Prediction of Temperature and Concentration Distributions of Distillation Sieve Trays by CFD

Tamkang Journal of Science and Engineering, Vol. 9, No 3, pp. 265278 (2006) 265 Prediction of Temperature and Concentration Distributions of Distillation Sieve Trays by CFD Mahmood-Reza Rahimi*, Rahbar Rahimi, Farhad Shahraki and Morteza Zivdar Department of Chemical Engineering, Sistan and Baluchistan University Zahedan 98164, Iran Abstract A three-dimensional two-fluid computational fluid dynamics (CFD) model is developed to predict concentration and temperature distributions on sieve trays of distillation columns and good simulation results are obtained. The dispersed gas phase and continuous liquid phase are modeled in the Eulerian framework as two interpenetrating phases with interphase momentum, heat and mass transfer. Closure models are developed for interphase transfer terms. The tray geometries and operating conditions are based on the experimental works of Dribika and Biddulph (AIChE. J., 32, 1864, 1986) and Yanagi and Sakata (Ind. Eng. Chem. Process. Des. Dev., 21, 712, 1982). The computational domain is considered to be equal to tray spacing. The main objective of this study has been to find the extent to which CFD can be used as a prediction tool for real behavior, and concentration and temperature distributions of sieve trays. The simulation results are shown that CFD is a powerful tool in tray design, analysis and trouble shooting, and can be considered as a new approach for efficiency calculations. Key Words: Computational Fluid Dynamics, Concentration Distribution, Temperature Distribution, Distillation, Sieve Tray 1. Introduction *Corresponding author. E-mail: mahmoodreza_rahimi@yahoo.com Distillation is a separation process of major importance in the chemical industries, and known as the energy-intensive process. Distillation is the first choice for separation of liquid mixtures, the separation occur as a result of differences in the volatilities of the constituent components in the mixture being separated. Therefore, distillation involves simultaneous mass and heat transfer between the liquid and vapor phases. Sieve trays as the contacting device are widely used in distillation columns for their simplicity and low construction cost. Tray design heavily relies on experience because little is known about the flow behavior and heat- and mass-transfer on the tray. The main reason for this is the poor understanding of the complex behaviors of the multiphase flow inside the tray. A good understanding of heat- and masstransfer and pressure drop fundamentals will enable the column designer effectively determine the optimal equipment design. Current practice of tray design and analysis, demonstrate that there are two major unresolved problems in analysis of tray hydrodynamics and performance. The first one is what flow patterns to expect for given geometry and operating conditions. The second problem is how to relate these flow patterns to tray performance parameters such as tray efficiency and pressure drop. The works of Rahimi et al. [1], and Gesit et al. [2], were efforts to answer the first problem. In this work concentration and temperature distributions of trays has been studied. The Murphree point and tray efficiencies can be obtained by these informations. There have been few attempts to model tray hydrodynamics using CFD simulation [18]. A single-phase model of Mehta et al. [3], can only predict the liquid flow behavior. Fischer and Quarini [4], presented a 3-D tran-

266 Mahmood-Reza Rahimi et al. sient model for vapor-liquid hydrodynamics; they assumed a constant value of 0.44 for drag coefficient. Yu et al. [5], model is two-dimensional and divides flow into two regions. In the region near the tray deck, flow is three dimensional; it becomes two dimensional on region near to the free surface. Liu et al. [6], used a two-dimensional model for simulating the liquid flow pattern. The variation of gas flow direction along the dispersion height was ignored. Krishna et al. [7], and Van Baten and Krishna [8] have used a three dimensional two-phase CFD model for a 0.3 m sieve tray. Gesit, et al. [2], were developed a 3-D CFD model to predict the flow patterns and hydraulics of commercial-scale sieve trays. All of the previous CFD simulations of sieve trays concerned the hydraulic behavior of trays, and temperature and concentration distributions of both liquid and vapor phases not included in them. Concentration (and temperature) distributions are characteristics of tray performance, and determine the point and tray efficiencies and energy efficiency. This information (velocity, concentration and temperature distributions and hydraulic parameters) are essential for complete simulation of all tray behaviors, and determination of all required information. Wang et al. [9], used a 3-D pseudo-single-phase CFD model for liquid-phase velocity and concentration distribution on a distillation column tray. The column (overall) efficiency of a 10-trayed column was estimated. Their model does not predict point efficiency and vaporphase concentration distribution, and used constant value of vapor (and liquid) volume fractions. Rahimi et al. [10] were studied the hydrodynamics and mass transfer efficiency of sieve trays, by means of a 3-D two fluid CFD simulation. In this work a CFD simulation is developed to give the predictions of the fluid flow patterns, and heat and mass transfer of distillation sieve trays. The main objective has been to find the extent to which CFD can be used as a design and prediction tool for real behavior, concentration and temperature distributions, and efficiencies of industrial trays. Therefore, at first, CFD predictions of temperature and concentration profiles were compared with the experimental data of Dribika and Biddulph [11], and then the model used to predict concentration distribution of commercial scale tray of FRI [12]. The simulation results were in good agreement with experimental data. The simulation results are shown that CFD can be used as a powerful tool in tray design and analysis, and can be considered as a new approach for efficiency calculations. 2. Model Equations The dispersed gas and the continuous liquid phases are modeled in the Eulerian frame work as two interpenetrating phases having separate transport equations. The basic derivation of the multiphase flow transport equations has been reported elsewhere [13,14] and therefore will not be described further in this article. The two-fluid conservation equations for adiabatic two-phase flow are as follows: Continuity equations Gas phase: t V r. r S 0 G G G G G LG Liquid phase: t r. r S 0 L L L LV L LG (1) (2) S LG is the rate of mass transfer from liquid phase to the Gas phase and vice versa. Mass transfer between phases must satisfy the local balance condition: S LG S GL Momentum conservation Gas phase: r V.(r ( V V )) r P t T.(r ( V ( V ) )) r g M G G G G G G G G G G eff,g G G G G GL Liquid phase: r LLVL.(r L( LVL VL)) rlpl t T.(r ( V ( V ) )) r g M L eff,l L L L L GL (3) (4) (5) M GL describes the interfacial forces acting on each phase due to the presence of other phase.

Prediction of Temperature and Concentration Distributions of Distillation Sieve Trays by CFD 267 Volume conservation equation This is simply the constraint that the volume fractions sum to unity: r r 1 L G (6) Pressure constraint The complete set of hydrodynamic equations represent 9 (4N P +1) equations in the 10 (5N P ) unknowns U L, V L,W L,r L,P L,U G, V G,W G,r G,P G. We need one (N P 1) more equation to close the system. This is given by constraint on the pressure, namely that two phases share the same pressure field: P L =P G =P Energy conservation Gas phase: (rggh G) (rggvgh G) q ( Q LG SLGh LG) t Liquid phase: (7) (rllh L) (rllvlh L) q ( Q LG SLGh LG) t (8) h L and h G are specific enthalpies of phase L and G, respectively. The first term in the parentheses on the right hand side of above equations is the energy transfer between phases, and the second term is the energy transfer associated with the mass transfer between phases. Heat transfer between phases must satisfy the local balance condition: Q LG = Q GL (9) Mass-Transfer equations Transport equations for mass fraction of light component A can be written Gas phase: (rggy A) [r G( GVGYA GD AG( Y A))] SLG 0 t (10) Liquid phase: (rllx A) [r L( LVLX A LD AL( X A))] SLG 0 t (11) Closure Models The closure models are required for interphase transfer quantities, momentum, heat and mass transfer, and turbulent viscosities. The turbulence viscosities were related to the mean flow variables by using the standard k model. The k model is well treated in literature [13,14]. The rate of energy transfer between phases can be written: Q a (T T ) LG LG e L G (12) LG represents heat transfer coefficient between phases. An appropriate value of heat transfer coefficient can be obtained by using suitable correlations of Nusselt number [15]. In the absence of sufficient reliable data, the effect of other transport phenomena on the momentum transfer (coupling) was neglected. The interphase momentum transfer term M GL is basically interphase drag force per unit volume. With the gas as the disperse phase, the equation for M GL is 3 C M r V V ( V V ) D GL G L G L G L 4dG (13) C D is drag coefficient. Its value for the case of distillation is not well known. However, Fisher and Quarini [4] assumed a constant value of 0.44. This value is appropriate for large bubbles of spherical cap shape. However, for the froth flow regime, which is dominant region in distillation, it is not applicable. Further, the bubbles are from 1020 mm in diameter with bubble rise velocity of 1.5 m/s, to 25 mm in diameter, with rise velocity of about 0.25 m/s [16]. Therefore any equation for C D that is independent of bubble diameter seems most appropriate. Krishna et al. [7], have used an equation for drag term that is developed from their studies on the bubble column. The drag coefficient, C D, has been estimated using

268 Mahmood-Reza Rahimi et al. the drag correlation of Krishna et al. [17], a relation proposed for the rise of a swarm of large bubbles in the churn-turbulent regime C D 4 L G 1 gdg 3 V L 2 slip (14) Where the slip velocity, V slip = V G V L, is estimated from the gas superficial velocity, V s, and the average gas holdup fraction in the froth region V slip Vs r G (15) For the average gas holdup fraction, Bennett et al. [18] correlation was considered. 0.91 G rg 1exp 12.55Vs L G (16) From eqs. 13 to 15 the interphase momentum transfer term as a function of local variables becomes: 2 rg M g r r V V ( V V ) GL 2 L G G L G L G L 1.0 rg Vs (17) This relation is independent of bubble diameter, and is suitable for CFD use. A vast amount of data of mass transfer coefficient is not available in the case of sieve tray; however, the available data are average values and therefore are not suitable for rigorous CFD studies of mass transfer on sieve trays of distillation columns. The mass-transfer rate can be calculated by one of the following two equations S k a M (x x ) I LG L e A A A S k a M (y y ) I LG G e A A A (18) (19) I I The interfacial concentrations x A and y A are in equilibrium y I A mx I A (20) The value of m was determined by the equilibrium data of Dribika and Biddulph [11]. Combining eqs. 18, 19 and 20 results in deleting the interface concentrations x A I, y A I : S K am (y y ) K am (x x ) * * LG OG e A A A OL e A A A (21) Where K OG = 1/(1/k G + m/k L ), K OL = 1(1/mk G + 1/k L ) * and ya mxa is the vapor composition in equilibrium with x A. The local mass-transfer rate S LG is calculated by above equation. Using Higbie [19] penetration theory is a fundamental approach to mass transfer mechanism in distillation [11,18,20]. Therefore the liquid and gas mass transfer coefficient is given by Eqs.22 and 23, respectively. k L D 2 D AL L AG kg 2 G (22) (23) D AL and D AG are diffusion coefficients in liquid and gas phases, respectively. The contact time for vapor in the d G froth region G is defined as G, where V P is velocity of vapor through the tray perforations. The con- VP tact time for liquid, L,is d, where average rise veloc- VG ity, V R, of bubbles through the froth is given by: V R A P VP V B A B (1 ) (1 ) L R (24) A P /A B is perforated area to total bubbling area ratio, and V B is vapor velocity over the bubbling area. Physical properties, diffusion coefficients of gas and liquid phases and slope of equilibrium line are given as function of concentration for two binary systems [11]. Taylor and Krishna [16] mentioned that only 10% of mass transfer occurs by bubbles of small size, whilst 90% of mass transfer is due to bubbles of large size. Hence, in one approach the characteristic length, d G, may be assumed to be equal to mean diameter of bubbles. The ef- L

Prediction of Temperature and Concentration Distributions of Distillation Sieve Trays by CFD 269 fective vapor-liquid interfacial area can be determined directly from the liquid holdup and the mean bubble diameter by the following equation: a e 6(1- L ) d G (25) It is known that closure models have important effects on the accuracy of final results of a CFD simulation [14]. Therefore, their determination is the most important part in each CFD simulation. But, unfortunately in the case of sieve tray, these models are not presented or no tested for CFD applications. Therefore further improvement and refinement of the required closure models, if more refined experimental data on flow and concentration distributions become available, can be subject of future investigations. 3. Flow Geometries The main aims of this work are at first the studying of hydrodynamics and mass and heat transfer of sieve trays, and then using this data to obtain point and tray efficiencies. Unfortunately, the coexisting experimental data on hydraulics, concentration and temperature distributions, and efficiencies are very rare. The work of Dribika and Biddulph is unique in this way, because this work contains all required data needed in this work. Dribika and Biddulph [11] were reported hydraulics parameters (clear liquid height and froth height), concentration and temperature distributions, and Murphree point and tray efficiencies as function of concentration for two binary systems (EtOH/nPrOH and MeOH/nPrOH) in a rectangular tray column. The composition and temperature profiles across the tray were measured and used to infer the values of point efficiencies. The flow regime on Dribika and Biddulph [11] experiments is nearly plug flow. In this work at first the proposed simulation was used for determination of hydraulic parameters, concentration and temperature profiles of Dribika and Biddulph [11] large rectangular sieve tray. The simulation results were in good agreement to experimental data of Dribika and Biddulph [11]. Fluid flow on commercial-scale columns may contain non-uniformities, which cause deviations from plug flow regime. The ability of this simulation was tested by simulation of FRI commercial-scale trays, used by Yanagi and Sakata [12]. Thus this model was developed to ascertain the influence of the flow non-uniformities (recirculation, back mixing, pooling zones, dead zones and etc) on hydraulics and performance of sieve trays. The experimental rig of Dribika and Biddulph [11] consists of three rectangular distillation trays having dimensions of 1067 89 mm, which the middle one being the test-tray. The test-tray was designed with six equally spaced points for sampling and temperature measurement along the centerline where mentioned by points S in Figure 1, details of the tray are given in Table 1. The col- Figure 1. Detail of rectangular tray showing sample/temperature points. Table 1. Tray specifications a) Rectangular tray b) Circular tray Weir length 83 mm Diameter 1.2 Liquid flow path 991 mm Downcomer area, m 2 0.14 Tray spacing 154 mm Hole area, m 2 0.118 Hole diameter 1.8 mm Hole diameter and spacing, mm mm 12.7 30.2 Percentage free area 8% Perforated sheet, material 316 SS Outlet weir height 25 mm Perforated sheet, thickness, mm 1.5 Inlet weir height 4.8 mm Outlet weir, height length, mm mm 25.4, 50.8 940 Inlet weir none Tray spacing, mm 610 Effective bubbling area, m 2 0.859 Edge of hole facing vapor flow sharp Clearance under downcomer, mm 22, 38

270 Mahmood-Reza Rahimi et al. umn was operated at total reflux and atmospheric pressure, and carried out at a vapor phase F s factor of 0.4 m/s (kg/m 3 ) 1/2 and covered a wide range of composition. All the hot surfaces of the equipment are insulated with 50 mm thick glass fiber material and aluminum cladding, therefore, the column is adiabatic, and this adiabatic form of CFD equations is applicable. A schematic of the test tray is shown in Figure 1.The details of FRI 1.2 m circular tray are given in Table 1. 4. Wall and Boundary Conditions In this steady state simulation, the following boundary conditions are specified. A uniform liquid and gas inlet velocity, temperature, and concentration profiles are used. Uniform vapor velocity: V = hole Uniform liquid velocity: U = L,in Q G n h A h Q L A cl (26) (27) Where A cl =h ap L w For scalar variables (temperature, species concentrations, physical properties, and soon): in = set (28) Liquid is considered as a pure phase, means that only liquid enters through the downcomer clearance. This is a good approximation for rectangular tray, because at this F factor (0.4) the entrainment was found to be less than 0.02 and this value would have negligible effect on the flow rates [11]. In addition negligible weeping was observed by the investigators. For circular tray this assumptions were used in hydrodynamics study [2,10]. The gas volume fraction at the inlet holes was specified to be unity. The liquid- and vapor-outlet boundaries were specified as mass flow boundaries with fractional mass flux specifications. At the liquid outlet, only liquid was assumed to leave the flow geometry and only gas was assumed to exit through the vapor outlet. These specifications are in agreement with the specifications at the gas inlet and liquid inlet, where only one fluid was assumed to enter. A no-slip wall boundary condition was specified for the liquid phase and a free slip wall boundary condition was used for the gas phase. The flow conditions at the outlet weir are considered as fully developed in velocity, temperature and concentration. The normal direction gradients of temperature and concentration at the walls are zero. The mathematical forms of all above boundary conditions can be found in the CFX Manual [21] and Ranade [14], they are not repeated here. 5. Simulation Results and Discussion Simulations were conducted using high speed dual processor machines (2 2.4 GHZ) run in parallel. CFD analysis was carried out using CFX 5.7 of Ansys, Inc. The solution procedure is based on the finite-volume method of the SIMPLEC algorithm. Interphase transfer terms are added into CFX via user defined routines. The whole tray spacing, from liquid inlet to the outlet weir, was considered in the simulations, even though the primary focus is in the froth section. This resulted in a better numerical convergence as well as providing us with the ability to assess the froth height from the simulations. Hydraulic parameters such as clear-liquid height and froth height were calculated at each time step. Runs continued until quasi-steady-state has reached, in other words, a simulation was deemed to have converged whenever the clearliquid height value reached a value no appreciable change in successive time steps. Although many of the simulations were inherently transient, an averaged quantity like the clear-liquid height appears to have reached a steady value; this criterion was used to terminate a simulation [2], even if local values were changing in successive time steps in a bounded, chaotic manner. Several runs were taken as low as 16h to about 3 weeks CPU time to be completed. 5.1 Rectangular Tray 5.1.1 Hydrodynamics Dribika and Biddulph [11] have been presented the

Prediction of Temperature and Concentration Distributions of Distillation Sieve Trays by CFD 271 average clear liquid height and froth height. Therefore these quantities from the simulation results, has been presented in this work, in order to compare the simulation results against their experimental data. The average values of liquid holdup and froth height for each run (at each average liquid composition x m ) where shown in Figures 2 and 3, respectively. Van Batten and Krishna [8] and Gesit et al [2] and Rahimi et al. [10] found that CFD give clear liquid height values larger than the experimental ones. It is required to discuss the reason of this difference between these data. Bennet et al [18] correlation is good for prediction of clear-liquid height, for trays operating in the froth regions. Van Batten and Krishna [8] also found the CFD to give clear-liquid height values that are larger than the experimental ones. They reasoned that this happened because the Bennet et al correlation used in the interphase momentum drag term ignores coalescence caused by impurities. Gesit et al [2] discussed their interpretation as follows: It is known that the Bennet et al. [18] correlation over predicts the liquid holdup fraction in froth. From drag coefficient term (eq. 8 in this work), at a given gas flow rate the use of the Bennet et al. [18] correlation amounts to using a constant multiplier as a drag coefficient. This constant factor is inversely proportional to the average liquid holdup fraction, but it is proportional to the second power of the average gas holdup fraction. Over predicting the average liquid holdup fraction re- Figure 2. Variation of liquid holdup with mean liquid composition, rectangular tray, F s = 0.4, (a) MeOH/nPrOH system, (b) MeOH/nPrOH system, (c) liquid holdup of rectangular tray F s = 0.4, Xm = 0.4960, EtOH/nPrOH. Figure 3. Variation of froth height with mean liquid composition, rectangular tray, F s = 0.4, (a) MeOH/nPrOH system, (b) EtOH/nPrOH system.

272 Mahmood-Reza Rahimi et al. sults in a reduction in the interphase drag term. The gas then does not exert enough drag force on the liquid. This can be thought of as if the tray were operating at a slightly lower gas rate than the actual one, which results in a larger clear-liquid height. However, these interpretations are not satisfactory. Use of governing equations, derived based on the assumption of a single bubble size, generally lead to significant over prediction of gas volume fraction, thought comparison of liquid phase mean velocity is not bad, for example Kumar et al. [24] was observed such behavior in studying bubble columns. 5.1.2 Velocity Profiles The U-velocity of liquid phase at the plane normal to the direction of liquid flow is shown in Figure 4a. The U velocity of liquid in the transverse direction to the liquid flow is shown in Figures 4b and c. The trend of velocity variation versus z is similar to circular tray of Gesit et al. [2] and Rahimi et al. [10] and confirms the validity of the simulation results. The velocities or velocity distributions were not presented by Dribika and Biddulph [12], therefore any comparison between simulated and experimental data is not possible. The rectangular tray have high aspect ratio and low-diameter holes, the results for this tray was clearly shown that the gas flow rate distribution is nonuniform along the tray, because of existence of hydraulic gradient and effect of relatively high residual pressure drop. 5.1.3 Compositions Profiles Dribika and Biddulph [11] have presented the liquid concentration and temperature profiles at various compositions at F s = 0.4 and total reflux condition. The simulation results of concentration and temperature were compared against their experimental data. The tray length was divided into 6 sections, in order to compare CFD results with experimental data. The mean liquid composition (concentration), for each section was determined by integration. Unfortunately, the exact position and geometry of the probes was not mentioned in the Biddulph and Coworkers series of papers. This may be a source of difference between experimental data and simulation results. In Figures 5 and 6 the predicted composition profiles using the CFD model, for MeOH/nPrOH and EtOH/ nproh pairs, were compared against experimental data of Dribika and Biddulph [11]. The obtained results are in close agreement with experimental data, and the trend of CFD results is exactly correct. Since the column was operated at total reflux conditions, the vapor compositions is related to the liquid compositions according to equation y n+1 =x n, the CFD results are generally in good agreement with this equation. The mean average error is about 0.005 that may be due to truncation errors and uncertainties in closure models used in these simulations. Though the composition profiles are irregular, the average concentration across the profiles closely follows Figure 4. (a) Liquid U-velocity profile in the direction to the liquid flow, Liquid U-velocity profile in the transverse direction to the liquid flow, Rectangular tray Fs = 0.4, at two positions: (b) x/l = 0.63, (c) x/l = 0.88.

Prediction of Temperature and Concentration Distributions of Distillation Sieve Trays by CFD 273 Figure 5. Center-line liquid composition profiles for rectangular tray, EtOH/nPrOH binary system, (a) x m = 0.1910, (b) x m = 0.4960. Figure 6. Center-line liquid composition and liquid composition contours for rectangular tray, MeOH/nPrOH binary system. (a) x m = 0.7710, (b) x m = 0.2790. the plug flow profiles. A Peclet number of about 39 was reported for this system [11], this value indicates that conditions are approaching plug flow on this study. The fact that for practical distillation trays the liquid phase approaches plug flow is even true for relatively small diameter columns. The simulation results of compositions may be used for calculation of Murphree point and tray efficiencies [4], and column overall efficiency [25]. 5.1.4 Liquid Temperature Profiles The predicted liquid temperature profiles, for MeOH/ nproh and EtOH/nPrOH systems, respectively, are shown in Figures 7 and 8 and compared with experimental data of Dribika and Biddulph [11]. The predictions are generally in very close agreement with experimental data. Mean temperature in each cell is calculated by integration. The temperature in downcomer was very close to the bubble-point temperatures. In the case of MeOH/nPrOH system, there is slight vaporization in downcomers, probably due to large temperature difference in this system [11]. The effect of this phenomenon on the point efficiency is small. Lockett and Ahmed [22] and Ellis and Shelton [23], who used methanol-water system, observed similar phenomenon, heat transfer produced due to variation of temperature from tray to tray. The temperature profiles of MeOH/nPrOH system illustrate that effect of this phenomenon on the efficiency being small, the average difference between experimental and predicted values of Dribika and Biddulph [11] is about 2% and agrees with the conclusions of Lockett and Ahmed [22]. The results confirm that at the condition of Dribika and Biddulph experiments the plug liquid flow is acceptable. In large diameter trays the variation of liquid concentration and temperature in transverse direction may be important, and flow non-uniformities may be existed. Concentration and temperature profiles were observed to have a minor difference, because different equation forms were used for heat and mass transfer coefficients in simulations. The accuracy of CFD simulation results are related to the closure models, but in the case of

274 Mahmood-Reza Rahimi et al. Figure 7. Center-line temperature profiles for rectangular tray, MeOH/nPrOH binary system. (a) x m = 0.2790, (b) x m = 0.5550. Figure 8. Centerline temperature profiles and temperature contours for rectangular tray, EtOH/nPrOH binary system, (a)x m = 0.4960, (b)x m = 0.3420. sieve tray, these models are not presented or no tested for CFD application. Furthermore, most of them are developed based on the macroscopic quantities, where are not suitable for detailed microscopic modeling. Therefore, future developments must be focused on the development of reliable correlations for this coefficients as well as closure models. 5.2 Tray Efficiency Increase of separation efficiency as well as its prediction has been a major task in design and operation of distillation columns. Murphree tray efficiency can be calculated, directly from CFD results, when concentration and temperature distributions were determined. The predicted and experimental tray efficiencies were shown against the mean liquid compositions in Figure 9. All the experimental runs (for the two binary systems) were made at conditions that the vapor phase (F s ) factor was about 0.4. Figure 9. Murphree tray efficiency vs. mean liquid composition, MeOH/nPrOH binary system. At this F factor negligible weeping was observed and the entrainment was found to be less than 0.02, this value would have a negligible effect on the efficiency [11]. These conditions are in agreement with our initial assumptions that each phase is entered to tray as a single

Prediction of Temperature and Concentration Distributions of Distillation Sieve Trays by CFD 275 phase. The predication of industrial tray efficiencies on distillation column is down usually by the following procedures [11]: Comparison with the tray efficiency of similar operating columns Scaling up from laboratory columns Empirical correlation Theoretical to semi theoretical mass-transfer methods The reliable experimental data of tray hydrodynamics and efficiency are rare, because experiments for trays are expensive and take a long time. CFD predictions are in good agreement with experimental data and are shown that CFD is a powerful method for sieve tray design and analysis; it may be used as a virtual experiment tool for distillation. Therefore, CFD is the best and surest method of tray efficiency calculation, and can be considered as new procedure that is able to overcome many of the limitations associated with the experiments. 5.3 Circular Tray The proposed model can be used for circular trays, too. Yanagi and Sakata [12] studied the performance of the FRI commercial scale sieve tray, 1.2 m diameter, at total reflux condition. The CFD model was solved for this column. The calculation procedure for circular tray is similar to rectangular tray. A tray with symmetry boundary conditions for velocity, and temperature and concentration at the tray center were used in order to reduce the calculation domain. The concentration distribution obtained from CFD results was shown in Figure 10. Figure 10. Liquid composition profile for Yanagi and Sakata (1982) sieve tray. 6. Conclusion A three dimensional two-fluid CFD model was developed in the Eulerian framework to predict temperature and concentration distributions of sieve trays. The tray geometries and operating conditions are based on the large rectangular tray of Dribika and Biddulph [11] and FRI commercial-scale sieve tray [12]. The hydraulics parameters and concentration and temperature distributions were determined. The CFD predictions are in good agreement with experimental data. In the case of rectangular tray, though the composition profiles are irregular, the average concentration profiles closely follows the plug flow profiles. The results confirm that at the condition of Dribika and Biddulph experiments the plug liquid flow is acceptable. In large diameter trays the variation of liquid concentration and temperature in transverse direction may be important, and flow non-uniformities may be existed. Concentration and temperature profiles were observed to have a minor difference, because different equation forms were used for heat and mass transfer coefficients in simulations. Despite the use of simple correlations for closure models, the obtained efficiencies are very close to experimental data. Therefore, CFD is the best and surest method of tray efficiency calculation, and can be considered as a new procedure that is able to overcome many of the limitations associated with the experiments; it may be used as a virtual experiment tool for distillation. The accuracy of CFD simulation results are related to the closure models, but in the case of sieve tray, these models are not presented or no tested for CFD application. Therefore, future developments must be focused on the development of reliable correlations for this coefficients as well as closure models. As predicted by Gesit et al. [2] and Rahimi et al. [10] inclusion of interphase mass (and heat) transfer relations, in CFD model, give much more accurate results. This study was shown that CFD can be used as a powerful tool for sieve tray design, simulation, visualization and trouble shooting. By means of CFD a virtual experiment can be developed to evaluate the tray performance. This study is a basis for development of new approaches for calculation of point and Murphree tray efficiencies by CFD.

276 Mahmood-Reza Rahimi et al. 7. Nomenclature A B = tray bubbling area, m 2 A cl = down comer clearance area, m 2 A h = hole area, m 2 A P = perforated area, m 2 a e = effective interfacial area per unit volume, m 1 C D = drag coefficient d G = mean bubble diameter, m D AG = diffusion coefficient of A in gas phase, m/s 2 D AL = diffusion coefficient of A in liquid phase, m/s 2 F S = F factor = V S G g = gravity acceleration, m/s 2 g = gravity vector, m/s 2 h G = specific enthalpy of gas, kj/kg h L = specific enthalpy of liquid, kj/kg h LG =(h L h G ) k L = liquid phase mass transfer coefficient, m/s k G = gas phase mass transfer coefficient, m/s K og = gas phase overall mass transfer coefficient, m/s K ol = liquid phase overall mass transfer coefficient, m/s L = length of flow path an tray, m M GL = interphase momentum transfer, kg.m 2.s 2 M A = molecular weight of component A m = slope of equilibrium line n h = number of holes P = total pressure, Nm 2 P G = gas-phase pressure, N.m 2 P L = liquid-phase pressure, N.m 2 q = flux of enthalpy, w/m 2 Q L = liquid volumetric flow rate, m 3 /s Q LG = energy transfer between liquid and gas phases, w/m 3 Q G = gas volumetric flow rate, m 3 /s r G = gas-phase volume fraction, dimensionless r G = average gas holdup fraction in froth, dimensionless r L = liquid-phase volume fraction, dimensionless S LG = rate of interphase mass transfer, kg/m 3 s t = time, s T = temperature, k U = x-component of velocity, m/s V = y-component of velocity, m/s V B = vapor velocity over the bubbling area, m/s V G = gas-phase velocity vector, m/s V L = liquid-phase velocity vector, m/s V P = vapor velocity through the tray perforations, m/s V R = bubble rise velocity, m/s V S = gas phase superficial velocity based on bubbling area, m/s V slip = slip velocity, m/s W = z-component of velocity, m/s w = weir length, m X A = mass fraction of A in liquid phase Y A = mass fraction of A in gas phase x A = mole fraction of A in liquid phase x * A I x A = equilibrium mole fraction = interfacial mol fraction in liquid phase y A = mole fraction of A in gas phase y * A I y A = equilibrium mole fraction = interfacial mol fraction in gas phase x, y, z = coordination s, distance from origin, m Greek letters L = average liquid holdup fraction in froth L,G = heat transfer coefficient between Liquid and Gas phase, W/m 2.k eff,g = effective viscosity of gas, kg.m 1.s 1 eff,l = effective viscosity of liquid, kg.m 1.s 1 G = gas-phase density, kg/m 3 L = liquid-phase density, kg/m 3 G = gas contact time, s L = liquid contact time, s = all scalar variables (except pressure) Subscripts A = component A L = liquid phase G = gas phase Superscripts * = equilibrium

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278 Mahmood-Reza Rahimi et al. in Bubble Columns, Chem. Eng. Sci., Vol. 49, p. 5637 (1994). [25] Rahimi, M. R., CFD Simulation of Hydrodynamics and Mass Transfer of Sieve Tray Distillation Columns, Ph. D. dissertation in chemical engineering, Sistan and Baluchistan University, Iran (2005). Manuscript Received: Jul. 21, 2005 Accepted: Oct. 3, 2005