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Detailed Investigation of Multiphase (Gas–Liquid and Gas–Liquid–Liquid) Flow Behaviour on Inclined Plates
0263–8762/06/$30.00+0.00 # 2006 Institution of Chemical Engineers Trans IChemE, Part A, February 2006 Chemical Engineering Research and Design, 84(A2): 147– 154
www.icheme.org/journals doi: 10.1205/cherd.05110
DETAILED INVESTIGATION OF MULTIPHASE (GAS – LIQUID AND GAS – LIQUID– LIQUID) FLOW BEHAVIOUR ON INCLINED PLATES A. HOFFMANN , I. AUSNER, J.-U. REPKE and G. WOZNY Technical University of Berlin, Institute of Process and Plant Technology, Berlin, Germany
T
his paper deals with the detailed investigation of homogeneous and heterogeneous liquid flow behaviours as it e.g., appears on distillation column packings. The flow is investigated experimentally as well as numerically. One main aspect is the validation of a multiphase CFD code for this complex application, which offers various difficulties like film flow and film break-up with rivulet and droplet flow. Experimental data of the flow is obtained with optical methods; numerical investigations are carried out with CFX 5, Ansys Inc. The multiphase flow in the first case is composed of one liquid phase and one gas phase (two-phase flow) and in the second case of two immiscible liquid phases and one gas phase (three-phase flow). For validation surface velocities and the spreading of the liquid phases are taken into account as well as morphologies of the flow. Keywords: two- and three-phase flow; film flow with break-up; CFD; optical measuring methods.
INTRODUCTION
liquid –liquid – vapour conditions (Villain et al., 2005). The long term target of this project is to develop a predictive model for multiphase operations which takes the local flow behaviour into account. Therefore prerequisite steps have to be taken. It was found that the liquid flow behaviour on packings reaches from film flow to rivulet and droplet flow, which becomes even more complex with the appearance of a second liquid phase (Repke and Wozny, 2002). Since flow measurements inside the packing are very difficult and highly expensive to perform, computational fluid dynamic (CFD) simulations are considered as an alternative to experiments. Nevertheless this highly complex special flow behaviour makes it necessary to validate the existing models capable of describing such flows. For the validation it is sufficient to reduce the complexity by examining inclined plates without counter-current gas flow. Each phase is considered as a continuous fluid and interacts with the other phases. The liquids may act as films or rivulets and droplets.
In the area of distillation, packed columns have become very popular during last few decades. This is due to higher loading capacities and separation efficiencies compared to traditional tray columns for most applications. The efficiency of the packed column strongly depends on the flow behaviour of the liquid inside the packing. Since this can change rapidly in the range of only a few inches, it seems reasonable to consider the local flow behaviour in the column models. This especially applies to threephase distillation where two immiscible liquid phases run counter-current to a vapour phase. Here the phases strongly interact with each other (Repke and Wozny, 2002). Designing columns for this application requires the knowledge of the flow behaviour since it is essential to have the right interfacial areas between each phase pair. Although various non-equilibrium models exist for two-phase distillation (Billet and Schultes, 1995; Brunazzi and Paglianti, 1997; Rocha et al., 1993) up to now models which take the local flow behaviour into consideration are not abundant in literature. For three-phase distillation (Repke and Wozny, 2004) developed a model which uses the twophase parameters from (Billet and Schultes, 1995). Lately, these parameters have been tuned to match the
EXPERIMENTS The experimental setup is shown in Figure 1: each liquid is delivered separately through a feeding tube onto the plate by a peristaltic pump. In case of only one liquid phase, it is also possible to deliver this liquid over an overflowing weir to make the formation of a film inlet condition easier. The plate is a rolled stainless steel plate with a flow field length of 0.06 m, a flow field width of 0.05 m and inclination angles varied between 458 and 608 referring to the horizontal,
Correspondence to: A. Hoffmann, Technical University of Berlin, Institute of Process and Plant Technology, Strasse d. 17 Juni 135, Sekr. KWT-9, D-10623 Berlin, Germany. E-mail: [email protected]
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HOFFMANN et al.
Figure 1. Experimental setup.
which are common used inclinations of commercial structured packings. A basin is mounted below the plate to collect the liquids and to separate the phases. The liquid loads are measured by Rota-meters. A CCD camera enables the flow regime, the wetted area of the plate, and the surface velocities to be observed. The surface velocities are determined using a Particle Tracking Velocimetry (PTV) method (Adrian, 1991): tracers which move accurately with the flow are detected and their velocity is measured. As tracers light weight particles (ISOSPHERES 300B, Omega Minerals GmbH, and Scotchlite Glass Bubbles K1 of 3 M), which rise to the liquid surface, are used as well as waves on the liquid film and fronts of rivulets and droplets. It was found that the different types of tracers lead all to the same distribution of velocities (Ausner et al., 2004). Hence it is not necessary to distinguish between the tracers during the measurement. A strobe light with 250 flashes per second double exposes the pictures of the tracers taken by the camera. The distances between the two exposures of each tracer are measured with the image analysis software SigmaScan Pro 5, SPSS Inc. Finally, the tracer velocity is obtained by the measured distance multiplied with the known stroboscope frequency and is assigned to the relevant liquid phase. Also, the spreading of the liquids is measured on these pictures. Due to the application of a camera a full field view of the flow behaviour on the plate is given. That enables the determination of the shadow areas, i.e., the interfacial area of each liquid phase projected on to the plate. NUMERICS The simulations are carried out with the commercial tool CFX 5, ANSYS Inc. It provides various multiphase models. The one considered here is a Euler –Euler model, which is simplified under the assumption that there is no slip velocity at the interfaces. This leads to one set of equations for all phases and an additional variable for the volume fraction for each phase. This results into a model similar to the well known volume of fluid (VOF) model introduced by (Hirt and Nichols, 1981). The surface tension is taken into account by using the continuous surface force model (CSF) by (Brackbill et al., 1992). Contact angles are implemented by setting the angle of the gradient of the volume fraction at the wall boundary condition. Different geometries are implemented and investigated. A two-dimensional mesh with symmetry boundaries at the sides is applied, but the main focus of the investigation
Figure 2. Geometry with boundary conditions implemented in CFX.
lies on three-dimensional (3D) geometries with symmetry and wall boundaries. The 3D mesh with the symmetry boundaries at the sides uses a plate width of 0.02 m which helps to reduce the mesh size and with that the computing time. The second 3D geometry which is shown in Figure 2 resembles the experimental setup of a 0.06 0.05 m2 steel plate held by steel supports on the left and on the right hand side. As can be seen in Figure 2 (right) the grid is refined in direction to the plate as well as to the side walls. The inlet conditions are varied between a film inlet and jet inlets to consider the experimental feeding options of an overflowing weir and a feeding tube. A constant pressure is given at the outlets. The plates and the plate supports are implemented as no-slip walls with given contact angles, which lead to a formation of a liquid meniscus at each support. Above the supports, the contact angle is set to 1808 to avoid a too high meniscus. The top boundaries are set to free-slip walls. The physical properties of the liquids used in the simulations are shown in Table 1. As gas phase the physical properties of air are applied. RESULTS At first the results concerning two phase flow are presented. This is a necessary step before changing to threephase flow. It is important first to validate the different unsteady flow behaviors, which also occur with two liquids: film break-up, rivulet and droplet flow. The testing system here is water – air on an inclined steel plate. Water is chosen for its tendency to film break-up below critical loadings. For three phase flow toluene is introduced as the third phase. The air phase in both cases is considered just as a stationary phase without a velocity. The two-phase flow simulations are carried out with a film inlet condition of constant height and parabolic velocity profile and with inclination angles of 458 and 608.
Table 1. Physical properties of the liquids implemented in the simulations. Physical properties 23
Density r (kg m ) Kinematic viscosity n (m2 s21) Surface tension g (N m21) Static contact angle with air-steel u
Water
Toluene
Air
997 8.926 1027
867 6.817 1027
1.185 1.545 1025
0.0728 70–808
0.0285 88
— —
Trans IChemE, Part A, Chemical Engineering Research and Design, 2006, 84(A2): 147– 154
MULTIPHASE FLOW BEHAVIOUR ON INCLINED PLATES Since the difference in the results between both inclinations is quite low, mainly the results of the 608 inclination are presented here. In the three-phase flow simulations a constant inclination angle of 458 is chosen in order to save computation time. Additionally, presented three-phase simulations use the jet inlet boundary condition for keeping comparability with the three-phase experiments. Two-Phase Flow First, numerical studies had been carried out with the two-dimensional geometry. It was found that with twodimensional simulations it is not possible to get reliable results concerning the critical Reynolds number ReC , which is defined as the lowest film Reynolds number Re ¼
u d V_ ¼ bn n
(1)
at which the liquid phase forms a stable film. In this case, the liquid film already breaks up at higher Re numbers. This is due to the fact that break-up phenomena and rivulet or droplet flow are highly three dimensional effects and therefore cannot be predicted by 2D-simulations. But even 3D-simulations result in too high ReC in comparison to experiments if the geometry is not taken into account. Here, the boundary conditions have a crucial effect. The usage of symmetry boundary conditions on the sides does not resemble the experimental setup. The introduction of wall boundaries on the sides and the geometrical realization of the experiments result in a better fit to the experiments. This is shown in Figure 3 where the specific wetted area a¼
Awetted Aplate
(2)
is plotted over Re for different simulations together with experimental data. While one curve shows the simulation results of the 3D simulation with a contact angle of u ¼ 808 and a lower plate width b of 0.02 m (compared to the geometry shown in Figure 2 with b ¼ 0.05 m) and symmetry boundaries on the left and right hand side, the
Figure 3. Specific wetted area plotted as a function of Re number. Comparison between measurements and different simulations: lower simulated width with symmetry-boundaries and a contact angle of u ¼ 808, adjusted to experimental set-up with contact angles of u ¼ 808 and 708.
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other two curves use the 3D geometry of the experiments with different contact angles u. The contact angle of 808 is the one most given in literature for air and water on steel. This value is also applied in the simulations with reduced geometry. The value of 708 is derived from own measurements of contact angles on the plate used and has a deviation of +108. As can be seen in Figure 3, the critical Reynolds number, where the specific area falls below a ¼ 1, can be accurately predicted, given the correct contact angle and provided that similar geometries are considered. For this case, where the correct geometry (steel plate (polished) with b ¼ 50 mm), boundary conditions (film inlet with Re ¼ 168 (sim.) acc. to Re ¼ 162 (exp.) and walls as plate supports) and static contact angle (u ¼ 708) are applied, a qualitative comparison between experiment and simulation is shown in Figure 4. Both pictures show the same flow behaviour and its characteristics of break-up arches and entry length. Additionally, the same specific wetted area is measured in the experiment (a ¼ 0.53) and the simulation (a ¼ 0.55). Another validation parameter is the velocity. Due to the absence of accurate measurements, the simulated velocity profiles over the film thickness are compared to the well known Nusselt profile. The comparison of a closed film flow at Re ¼ 224 with slight wave formation at the surface shows nearly exact agreements of the parabolic profiles (Figure 5). Also the film thickness shows a very good agreement for this case (Hoffmann et al., 2005). In order to compare the results with the experiments, we have to restrict ourselves to the surface velocity. Figure 6 shows the surface velocity us of a droplet flow over the length of the plate x at Re 120 (112 in the simulations, 122 in the experiments). The measured surface velocity is shown in comparison to the simulated maximum as well as averaged surface velocities. The values are determined by dividing the plate into six horizontal regions, where the simulated values are obtained from an isosurface at water volume fraction of 0.36. In each region the local maximum velocity and the local area-averaged velocity of the isosurface are taken. The volume fraction value for defining the isosurface was determined by integrating the volume fraction and fitting the surface to match this result. The three curves in Figure 6 have the same trend, which shows significant locations on the plate: at x between 0.015 m and 0.02 m the initial rivulets break up and droplets are formed, after that the droplets accelerate to the end of the plate. The film inlet condition in the simulation is not able to maintain film flow after the first few cells so that rivulets are formed right at the beginning of the plate. This is close to the experiments where no film flow is formed under these conditions. As can be seen in Figure 6 the local maximum velocity agrees with the measured values accurately, while the averaged velocity leads to lower values. This observation can be explained with the different methods of velocity determination in the experiments and the simulations. In the experiments, the PTV method can only detect the higher velocities at the top region of the droplets or rivulets due to the surface curvature. On the other hand, the area-averaged values from the simulations represent the whole surface, which also includes the low-velocity zone near the plate. For this reason, the simulated velocities, which represent
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Figure 4. Qualitative comparison between (a) simulation (Re ¼ 168), and (b) experiment (Re ¼ 162) of water on a 608 inclined polished steel plate.
the experiments best, shift from the maximum values for droplets to the area-averaged for film flow. Rivulets are best described by a weighted average depending on the droplet portion of the whole flow behaviour. A comparison of the velocity trend at different flow behaviours due to different flow rates is shown in Figure 7. Again the simulated surface velocity is plotted over the length of the plate x for three Re numbers. Re ¼ 224 represents a closed film flow with a high initial velocity and low acceleration. At Re ¼ 168 the film breaks up and a rivulet is formed at x of about 0.03 m that accelerates to the end of the plate. The third curve shows the surface velocity of a droplet flow at Re ¼ 112 that moves with a strong acceleration. For continuity reasons, all three curves represent the area-averaged velocities. For the interpretation of this plot, one should
keep in mind that the rivulet and droplet flow tend to higher surface velocities as shown above. Regarding the distillation process, the simulation results shown in Figure 7 lead to an important effect: in absence of a counter-current gas flow the gravitational acceleration of rivulets and droplets may result in higher velocities and with that in lower residence time inside the packing than with film flow. This is due to the fact that the film reaches a relatively low constant film thickness and film velocity while the rivulets and droplets are thicker and do not encounter as much friction as films. This effect might be reversed by introduction of a counter-current gas flow where the higher surface area (compared to the volume) of droplets and rivulets can lead to a stronger interaction between gas and liquid, which still has to be investigated. Three-Phase Flow When adding a second liquid which is immiscible with the first one (which occurs in various chemical engineering
Figure 5. Comparison of simulated velocity profile and theoretical Nusselt solution at Re ¼ 224.
Figure 6. Profile of the surface velocity along the length of the plate for a water droplet flow, Re 120.
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Figure 7. Simulated surface velocity profiles along the length of the plate for different water flow behaviours. Figure 9. Comparison of multiphase film flow between simulation (a) and experiment (b): water forms rivulets and droplets above and below the toluene film.
processes) the flow behaviour becomes much more complex. Here toluene is added to water. In this case we observe film flow of the organic phase (toluene) and rivulet and/or droplet flow of the aqueous phase (Figure 8). At low liquid loadings the order in which the liquids are delivered onto the plate also has an impact on the flow behaviour: while water forms rivulets and droplets, which flow on top of the toluene film when fed onto the toluene film [Figure 8(a)—further on defined as feed configuration number 1], it tends to forming rivulets flowing below the toluene film surface when fed above the toluene inlet [Figure 8(b)—feed configuration number 2]. At higher loadings of Re . 100 (especially the water load has a great impact) these two behaviours blend into each other for both feeding options. Figure 9 displays this case for both experiment and simulation. Water forms rivulets which are covered by the toluene film and droplets which are running on the toluene surface. Figure 9 shows the good agreement of the morphological comparison between simulation and experiment. A flow behaviour like this is not as depending on the liquid load as a single liquid flow. One of the two phases will likely form a stable film while the other phase will break-up even at loading high above the critical one. Nevertheless, the flow behaviour of a two-liquid flow is not just a superposition of the two single-liquid flows.
Figure 8. Morphological comparison between the different feed configurations: (a) water is fed onto the toluene phase and forms droplets on the toluene film; and (b) water is fed above the toluene phase and forms rivulets below the closed toluene film.
The two liquids interact strongly with each other. Both liquids are slower than in the single liquid case and the film is accelerated in the vicinity of the rivulets and droplets while these are decelerated by the film. That mutual interaction is shown in Figure 10 where a simulation result of water –toluene-flow is displayed with the surface velocity as a grey scale. Here a dark colour means high velocity and bright colour lower velocity. The black colour displays the interfacial contact line of the system water/toluene/air which appears where water phase cuts toluene film surface. Water flow below the toluene phase is indicated by high surface velocity of the toluene film. In order to reduce the number of necessary experiments for the validation, a factorial design (Montgomery et al., 1998) is chosen which varies the three parameters water load, toluene load and the order in which the two liquids are fed onto the plate, i.e., the feed configuration. The set points chosen here are given in Table 2. The liquid loadings lie within the measured region for the single liquid case. The experimental results of that factorial design on a 458 inclined plate are used to formulate empirical equations,
Figure 10. Simulated surface velocity of the multiphase flow. Water phase above the toluene phase is labelled by black surroundings.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2006, 84(A2): 147 –154
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HOFFMANN et al. Table 2. Factorial design of three-phase experiments.
Factor
Values
Re-number toluene feed Feed configuration number Re-number water feed
A
70
164
B
1 ! Configuration 1
2 ! Configuration 2
C
72
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which express the interaction between the liquids and enable the prediction of the surface velocity for a set of known parameters: uW ¼ (0:574 þ 0:023 XA 0:017 XB m þ 0:022 XB XC ) s uT ¼ (0:396 þ 0:035 XA 0:054 XB 0:035 XA XB þ 0:037 XB XC )
(3) m s
(4)
with the normalized parameters ReT 117 47 ReW 110 XB ¼ 38 NoFC 1:5 XC ¼ 1:5
XA ¼
(5a) (5b) (5c)
In the parameter definition equations (5a – c) ReT is the Re number of the toluene load, ReW represents the water Re number and NoFC is the number of feed configuration defined above. As can be seen in equations (3) and (4), linear dependences are assumed for the surface velocities for water and toluene from these parameters. This assumption is valid with good accuracy for the small investigated range
of Re numbers: ReT and ReW between 60 and 170. NoFC is a discrete value and can be chosen as 1 or 2. In order to validate the numerics, the one part of the factorial design which feds the water above the toluene (feed configuration 2) is simulated in CFX on a 458 inclined plate. Figure 11 shows a comparison of the numerical solution to the equations (3) and (4). In Figure 11(a) the surface velocities at a constant ReT of 160 are plotted as a function of RW . It can be seen that the water surface velocities remain on a constant level for different ReW , i.e., the influence of the water load on the water surface velocity is small. In comparison the toluene surface velocities show a significant decrease with increasing water load. These trends are found in the experimental results [equations (3) and (4)] as well as in the simulations. As expected, quantitative comparisons between the simulated and measured surface velocities show for the toluene phase that the measured values are well described by the area-averaged values from CFD simulations while the water surface velocities are better represented by an average which is shifted towards the maximum surface velocities. As shown above, this observation is also found in single-liquid flows. The weighted average in Figure 11 is taken from the equation uweighted ¼
2 2uavg þ umax 3
(6)
Figure 11(b) shows the water and toluene surface velocities as a function of ReT at a constant ReW of 70. Here the surface velocities computed with equations (3) and (4) increase with increasing ReT which is also found for the averaged surface velocities from the CFD simulations. The quantitative comparisons again lead to good agreements between the toluene surface velocity from equation (4) and the area averaged surface velocity from simulation. And also the water surface velocity from equation (3) is fitted best by the weighted average velocity from the simulations. In analogy to single liquid flows, that shift of the water surface velocity to higher values is expected since the
Figure 11. Comparison between simulated and measured multiphase surface velocity trends: (a) surface velocity trends for constant ReT ¼ 163.5, and (b) surface velocity trends for constant ReW ¼ 76.8.
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Figure 12. Comparison between the simulated and experimental surface velocities for (a) the water, and (b) the toluene phase.
surface area average is calculated for the whole surface of the water rivulet, where the area near the plate with its lower velocities weigh more in this rivulet flow than in film flow conditions. In comparison to this, the experimental data represent higher velocities of the water rivulet due to the measurement technique. That phenomenon is presented in Figure 12, too. In the chart (a), the measured water surface velocity is compared to the simulated surface velocities and in the chart (b), it is shown for toluene surface velocities. Ideally all the points of each chart should be found on the angle bisector. From Figure 12 it can be seen, that the best fit for measured water surface velocity is the weighted average surface velocity and the measured toluene surface velocities are best represented by the area averaged surface velocity.
CONCLUSIONS The complex flow behavior of homogeneous and heterogeneous liquids on inclined plates is investigated in detail. Industrial applications often do not show ideal performance of the occurring liquids. Complete wetting liquids are already investigated in literature. Unfortunately, in reality the liquids mostly are only partly wetting the plates. This leads to highly complex flow behaviours, which are analysed here with experiments as well as with numerical investigations. It is shown that the simulations meet the experiments very well. Intricate flow behaviours like film break-up, rivulet and droplet flow are represented by the calculations correctly. Two-phase flows of air and one liquid show the expected behaviour of film flow above a critical Reynolds number and rivulet and droplet formation below. The transition between these flow regimes is also predicted correctly. Validation by the data of surface velocities and shadow areas shows good quantitative agreement. Three-phase flow of gas and a film of two immiscible liquids is analysed here for the first time. It is shown that experiments and simulations compare well, too. Here one liquid phase (toluene) always forms film flow, while the other liquid (water) forms rivulets and droplets, which flow above and below the film surface. The two phases strongly interact with each other, which is verified by
experiments and simulations. When comparing the surface velocities it is necessary to keep the limitation of the measurement technique in mind, which leads to higher averaged velocities for rivulets and droplets than the calculation algorithm, which also accounts for low-velocity regions near the plate and below the film surface. By taking this into account, the validation with surface velocities shows good agreement for both phases in values and trends as well. The results show that for these complex flows reliable simulations have to be carried out in three dimensions. Here, also the geometry as well as the boundary conditions have an important impact on the accuracy. The strong dependency on the geometry leads to the necessity of implementing the packing geometry with highly resolving meshes. Therefore the calculation efforts increase strongly making it pointless to simulate complete packed columns with current available computational capacities. Practically, representative sections of the packing must be identified to reach a conclusion for the model. Next the model will be developed using these simulations, but also experiments and theoretical considerations. These detailed investigations are necessary for understanding the complex flow behaviour in many industrial applications, where these flows are occurring. The complete knowledge of the flow performance is essential for predicting the behaviour and developing a designing method in the future.
NOMENCLATURE a Aplate Awetted b d NoFC n Re Rec ReT ReW u u
specific wetted area, m2 m22 area of the full plate, m2 wetted area of the plate, m2 width of the plate, m film thickness, m number of feed configuration, parameter of factorial design kinematic viscosity, m2 s21 film Reynolds number critical Re number Re number of the toluene load Re number of the water load contact angle, degree average film velocity, m s21
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154 uavg uExp umax us uSim uT uW uweighted V_ x XA , XB , XC
HOFFMANN et al. area averaged surface velocity from the simulated isosurface, m s21 surface velocity from the experiments, m s21 maximum surface velocity from the simulated isosurface, m s21 surface velocity, m s21 surface velocity from the simulations, m s21 surface velocity of the toluene phase, m s21 surface velocity of the water phase, m s21 weighted average of the surface velocity, m s21 flow rate, m3 s21 length of the plate, m parameter of the factorial design
REFERENCES Adrian, R.J., 1991, Particle-imaging techniques for experimental fluid mechanics, Annu Rev Fluid Mech, 23: 261– 304. Ausner, I., Hoffmann, A., Repke, J.-U. and Wozny, G., 2004, Analyzing the surface velocity field of multiphase film flow, in Celata, G.P., Di Marco, P., Mariani, A. and Shah, R.K. (eds). Proceedings of 3rd International Symposium on Two-Phase Flow Modelling and Experimentation, 727– 733 (ETS Pisa, Italy). Billet, R. and Schultes, M., 1995, Fluid dynamics and mass transfer in the total capacity range of packed columns up to the flood point, Chem Eng Technol, 18: 371– 379. Brackbill, J.U., Kothe, D.B. and Zemach, C., 1992, A continuum method for modelling surface tension, J Comp Phys, 100: 335 –354. Brunazzi, E. and Paglianti, A., 1997, Liquid-film mass-transfer coefficient in a column equipped with structured packings, Ind Eng Chem Res, 36: 3792–3799.
Hirt, C.W. and Nichols, B.D., 1981, Volume of fluid (VOF) method for the dynamics of free boundaries, J Comp Phys, 39: 201–255. Hoffmann, A., Ausner, I., Repke, J.-U. and Wozny, G., 2005, Fluid dynamics in multiphase distillation processes in packed towers, Comp Chem Eng, 29: 1433–1437. Montgomery, D.C., Runger, G.C. and Hubele, N.F., 1998, Engineering Statistics (Wiley, New York, USA). Repke, J.-U. and Wozny, G., 2004, A short story of modelling and operation of three-phase distillation in packed columns, Ind Eng Chem Res, 24(43): 7850–7860. Repke, J.U. and Wozny, G., 2002, Experimental investigations of threephase distillation in a packed column, Chem Eng Technol, 25(2): 513–519. Rocha, J.A., Bravo, J.L. and Fair, J.R., 1993, Distillation columns containing structured packings: a comprehensive model for their performance. Part 1: hydraulic models, Ind Eng Chem Res, 32: 641–651. Villain, O., Faber, R., Li, P., Repke, J.-U. and Wozny, G., 2005, ThreePhase Distillation in Packed Towers: Short-Cut Modelling and Parameter Tuning, 29.5.– 1.6.2005 (ESCAPE 15, Barcelona, Spain).
ACKNOWLEDGEMENTS The authors gratefully appreciate the founding and support by the German Research Foundation (DFG) and the Research Center for Fluid Systems Technology, Technical University of Berlin. The manuscript was received 9 May 2005 and accepted for publication after revision 1 February 2006.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2006, 84(A2): 147– 154
www.icheme.org/journals doi: 10.1205/cherd.05110
DETAILED INVESTIGATION OF MULTIPHASE (GAS – LIQUID AND GAS – LIQUID– LIQUID) FLOW BEHAVIOUR ON INCLINED PLATES A. HOFFMANN , I. AUSNER, J.-U. REPKE and G. WOZNY Technical University of Berlin, Institute of Process and Plant Technology, Berlin, Germany
T
his paper deals with the detailed investigation of homogeneous and heterogeneous liquid flow behaviours as it e.g., appears on distillation column packings. The flow is investigated experimentally as well as numerically. One main aspect is the validation of a multiphase CFD code for this complex application, which offers various difficulties like film flow and film break-up with rivulet and droplet flow. Experimental data of the flow is obtained with optical methods; numerical investigations are carried out with CFX 5, Ansys Inc. The multiphase flow in the first case is composed of one liquid phase and one gas phase (two-phase flow) and in the second case of two immiscible liquid phases and one gas phase (three-phase flow). For validation surface velocities and the spreading of the liquid phases are taken into account as well as morphologies of the flow. Keywords: two- and three-phase flow; film flow with break-up; CFD; optical measuring methods.
INTRODUCTION
liquid –liquid – vapour conditions (Villain et al., 2005). The long term target of this project is to develop a predictive model for multiphase operations which takes the local flow behaviour into account. Therefore prerequisite steps have to be taken. It was found that the liquid flow behaviour on packings reaches from film flow to rivulet and droplet flow, which becomes even more complex with the appearance of a second liquid phase (Repke and Wozny, 2002). Since flow measurements inside the packing are very difficult and highly expensive to perform, computational fluid dynamic (CFD) simulations are considered as an alternative to experiments. Nevertheless this highly complex special flow behaviour makes it necessary to validate the existing models capable of describing such flows. For the validation it is sufficient to reduce the complexity by examining inclined plates without counter-current gas flow. Each phase is considered as a continuous fluid and interacts with the other phases. The liquids may act as films or rivulets and droplets.
In the area of distillation, packed columns have become very popular during last few decades. This is due to higher loading capacities and separation efficiencies compared to traditional tray columns for most applications. The efficiency of the packed column strongly depends on the flow behaviour of the liquid inside the packing. Since this can change rapidly in the range of only a few inches, it seems reasonable to consider the local flow behaviour in the column models. This especially applies to threephase distillation where two immiscible liquid phases run counter-current to a vapour phase. Here the phases strongly interact with each other (Repke and Wozny, 2002). Designing columns for this application requires the knowledge of the flow behaviour since it is essential to have the right interfacial areas between each phase pair. Although various non-equilibrium models exist for two-phase distillation (Billet and Schultes, 1995; Brunazzi and Paglianti, 1997; Rocha et al., 1993) up to now models which take the local flow behaviour into consideration are not abundant in literature. For three-phase distillation (Repke and Wozny, 2004) developed a model which uses the twophase parameters from (Billet and Schultes, 1995). Lately, these parameters have been tuned to match the
EXPERIMENTS The experimental setup is shown in Figure 1: each liquid is delivered separately through a feeding tube onto the plate by a peristaltic pump. In case of only one liquid phase, it is also possible to deliver this liquid over an overflowing weir to make the formation of a film inlet condition easier. The plate is a rolled stainless steel plate with a flow field length of 0.06 m, a flow field width of 0.05 m and inclination angles varied between 458 and 608 referring to the horizontal,
Correspondence to: A. Hoffmann, Technical University of Berlin, Institute of Process and Plant Technology, Strasse d. 17 Juni 135, Sekr. KWT-9, D-10623 Berlin, Germany. E-mail: [email protected]
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HOFFMANN et al.
Figure 1. Experimental setup.
which are common used inclinations of commercial structured packings. A basin is mounted below the plate to collect the liquids and to separate the phases. The liquid loads are measured by Rota-meters. A CCD camera enables the flow regime, the wetted area of the plate, and the surface velocities to be observed. The surface velocities are determined using a Particle Tracking Velocimetry (PTV) method (Adrian, 1991): tracers which move accurately with the flow are detected and their velocity is measured. As tracers light weight particles (ISOSPHERES 300B, Omega Minerals GmbH, and Scotchlite Glass Bubbles K1 of 3 M), which rise to the liquid surface, are used as well as waves on the liquid film and fronts of rivulets and droplets. It was found that the different types of tracers lead all to the same distribution of velocities (Ausner et al., 2004). Hence it is not necessary to distinguish between the tracers during the measurement. A strobe light with 250 flashes per second double exposes the pictures of the tracers taken by the camera. The distances between the two exposures of each tracer are measured with the image analysis software SigmaScan Pro 5, SPSS Inc. Finally, the tracer velocity is obtained by the measured distance multiplied with the known stroboscope frequency and is assigned to the relevant liquid phase. Also, the spreading of the liquids is measured on these pictures. Due to the application of a camera a full field view of the flow behaviour on the plate is given. That enables the determination of the shadow areas, i.e., the interfacial area of each liquid phase projected on to the plate. NUMERICS The simulations are carried out with the commercial tool CFX 5, ANSYS Inc. It provides various multiphase models. The one considered here is a Euler –Euler model, which is simplified under the assumption that there is no slip velocity at the interfaces. This leads to one set of equations for all phases and an additional variable for the volume fraction for each phase. This results into a model similar to the well known volume of fluid (VOF) model introduced by (Hirt and Nichols, 1981). The surface tension is taken into account by using the continuous surface force model (CSF) by (Brackbill et al., 1992). Contact angles are implemented by setting the angle of the gradient of the volume fraction at the wall boundary condition. Different geometries are implemented and investigated. A two-dimensional mesh with symmetry boundaries at the sides is applied, but the main focus of the investigation
Figure 2. Geometry with boundary conditions implemented in CFX.
lies on three-dimensional (3D) geometries with symmetry and wall boundaries. The 3D mesh with the symmetry boundaries at the sides uses a plate width of 0.02 m which helps to reduce the mesh size and with that the computing time. The second 3D geometry which is shown in Figure 2 resembles the experimental setup of a 0.06 0.05 m2 steel plate held by steel supports on the left and on the right hand side. As can be seen in Figure 2 (right) the grid is refined in direction to the plate as well as to the side walls. The inlet conditions are varied between a film inlet and jet inlets to consider the experimental feeding options of an overflowing weir and a feeding tube. A constant pressure is given at the outlets. The plates and the plate supports are implemented as no-slip walls with given contact angles, which lead to a formation of a liquid meniscus at each support. Above the supports, the contact angle is set to 1808 to avoid a too high meniscus. The top boundaries are set to free-slip walls. The physical properties of the liquids used in the simulations are shown in Table 1. As gas phase the physical properties of air are applied. RESULTS At first the results concerning two phase flow are presented. This is a necessary step before changing to threephase flow. It is important first to validate the different unsteady flow behaviors, which also occur with two liquids: film break-up, rivulet and droplet flow. The testing system here is water – air on an inclined steel plate. Water is chosen for its tendency to film break-up below critical loadings. For three phase flow toluene is introduced as the third phase. The air phase in both cases is considered just as a stationary phase without a velocity. The two-phase flow simulations are carried out with a film inlet condition of constant height and parabolic velocity profile and with inclination angles of 458 and 608.
Table 1. Physical properties of the liquids implemented in the simulations. Physical properties 23
Density r (kg m ) Kinematic viscosity n (m2 s21) Surface tension g (N m21) Static contact angle with air-steel u
Water
Toluene
Air
997 8.926 1027
867 6.817 1027
1.185 1.545 1025
0.0728 70–808
0.0285 88
— —
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MULTIPHASE FLOW BEHAVIOUR ON INCLINED PLATES Since the difference in the results between both inclinations is quite low, mainly the results of the 608 inclination are presented here. In the three-phase flow simulations a constant inclination angle of 458 is chosen in order to save computation time. Additionally, presented three-phase simulations use the jet inlet boundary condition for keeping comparability with the three-phase experiments. Two-Phase Flow First, numerical studies had been carried out with the two-dimensional geometry. It was found that with twodimensional simulations it is not possible to get reliable results concerning the critical Reynolds number ReC , which is defined as the lowest film Reynolds number Re ¼
u d V_ ¼ bn n
(1)
at which the liquid phase forms a stable film. In this case, the liquid film already breaks up at higher Re numbers. This is due to the fact that break-up phenomena and rivulet or droplet flow are highly three dimensional effects and therefore cannot be predicted by 2D-simulations. But even 3D-simulations result in too high ReC in comparison to experiments if the geometry is not taken into account. Here, the boundary conditions have a crucial effect. The usage of symmetry boundary conditions on the sides does not resemble the experimental setup. The introduction of wall boundaries on the sides and the geometrical realization of the experiments result in a better fit to the experiments. This is shown in Figure 3 where the specific wetted area a¼
Awetted Aplate
(2)
is plotted over Re for different simulations together with experimental data. While one curve shows the simulation results of the 3D simulation with a contact angle of u ¼ 808 and a lower plate width b of 0.02 m (compared to the geometry shown in Figure 2 with b ¼ 0.05 m) and symmetry boundaries on the left and right hand side, the
Figure 3. Specific wetted area plotted as a function of Re number. Comparison between measurements and different simulations: lower simulated width with symmetry-boundaries and a contact angle of u ¼ 808, adjusted to experimental set-up with contact angles of u ¼ 808 and 708.
149
other two curves use the 3D geometry of the experiments with different contact angles u. The contact angle of 808 is the one most given in literature for air and water on steel. This value is also applied in the simulations with reduced geometry. The value of 708 is derived from own measurements of contact angles on the plate used and has a deviation of +108. As can be seen in Figure 3, the critical Reynolds number, where the specific area falls below a ¼ 1, can be accurately predicted, given the correct contact angle and provided that similar geometries are considered. For this case, where the correct geometry (steel plate (polished) with b ¼ 50 mm), boundary conditions (film inlet with Re ¼ 168 (sim.) acc. to Re ¼ 162 (exp.) and walls as plate supports) and static contact angle (u ¼ 708) are applied, a qualitative comparison between experiment and simulation is shown in Figure 4. Both pictures show the same flow behaviour and its characteristics of break-up arches and entry length. Additionally, the same specific wetted area is measured in the experiment (a ¼ 0.53) and the simulation (a ¼ 0.55). Another validation parameter is the velocity. Due to the absence of accurate measurements, the simulated velocity profiles over the film thickness are compared to the well known Nusselt profile. The comparison of a closed film flow at Re ¼ 224 with slight wave formation at the surface shows nearly exact agreements of the parabolic profiles (Figure 5). Also the film thickness shows a very good agreement for this case (Hoffmann et al., 2005). In order to compare the results with the experiments, we have to restrict ourselves to the surface velocity. Figure 6 shows the surface velocity us of a droplet flow over the length of the plate x at Re 120 (112 in the simulations, 122 in the experiments). The measured surface velocity is shown in comparison to the simulated maximum as well as averaged surface velocities. The values are determined by dividing the plate into six horizontal regions, where the simulated values are obtained from an isosurface at water volume fraction of 0.36. In each region the local maximum velocity and the local area-averaged velocity of the isosurface are taken. The volume fraction value for defining the isosurface was determined by integrating the volume fraction and fitting the surface to match this result. The three curves in Figure 6 have the same trend, which shows significant locations on the plate: at x between 0.015 m and 0.02 m the initial rivulets break up and droplets are formed, after that the droplets accelerate to the end of the plate. The film inlet condition in the simulation is not able to maintain film flow after the first few cells so that rivulets are formed right at the beginning of the plate. This is close to the experiments where no film flow is formed under these conditions. As can be seen in Figure 6 the local maximum velocity agrees with the measured values accurately, while the averaged velocity leads to lower values. This observation can be explained with the different methods of velocity determination in the experiments and the simulations. In the experiments, the PTV method can only detect the higher velocities at the top region of the droplets or rivulets due to the surface curvature. On the other hand, the area-averaged values from the simulations represent the whole surface, which also includes the low-velocity zone near the plate. For this reason, the simulated velocities, which represent
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HOFFMANN et al.
Figure 4. Qualitative comparison between (a) simulation (Re ¼ 168), and (b) experiment (Re ¼ 162) of water on a 608 inclined polished steel plate.
the experiments best, shift from the maximum values for droplets to the area-averaged for film flow. Rivulets are best described by a weighted average depending on the droplet portion of the whole flow behaviour. A comparison of the velocity trend at different flow behaviours due to different flow rates is shown in Figure 7. Again the simulated surface velocity is plotted over the length of the plate x for three Re numbers. Re ¼ 224 represents a closed film flow with a high initial velocity and low acceleration. At Re ¼ 168 the film breaks up and a rivulet is formed at x of about 0.03 m that accelerates to the end of the plate. The third curve shows the surface velocity of a droplet flow at Re ¼ 112 that moves with a strong acceleration. For continuity reasons, all three curves represent the area-averaged velocities. For the interpretation of this plot, one should
keep in mind that the rivulet and droplet flow tend to higher surface velocities as shown above. Regarding the distillation process, the simulation results shown in Figure 7 lead to an important effect: in absence of a counter-current gas flow the gravitational acceleration of rivulets and droplets may result in higher velocities and with that in lower residence time inside the packing than with film flow. This is due to the fact that the film reaches a relatively low constant film thickness and film velocity while the rivulets and droplets are thicker and do not encounter as much friction as films. This effect might be reversed by introduction of a counter-current gas flow where the higher surface area (compared to the volume) of droplets and rivulets can lead to a stronger interaction between gas and liquid, which still has to be investigated. Three-Phase Flow When adding a second liquid which is immiscible with the first one (which occurs in various chemical engineering
Figure 5. Comparison of simulated velocity profile and theoretical Nusselt solution at Re ¼ 224.
Figure 6. Profile of the surface velocity along the length of the plate for a water droplet flow, Re 120.
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Figure 7. Simulated surface velocity profiles along the length of the plate for different water flow behaviours. Figure 9. Comparison of multiphase film flow between simulation (a) and experiment (b): water forms rivulets and droplets above and below the toluene film.
processes) the flow behaviour becomes much more complex. Here toluene is added to water. In this case we observe film flow of the organic phase (toluene) and rivulet and/or droplet flow of the aqueous phase (Figure 8). At low liquid loadings the order in which the liquids are delivered onto the plate also has an impact on the flow behaviour: while water forms rivulets and droplets, which flow on top of the toluene film when fed onto the toluene film [Figure 8(a)—further on defined as feed configuration number 1], it tends to forming rivulets flowing below the toluene film surface when fed above the toluene inlet [Figure 8(b)—feed configuration number 2]. At higher loadings of Re . 100 (especially the water load has a great impact) these two behaviours blend into each other for both feeding options. Figure 9 displays this case for both experiment and simulation. Water forms rivulets which are covered by the toluene film and droplets which are running on the toluene surface. Figure 9 shows the good agreement of the morphological comparison between simulation and experiment. A flow behaviour like this is not as depending on the liquid load as a single liquid flow. One of the two phases will likely form a stable film while the other phase will break-up even at loading high above the critical one. Nevertheless, the flow behaviour of a two-liquid flow is not just a superposition of the two single-liquid flows.
Figure 8. Morphological comparison between the different feed configurations: (a) water is fed onto the toluene phase and forms droplets on the toluene film; and (b) water is fed above the toluene phase and forms rivulets below the closed toluene film.
The two liquids interact strongly with each other. Both liquids are slower than in the single liquid case and the film is accelerated in the vicinity of the rivulets and droplets while these are decelerated by the film. That mutual interaction is shown in Figure 10 where a simulation result of water –toluene-flow is displayed with the surface velocity as a grey scale. Here a dark colour means high velocity and bright colour lower velocity. The black colour displays the interfacial contact line of the system water/toluene/air which appears where water phase cuts toluene film surface. Water flow below the toluene phase is indicated by high surface velocity of the toluene film. In order to reduce the number of necessary experiments for the validation, a factorial design (Montgomery et al., 1998) is chosen which varies the three parameters water load, toluene load and the order in which the two liquids are fed onto the plate, i.e., the feed configuration. The set points chosen here are given in Table 2. The liquid loadings lie within the measured region for the single liquid case. The experimental results of that factorial design on a 458 inclined plate are used to formulate empirical equations,
Figure 10. Simulated surface velocity of the multiphase flow. Water phase above the toluene phase is labelled by black surroundings.
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HOFFMANN et al. Table 2. Factorial design of three-phase experiments.
Factor
Values
Re-number toluene feed Feed configuration number Re-number water feed
A
70
164
B
1 ! Configuration 1
2 ! Configuration 2
C
72
148
which express the interaction between the liquids and enable the prediction of the surface velocity for a set of known parameters: uW ¼ (0:574 þ 0:023 XA 0:017 XB m þ 0:022 XB XC ) s uT ¼ (0:396 þ 0:035 XA 0:054 XB 0:035 XA XB þ 0:037 XB XC )
(3) m s
(4)
with the normalized parameters ReT 117 47 ReW 110 XB ¼ 38 NoFC 1:5 XC ¼ 1:5
XA ¼
(5a) (5b) (5c)
In the parameter definition equations (5a – c) ReT is the Re number of the toluene load, ReW represents the water Re number and NoFC is the number of feed configuration defined above. As can be seen in equations (3) and (4), linear dependences are assumed for the surface velocities for water and toluene from these parameters. This assumption is valid with good accuracy for the small investigated range
of Re numbers: ReT and ReW between 60 and 170. NoFC is a discrete value and can be chosen as 1 or 2. In order to validate the numerics, the one part of the factorial design which feds the water above the toluene (feed configuration 2) is simulated in CFX on a 458 inclined plate. Figure 11 shows a comparison of the numerical solution to the equations (3) and (4). In Figure 11(a) the surface velocities at a constant ReT of 160 are plotted as a function of RW . It can be seen that the water surface velocities remain on a constant level for different ReW , i.e., the influence of the water load on the water surface velocity is small. In comparison the toluene surface velocities show a significant decrease with increasing water load. These trends are found in the experimental results [equations (3) and (4)] as well as in the simulations. As expected, quantitative comparisons between the simulated and measured surface velocities show for the toluene phase that the measured values are well described by the area-averaged values from CFD simulations while the water surface velocities are better represented by an average which is shifted towards the maximum surface velocities. As shown above, this observation is also found in single-liquid flows. The weighted average in Figure 11 is taken from the equation uweighted ¼
2 2uavg þ umax 3
(6)
Figure 11(b) shows the water and toluene surface velocities as a function of ReT at a constant ReW of 70. Here the surface velocities computed with equations (3) and (4) increase with increasing ReT which is also found for the averaged surface velocities from the CFD simulations. The quantitative comparisons again lead to good agreements between the toluene surface velocity from equation (4) and the area averaged surface velocity from simulation. And also the water surface velocity from equation (3) is fitted best by the weighted average velocity from the simulations. In analogy to single liquid flows, that shift of the water surface velocity to higher values is expected since the
Figure 11. Comparison between simulated and measured multiphase surface velocity trends: (a) surface velocity trends for constant ReT ¼ 163.5, and (b) surface velocity trends for constant ReW ¼ 76.8.
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Figure 12. Comparison between the simulated and experimental surface velocities for (a) the water, and (b) the toluene phase.
surface area average is calculated for the whole surface of the water rivulet, where the area near the plate with its lower velocities weigh more in this rivulet flow than in film flow conditions. In comparison to this, the experimental data represent higher velocities of the water rivulet due to the measurement technique. That phenomenon is presented in Figure 12, too. In the chart (a), the measured water surface velocity is compared to the simulated surface velocities and in the chart (b), it is shown for toluene surface velocities. Ideally all the points of each chart should be found on the angle bisector. From Figure 12 it can be seen, that the best fit for measured water surface velocity is the weighted average surface velocity and the measured toluene surface velocities are best represented by the area averaged surface velocity.
CONCLUSIONS The complex flow behavior of homogeneous and heterogeneous liquids on inclined plates is investigated in detail. Industrial applications often do not show ideal performance of the occurring liquids. Complete wetting liquids are already investigated in literature. Unfortunately, in reality the liquids mostly are only partly wetting the plates. This leads to highly complex flow behaviours, which are analysed here with experiments as well as with numerical investigations. It is shown that the simulations meet the experiments very well. Intricate flow behaviours like film break-up, rivulet and droplet flow are represented by the calculations correctly. Two-phase flows of air and one liquid show the expected behaviour of film flow above a critical Reynolds number and rivulet and droplet formation below. The transition between these flow regimes is also predicted correctly. Validation by the data of surface velocities and shadow areas shows good quantitative agreement. Three-phase flow of gas and a film of two immiscible liquids is analysed here for the first time. It is shown that experiments and simulations compare well, too. Here one liquid phase (toluene) always forms film flow, while the other liquid (water) forms rivulets and droplets, which flow above and below the film surface. The two phases strongly interact with each other, which is verified by
experiments and simulations. When comparing the surface velocities it is necessary to keep the limitation of the measurement technique in mind, which leads to higher averaged velocities for rivulets and droplets than the calculation algorithm, which also accounts for low-velocity regions near the plate and below the film surface. By taking this into account, the validation with surface velocities shows good agreement for both phases in values and trends as well. The results show that for these complex flows reliable simulations have to be carried out in three dimensions. Here, also the geometry as well as the boundary conditions have an important impact on the accuracy. The strong dependency on the geometry leads to the necessity of implementing the packing geometry with highly resolving meshes. Therefore the calculation efforts increase strongly making it pointless to simulate complete packed columns with current available computational capacities. Practically, representative sections of the packing must be identified to reach a conclusion for the model. Next the model will be developed using these simulations, but also experiments and theoretical considerations. These detailed investigations are necessary for understanding the complex flow behaviour in many industrial applications, where these flows are occurring. The complete knowledge of the flow performance is essential for predicting the behaviour and developing a designing method in the future.
NOMENCLATURE a Aplate Awetted b d NoFC n Re Rec ReT ReW u u
specific wetted area, m2 m22 area of the full plate, m2 wetted area of the plate, m2 width of the plate, m film thickness, m number of feed configuration, parameter of factorial design kinematic viscosity, m2 s21 film Reynolds number critical Re number Re number of the toluene load Re number of the water load contact angle, degree average film velocity, m s21
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154 uavg uExp umax us uSim uT uW uweighted V_ x XA , XB , XC
HOFFMANN et al. area averaged surface velocity from the simulated isosurface, m s21 surface velocity from the experiments, m s21 maximum surface velocity from the simulated isosurface, m s21 surface velocity, m s21 surface velocity from the simulations, m s21 surface velocity of the toluene phase, m s21 surface velocity of the water phase, m s21 weighted average of the surface velocity, m s21 flow rate, m3 s21 length of the plate, m parameter of the factorial design
REFERENCES Adrian, R.J., 1991, Particle-imaging techniques for experimental fluid mechanics, Annu Rev Fluid Mech, 23: 261– 304. Ausner, I., Hoffmann, A., Repke, J.-U. and Wozny, G., 2004, Analyzing the surface velocity field of multiphase film flow, in Celata, G.P., Di Marco, P., Mariani, A. and Shah, R.K. (eds). Proceedings of 3rd International Symposium on Two-Phase Flow Modelling and Experimentation, 727– 733 (ETS Pisa, Italy). Billet, R. and Schultes, M., 1995, Fluid dynamics and mass transfer in the total capacity range of packed columns up to the flood point, Chem Eng Technol, 18: 371– 379. Brackbill, J.U., Kothe, D.B. and Zemach, C., 1992, A continuum method for modelling surface tension, J Comp Phys, 100: 335 –354. Brunazzi, E. and Paglianti, A., 1997, Liquid-film mass-transfer coefficient in a column equipped with structured packings, Ind Eng Chem Res, 36: 3792–3799.
Hirt, C.W. and Nichols, B.D., 1981, Volume of fluid (VOF) method for the dynamics of free boundaries, J Comp Phys, 39: 201–255. Hoffmann, A., Ausner, I., Repke, J.-U. and Wozny, G., 2005, Fluid dynamics in multiphase distillation processes in packed towers, Comp Chem Eng, 29: 1433–1437. Montgomery, D.C., Runger, G.C. and Hubele, N.F., 1998, Engineering Statistics (Wiley, New York, USA). Repke, J.-U. and Wozny, G., 2004, A short story of modelling and operation of three-phase distillation in packed columns, Ind Eng Chem Res, 24(43): 7850–7860. Repke, J.U. and Wozny, G., 2002, Experimental investigations of threephase distillation in a packed column, Chem Eng Technol, 25(2): 513–519. Rocha, J.A., Bravo, J.L. and Fair, J.R., 1993, Distillation columns containing structured packings: a comprehensive model for their performance. Part 1: hydraulic models, Ind Eng Chem Res, 32: 641–651. Villain, O., Faber, R., Li, P., Repke, J.-U. and Wozny, G., 2005, ThreePhase Distillation in Packed Towers: Short-Cut Modelling and Parameter Tuning, 29.5.– 1.6.2005 (ESCAPE 15, Barcelona, Spain).
ACKNOWLEDGEMENTS The authors gratefully appreciate the founding and support by the German Research Foundation (DFG) and the Research Center for Fluid Systems Technology, Technical University of Berlin. The manuscript was received 9 May 2005 and accepted for publication after revision 1 February 2006.
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