Hydrodynamics and Mass-Transfer Analysis of a Distillation Ripple

Article pubs.acs.org/IECR

Hydrodynamics and Mass-Transfer Analysis of a Distillation Ripple Tray by Computational Fluid Dynamics Simulation Bin Jiang,†,‡ Pengfei Liu,† Luhong Zhang,*,† Yongli Sun,†,‡ Huajin Wang,† Yuhua Liu,§ and Zhao Fang§ †

School of Chemical Engineering and Technology and ‡National Engineering Research Center for Distillation Technology, Tianjin University, Tianjin, People’s Republic of China § Peiyang National Distillation Technology Corporation Limited Company, Tianjin, People’s Republic of China S Supporting Information *

ABSTRACT: A 3D two-phase computational fluid dynamics model in the Eulerian−Eulerian framework was developed to predict the hydrodynamics, mass-transfer behaviors, and tray efficiency of dual-flow trays: ripple trays. Interaction between the two phases occurs via interphase momentum and mass transfer. Mass-transfer coefficients were estimated using the Higbie penetration theory model. The simulated results were compared with the experimental data obtained from distillation of cyclohexane and n-heptane at total reflux. The results show that vapor and liquid flow countercurrently through the tray holes and four main hydrodynamic regimes are distinguished at different vapor/liquid loadings (Fs factor). It was found that the mass transfer of the spray zone above the froth was also significant, especially at lower loadings. In addition, the results indicated that the efficiency of a ripple tray was a strong function of the open hole area and Fs factor.

1. INTRODUCTION Sieve trays have been widely employed in many chemical and petroleum separation processes, such as distillation, absorption, extraction, etc. Because of the distillation processes’ high-energyconsuming operations, the prediction and improvement of the mass-transfer efficiency have always attracted a considerable amount of attention and effort. Dual-flow trays are trays in which liquid and vapor flow countercurrently through the same holes. These trays possess greater capacity and lower pressure drop than trays with downcomers because the fluid can flow through the entire cross section of the column.1 Turbogrid and ripple trays are special forms of dual-flow trays, which are used for special services, especially when openings of a cross-flow tray might foul. Ripple trays are made from sheet metal that is perforated in the flat and then bent into sinusoidal waves, with their first appearance about 60 years ago.2 A number of standard types of ripple trays have been developed to provide flexibility in most of the design conditions encountered.3 In the early investigation, most attention was paid to understanding the hydrodynamics of the dual-flow trays.4−8 Very little has been done to model the mass-transfer efficiency of dual-flow trays. Hutchinson and Baddour3 evaluated the effect of varying loadings and reflux ratios on the efficiency with an ethanol−water system in an 18-in.-diameter copper column containing three copper ripple trays. Furzer and Duffy9 developed the theory of mass transfer on multiple sieve plates without downcomers by increasing the number of plates in the column. The visualization experiments measured severe segregation of the phases and poor vapor−liquid contact, which lowers the overall column efficiencies. Miyahara et al.10 investigated the gas−liquid interfacial area and liquid-phase mass-transfer coefficients in both the froth and transition regimes, which showed different relationships between the interfacial area and the free area of the plates. Xu et al.1 experimentally investigated the dual-flow-tray efficiency in a 300-mm-diameter © 2013 American Chemical Society

distillation column using methanol−water and methanol− isopropyl alcohol systems in 1994, which proved that dual-flow trays are more suitable for distillation operations where the physical properties of the mixture do not vary significantly with composition. However, the model they proposed was based on the assumption that essentially all of the interphase mass transfer occurs within the liquid-continuous froth immediately above the tray floor. Garcia and Fair11 proposed a rational method for the analysis and design of dual-flow-tray distillation columns based on a large number of performance data on larger-scale trays without downcomers. They divided the tray spacing into two zones: the liquid-continuous froth zone and the vapor-continuous spray zone. The model presumed that the majority of the mass transfer occurred in the froth zone and the spray zone was available for additional mass transfer. In the froth zone, the mass-transfer behavior was treated the same as that in a cross-flow froth, while an empirical correlation was employed to account for mass transfer in the spray zone. Domingues et al.12 proposed a new method inserted in the Aspen Plus 12.1 simulator to predict the overall efficiency of columns with valve and dual-flow trays. There have been many attempts to model mass-transfer efficiencies of sieve trays with downcomers using computational fluid dynamics (CFD) techniques. Wang et al.13 presented a 3D CFD model for describing the liquid-phase flow and concentration distribution on both a single tray and all trays of a distillation column with 10 sieve trays under total reflux. Sun et al.14 proposed a new turbulent model for solving the turbulent mass-transfer equation in order to predict the turbulent masstransfer diffusivity Dt. Rahimi et al.15 developed a 3D two-phase CFD model to predict the hydrodynamics and heat and mass Received: Revised: Accepted: Published: 17618

August 27, 2013 November 5, 2013 November 15, 2013 November 15, 2013 dx.doi.org/10.1021/ie402822w | Ind. Eng. Chem. Res. 2013, 52, 17618−17626

Industrial & Engineering Chemistry Research

Article

transfer of sieve trays. The simulation results show that CFD can be used as a powerful tool in tray design and analysis. Noriler et al.16 modeled a 3D, two-phase, and transient simulation with chemical species, energy, and momentum conservation balances. They obtained the volume fraction, velocity, temperature, and concentration profiles as a function of time and position on the distillation sieve tray. Rahimi et al.17 studied the effects of the holes and bubble diameters of two trays with similar geometry using a 3D two-phase CFD model in Eulerian−Eulerian framework. In addition, they found that using the SRS model reduces the sensitivity of the simulation results to the bubble diameters. In the present work, a CFD model is developed to give a prediction of the fluid-flow patterns, hydraulics, and masstransfer efficiency of ripple trays without downcomers. Also, the effects of the vapor/liquid load (Fs factor) and open hole area on the tray efficiency have been studied. Therefore, at first, a brief introduction about the experimental apparatus and method for measuring the pressure drop and concentration of samples is presented. Then the calculation method including the theoretical approach, governing equations, and closure equations is described. Next, a summary of the flow geometries and boundary conditions is given. Finally, comparisons between the simulation results and experimental data are drawn to verify the accuracy of the models and give a conclusion of this research.

Table 1. Ripple Tray Specifications characteristics

geometry 1

geometry 2

wavelength L (mm) wave depth H (mm) hole diameter d (mm) hole spacing t (mm) percentage of free area (%)

50.8 12.7 8 20 14.2

50.8 12.7 8 24 9.9

shown in Figure 2. All samples were analyzed using an Abbe refractometer operated isothermally at 35 °C, giving an accuracy

Figure 2. Gas and liquid sampler devices.

of ±0.0026 mole fraction. Two or three injections were made for each sample to decrease the experimental errors.

2. EXPERIMENT Experimental data were obtained in a 308-mm-diameter stainless steel distillation column with a cyclohexane/n-heptane system. The column contained four identical ripple trays spaced 300 mm apart, with the second one on top being the testing tray. All of the hot surfaces of the equipment are insulated with 50-mm-thick rubber material. Ripple trays shown in Figure 1 are composed of

3. MATHEMATICAL MODEL The model includes the flow and mass transfer of gas and liquid in the Eulerian−Eulerian framework in which each phase was treated as interpenetrating phases having separate transport equations. Both gas and liquid phases were treated as continuous phases, and the volume-averaged conservation equations were numerically solved for each phase. The model is based on the following assumptions:17 (1) The steady-state assumption is acceptable. (2) For the ideal mixture, the heats of mixing can be neglected. Therefore, the energy balance equations were not solved in the model. 3.1. Governing Equations. Continuity Equations. For the gas phase: ∂ (γ ρ ) + ∇·(γGρG UG) + SLG = 0 (1) ∂t G G For the liquid phase: ∂ (γ ρ ) + ∇·(γLρL UL) − SLG = 0 ∂t L L

Figure 1. Photographs of the ripple trays.

(2)

SLG is the rate of mass transfer from the liquid phase to the gas phase and vice versa. Mass transfer between phases must satisfy the local balance condition: SLG = −SGL. Momentum Conservation.

vertical rims bolted together in the shell, and the complete tray is clamped to a narrow support ring. Packing is used as a sealing material to avoid weeping. The adjacent trays were installed at 90° to each other from the direction of the waves. Each tray was equipped with thermocouples with an accuracy of 0.1 °C and a U-tube manometer to measure the pressure drop. Detailed dimensions of the trays are presented in Table 1. The column was run for 4−5 h to establish steady-state conditions at total reflux and ambient pressure. The boil-up rate being adjusted by the temperature of the conducting oil was measured by a rotameter placed in the reflux line. Gas samples were taken above and below this tray through a baffled conical sampler to remove entrained droplets.18 Liquid samples were taken from the bottom of the test tray through a half-pipe device. These sample devices are

For the gas phase: ∇·[γG(ρG UGUG)] = − γG∇PG + ∇·{γGμeff,G [∇UG + (∇UG)T ]} − MLG

(3)

For the liquid phase: ∇·[γL(ρL ULUL)] = −γL∇ρL + ∇·{γLμeff,L [∇UL + (∇UL)T ]} + MLG

(4)

MLG describes the interfacial forces acting on each phase because of the presence of the other phase. 17619

dx.doi.org/10.1021/ie402822w | Ind. Eng. Chem. Res. 2013, 52, 17618−17626


Article

Sct = νt/Dt was adopted for Dt, where Sct was equal to 0.9. The rate of interphase mass transfer was calculated by one of the following equations:28

Volume Conservation Equation. This is simply the constraint that the volume fractions sum to unity: γG + γL = 1

(5)

SLG = K OGaeMA (yA − yA *) = K OLaeMA (xA* − xA )

Pressure Constraint. Two phases share the same pressure field: PG = PL = P

where KOG = 1/(1/kG + m/kL), KOL = 1/(1/mkG + 1/kL), and yA* = mxA is the vapor composition in equilibrium with xA. Two theoretical models for mass transfer are commonly invoked: film theory and penetration theory. Film theory, first proposed by Nernst and Brunner29 and further developed by Lewis and Whitman,30 assumes that a stagnant film exists in the interface. The basic concept of film theory is that the resistance to diffusion can be considered equivalent to that in a stagnant film of a certain thickness. The implication is that the coefficient kL varies with the first power of DAL, which is rarely true, but this does not detract from the value of the theory in many applications. Film theory is often used as a basis for complex problems of multicomponent diffusion or diffusion plus chemical reaction. However, the fictitious nature of film theory may lead to erroneous results in many actual mechanisms of mass transfer. In particular, when fluid particles rise or fall in infinite media with turbulent motion, it appears unlikely that the surface layer on each particle keeps its identity throughout all times.31 Penetration theory was first proposed by Higbie32 and later modified by Danckwerts.33 It postulates fluid convection right up to the interface. At the interface, a small fluid volume element of one phase is momentarily in contact with the other phase for some exposure time, θL, after which the volume element is mixed back into the bulk fluid. The resulting expression for the masstransfer coefficient is

(6)

Mass-Transfer Equations. Transport equations for the mass fraction of light component A can be written as follows: For the gas phase: ∂ (γ ρ YA ) + ∇·{γG[ρG UGYA − ρG (DAG + Dt)(∇YA)]} − SLG = 0 ∂t G G

(7)

For the liquid phase: ∂ (γ ρ XA ) + ∇·{γL[ρL ULXA − ρL (DAL + Dt)(∇XA )]} + SLG = 0 ∂t L L

(8)

3.2. Closure Models. In order to solve eqs 1−8, additional equations are required for interphase transfer quantities, momentum, mass transfer, and turbulent viscosities. Turbulence viscosities were related to the mean-flow variables using the shear stress transport (SST) model19 for the liquid and gas phases, respectively. The interphase momentum exchange term MLG is mainly the interphase drag force per unit volume.20−22 The equation for MLG can be written as MLG =

3 CD γ ρ |UG − UL|(UG − UL) 4 dG G L

(9)

where CD is the dimensionless drag coefficient, which has different correlations to various dispersed multiphase flow.

kL = 2

DAL πθL

(14)

kG = 2

DAG πθG

(15)

For the Stokes regime: C D = 24/Re ,

Re ≪ 1

(10)

where Re = ρLUGdG/μL. For the inertial regime, also known as the turbulent regime, the drag coefficient becomes independent of the Reynolds number: C D = 0.44,

1000 ≤ Re ≤ (1−2) × 105

where DAL and DAG are diffusion coefficients in the liquid and gas phases. Also, θG and θL are the exposure times for liquid and gas in the froth region, respectively. θG is defined as θG = dG/VP, where VP is the velocity of vapor through tray perforations. θL = dG/VR, where the average rise velocity VR of bubbles through the froth is given by

(11)

In the transitional region between the viscous and inertial regimes, 0.1 < Re < 1000 for spherical particles, both viscous and inertial effects are important. Hence, the drag coefficient is a complex function of the Reynolds number, which must be determined from experiment. In our study, the Reynolds number of geometry 1 under different Fs factors ranges from 6.29 × 103 to 2.22 × 104 and the Reynolds number of geometry 2 under different Fs factors ranges from 3.55 × 103 to 1.87 × 104. Therefore, a drag coefficient CD of 0.44 was chosen as referenced by the CFX 13.0 tutorial,23 which has been successfully employed by Fischer and Quarini24 and Li et al.25 For the average gas-holdup fraction, the Bennett et al.26 correlation was used. ⎡ ⎛ ρG γG = 1 − exp⎢⎢ − 12.55⎜⎜US ρL − ρG ⎝ ⎣

⎞0.91⎤ ⎟ ⎥ ⎟ ⎥ ⎠ ⎦

(13)

( ) A

VP AP VS B = VR = 1 − γL 1 − γL

(16)

AP/AB is the perforated area to the bubbling area ratio. dG is assumed to be equal to the mean diameter of the bubbles; it was mentioned by Taylor and Krishna34 that 90% of mass transfer occurred by bubbles of large size, while only 10% of mass transfer was due to bubbles of small size. An alternate form of the penetration theory, known as the surface-renewal model, was developed by Danckwerts,33 who considered the case in which elements of fluid at a transfer surface are randomly replaced by fresh fluid from the bulk stream. An exponential distribution of ages or contact times results, and the mass-transfer coefficient is given by

(12)

The turbulent mass-transfer diffusivity Dt depends not only on the fluid dynamic properties (e.g., turbulence viscosity of the fluid) but also on the fluctuation of the concentration in turbulent flow.27 An empirical correlation Schmidt number

kL =

DAL s

(17)

where s is the fractional rate of surface renewal. 17620



Article

the “opening” boundary condition for gas outflow. At the bottom face of the column, there were gas inlet and liquid outlet boundaries. At the beginning of the simulation, the liquid outlet was filled up to a certain height of liquid lower than the height of the gas inlet pipe. The mass-flow and velocity-flow inlets were specified for the liquid and gas phases, respectively. At the liquid inlet, only liquid was assumed to enter the flow geometry and only gas was assumed to get into the gas inlet. Constant mass fraction values for entering the gas and liquid phases were used. The gas and liquid outlet specifications were in agreement with specifications in the inlet where only one phase was assumed to enter. The relative static pressure was specified at the outlet boundary. A no-slip wall boundary condition was specified for all walls in the flow field. Automatic near-wall treatment in CFX was employed as default in the SST model, which automatically switches from wall functions to a low-Re near wall formulation as the mesh is refined.36 At the symmetric plane, a symmetry boundary condition was set.

Jajuee et al.31 also proposed the surface-renewal-stretch (SRS) model responding to fluid−fluid interacting systems according to the penetration theory of mass transfer. Also, the SRS masstransfer model was first tested in CFD simulation of distillation by Rahimi et al.17 Although Higbie theory is a special case of what may be a more realistic picture of the processes occurring during absorption into an agitated fluid where, in fact, eddies are exposed for varying lengths of time, it has been widely used to simulate gas−liquid mass transfer in distillation columns.35,28,15,17 Considering the wide application of Higbie theory in the simulation of kinds of sieve-tray distillation columns, we tried to apply Higbie theory to ripple-tray simulation in this work.

4. FLOW GEOMETRIES AND BOUNDARY CONDITIONS The model geometries and boundaries are shown in Figure 3. Considering that the geometry and flow are symmetrical, only

5. RESULTS AND DISCUSSION The simulations were carried out with a commercial CFD package, CFX 13.0 (ANSYS Inc.). The model equations were solved numerically with the finite-volume method. A highresolution advection scheme was used for the hydrodynamics and mass-transfer equations and upwind for the turbulence equations. A physical time scale of 0.3 s and the default target root-mean-square residual value 1.0 × 10−4 that is sufficient for

Figure 3. Geometries of simulated tray and boundary conditions: (a) geometry 1; (b) geometry 2. Figure 4. Vapor-phase cyclohexane mole fraction at the outlet for the testing tray.

half of the ripple tray was computed so as to save computational time and physical time. The mesh preparation for the geometry was performed in ICEM CFD 13.0. The total numbers of unstructured tetrahedral cells up to 1158869 for geometry 1 and 1141333 for geometry 2 were set after thorough preliminary simulations until grid-independent solutions were yielded. Calculations were performed with four mesh sizes consisting of 5.76 × 105, 8.64 × 105, 1.14 × 106, and 1.54 × 106 cells to examine the effect on the solutions for geometry 2. Different mesh sizes were used in different positions of the computational domain. Finer meshes were used near the tray floor, which is the main region for gas−liquid contact than those away from the tray. The mesh size ranges from 2.8 × 10−11 to 2.4 × 10−6 m3 for geometry 1 and from 1.5 × 10−11 to 2.4 × 10−6 m3 for geometry 2. In this steady-state simulation, the following boundary conditions for each phase were specified at all inside and external boundaries of the simulated domain. At the top face of the column, equilateral triangle arranged holes were set for the liquid inlet boundary. The remaining region of the top face was set as

Figure 5. Clear liquid and froth heights at varying Fs. 17621



Article

Figure 6. Liquid-volume fraction contours for geometries 1 (a) and 2 (b).

actual value at lower Fs factor and underestimates the actual value at higher Fs factor. The mean absolute error of less than 5% was acceptable, and the model was validated satisfactorily. 5.2. Hydrodynamics. Hydrodynamics regimes of phase contact are mainly affected by the vapor/liquid load (Fs factor) and open hole area. The froth and clear liquid heights were considered to be the key hydraulic parameters, which had a direct effect on the mass-transfer efficiency. The simulated results of the two geometries were compared in Figure 5. It is shown that by an increase of the Fs factor, the froth height is increased for both geometries. On the other hand, it is found that the clear liquid height has a maximum value in the presence of variant Fs factors. Comparisons show that the clear liquid and froth heights for geometry 1 are both higher than those of geometry 2. Also, the corresponding Fs factor at the maximum value of the clear liquid height for geometry 1 is greater than that of geometry 2. These

engineering application were adopted. A double-precision solver was executed to improve convergence for interphase masstransfer cases. Runs were continued until quasi-steady-state was reached; in other words, a simulation was deemed to have converged whenever the clear liquid height value reached a value with no appreciable change in successive time steps.28 5.1. Validation of the Model. To validate the model, the vapor cyclohexane mole fraction at the outlet versus increasing Fs factor was computed and compared with the experimental data. Comparisons in Figure 4 have shown that there was a close agreement between the experimental and simulated data. It is obvious that the model using either of the geometries underestimates the experimental results at lower Fs factor and overestimates the experimental results at higher Fs factor. The reason is that the turbulent mass-transfer diffusivity Dt calculated by an empirical correlation Schmidt number Sct = νt/Dt overestimates the 17622



Article

The liquid-volume fraction contours on the XY plane at Z = 0, which represented the hydrodynamics of the gas−liquid dispersions and the transition zones between various regimes, are shown in Figure 6 for different Fs factors. Four main regimes are distinguished in the present study. A wetting regime exists at the beginning of the vapor/liquid contact at a lower Fs factor. There is a thin liquid holdup in the wave trough and a film liquid wetting the wave peak. As the Fs factor increases, a bubbling regime is formed and the clear liquid height increases gradually. It is characterized by a uniform bubbling through the tray holes and a sharp increasing forth height. Then, a froth regime occurs at high vapor and liquid load. It is characterized by a very turbulent froth in which circulation (up at the center and down near the walls) is set up and liquid weeps mainly near the walls.4 Finally, the vapor/liquid contact reaches a fluctuating regime with a higher Fs factor. In this regime, the froth height increases continually and liquid entrainment occurs. Given the vapor/ liquid contact area and the entrainment, lower froth height and higher forth height are not good for mass transfer. Bubbling (BC and B′C′ in Figure 5) and froth (CD and C′D′ in Figure 5) regimes are feasible operating regimes in industry application. Figure 7 showed the liquid velocity component values versus the diameter of the tray, X, at Y = 10 mm and Z = 0, for geometry 2. The horizontal velocity of the liquid on the ripple tray

Figure 7. Components of the liquid velocity across the tray at Y = 10 mm and Z = 0 (geometry 2).

phenomena can be attributed to the different open hole areas. It is believed that the larger the open hole area, the greater the capability but the lower the efficiency. These are observable vividly in Figure 6a,b.

Figure 8. Vapor-phase cyclohexane mole fraction on the XY plane at Z = 0 for geometries 1 (a) and 2 (b). 17623



Article

of Figure 8 shows that, to obtain the same result of mass transfer, geometry 1, which has a larger open hole area, should be operated at a higher Fs factor than geometry 2 with a lower open hole area. This also illustrated the previous studies that the larger the open hole area, the greater the capability but the lower the efficiency. These may be ascribed to the froth height and vapor/ liquid interfacial area. Figure 9 illustrates the vapor/liquid interfacial area density on the horizontal plane XZ at varying Fs factors for geometry 2. The Y = 0 plane divided the tray space into a spray zone (Y < 0) and a froth zone (Y > 0). At lower Fs factors, the interfacial area in the spray zone almost equals that in the froth zone. Therefore, the contribution of mass transfer in the spray zone should not be neglected at lower Fs factors. With the increased Fs factor, the interfacial area in the froth zone markedly increased and the mass transfer in the spray zone was negligible compared with that in the froth zone. This fact was observed in the Garcia and Fair11 study, in which they pointed out that the predicted value, which did not consider the contribution of the spray zone, was evidently lower than the observed value and proposed a low load discount factor Ψ′ calculated from the experimental data to improve the model precision at lower loadings. This was also observable in Figure 10, which illustrated contours of the vapor/liquid interfacial area density on the horizontal plane XZ at Fs = 0.807 (m/s)(kg/m3)0.5 for geometry 2. Figure 9 also explained the effect of the Fs factor on the mass-transfer efficiency. At both low and high Fs factors, the vapor/ liquid interfacial area density remained lower, which contributes little to mass transfer between the two phases. The extreme point in Figure 9 just appeared near the plane of the clear liquid height. 5.4. Tray Efficiency. The Murphree tray efficiency, defined by comparing an ideal tray with a real tray, is the most applied definition of the tray efficiency. The Murphree tray efficiencies for the testing tray were calculated from the definition y − yn + 1 EnMV = n yn * − yn + 1 (18)

Figure 9. Vapor/liquid interfacial area density on the horizontal plane XZ for geometry 2.

approximately equaled zero, and almost all of the liquid flowed down through tray holes at a lower Fs factor. With increasing Fs factor, the upward velocity of the liquid increased, especially in holes near the wave peaks. Also, the liquid on the tray occurred in random flow at a horizontal direction, especially in froth and fluctuating regimes. This is different from the trays with downcomers, on which the cross-flow of liquid occurs. 5.3. Mass Transfer. Given that vapor and liquid flow countercurrently through the same open holes, the radial concentration gradient in both the liquid and vapor phases can be neglected if no serious channeling of fluids occurs on the tray. In Figure 8, the cyclohexane mole fraction in the vapor phase on the XY plane at Z = 0 for different Fs factors can be observed. The composition profiles can be noted through a comparison with Figure 4. When the liquid flows downward through the tray and contacts with the vapor upward through tray holes, cyclohexane in the liquid phase is absorbed by the gas phase and n-heptane is desorbed into the liquid phase. With fluid flow through the ripple tray, the concentration of cyclohexane in the vapor phase increases, and therefore the concentration of cyclohexane in the liquid phase decreases. The red regions in Figure8, similar to the liquid-phase regions discussed in Figure 6, represent the main mass-transfer regions. Although the vapor volume fraction is almost zero, the larger vapor/liquid interfacial area and longer contact time contribute to a higher concentration of the vapor cyclohexane region. Parts a and b of Figure 8 both show that, at low and high Fs factors, the concentration gradient in the vapor phase was lower, so the flux of mass transfer between two phases was fewer. At an appropriate vapor/liquid load, the efficiency of mass transfer between two phases is kept higher. A comparison of parts a and b

where yn * = mnxn

(19)

The tray efficiencies of simulated results and experimental data are compared in Figure 11. Obviously, the tray efficiency (EMV) increases with increasing Fs factor for ripple trays. The masstransfer coefficient and vapor/liquid interfacial area are believed to cause this phenomenon. As the Fs factor increases, the masstransfer coefficients may increase because of a higher turbulence of fluids. Also, the froth height and therefore the vapor/liquid interfacial area increase. This is one characteristic of dual-flow

Figure 10. Contours of the liquid and vapor interfacial area density on the horizontal plane XZ at Fs = 0.807 (m/s)(kg/m3)0.5 for geometry 2. 17624



Article

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was supported financially by the Program for Chang Jiang Scholars and Innovative Research Terms in Universities (Grant IRT0936).

■

NOMENCLATURE AB ray bubbling area, m2 AP open hole area, m2 ae effective interfacial area per unit volume, m−1 CD drag coefficient d hole diameter of the ripple tray, m dG mean bubble diameter, m DAG vapor molecular diffusivity, m2/s DAL liquid molecular diffusivity, m2/s Dt turbulent mass-transfer diffusivity, m2/s MV E Murphree tray efficiency Fs F factor = VS(ρG)1/2, (m/s)(kg/m3)0.5 g gravity acceleration, m/s2 H wave height of the ripple tray, m HF froth height, m HL clear liquid height, m kG gas-phase mass-transfer coefficient, m/s kL liquid-phase mass-transfer coefficient, m/s KOG gas-phase overall mass-transfer coefficient, m/s KOL liquid-phase overall mass-transfer coefficient, m/s MA molecular weight of component A, g/mol MLG interphase momentum transfer, kg/m2·s2 P total pressure, N/m2 PG gas-phase pressure, N/m2 PL liquid-phase pressure, N/m2 Re Reynolds number s fractional rate of surface renewal SLG rate of interphase mass transfer, kg/m3·s t hole spacing of the ripple tray, m u velocity in the x direction, m/s UG gas-phase velocity vector, m/s UL liquid-phase velocity vector, m/s v velocity in the y direction, m/s VS gas-phase superficial velocity based on the bubbling area, m/s Vt velocity vector, m/s VP vapor velocity through the tray holes, m/s VR bubble rise velocity, m/s w velocity in the z direction, m/s X, Y, Z coordinates, distance from origin, m XA mass fraction of A in the liquid phase YA mass fraction of A in the gas phase xA mole fraction of A in the liquid phase yA mole fraction of A in the gas phase yA * equilibrium mole fraction

Figure 11. Effect of Fs on the tray efficiency for geometries 1 and 2.

trays that is different from trays with downcomers.1 Figure 11 also shows that ripple trays with lower open hole area are more efficient than ripple trays with greater open hole area at the same Fs factor.

6. CONCLUSIONS In the present study, a 3D multiphase CFD model was developed in the Eulerian−Eulerian framework to predict the hydrodynamics, mass-transfer behavior, and tray efficiency of ripple trays. Two types of ripple trays with different open hole areas were simulated. The experimental data were obtained in a 308-mm-diameter column with cyclohexane and n-heptane at total reflux. The effects of the open hole area and Fs factor on the hydrodynamics and mass-transfer behavior were investigated. The CFD predictions, in good agreement with the experimental data, exhibited some known features of the two-phase flow field and mass-transfer behavior on trays. As dual-flow trays, the vapor and liquid phases contacted countercurrently through the ripple tray and interphase momentum and mass transfer occurred. The simulated results showed four distinguished hydrodynamic regimes based on the clear liquid and froth heights at different vapor/liquid loads (Fs factor). It has been concluded that the efficiency of the ripple tray is markedly affected by vapor/liquid loadings (Fs factor) and tray open hole areas. The froth height will affect the vapor/liquid contact time; therefore, the mass-transfer efficiency differs. The calculated results have proven the fact that ripple trays with larger open hole area have greater capability with lower efficiency. The study showed that mass transfer in the spray zone, where all of the downflow liquid comes into contact with the rising vapor, made a significant contribution to the tray efficiency. The additional mass transfer in the spray zone must be considered, especially at lower Fs factors. In addition, it has been obtained that the ripple tray efficiency increases with increasing Fs factor, unlike the tray with downcomers.

■

ASSOCIATED CONTENT

Greek Letters

S Supporting Information *

θG θL ρG ρL γG γL γL νt

Dimensions of the ripple tray and the mesh layout on the tray and holes surfaces. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel/Fax: +86 22 27400199. 17625

gas contact time, s liquid contact time, s gas-phase density, kg/m3 liquid-phase density, kg/m3 gas-phase volume fraction liquid-phase volume fraction average liquid holdup fraction in froth turbulent viscosity, m2/s dx.doi.org/10.1021/ie402822w | Ind. Eng. Chem. Res. 2013, 52, 17618−17626


Article

μeff,G effective viscosity of gas, kg/m·s μeff,L effective viscosity of liquid, kg/m·s

(22) Krishna, R.; Van Baten, J. M. Modelling Sieve Tray Hydraulics Using Computational Fluid Dynamics. Chem. Eng. Res. Des. 2003, 81, 27−38. (23) ANSYS CFX release 13.0, ANSYS CFX-Solver Manager User’s Guide; ANSYS Inc.: Canonsburg, PA, 2010. (24) Fischer, C. H.; Quarini, G. L. Three-dimensional heterogeneous modelling of distillation tray hydraulics. In AIChE annual meeting, Miami Beach, FL, 1998. (25) Li, X.; Zhang, H.; Gao, X.; Zhang, R.; Li, H. Hydrodynamic Simulations of Seepage Catalytic Packing Internal for Catalytic Distillation Column. Ind. Eng. Chem. Res. 2012, 51, 14236−14246. (26) Bennett, D. L.; Agrawal, R.; Cook, P. J. New Pressure Drop Correlation for Sieve Tray Distillation Columns. AIChE J. 1983, 29, 434−442. (27) Sun, Z. M.; Yu, K. T.; Yuan, X. G.; Liu, C. J. A modified model of computational mass transfer for distillation column. Chem. Eng. Sci. 2007, 62, 1839−1850. (28) Rahimi, M.-R.; Rahimi, R.; Shahraki, F.; Zivdar, M. Prediction of Temperature and Concentration Distributions of Distillation Sieve Trays by CFD. Tamkang J. Sci. Eng. 2006, 9, 265−278. (29) Nernst, W. Z.; Brunner, E. Z. Theorie der Reaktionsgeschwindigkeit in heterogenen Systemen. Z. Phys. Chem. 1904, 47, 52−55. (30) Lewis, W. K.; Whitman, W. G. Principles of Gas Absorption. Ind. Eng. Chem. 1924, 16, 1215−1220. (31) Jajuee, B.; Margaritis, A.; Karamanev, D.; Bergougnou, M. A. Application of surface-renewal-stretch model for interface mass transfer. Chem. Eng. Sci. 2006, 61, 3917−3929. (32) Higbie, R. The rate of absorption of a pure gas into a still liquid during short periods of exposure. Trans. AIChE 1935, 31, 365−389. (33) Dankwerts, P. V. Significance of liquid-film coefficients in gas absorption. Ind. Eng. Chem. Res. 1951, 43, 1460−1467. (34) Taylor, R.; Krishna, R. Multicomponent mass transfer; John Wiley and Sons, Inc.: New York; 1993. (35) Dribika, M. M.; Biddulph., M. W. Scaling-up distillation efficiency. AIChE J. 1986, 32, 1864−1875. (36) ANSYS CFX release 13.0, ANSYS CFX-Solver Modeling Guide; ANSYS Inc.: Canonsburg, PA, 2010.

Subscripts

A eff G L t

■

component A effective property gas phase liquid phase turbulent property

REFERENCES

(1) Xu, Z. P.; Afacan, A.; Chuang, K. T. Efficiency of dualflow trays in distillation. Can. J. Chem. Eng. 1994, 72, 607−613. (2) Hutchinson, M. H. Fractionating Tray. U.S. Patent 2,767,967, 1956 (3) Hutchinson, M.; Baddour, R. Ripple trays:a new tool for vaporliquid contacting. Chem. Eng. Prog. 1956, 52, 503−508. (4) Shoukry, E.; Cermak, J.; Kolar, V. On the hydrodynamics of sieve plates without downcomers. I. Dynamics nature of the gas liquid dispersions. Chem. Eng. J. 1974, 8, 27−40. (5) Shoukry, E.; Kolar, V. On the hydrodynamics of sieve plates without downcomers. II. A model of plate operation and the phenomenon of multiplicity of steady state. Chem. Eng. J. 1974, 8, 41−51. (6) Takahashi, T.; Miyahara, T.; Tano, T.; Akagi, Y. Hydrodynamic characteristics of sieve trays having large free areas without downcomers. J. Chem. Eng. Jpn. 1986, 19, 339−341. (7) Furzer, I. A. Froth Heights on Dualflow Trays with a Ternary Azeotropic System of Ethyl Acetate−Ethanol−Water. Ind. Eng. Chem. Res. 2000, 39, 1430−1436. (8) Billet, R. Separation tray without downcomers. Chem. Eng. Technol. 2001, 24, 1103−1112. (9) Furzer, I. A.; Duffy, G. J. Mass transfer on sieve plates without downcomers. Chem. Eng. J. 1977, 14, 217−224. (10) Miyahara, T.; Kurihara, M.; Asoda, M.; Takahashi, T. Gas−Liquid Interfacial Area and Liquid-Phase Mass Transfer Coefficient in Sieve Plate Columns without Downcomer Operating at High Gas Velocities. J. Chem. Eng. Jpn. 1990, 23, 280−285. (11) Garcia, J. A.; Fair, J. R. Distillation sieve trays without downcomers:prediction of performance characteristics. Ind. Eng. Chem. Res. 2002, 41, 1632−1640. (12) Domingues, T. L.; Secchi, A. R.; Mendes, T. F. Overall efficiency evaluation of commercial distillation columns with valve and dualflow trays. AIChE J. 2010, 56, 2323−2330. (13) Wang, X. L.; Liu, C. J.; Yuan, X. G.; Yu, K. T. Computational fluid dynamics simulation of three-dimensional liquid flow and mass transfer on distillation column. Ind. Eng. Chem. Res. 2004, 43, 2556−2567. (14) Sun, Z. M.; Liu, B. T.; Yuan, X. G.; Liu, C. J.; Yu, K. T. New turbulent model for computational mass transfer and its application to a commercial-scale distillation column. Ind. Eng. Chem. Res. 2005, 44, 4427−4434. (15) Rahimi, R.; Rahimi, M. R.; Zivdar, M. Efficiencies of Sieve Tray Distillation Columns by CFD Simulation. Chem. Eng. Technol. 2006, 29, 326−335. (16) Noriler, D.; Barros, A. A. C.; Maciel, M. R. W.; Meier, H. F. Simultaneous Momentum, Mass, and Energy Transfer Analysis of a Distillation Sieve Tray Using CFD Techniques: Prediction of Efficiencies. Ind. Eng. Chem. Res. 2010, 49, 6599−6611. (17) Rahimi, R.; Mazarei Sotoodeh, M.; Bahramifar, E. The effect of tray geometry on the sieve tray efficiency. Chem. Eng. Sci. 2012, 76, 90− 98. (18) Scheffe, R. D.; Weiland, R. H. Mass-transfer characteristics of valve trays. Ind. Eng. Chem. Res. 1987, 26, 228−236. (19) ANSYS CFX release 13.0, ANSYS CFX-Solver Theory Guide; ANSYS Inc.: Canonsburg, PA, 2010. (20) Krishna, R.; Baten, J. M. V.; Ellenberger, J.; Higler, A. P.; Taylor, R. CFD Simulations of Sieve Tray Hydrodynamics. Trans. Inst. Chem. Eng. 1999, 77, 639−646. (21) Baten, J. M. v.; Krishna, R. Modelling sieve tray hydraulics using computational fluid dynamics. Chem. Eng. J. 2000, 77, 143−151. 17626


Hydrodynamics and Mass-Transfer Analysis of a Distillation Ripple

Recommend Documents