Korean J. Chem. Eng., 22(3), 441-451 (2005) Simulation and Analysis of Extractive Distillation Process in a Valve Tray Column Using the Rate Based Model Sasmita Pradhan and Aravamudan Kannan† Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India (Received 6 September 2004 • accepted 14 February 2005) Abstract−Valve trays are becoming popular in the chemical process industries owing to their flexibility to handle a wide range of vapor throughputs. Using the rigorous rate based model, the importance of the non-equilibrium approach is demonstrated for a typical extractive distillation process in a Glitsch V-1 valve tray column. Simulation results based on an in-house developed code indicated that the rate based model predictions for a valve tray column operation showed significant differences relative to the equilibrium model. Even small errors in product purities translated into non- optimal feed stage locations and inaccurate number of stages required. The counter-intuitive effect of high reflux ratio on separation is explained. Key words: Valve Tray Column, Extractive Distillation, Rate-based Model, Distillation Column Design INTRODUCTION transfer coefficients using the film theory are summarized in Table 3. The rate based model has been extensively applied in several ap- A major part of the operations in a chemical process plant is cen- plications. These are briefly reviewed below. tered on separation processes, which typically include distillation In one of the earlier studies, Lee et al. [1997] investigated the columns, absorbers and extractors. It is essential to ensure accurate packed distillation columns with a rate based model. Springer et al. design of this equipment, since even a small difference between [2002] recommended the model for predicting the distillation bound- the separation achieved and target specified may have considerable ary crossing characteristics observed in ternary azeotropic distillation environmental and economic implications. The present work em- processes. Pyhalahti and Jakobsson [2003] developed a rate based phasizes distillation since it is usually the first choice to meet sep- mixed pool model and recommended its application for absorbers aration requirements. with high exothermic reactions. Sanpui and Khanna [2003] have Conventionally, multistage separation processes were modeled investigated the selection of mass transfer correlations for rate based in terms of the equilibrium stage model, which assumes the attain- liquid-liquid extraction models. Peng et al. [2003] developed rate ment of thermodynamic equilibrium between the contacting phases. based and equilibrium models for the production of tert-amyl methyl However, multicomponent diffusion phenomena may involve cou- ether (TAME) in packed columns using gPROMS software. These pling of concentration gradients of different species leading to uncom- authors recommended simplification of the rate based model for mon behaviour such as reverse diffusion, diffusion barrier, osmotic model based control. Kloker et al. [2003] studied the influence of diffusion etc. [Toor, 1957, 1964]. For systems exhibiting strong ther- operating conditions and column configuration on the performance modynamic non-ideality, the efficiencies could vary significantly of reactive distillation columns with liquid-liquid separators. Mor- and can even lie between −∝ to +∝. Hence, multicomponent Mur- taheb and Kosuge [2004] studied the simulation and optimization phree efficiencies and their variation with respect to component as of a heterogeneous azeotropic distillation process in a sieve tray well as stage are difficult to estimate and incorporate into the equi- column. Hoffman et al. [2004] studied the scale up characteristics of librium model. The development of the rigorous non-equilibrium or the structured packing, MULTIPAK®, that was applied in methyl rate based model, described in detail by Taylor and Krishna [1993] acetate synthesis. Kenig et al. [2004] described the features of the obviated the need for use of Murphree efficiencies for multicom- advanced rate based simulation tools in reactive distillation that in- ponent systems. Briefly, this model considers each phase to be sep- cluded reaction in the film and catalyst efficiency. Higler et al. [2004] arated by an interface through which heat and mass transfer occur. have used the nonequilibrium stage modeling for three phase distil- The transport of mass and heat through both phases implies the ex- lation. First, the equilibrium 2 phase model was solved to generate istence of concentration and temperature gradients in both phases. initial guesses for solving the equilibrium three phase model. These While the temperature gradient was continuous across the inter- results in turn were used to solve the rigorous three phase rate based face, the concentration at the interface was related by the equilib- model. Noeres et al. [2004] adopted dynamic simulation of cata- rium relationship. The MERSQ equations developed for the rate- lytic distillation columns in methyl acetate synthesis. For offline based model are summarized in Table 1. The equilibrium model and online optimization and control reduced order and simplified equations corresponding to reboiler and condenser are summarized models were applied. While the rate based model is rigorous, it can in Table 2. The procedures for estimating the multicomponent mass also become difficult to implement for dynamic simulations, opti- mization and control. Further, the parameters of the model such as †To whom correspondence should be addressed. the mass transfer coefficients may be difficult to estimate accurately. E-mail: [email protected] Equilibrium based models can serve as useful limits to the rate based 441 442 S. Pradhan and A. Kannan Table 1. MERSQ equations for column stages modeled as non-equilibrium stages [Taylor and Krishna, 1993] Liquid phase Vapor phase Interface Significance (jth stage, i=1, 2, …, c) (jth stage, i=1, 2, …, c) (jth stage i=1, 2, …, c) L L L V V V Component Material (1+r j)Ljxij −Lj−1xi, j−1−f ij −Nij =0 (1+rj)Vjyij −Vj+1yi, j+1−f ij −Nij =0 - L V balances (Mij and Mij) L L L L V V Total material balances (1+r j)Lj−Lj−1−Fj−Ntj =0 (1+r j)Vj−Vj+1−F j+Ntj =0 - L V (Mtj and Mtj) where where L c L L c L V c V V c V Fj = ∑f ij and Ntj = ∑Nij Fj = ∑f ij and Ntj = ∑Nij i=1 i=1 i=1 i=1 L L L L LF V V V V VF Energy balances in the bulk (1+r j)LjH j−Lj−1H j−1−Fj Hj (1+r j )VjH j−Vj+1H j+1−Fj Hj L V L L V V phases (Ej and E j) +Q j−e j=0 +Q j+e j=0 V L Energy balance at the --ej−ej=0 I V L interface (Ej) where e j and ej are given by c V• V I V V ajhj ()Tj − Tj + ∑NijHij; i=1 c L I L L L ajhj ()Tj − Tj + ∑NijHij i=1 L V Rate equations Nij −Nij=0 i=1, 2, …, c−1 Nij −Nij=0 i=1, 2, …, c−1 - L V L L L V V V (Rij and Rij) where Ni = Ji + xiNt where Ni = Ji + yiNt c c Constraint at the interface --I I LI VI ∑xij −1= 0; ∑yij −1= 0 (Sj , Sj ) i=1 i=1 I I I I Equilibrium relationship (Qij)- - Kijxij −yij =0 No. of Equations 2c+1 2c+1 c+3 Table 2. MESH equations for reboiler and condenser modeled as equilibrium stages [Taylor and Krishna, 1993] Significance Equation (I=1, 2, …, c) V L Component material balances (Mij)Mij ≡(1+r j )Vjyij +(1+rj)Ljxij −Vj+1yi, j+1−Lj−1xi, j−1−fij =0 V L V L V L Total material balance (Mtj) (1+r j )Vj+(1+rj)Lj−Vj+1−Lj−1−Fj=0 where fij =fij +f ij and Fj=Fj +Fj V V L L V L F Energy balance (Ej)Hj≡(1+r j )VjH j+(1+rj)LjHj −Vj+1H j+1−Lj−1H j−1−FjH j+Qj=0 where F V VF L LF V L FjH j =Fj Hj +Fj Hj and Qj=Qj +Qj c Mole fraction constraint (Sj) ∑()xij − yij = 0 i=1 Equilibrium relationship (Ei, j)Kijxij−yij=0 No. of Equations 2c+3 Table 3. Estimation of multi-component mass transfer coefficient matrices in the non-equilibrium model by film theory [Taylor and Krishna, 1993] Parameter Equations V V c I Multicomponent mass mi mk ()J = []k ()y − y Rii = ----- + ∑------ i=1, 2, … c−1 transfer coefficient matrices κic k=1 κik and ki≠ V L L L I [k ] and [k ] ()J = []k ()x − x ⎛⎞1 1 R = − m ----- − ----- ij i⎝⎠ i=1, 2, … c−1 where κij κic −1 []k = []R []Γ mi is the mole fraction of appropriate phase and κij is the binary mass transfer coefficient For liquid and vapor phases, the thermodynamic correction factors (Γ L and Γ V) are given by : L ∂lnγi i, j=1, 2, … c−1 Γ = δ + x ----------- ij ij i ∂x j TP,,Σ V ∂lnϕi Γ = δ + x ------------ ij ij i ∂x j TP,,Σ models and have also been used in recent times in the analysis of SCOPE OF THE CURRENT STUDY complex distillation processes for e.g. by Kim et al. [2004] and As- sabumrungrat et al. [2004]. Valve tray distillation columns are considered in this work since May, 2005 Simulation and Analysis of Extractive Distillation Process in a Valve Tray Column Using the Rate Based Model 443 they have significant advantages over conventional sieve trays owing Table 4. Degrees of freedom analysis for the rate based model equa- to their high turn down ratio. This gives them the flexibility to handle tions a wide range of vapor flow rates ranging from a minimum through- Variables Equations put to the normal or design throughput [Kister, 1992].