Efficiencies of sieve tray distillation columns by CFD simulation

Full Paper Efficiencies of Sieve Tray Distillation Columns by CFD Simulation By Rahbar Rahimi*, Mahmood Reza Rahimi, Farhad Shahraki, and Mortaza Zivdar DOI: 10.1002/ceat.200500285 A 3-D two-fluid CFD model in the Eulerian-Eulerian framework was developed to predict the hydrodynamics and heat and mass transfer of sieve trays. Interaction between the two phases occurs via interphase momentum and heat and mass transfer. The tray geometries are based on the large rectangular tray of Dribika and Biddulph and FRI commercial-scale sieve tray of Yanagi and Sakata. In this work a CFD simulation is developed to give predictions of the fluid flow patterns, hydraulics, and mass transfer efficiency of distillation sieve trays including a downcomer. 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. Despite the use of simple correlations for closure models, the efficiencies obtained are very close to experimental data. The results show that values of point efficiency vary with position on the tray because of variation of affecting parameters, such as velocities, temperature and concentration gradients, and interfacial area. The simulation results show 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 and as a new tool for testing mixing models in both phases. CFD can be used as a “virtual experiment” to simulate tray behavior under operating conditions. 1 Introduction Distillation is a separation process of major importance in chemical and petroleum industries. The worldwide throughput of distillation columns in 1992 was estimated as [1]: Oil refining: 3.7 Billion tonnes/year; chemicals and petrochemicals: 130 Million tonnes/year; and natural gas processing 1.4 Billion tonnes/year. Porter [2] estimated that the throughput of distillation columns is at least $ 500 billion/ year. Increasing separation efficiency as well as its prediction has been a major task in design and operation of distillation columns. Efforts to maximize the efficiency of distillation columns are still justified on economic grounds [3]. Determination of the theoretical stages required for a desired separation is the first stage of distillation column design, thereafter, by using column efficiency, the actual number of trays is determined. This column efficiency is calculated from the Murphree tray efficiency, and this efficiency is calculated from the point efficiency. Therefore, knowledge of the point efficiency is essential for design of trayed distillation columns. The predication of industrial tray efficiencies on distillation columns is usually done by the following procedures [4]: – Comparison with the tray efficiency of similar operating columns. – Scaling-up from laboratory columns. – Empirical correlation. – Theoretical to semi-theoretical mass transfer methods. – [*] 326 R. Rahimi (author to whom correspondence should be addressed, [email protected]), M. R. Rahimi, F. Shahraki, M. Zivdar, Department of Chemical Engineering, Sistan and Baluchistan University, Zahedan, 98164, Iran. The best and surest method of tray efficiency calculation to date is to use the value of a similar column as a reference [4]. Unfortunately, such data are seldom available, though where they do exist they should be used as the basis for efficiency of separation [4]. On the other hand, the prediction of point efficiency remains uncertain, and little real progress has been achieved since the AIChE Bubble Tray design Manual [5] was published. The AIChE semi-empirical correlation was based on the assumption that point efficiencies were real and measurable. However, it is clear that direct measurement of this quantity is difficult. Various methods were found to overcome this problem. Klemola [4] lists references for tray efficiency correlations. For each of these methods, the conversion of point efficiency to tray efficiency relies on the choice of the mixing model to be used. The liquid mixing on the tray has been modeled using several approaches [5–8]. More recent works have introduced mixing models of increasing complexity [9–11]. The correct prediction of point efficiencies is subject to question and there is not a unified model to predict its variation along the tray. Point efficiency should be properly based on vapor-liquid mass transfer fundamentals and transport between phases in the turbulent two phase dispersion. Sieve trays are widely used in distillation, absorption, and liquid-liquid extraction columns for their simplicity, and hence low construction cost. There have been few attempts to model sieve tray hydrodynamics using CFD simulation [12–19]. Gesit, et al. [12] developed a 3-D CFD model to predict the flow patterns and hydraulics of commercial-scale sieve trays. Wang et al. [19] 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 ten-trayed column was estimated. Their © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eng. Technol. 2006, 29, No. 3 Full Paper model does not predict point efficiency and vapor-phase concentration distribution, and used constant values for vapor (and liquid) volume fractions. Rahimi et al. [20] studied the hydrodynamics of sieve trays by means of a 3-D two fluid CFD simulation. The velocity, concentration, and temperature distributions were determined [21]. In this work, a CFD simulation is developed to give predictions of the fluid flow patterns, hydraulics, and mass transfer efficiency of distillation sieve trays including a downcomer. 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 of rectangular trays were used for calculation of the Murphree point and tray efficiencies, and results were compared against the experimental data of Dribika and Biddulph [22]. Then the model was used to predict efficiencies of the commercial-scale tray FRI used in Yanagi and Sakata’s experiments [23]. The simulation results show 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. This simulation can be used as a “virtual experiment” instead of “warm measurements”, which are very expensive and time consuming. CFD can be used as a tool for testing mixing models in liquid and vapor phases. 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 (3) 2.2 Momentum Conservation – Gas phase: ∂ r q V † ‡ ∇: rG qG VG VG †† ˆ ∂t G G G (4) T rG ∇PG ‡ ∇: rG leff;G ∇VG ‡ ∇VG † †† ‡ rG qG g MGL – Liquid phase: ∂ r q V † ‡ ∇: rL qL VL VL †† ˆ ∂t L L L (5) T rL ∇PL ‡ ∇: rL leff;L ∇VL ‡ ∇VL † †† ‡ rL qL g ‡ MGL MGL describes the interfacial forces acting on each phase due to the presence of the other phase. 2.3 Volume Conservation Equation This is simply the constraint that the volume fractions sum to unity: 2 Model Equations The dispersed gas and the continuous liquid are modeled in the Eulerian frame work as two interpenetrating phases having separate transport equations. Thus, for each phase the time and volume averaged conservation equations are numerically solved. The basic derivation of the multiphase flow transport equations has been reported elsewhere [24, 25] and therefore will not be described further in this article. The two-fluid conservation equations for adiabatic twophase flow are as follows1): rL + rG = 1 (6) 2.4 Pressure Constraint The complete set of hydrodynamic equations represent nine (4NP + 1) equations in the ten (5NP) unknowns: VL, UL, WL, rL, PL, VG, UG, WG, rG, PG. We need one (NP – 1) more equation to close the system. This is given by constraint on the pressure, namely that the two phases share the same pressure field: PL = PG = P. 2.1 Continuity Equations 2.5 Energy Conservation – Gas phase: ∂ r q † ‡ ∇: rG qG VG † ‡ SLG ˆ 0 ∂t G G – Gas phase: (1) – Liquid phase: ∂ r q † ‡ ∇: rL qL VL † ∂t L L SLG ˆ 0 – 1) (2) ∂ r q h † ‡ ∇: rG qG VG hG † ˆ ∂t G G G (7) ∇:q ‡ QLG ‡ SLG hLG † – Liquid phase: ∂ r q h † ‡ ∇: rL qL VL hL † ˆ ∂t L L L ∇:q QLG ‡ SLG hLG † List of symbols at the end of the paper. Chem. Eng. Technol. 2006, 29, No. 3 © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.com (8) 327 Full Paper hL and hG are the specific enthalpies of phases L and G, respectively. The first term in parentheses on the right hand side of the 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 the phases must satisfy the local balance condition: QLG = –QGL (9) to 2–5 mm in diameter with rise velocity of about 0.25 m/s [27]. Therefore, an equation for CD that is independent of bubble diameter seems most appropriate. Krishna et al. [17] have used an equation for the drag term that was developed from their studies on the bubble column. The drag coefficient CD has been estimated using the drag correlation of Krishna et al. [28], a relation proposed for the rise of a swarm of large bubbles in the churn-turbulent regime: 4 qL qG 1 gdG 2 3 qL Vslip (14) 2.6 Mass Transfer Equations CD ˆ Transport equations for the mass fraction of light component A can be written: – Gas phase: Where the slip velocity, Vslip = |VG–VL| , is estimated from the gas superficial velocity Vs and the average gas holdup fraction in the froth region: ∂ r q Y † ‡∇:‰rG qG VG YA ∂t G G A Vslip ˆ qG DAG ∇YA ††Š SLG ˆ 0 (10) – Liquid phase: ∂ r q X † ‡ ∇: ‰rL qL VL XA ∂t L L A qL DAL ∇XA ††Š ‡ SLG ˆ 0 (11) Vs rG (15) For the average gas holdup fraction, Bennett et al. [29] considered the correlation: "  r0:91 # qG rG ˆ 1 exp 12:55 Vs (16) qL qG From Eqs. (13–15) the interphase momentum transfer term as a function of local variables becomes [17]: 2.7 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–e model. The rate of energy transfer between phases can be written: QLG = bLG ae (TL – TG) (12) bLG represents the heat transfer coefficient between phases. An appropriate value of the heat transfer coefficient can be obtained by using suitable correlations of the Nusselt number [26]. 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 MGL is basically the interphase drag force per unit volume. With the gas as the disperse phase, the equation for MGL is: MGL ˆ 3 CD r q jV 4 dG G L G VL j VG VL † http://www.cet-journal.com rG †2 g qL 1:0 rG †V2s qG †rG rL j VG V L †j V G VL † (17) This relation is independent of bubble diameter and is suitable for CFD use. A vast amount of data for the mass transfer coefficient is not available in the case of sieve trays; in addition, 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: SLG ˆ kL ae MA xA xIA † (18) SLG ˆ kG ae MA yIA yA † (19) The interfacial concentrations xIA and yIA are in equilibrium: (13) CD is the drag coefficient. Its value for the case of distillation is not well known. However, Fisher and Quarini [14] 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 the dominant region in distillation, it is not applicable. Further, the bubbles are from 10–20 mm in diameter with a bubble rise velocity of 1.5 m/s 328 MGL ˆ yIA ˆ mxIA (20) The value of m was determined from the equilibrium data [22]. Combining Eqs. (18–20) results in deleting the interface concentrations xIA, yIA : SLG ˆ KOG ae MA yA © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim yA † ˆ KOL ae MA xA xA † (21) Chem. Eng. Technol. 2006, 29, No. 3 Full Paper Where KOG = 1/(1/kG + m/kL), KOL = 1/(1/mkG + 1/kL), and yA ˆ mxA is the vapor composition in equilibrium with xA. The local mass transfer rate SLG is calculated from the above equation. Higbie penetration theory [30] has been widely used to simulate the gas-liquid mass transfer in distillation columns [9, 22, 31, 32]. In all of these works the time averaged values of mass transfer coefficients were used in steady-state processes. The Higbie model assumes that the composition of the film does not stay stagnant as in the film model. The exposure time is determined by the hydrodynamic properties of the system and is the only parameter required to account for their effect on the transfer coefficient KL. During this short time, the element of liquid absorbs the same amount of gas per unit area as thought it were stagnant and infinitely deep. Higbie [30] deduced that the time averaged liquid and gas mass transfer coefficients take the form: s DAL (22) kL ˆ 2 phL s DAG kG ˆ 2 (23) phG DAL and DAG are diffusion coefficients in the liquid and gas phases, respectively. The contact time for vapor in d the froth region hG is defined as hG ˆ G , where VP is the VP velocity of vapor through the tray perforations. The contact d time for liquid hL is G , where the average rise velocity VR of VR bubbles through the froth is given by:   AP VP Vs AB ˆ (24) VR ˆ 1 aL † 1 aL † AP/AB is the perforated area to total bubbling area ratio. Taylor and Krishna [27] 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 dG may be assumed to be equal to the mean diameter of the bubbles. The effective vapor-liquid interfacial area can be determined directly from the liquid holdup and the mean bubble diameter by the following equation: ae ˆ 61 dG aL † (25) It is known that closure models have important effects on the accuracy of the final results of a CFD simulation. Therefore, their determination is the most important part in each CFD simulation. But, unfortunately, in the case of sieve trays these models are not presented or not tested for CFD application. Therefore, further improvement and refinement of the closure models is required, in order that if more refined experimental data on flow and concentration distributions become available they can be the subject of future investigations. Chem. Eng. Technol. 2006, 29, No. 3 A set of conditions must be used at the interface. The continuity at the interface for transport quantities, and correlation between parameters at the interface were mentioned by a set of conditions used at the vapor-liquid interface: Ki xi ji ˆ yi ji (26a) TL i ˆ TV i (26b) NLA i ˆ NV A i (26c) EL i ˆ EV i (26d) VS ˆ jVG (26e) VL j At the vapor-liquid interface we assume phase equilibrium, described by Eqs. (26a) and (26b). Furthermore, the fluxes of mass NA and energy E are continuous across the interface, by Eqs. (26c) and (26d), and the velocities of the two phases are related by Eq (26e). The above conditions were considered to obtain the correlations of this CFD work. Eqs. (26b) and d) were considered in the interphase energy transfer term, Eq. (26e) in the interphase momentum transfer term, and Eqs. (26a) and c) in the interphase mass transfer term. Therefore, the interface conditions were automatically considered and included in the correlations of this CFD model. 3 Flow Geometries In this work, the proposed simulation was first used to emulate the data of Dribika and Biddulph [22] using a large rectangular sieve tray, for determination of hydraulic parameters, temperature, and concentration profiles. The simulation results were compared against the experimental data, after which the FRI tray used by Yanagi and Sakata [23] was simulated. The experimental rig of Dribika and Biddulph [22] consists of three rectangular distillation trays having dimensions of 1067 by 89 mm, 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, indicated by points “S” in Fig. 1, details of the tray are given in Tab. 1. The column was operated at total reflux and atmospheric pressure, with a vapor phase Fs factor of 0.4 m/s (kg/m3)1/2, and covered a wide range of compositions. Figure 1. Details of rectangular tray showing sample/temperature points. © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.com 329 Full Paper Table 1. Tray specifications. a) Rectangular tray Weir length b) Circular tray 83 mm Diameter 1.2 2 Liquid flow path 991 mm Downcomer area,m 0.14 Tray spacing 154 mm Hole area, m2 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 Effective bubbling area, m sharp Clearance under downcomer, mm 22, 38 4 Wall and Boundary Conditions In this steady state simulation, the following boundary conditions are specified. Uniform liquid inlet velocity, temperature, and concentration profiles are used and liquid is considered as a pure phase, meaning that only liquid enters through the downcomer clearance. This is a good approximation for rectangular trays, 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 [22]. In addition, negligible weeping was observed by the investigators. For the circular tray these assumptions were used in the hydrodynamics study [12, 20]. 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 phase 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 http://www.cet-journal.com 0.859 Edge of hole facing vapor flow 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 the adiabatic form of the CFD equations is applicable. A schematic of the test tray is shown in Fig. 1. The details of the FRI 1.2 m circular tray are given in Tab. 1. 330 610 2 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 are described in full in the CFX Manual [33], and hence they are not repeated here. 5 Simulation Results and Discussion Most of the simulations were conducted using high speed dual processor machines (2 × 2.4 GHz) run in parallel. The details of numerical methods for transient simulations were presented by Rahimi et al. [20]. CFD analysis was carried out using a CFX5.7 of Ansys, Inc. Simulations were conducted with CPU times per CFD simulations, for convergence, varying from as low as 16 h to about three weeks. 5.1 Rectangular Tray 5.1.1 Compositions Profiles Dribika and Biddulph [22] have presented the liquid concentration and temperature profiles at various compositions at Fs = 0.4 and total reflux. The simulation results for concentration and temperature were compared against their experimental data. The tray length was divided into six 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 © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eng. Technol. 2006, 29, No. 3 Full Paper and coworkers series of papers. This may be a source of difference between experimental data and simulation results. In Fig. 2 the predicted composition profiles using the CFD model for MeOH/nPrOH and EtOH/nPrOH pairs were compared against experimental data [12]. The obtained results are in close agreement with the experimental data, and the trend of the CFD results fits exactly. Since the column was operated under total reflux conditions, the vapor compositions are related to the liquid compositions according to the equation yn+1 = xn; the CFD results are generally in good agreement with this equation. The mean average error is about 0.005, which may be due to truncation errors and uncertainties in the closure models used in these simulations. a) and Biddulph [22]. The predictions are generally in very close agreement with the experimental data. The mean temperature in each cell is calculated by integration. The temperature in the downcomer was very close to the bubblepoint temperatures. In the case of the MeOH/nPrOH system there is slight vaporization in the downcomers, probably due to large temperature differences in this system [22]. The effect of this phenomenon on the point efficiency is small. Lockett and Ahmed [34] and Ellis and Shelton [35], who used methanol-water systems, observed a similar phenomenon, heat transfer produced due to variation of the temperature from tray to tray. The temperature profiles of the MeOH/nPrOH system illustrate that the effect of this phenomenon on the efficiency is small, the average difference between experimental and predicted values is about 2 % and agrees with the conclusions of Lockett and Ahmed [34]. 367 TK 363 359 Exp. data CFD 355 0 0,2 0,4 0,6 0,8 Dimensionless lenth,x/L 1 Liquid composition,X 0,75 Exp. data 0,6 CFD Figure 3. Centerline temperature and temperature profiles for the rectangular tray, EtOH/nPrOH binary system, (xm = 0.4960). 0,45 0,3 0,15 0 0 0,2 0,4 0,6 0,8 1 dimensionless coordinate,x/L b) The results confirm that under the conditions of Dribika and Biddulph’s experiments the mixed liquid flow in the transverse direction is acceptable, but in large diameter trays the variation of liquid concentration in the transverse direction may be important. 5.1.3 Point and Tray Efficiencies Figure 2. Centerline liquid composition and liquid composition profiles for the rectangular tray, MeOH/nPrOH binary system. a) xm = 0.2790, b) xm = 0.7710. 5.1.2 Liquid Temperature Profiles The predicted liquid temperature profiles for MeOH/ nPrOH and EtOH/nPrOH systems, respectively, are shown in Fig. 3 and compared with experimental data of Dribika Chem. Eng. Technol. 2006, 29, No. 3 When the concentration and temperature of the whole tray is determined, Murphree point and tray efficiencies can be calculated directly from CFD results by related definitions as follows. The tray was divided into six cells in the liquid flow direction. By integration on the y and z directions (see Fig. 1), the average value of temperature and concentration was calculated for each cell, then each cell efficiency was calculated by the following equations. For each cell (n, i), the point efficiency for vapor was calculated as follows: © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.com 331 Full Paper yni yni yn yn 1;i (27) 1;i yni ˆ mni :xni (28) The value of mni was calculated from the equilibrium data of Dribika and Biddulph [22]. The value yn–1,i was calculated by surface integration, just below the tray “n” and value of yni and just above the froth of the cell “i” of the tray “n”. The average outlet liquid concentration of the cell (n, i) was calculated by integration on a liquid outlet face of the cell. Dribika and Biddulph used a plug flow model for vapor and mixed model for liquid. The results of this work show that this is a good representation of tray hydrodynamics in this case, and this is confirmed by the velocity profiles of this tray, because these profiles show that the gas encounters almost no sideways force and appears to flow in an approximately straight path. Likewise, no (or small) vertical displacement of the liquid streamlines are seen at this gas flow rate (Fs = 0.4). The work of Dribika and Biddulph was done at low to moderate gas flow rates (Fs = 0.2–0.4), hence the assumption of a plug flow regime for the gas phase is reasonable. For each tray the Murphree tray efficiencies were calculated from the definition: EMV ˆ n yn yn yn‡1 yn‡1 (31) (32) Hence: yn+1 = xn (33) The same result is obtained for the stripping section. The values of xn and yn+1 are averaged values for the liquid and vapor phases, and are calculated by integration of related profiles at the outlet weir and just below the tray n, respectively. Combining Eqs. (29), (30), and (33): EMV ˆ n yn xn y =x 1 ˆ n n mn 1 mn :xn xn 332 http://www.cet-journal.com 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 78 77,8 77,6 77,4 77,2 77 CFD Efficiency CFD X 76,8 0 0,2 0,4 0,6 Dimensionless length, x/L 0,8 1 (30) And the overall mass balance is: Vn+1 = Ln In Fig. 4 the variation of point efficiency and liquid composition profile along the centerline of the tray for the MeOH/nPrOH binary system, at a run corresponding to the mean liquid composition xm = 0.771, is presented. Dribika and Biddulph [22] used a constant value for point efficiency, as a function of liquid concentration, for each run. With reference to the results of this study; this is not a good assumption for long flow path trays and for high aspect ratio trays. Figure 4. Point efficiency and liquid composition profile along the centerline of the rectangular tray, MeOH/nPrOH binary system (xm = 0.771). The value of m was determined from the equilibrium data of Dribika and Biddulph [22]. Considering a column operated at total reflux, no product is withdrawn from the column; therefore, the mass balance of any component performed around any tray is: Vn‡1 :yn‡1 ˆ Ln :xn (35) 0 76,6 (29) Where: yni ˆ mn :xn Where mn for each tray is calculated as: Z1 Ncell 1 X m mn ˆ mni d w† ˆ Ncell iˆ1 ni Ep EPni ˆ (34) The results confirm that under the conditions of Dribika and Biddulph’s experiments the mixed liquid flow in the transverse direction is acceptable, but in large diameter trays the variation of liquid concentration in the transverse direction may be important. In this study each point of mean liquid composition belongs to a computer run. The average (mean) liquid and vapor compositions in each run were determined as discussed previously, and then related values of efficiencies were calculated as described above. The predicted and experimental tray efficiencies are shown against the mean liquid compositions in Fig. 5. All the experimental runs (for the two binary systems) were made under conditions such that the vapor phase Fs factor was about 0.4. At this F factor the entrainment was found to be less than 0.02, and this value would have a negligible effect on the efficiency [22]. In addition, negligible weeping was observed [22]. These conditions are in agreement with the initial assumptions that each phase is pure and entered into the tray as a single phase. With reference to Fig. 5, it can be observed that higher tray efficiencies were obtained at the lower concentration range of the more volatile component. In addition, in the middle to higher range of composition used in the two systems, the tray efficiencies for the EtOH/nPrOH system are © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eng. Technol. 2006, 29, No. 3 Full Paper a) b ) CFD results Exp. data Dribika model 130 145 Exp. data Dribika model CFD results Emv Emv 130 110 115 100 90 85 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 Mean Liquid Composition,X Mean liquid composition 0.9 Figure 5. Murphree tray efficiency vs. mean liquid composition, a) MeOH/nPrOH binary system, b) EtOH/nPrOH. 5.2 Circular Tray The proposed model can be used for circular trays, too. Yanagi and Sakata [23] studied the performance of the FRI commercial-scale sieve tray, 1.2 m diameter, under total reflux conditions. The CFD model was solved for this column. The calculation procedure for circular trays is similar to that for rectangular trays. Two cases were used. The first one is a single tray with a symmetry boundary condition for velocity, temperature and concentration at the tray center used in order to reduce the calculation domain. The liquid composition profile for the Yanagi and Sakata [23] tray is shown in Fig. 6. The second case is a column with ten trays under total reflux conditions. In the latter case, the liquid concentration and temperature at the output of each tray was calculated at the outlet weir location by averaging the liquid flow at the plane perpendicular to the liquid flow. The input vapor concentration entered to each tray was obtained by averaging on a plane parallel to the tray floor just below the tray. According to this model, mass transfer does not take place outside the dispersion; therefore, this vapor composition is equal to the outlet vapor composition from the tray below. Murphree tray efficiencies were calculated by related definitions. The efficiencies calculated from the CFD results are Figure 6. Liquid composition profile for Yanagi and Sakata [23] sieve tray. Chem. Eng. Technol. 2006, 29, No. 3 shown in Fig. 7 and compared with the experimental data of Yanagi and Sakata [23]. 1 cC6-nC7 0.9 Tray efficiency higher than for the MeOH/nPrOH system; this effect was observed and discussed by Dribika and Biddulph [22]. In the composition range of the experiments the slope of equilibrium curves is similar for the two binary systems, therefore, the higher tray efficiencies were probably due to the higher point efficiencies in the system EtOH/nPrOH, Dribika and Biddulph [22] observed this effect, too. 0.8 0.7 0.6 0.5 experimental data 0.4 CFD results 0.3 1 2 3 4 5 6 Tray no. 7 8 9 10 Figure 7. Tray efficiency for a column having ten trays, as used by Yanagi and Sakata [23]. 6 Conclusion A 3-D two-fluid CFD model was developed in the Eulerian framework to predict the hydrodynamics and heat and mass transfer performance of sieve trays. The tray geometries are based on the large rectangular tray of Dribika and Biddulph [22] and FRI commercial-scale sieve tray [23]. The hydraulics parameters, such as clear liquid height, froth height, holdup of both phases, velocity, and temperature and concentration distributions, were determined. The Murphree point efficiencies and tray efficiencies were calculated. The CFD predictions are in good agreement with the experimental data. This study has shown that CFD can be used as a powerful tool for sieve tray design, simulation, and visualization. By means of CFD a virtual experiment can be developed to evaluate the tray performance. CFD can be used as a troubleshooting tool, also. Calculation of point and Murphree tray efficiencies by CFD is a first effort to develop a new approach in this way. CFD is the best and surest method of tray efficiency calculation, and can be considered as a new procedure that has the ability to overcome the “last frontier” of efficiency prediction. © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.com 333 Full Paper As predicted by Gesit et al. [12] and mentioned by Rahimi et al. [20], inclusion of interphase mass (and heat) transfer relations in the CFD model gives much more accurate results. The results of the CFD model are dependent on the closure models. But, unfortunately, these models are not available in the case of distillation; therefore, there is clearly room for further improvement in this field. Future works can be focused on development and refinement of closure laws for interphase momentum, heat and mass transfer, and coupling between them, and development of the required correlations based on bubble diameter. Received: August 31, 2005 T T U V VG VL VP [s] [K] [m/s] [m/s] [m/s] [m/s] [m/s] VR VS [m/s] [m/s] Vslip W w [m/s] [m/s] [–] XA YA xA xm xA xIA [–] [–] [–] [–] [–] [–] yA yA yIA x, y, z [–] [–] [–] [m] Symbols used AB AH AP ae [m2] [m2] [m2] [m–1] CD dG DAG phase DAL [–] [m] [m/s2] FLV [–] FS g g hG hL hLG kL kG KOG [m/s2] [m/s2] [m/s2] [kJ/kg] [kJ/kg] [–] [m/s] [m/s] [m/s] KOL [m/s] MGL MA M P PG PL Q QL QLG [kg m–2 s–2] [g mol–1] [–] [N m–2] [N m–2] [N m–2] [W/m2] [m3/s] [W/m3] rG rG rL SLG [–] [–] [–] [kg/m3s] 334 http://www.cet-journal.com [m/s2] tray bubbling area total area of holes perforated area effective interfacial area per unit volume drag coefficient mean bubble diameter diffusion coefficient of A in gas diffusion coefficient of A in liquid phase p flow parameter = L/G qG =qL, L, G = liquid, gas mass flow rate, respectively p F factor = VS qG gravity acceleration gravity vector specific enthalpy of gas specific enthalpy of liquid (hL – hG) liquid phase mass transfer coefficient gas phase mass transfer coefficient gas phase overall mass transfer coefficient liquid phase overall mass transfer coefficient interphase momentum transfer molecular weight of component A slope of equilibrium line total pressure gas-phase pressure liquid-phase pressure flux of enthalpy liquid volumetric flow rate energy transfer between liquid and gas phases gas-phase volume fraction average gas holdup fraction in froth liquid-phase volume fraction rate of interphase mass transfer time temperature x-component of velocity y-component of velocity gas-phase velocity vector liquid-phase velocity vector vapor velocity through the tray perforations bubble rise velocity gas phase superficial velocity based on bubbling area slip velocity z-component of velocity dimensionless distance from tray inlet mass fraction of A in liquid phase mass fraction of A in gas phase mole fraction of A in liquid phase mean liquid mole fraction equilibrium mole fraction interfacial mol fraction in liquid phase mole fraction of A in gas phase equilibrium mole fraction interfacial mol fraction in gas phase coordinates, distance from origin Greek symbols bL,G [W/m2 K] meff,G meff,L qG qL hG hL [kg m–1 s–1] [kg m–1 s–1] [kg/m3] [kg/m3] [s] [s] heat transfer coefficient between Liquid and Gas phase effective viscosity of gas effective viscosity of liquid gas-phase density liquid-phase density gas contact time liquid contact time Subscripts and Superscripts A I L G * component A interface liquid phase gas phase equilibrium References [1] [2] [3] [4] S. 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