulted in a three order of magnitude difference in dispersion in pilot studies of air injected into water in a 2.44 m tall pilot scale bubble column (Rice and Littlefield [9]). In full scale reactors, the arrangement of baffles dominates reactor hydrodynamics (T 10 /θ); gas injection scheme (distribution of gas injection between reactor compartments) plays a less significant role (Do-Quang et al. [10]). The spacing of spargers and their proximity to reactor walls influence reactor hydrodynamics, given the tendency of bubble plumes to migrate toward each other (Freire et al. [11]) or toward reactor walls (Machina et al. [12]). Using drift flux analysis and experimentation, Hasan et al. [13] observed that holdup in bubble columns differs significantly for cocurrent and countercurrent modes of operation. For countercurrent operation in the ideal bubbly flow regime, Argo and Cova [14] determined that gas superficial velocity influences on dispersion more than liquid superficial velocity. 1.2 Review of prior numerical studies Numerous CFD studies have been made of bubble columns with non-flowing liquid phase for exploring the submodels best suited for reproducing bubble column hydrodynamics in general and momentum exchange between phases and bubble break-up and coalescence in specific. Significant differences between reported studies are treatment of the dispersed phase (Eulerian (e.g., Olmos et al. [15]; Pfleger et al. [16]; van Baten and Krishna [17]) or Lagrangian (e.g., Laín et al. [18])), distribution of bubble diameters (monodisperse (e.g., Pfleger et al. [16]) two size groups (e.g., van Baten and Krishna [17]) or a distribution of bubble diameters (e.g., Olmos et al. [15])) and bubble drag model. Among researchers who have performed CFD studies of ozone bubble contactors, Cockx et al. [19] modelled relevant physics in the greatest detail. That study used an Eulerian-Eulerian approach with a monodisperse gas phase (3 mm bubble diameter) and uniform drag coefficient of Experimental and numerical methods 2.1 Experimental methods Tracer studies were performed in the countercurrent flow bubble column shown in Figure 1. Water enters the column via two ports at the bottom of the collar that encloses the top of the column. The space between the column and collar is packed with 7 mm glass beads. Water flows out of the column through four symmetric ports located approximately 3 cm below the bottom of the diffuser. The volume of the column below the diffuser is also packed with glass beads. Air flows into column via a spherical 2.5 cm diameter fine porous diffuser and leaves the reactor at the water surface.

4 38 Computational Methods in Multiphase Flow III Water in 1.83 m (6 ft) 7.6 cm (6 in) Figure 1: Experimental apparatus. Step tracer studies (NaCl tracer) were performed at a liquid flow rate of 6.6 L/min and at gas flow rates of 0, 0.5, 1, 2, 3 and 3.5 L/min. Gas flow was observed to be in the ideal bubbly regime at all gas flow rates, though, as will be described later, the liquid phase flow field and distribution of bubbles in the column changed significantly over the range of gas flow rates. During tracer studies, samples were taken at 15s intervals from a port approximately 6 cm downstream of the column s water discharge ports. All calculations were performed using conductivity rather than NaCl concentration since calibration studies confirmed linear dependence of conductivity on concentration over the anticipated concentration range. Prior to tracer studies the column was operated at the test water and gas flow rates for at least 3 theoretical residence times. During tracer experiments tracer was introduced to the column via step feed for 3 theoretical residence times, then tracer feed was replaced with tap water and tracer was washed out for at least three residence times. 2.2 Numerical model Water out Numerical studies were performed with the commercial finite volume CFD package CFX (ANSYS Europe Ltd. [20]) on a 480,000 element 3-dimensional unstructured mesh. Mesh density was chosen based on a grid resolution study and generated to provide high resolution at column walls and near the diffuser. An Eulerian-Eulerian two phase formulation was employed. The gas phase was approximated as monodisperse (2 mm diameter) with drag coefficient from the Grace model (Clift et al. [21]) and with bubble-enhanced turbulence (Sato and Sekoguchi [22]). Dirichlet water and air inlet boundaries were specified and gas escaped from the top of the column via a degassing boundary (no slip for the liquid phase, sink term for the gas phase). All calculations were 3-dimensional and unsteady. A second order upwind transient scheme with relatively small time steps (0.05 s) was required to achieve convergence to an RMS residual of within 10 iterations per time step. To

5 Computational Methods in Multiphase Flow III 39 produce representative quasi-steady results for inclusion in this paper, calculations were performed for approximately 10s of simulation time, after which variations in bubble plume shape became minor and bubble plume was seen to rotate in the column, though not with a fixed period. 3 Experimental observations As gas flow rate was increased during tracer studies, the behaviour of the bubble plume changed significantly, despite though no increase in bubble break-up or collisions was observed. At low gas flow rates, the plume rises vertically and increases in diameter with height, as shown in Figure 2(a). At higher gas flow rate (Figure 2(b)), the bubble plume rotates while rising, tending to migrate away from the column centreline and toward the wall. At some distance above the sparger (typically between 0.6 and 1 m), the plume expands to fill the entire column. (a) Low Q g (b) High Q g Figure 2: Bubble plume shapes. Residence time distributions (RTDs) corresponding to the range of gas flow rates tested are presented in Figure 3. The parameters θ and F are the normalized time (time/theoretical hydraulic residence time) and the normalized concentration, given as F = C Tracer C 0 for tracer feed or 1 C Tracer C 0 for washout (2) C Tracer,in C 0 C Tracer,in C 0 where C Tracer is the measured tracer conductivity, C 0 is the conductivity of the tap water feed (background) and C Tracer,in is the conductivity of the tracer at column inlet. The early portion of the RTD curves indicate that increased gas flow rates promote earlier breakthrough. This is due, in part, to gulfstreaming (upward flow of liquid phase in the bubble plume) and reduction of the effective column cross sectional area through which downward-flowing liquid passes.

6 40 Computational Methods in Multiphase Flow III F Early breakthrough No gas flow Q = 0.5 lpm Q = 1 lpm Q = 2 lpm Q = 3 lpm θ Figure 3: RTDs for 0 < Q g < 3 L/min Experimental 100 Reith Kim P e 10 Figure 4: Q g (L/min) Experimental and predicted Peclet number. Axial dispersion was estimated via RTD analyses (Haas et al. [23]). Candidate RTD models (inverse Gaussian, Gamma, two stream gamma and two stream inverse Gaussian) were fit to data and best-fit models were identified. F- tests were performed to ensure use of more highly parameterized models was justified by improvement in fit. For 0.5 l/min Q gas 2 l/min, a single stream inverse Gaussian distribution provided the best fit to RTD data. For 0 and 3 l/min gas flow, a two-stream inverse Gaussian distribution provided a statistically-significant better fit than the single stream model at 90% confidence level. Peclet number was estimated from the variance of the inverse Gaussian distribution via the relation 2( 1 epe ) (3) 2 P e σ 2 = 2 P e Figure 4 shows Peclet number calculated from experimental data and the relations found in Table 1. Experimental Peclet number falls sharply as gas flow

7 Computational Methods in Multiphase Flow III 41 increases from 0 to 0.5 L/min, is relatively constant (around 3.0) for moderate gas flow rate and falls as gas flow rate increases above 2 L/min. The Kim expression fits experimental data well at low and high gas flow rates and the Reith expression fits the data at moderate gas flow rate. In summary, three trends identified in RTD analyses indicate changed hydrodynamics as gas flow is increased above 2 L/min: early breakthrough observed in the RTD, significant improvement in RTD fit when a two-stream model is used, and significant reduction in Peclet number. φ g Numerical studies (a) Gas volume fraction Figure 5: (b) Plume shape Phase distribution. Contours of gas volume fraction, φ g, predicted at a gas flow rate of 2 L/min are shown in Figure 5(a). The plume does not rise symmetrically, but migrates in the column and finally migrates to the wall near the top of the column. The plume region, shown in Figure 5(b) is defined as the region within which the liquid phase velocity is upward. Note that there is upflow of liquid in the bubble plume over the entire reactor height and that the plume twists as it rises in the column. These figures illustrate non-axisymmetric plume rise and significantly different plume shape near the sparger compared with higher locations. In drinking water treatment, non-asymmetric flow as illustrated in Figure 5 creates the potential for short-circuiting of raw water and retards ozone mass transfer via poor mixing in the bubble plume and reduced contact of bubbles with raw water.

8 42 Computational Methods in Multiphase Flow III Figure 6: Spatial variations in mixing. Axial variation in mixing in the column is shown in Figure 6. Neglecting large-scale fluid motion, local mixing intensity is approximately proportional to the square root of the rate of turbulent energy dissipation (Droste [24]). Figure 6(a) shows contours of turbulent kinetic energy dissipation on a column midplane and Figure 6(b) is a plot of mean dissipation as a function of axial location. Average turbulent dissipation at axial location k, is calculated by: #elements ( φg ) ( P ) A i 1 ik, ik, ik, P = k (4) φ A = ( ) i = 1 g ik, ik, where A i,k is area of element i at axial location k. Mixing is non-uniform both axially and radially. Mixing is highest near the sparger (z < 0.5 m) and uniform in the rest of the column, except near the top where entrance effects dominate the flow. Mixing intensity is high inside the bubble plume and much lower outside the bubble plume. These results explain early breakthrough of tracer at high gas flow rates (Figure 3) the flow field is partitioned into a well-mixed portion rising in the bubble plume and a poorly mixed stream flowing downward. 5 Discussion Experiments and numerical studies were used to explore mixing phenomena in a countercurrent bubble column operating in the ideal bubbly regime. Nonuniform

9 Computational Methods in Multiphase Flow III 43 distribution of the gas phase and mixing became pronounced for gas flow rate higher than 2 L/min. At high gas flow rate the liquid flow field was partitioned into a fast-flowing stream flowing through a restricted area and a second stream dominated by large scale hydrodynamics. These findings indicate that dispersion relations for bubble column reactors are specific to the column mode of operation and height of bubble column. In very tall columns, axial variations in dispersion will be minor, but large-scale hydrodynamics may be different than in smaller reactors. The proposed numerical model was adequate to reproduce significant features in the flow field and results of CFD studies provided explanation for the unexpectedly early breakthrough of tracer during tracer studies at high gas flow rates. In subsequent studies additional experiments with a greater range of gas flow rates will be performed to allow characterization of the entire ideal bubbly flow regime. In concert with these studies, numerical tracer studies will be performed at several gas flow rates. Acknowledgements The authors gratefully acknowledge the Koerner Family Fellowship and the L.D. Betz Endowment for Environmental Engineering for support of this research. References [1] Langlais, B., D.A. Reckhow, and D.R. Brink, eds. Ozone in Water Treatment: Application and Engineering. ed. AWWARF and Compagnie Général des Eaux. 1991, Lewis Publishers, Inc.: Chelsea, MI [2] Bischoff, K.B. and J.B. Phillips, Longitudinal Mixing in Orifice Plate Gas-Liquid Reactors. Industrial and Engineering Chemistry Process Design and Development, (4): p [3] Reith, T., S. Renken, and B.A. Israël, Gas Hold-up and Axial Mixing in the Fluid Phase of Bubble Columns. Chemical Engineering Science, : p [4] Kim, J.-H., R.B. Tomiak, and B.J. Mariñas, Inactivation of Cryptosporidium Oocysts in a Pilot-Scale Ozone Bubble-Diffuser Contactor. I: Model Development. Journal of Environmental Engineering, 2002a. 128(6): p [5] Forret, A., et al., Influence of Scale on the Hydrodynamics of Bubble Column Reactors: an Experimental Study in Columns of 0.1, 0.4 and 1 m Diameters. Chemical Engineering Science, : p [6] Krishna, R., et al., Influence of Scale on the Hydrodynamics of Bubble Columns Operating in the Churn-Turbulent Regime: Experiments vs. Eulerian Simulations. Chemical Engineering Science, : p [7] Ruzicka, M.C., et al., Homogeneous-Heterogeneous Regime Transition in Bubble Columns. Chemical Engineering Science, : p [8] Ruzicka, M.C., et al., Effect of Bubble Column Dimensions on Flow Regime Transition. Chemical Engineering Science, : p

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