14th European Conference on Mixing Warszawa, 10-13 September 2012
CFD MODELLING OF HYDRODYNAMICS
IN SUPERCRITICAL FLUID EXTRACTION SYSTEMS
Jan Krzysztoforski, Marek Henczka
Warsaw University of Technology, Faculty of Chemical and Process Engineering, Waryńskiego 1, PL 00-645 Warsaw, Poland
m.henczka@ichip.pw.edu.pl
Abstract. A method for CFD modelling of hydrodynamics in supercritical fluid extraction (SFE)
systems was presented. Computational results obtained from the method were compared with experimental data for method validation. The course of SFE in a rotating disk contactor (RDC) column was simulated. In the presented method, the Euler-Euler multiphase approach was used and the dispersed phase drop size had a constant value based on experimental data. Local values of dispersed phase volume fraction were presented, as well as velocity fields for both phases and local values of turbulent energy dissipation rate. Computed values of the dispersed phase holdup in the RDC column show a reasonable agreement with experimental results. For the examined conditions, drop breakup and coalescence occur rather due to buoyancy effects than caused by the rotor energy input. The results show the capability of using CFD in order to predict and analyze the hydrodynamics of SFE systems. The presented method can be used for development of more complex methods with direct drop breakup and coalescence calculation and mass transfer simulation.
Keywords: supercritical fluids, SFE, extraction, hydrodynamics, CFD
1. INTRODUCTION
Nowadays, supercritical fluids are gaining new fields of applications in science and industry. One of the main applications of supercritical fluids is supercritical fluid extraction (SFE), where supercritical fluid is used as solvent for extraction of substances from liquids and solids, often replacing organic solvents. In practical applications, various SFE column designs are used, e.g. packed bed columns or rotating disk contactor (RDC) columns, where rotating disks enhance mass transfer in the two phase system.
Hydrodynamics and especially such phenomena as drop breakup and coalescence significantly influence the course of SFE processes. They affect both the interfacial area and mass transfer rate, which can lead to process intensification. Optimization of process conditions can be supported by computational modelling. CFD methods of extraction systems should be able to deliver reliable results, develop the knowledge about process mechanisms and support the design of extraction apparatus. However, this problem is complex because many phenomena have to be taken into account simultaneously. A review of drop breakup models was presented by Bałdyga et al. [1]. Numerous different approaches for numerical modelling of liquid-liquid extraction systems have already been presented [2,3].
CFD modelling of two-phase hydrodynamics, including drop breakup and coalescence analysis, in SFE systems has not been presented in the literature so far. The aim of this work is to present such a CFD modelling method and to validate it by means of available experimental data. A method validated for supercritical conditions would be useful, as due to
high pressure conditions direct visual observation of hydrodynamics is often difficult. It would also be a valuable contribution to apparatus design for supercritical technologies. A validated method for modelling SFE hydrodynamics can be used for development of a complex method, which takes into account both hydrodynamics a mass transfer phenomena.
A computational approach for modelling hydrodynamics in a countercurrent flow RDC column for a liquid-liquid system, using the Euler-Euler approach, was described by Drumm et al. [4]. The presented method is based on this approach, which has been developed and adapted to supercritical conditions, and exemplary modelling of a SFE system in a RDC column was carried out. The new method was validated by means of experimental results presented by Laitinen et al. [3], who investigated the course of SFE in a lab-scale countercurrent flow RDC column.
2. COMPUTATIONAL MODEL
The presented computational model enables to simulate two-phase hydrodynamics in a SFE extraction system. As in this kind of processes pressure gradients in the system are usually low and do not cause significant compressibility effects in the supercritical phase [5], both phases are considered as incompressible. The simulated phases are the water phase (continuous phase, phase 1) and the supercritical CO2 phase (dispersed phase, phase 2).
2.1 Physical properties
All calculations were carried out for the same conditions as in the experiments [3]: T=313 K and p=10 MPa. In this conditions, water density and dynamic viscosity are equal to
ρ1=992.99 kg/m3 and μ1=6.536·10-4 Pa·s [6], respectively. The density of supercritical carbon dioxide is ρ2=628.59 kg/m3 [7]. Viscosity of supercritical CO2 was calculated from a correlation by Heidaryan et al. [8]:
2 2 3 1 2 3 4 5 6 2 7 8 9 ln( ) (ln( )) (ln( )) 1 ln( ) (ln( )) 2 A A p A p A T A T A T μ A p A T A T + + + + + = + + + (1)
where p is the pressure, T – the temperature, and A1-A9 are coefficients. For the given conditions, μ2=4.022·10-5 Pa·s. The interfacial tension in this system is σ=0.00283 N/m2 [9]. 2.2 Multiphase model
For multiphase modelling, the Euler-Euler approach was chosen, as it describes well systems with significantly different velocity fields of the particular phases and it is suitable for cases, where the volume fraction of the dispersed phase is greater than 10% [10]. Water is the continuous phase and supercritical carbon dioxide the dispersed one. In the model, the Schiller-Naumann model [10] for the drag coefficient was used:
0.687 24(1 0.15 ) / 0.44 D Re Re Re 1000 C Re 1000 ⎧ + ≤ = ⎨ > ⎩ (2) where Re= 1d v( 1−v2) / 1 G G
ρ μ is the Reynolds number for one drop, calculated for the continuous phase density ρ1, the dispersed phase drop diameter d, the velocity vectors of the both phases vG1 and vG2, and for the continuous phase viscosity μ1. The dispersed phase drop size was assumed to be a constant value, derived from experimental data [3]. The flow was considered to be turbulent and the standard k-ε model of turbulence was used.
2.3 Geometry and mesh
The CFD simulations were carried out for two geometries: the first one (see Figure 1) consisted of one compartment of the RDC column and was used to validate the mesh. The compartment diameter is DC=35 mm, the rotor diameter is DR=21 mm, the stator opening
diameter is DS=24 mm, and the compartment height is h=20 mm. The second geometry (see
Figure 2) is a RDC column containing 5 compartments, a top section and a bottom section. Supercritical carbon dioxide flows upwards, and water flows downwards. Due to symmetry of the system, a 2D axisymmetric problem was solved for both geometries. The meshes consisted of 1260 and 14076 square elements (with 0,5 mm element side length), respectively. All calculations were carried out using ANSYS Workbench 14.0.
3. RESULTS AND DISCUSSION 3.1 Single-phase simulations
In order to validate the mesh, single-phase CFD simulations ware carried out for one compartment of the column. The liquid phase was water, and the open boundaries of the compartment (the top and the bottom boundary) were set to “periodic”. The computations were carried out for a steady state. In Figure 1, the geometry the compartment is presented, as well as velocity vectors and turbulent energy dissipation rate distribution. One can observe that the rotating disk produces two circulation loops situated below and above the rotating disk plane. The highest values of turbulent energy dissipation rate are present in the region near the outer section of the disk. These calculations were also carried out for finer meshes, but no significant changes in the flow field were observed.
geometry v1 [m/s] ε [m2/s3]
Figure 1. Single phase simulation results (N=300 rpm): Geometry, continuous phase velocity v1 and turbulent energy dissipation rate ε.
3.2 Two-phase simulations
For two-phase simulations, a different geometry was used. The geometry of a RDC column consist of 5 compartments, each of which had the same geometry as in the real RDC column used by Laitinen et al. in their experiments. In Figure 2, the geometry of the column is shown. At t=0, the top section was filled by the dispersed phase, while all other sections (five compartments and the bottom section) were filled with the continuous phase. All inlets and outlets were set to “velocity inlets”. Calculations were carried out for a transient flow with a time step Δt=0.001 s. During the calculations, dispersed phase holdup values where monitored for the whole domain and for particular compartments. The calculations were finished, when a steady state was reached, for which dispersed phase holdup values for particular compartments remained constant. The simulations were carried out for three different disk rotation speeds N (0, 150 and 300 rpm). The water and carbon dioxide flow rates were F1=1.6 kg/h and F2=12 kg/h, respectively. In Figure 2, detailed results for N=300 rpm are shown. The dispersed phase volume fraction is presented both for the whole column and for the fourth compartment. The trajectories of CO2 drops are clearly visible, as well as areas, where the dispersed phase is accumulated. The velocity vector flow fields for both phases show that there are circulation loops present in the continuous phase flow whereas the dispersed phase
drops rise without any circulation. The flow caused by the rotor is not sufficient to alter significantly the upward movement of the drops caused by buoyancy. The distribution of turbulent energy dissipation rate is more uniform than in the single phase system, although there are regions with a not fully developed turbulent flow. Hence, the k-ω model of turbulence or LES will be used in future calculations for more accurate results
column compartment 4
α2 [-] v1 [m/s] v2 [m/s]
α2 [-] ε [m2/s3]
Figure 2. Two-phase simulation results (N=300 rpm): Dispersed phase volume fraction α2, continuous
and dispersed phase velocity v1 and v2, respectively, and turbulent energy dissipation rate ε. For the dispersed phase, the holdup was calculated:
2 dispersed phase volume
dispersed phase volume + continuous phase volume
H = = α (3)
In Table 1, the values of computed holdup Hm and experimental holdup Hexp of the dispersed phase are compared for the three rotor speeds, and drop sizes are presented as well. The holdup obtained from the model was calculated as the mean holdup in compartment 4. The computational data show a quite good agreement with the experimental results, although the influence of rotor speed on holdup in the CFD results is not as strong as in the experiments.
Table 1. Computed versus experimental dispersed phase holdup
No. N [rpm] d [mm] Hm [-] Hexp [-]
1 0 1.80 0.110 0.090
2 150 1.65 0.111 0.120
3 300 1.55 0.112 0.130
Furthermore, the mechanisms of drop breakup and coalescence was investigated. Laitinen et al. [4] reported, that the change of rotor speed had a rather weak influence on the dispersed
phase drop size. In Figure 3, velocities for both phases and turbulent energy dissipation rate are shown for three different rotor speeds. One can see that rotation has little influence on the velocity fields. The zones with increased turbulent energy dissipation rate (which is a crucial parameter for breakup and coalescence mechanisms) are more evenly distributed with the increase of rotor speed, but even without any rotation there are zones with significant turbulent energy dissipation rates, namely the outermost edge of the rotor and the innermost edge of the stator. Hence, buoyancy seems to be the main factor causing the drops to undergo breakup and coalescence.
N [rpm] 0 150 300 v1 [m/s] v2 [m/s] ε [m2/s3]
Figure 3. Comparison of velocity v1 (continuous phase) , v2 (dispersed phase) and turbulent energy
dissipation rate ε for different rotor speeds N.
In order to confirm this hypothesis, the critical diameter dcrit, at which drops start to break, was calculated for different rotor speeds from a correlation for RDC columns [2]:
0.75 crit 1.23 R R
d = D We− (4)
where DR is the rotor diameter and WeR =ρ1D NR3 2/σ is the rotor Weber number, depending
on rotor diameter DR, rotor speed N, continuous phase density ρ1 and interfacial tension σ. This correlation does not take into account any effects related to buoyancy. In Table 2, critical diameters for different rotor speeds are compared with experimental drop sizes. For lower rotation speeds, critical drop sizes are significantly greater than experimental drop sizes. Such small drop sizes cannot be caused by the effects predicted by the correlation (2), and breakup
and coalescence is predominantly caused by buoyancy. For higher rotor speeds, the critical drop size decreases and for these rotor speeds the energy input from the rotor can considerably affect the drop size.
Table 2. Comparison of critical drop size dcrit (according to equation 4) and experimental drop size d.
N [rpm] 0 50 100 150 300 500
dcrit [mm] - 14.00 4.96 2.70 1.75 0.95
d[mm] 1.80 - - 1.65 1.55 -
4. SUMMARY AND CONCLUSIONS
A method for modelling hydrodynamics of SFE extraction systems was presented and validated using experimental results available in the literature. The model comprises a two-phase Euler-Euler approach with the supercritical fluid two-phase being the dispersed two-phase and the liquid being the continuous phase, with a constant drop size obtained from experimental data. CFD simulations were carried out for countercurrent supercritical extraction in a RDC column. Local dispersed phase holdup and velocity fields for both phases, as well as the turbulent energy dissipation rate were presented for constant flow rates and different rotor speeds. The results show a reasonable accordance with experimental results, concerning the dispersed phase holdup. The computations also confirmed the reason for a small change in drop size with the increase in rotor speed, as the main cause of drop breakup and coalescence was buoyancy. This work shows the capability of using CFD for modelling the hydrodynamics of SFE systems. This model is to be further developed, in order to be able to predict correctly drop size distributions and to simulate mass transfer in SFE systems.
The research was supported by scientific funds in 2010-2013 as a scientific project (N N209 175 238).
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