A fixed point methodology for the design of reactive distillation columns

Accepted Manuscript Title: A fixed point methodology for the design of reactive distillation columns Author: Hong Li Ying Meng Xingang Li Xin Gao PII: DOI: Reference:

S0263-8762(16)30098-3 http://dx.doi.org/doi:10.1016/j.cherd.2016.05.015 CHERD 2282

To appear in: Received date: Revised date: Accepted date:

3-3-2015 25-6-2015 18-5-2016

Please cite this article as: Li, H., Meng, Y., Li, X., Gao, X.,A fixed point methodology for the design of reactive distillation columns, Chemical Engineering Research and Design (2016), http://dx.doi.org/10.1016/j.cherd.2016.05.015 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Research Highlights

ip t cr us an M



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

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

We developed the fixed point design method for quadruple compositions reactive system by using the element concept. We solve the shortcoming of the element concept for the design of reactive distillation. The temperature is considered to every parameter on the separation and reaction account. We verify the correctness and effectiveness of the modified fixed point design method.

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A fixed point methodology for the design of reactive distillation columns Hong Lia, c, Ying Menga, Xingang Lia, b, c, Xin Gaoa, b,

School of Chemical Engineering and technology, Tianjin University, Tianjin 300072, China

Collaborative Innovation Center of Chemical Science and Engineering(Tianjin), Tianjin 300072, China

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c

National Engineering Research Center of Distillation Technology, Tianjin 300072, China

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b

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a

Abstract

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Reactive distillation (RD), one of the best-known examples of process

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intensification, has been received significant attention. Although the advantages of RD are well documented in the literature, the commercial applications of RD are still

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limited because of the rather complicated design methodology in multi-component

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reaction system. In this paper, a modified fixed point method for the design of reactive distillation column with the multi-component reactive system is developed and illustrated. The method is based on the theory of phase equilibrium, kinetic fixed points

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and element concept in the reactive distillation map. The proposed graphical presentation takes the effect of temperature on the separation and reaction into account, which helps in extrapolating the design details. Three example systems are employed to evaluate the modified fixed point methodology proposed. The results show that the



Corresponding author. Tel: +86-022-27404701(X.G.); Fax: +86-022-27404705(X.G.). E-mail: [email protected] (Xin Gao). 1

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methodology is feasible and computationally efficient even for the complex configurations and multi-component reaction systems. Keywords: Reactive distillation; process intensification; process design; fixed point

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method

1. Introduction

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Reactive distillation, combining reaction with separation in a single process unit,

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represents an exciting alternative for carrying out chemical reaction and separation

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respectively (Agreda and Lilly, 1990; DeGarmo et al., 1992). Compared with traditional technology, this technology has the potential to develop because of these

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following advantages: overcoming chemical equilibrium limitations, minimizing the

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production of undesirable byproducts, improving conversion and yield, improving energy efficiency and potentially reducing flowsheet complexity. However, due to the

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non-linear coupling of reactions, transport phenomena and separation, there is a price to pay in the area of increased complexity in simulation and design. At the present stage, the static and dynamic simulations of reactive distillation processes have been

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performed (Jacobs and Krishna, 1993; Abufares and Douglas, 1995). Nevertheless, the design technology of reactive distillation column is not only in a condition of development, but also relatively difficult to use and limiting. In recent years, many design methods of reactive distillation have been proposed, such as Statics analysis (Serafimov et al., 1999), Residue curve mapping technique (Malone and Doherty, 2000; Siirola, 1996), Attainable region technique (Feinberg, 2

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1999; Nisoli et al., 1997), Fixed-point design method (Buzad and Doherty, 1994; Okasinski and Doherty, 1998) and Conventional graphical techniques (Guo et al., Kang et al., 2014; Lee, 2002; Lee et al., 2002a; Lee et al., 2002b). Comparing these

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methods, it is found that the majority of existing methods, except for the fixed point design method, only can receive the feasibility of the reactive distillation process

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(Almeida-Rivera et al. 2004). Whereas, the fixed point design method can be used to

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particular design and achieve more output parameters than other methods. This

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allows for quick generation of alternative designs, for example, at different reboil ratios, catalyst loading, and/or product specifications, and takes into account heat

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effects, non-ideal vapor-liquid equilibrium and a distribution of liquid holdups on the

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reactive section. The fixed point design method could effectively design the kinetically controlled, stagewise reactive distillation columns.

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However, the fixed point method still has two defects. Firstly, this algorithm does not take into account the effects of temperature on reaction and separation. Temperature is the significant influence of reaction and distillation conditions, such as

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reaction equilibrium constant, rate constant and phase equilibrium. Reactive distillation, a coupling unit, has a significant limitation which is the need for a temperature favorable match between these two sections. So every influence of temperature should be considered to make the design temperature close to practical temperature of the reactive distillation column. Secondly, it is limited by its inherent graphical nature, which imposes practical limitations and complicates its extension to 3

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systems in which the number of components exceeds three. The element concept was applied to reactive distillation for the first time by Pérez Cisneros et al. (1997). This concept has been combined with reactive residue curve map to solve the reactive

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distillation with four components by Daza et al. (2003). This combination allows graphic representation of the reactive distillation processes in a simple way.

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Based on the element concept, the modified fixed point design methodology is

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developed for the reactive distillation with quaternary compositions in this work. It

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also introduces Z axis for temperature to solve the shortage of the element concept, which reduces the freedom in need of backward derivation. Because of the

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importance of the temperature, every of the temperature effects is considered in this

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modified fixed point method. Furthermore, the correctness and effectiveness of the fixed point method modified by the element concept is verified for three production

and TAME.

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processes of four compositions: MTBE (with inert constituents), Amyl acetate (AmA)

2. Methodology

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2.1. The element concept

The element concept is based on atom, molecule or fragment of molecule instead

of substance (Pérez Cisneros, 1998). The independent element number is usually equal to the number of compositions (reactants, products and inerts) involved in the reaction systems minus the number of the reactions (except for isomerization). Although the studied reactive mixtures are consisted of four components, the degrees 4

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of freedom are reduced to three on account of one reaction taking place without stoichiometric restriction. The principle of the element concept is that the amount of the element is not

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changed even though the non-symmetric stoichiometric reactions take place in the system. So the concept could be widely used to any esterification reaction and

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etherification reaction. Furthermore, due to these specialties, the element concept

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offers a new way to express the four compositions on the graph.

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For example, the reaction of methanol and acetic acid to produce methyl acetate and water can be represented as follow:

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Acetic Acid + Methanol ↔ Water + Methyl Acetate

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(CH)2O(H2O) + CH4O ↔ H2O + (CH)2O(CH4O) Here, (CH)2O is element A, H2O is element B, and CH4O is element C. So the

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component Acetic Acid is regarded as AB, the component Methyl Acetate is regarded as AC. The formula matrix of this reaction is written in Table 1. The relationship between the molar concept and the element concept can be seen

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through the formula matrix (or element composition matrix) in Table 1. From Table 1, we could achieve the definition of element fraction:

 Element Quantity j  Element fraction j     Total Quantitits of Elements 

(1)

In this work, we respectively discuss three different reactive systems with four compositions:

(a)

 i A  j B   k C

with

the

inert

component

D,

(b)

5

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 A A  B B   C C  D D , and (c)  i A  j B   k C with an isomer for the reactant or the product. In order to reflect these systems, we choose the etherification reaction of methyl tert-butyl ether (MTBE), the etherification reaction of tert amyl methyl

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ether (TAME), and the esterification reaction system of Amyl acetate.

2.2. The modified fixed point method

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To acquire the balances of the material and the enthalpy over the column,

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bottoms compositions and one distillate specification should be determined. Then the

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balances of the stage-to-stage are calculated from the reboiler to the feed tray on the stripping section. After achieving the compositions on the feed tray, the calculation is

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continued to the condenser by the equations of the rectifying section, as illustrated in

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Fig. 1.

There are some assumptions and system boundaries of the fixed point method

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have been given in the previous papers (Buzad and Doherty, 1994; Okasinski and Doherty, 1998). Firstly, the reaction takes place in the liquid phase on each tray of the column. Secondly, liquid and vapor phase is the ideal mixtures, respectively. Thirdly,

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vapor-liquid equilibrium is obtained. 2.2.1 Overall Column Balances

Based on the fixed point method, the overall and the component molar balances over the column are written as NT

F  D  B  T  H j r j j 1

where NT  N S  N R

(2)

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NT

Fx F ,i  DxD ,i  Bx B ,i  i  H j rj

i = 1...c-1

(3)

j 1

where Hj is the reactive liquid holdup on the tray j, the different value were chosen for the molar liquid holdup (Melles et al., 2000). νi is the stoichiometric coefficient which

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is positive for products and negative for reactants, and their summation is presented

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by νT.

rj k j f

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The reaction rate in the Eq. (2) is followed: j

(4)

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where kj is the reaction rate constant evaluated at the temperature of the tray j, and fj is

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the composition dependent term of the rate expression.

The Damkohler number is defined by the ratio of a characteristic liquid

H 0 k0 F

(5)

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Da 

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residence time (H/F) to a characteristic reactive time (1/kf) as follow:

where H0 is a reference reactive tray holdup, k0 is the kinetic rate constant evaluated at a reference temperature (i.e. reboiler temperature). Using this definition, the

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component molar balances over the column can be written as:  H  k   FxFi  DxDi  BxBi  i ( Da)( F )  j  j  f j  j 1  H 0  k0   NT

i 1 . . . c - 1

(6)

Solving Eq. (6), D/B and F/D are achieved as the following relationship involving the transformed composition variables and the mole fractions of the reference component.

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D   k  T xBk  B   k  T xDk

 X Bi  X Fi    X  X Fi Di  

(7)

F   k  T xDk  X Bi  X Di     D   k  T xFk  X Bi  X Fi 

(8)

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Therefore, F/B can be acquired through D/B and F/D. F F  D    B D B

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(9)

     

(10)

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   xi  i xk k Xi    T  1   xk k 

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where X represent the Ung-Doherty transforms given in the general form as:

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In addition, the liquid holdups in the stripping section and in the rectifying

(Melles et al., 2000).

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section are respectively assumed as constants, although they can vary from tray to tray

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Finally the overall enthalpy balance is given as follow: NT

FE F  Qr  DED  BE B  Qc   Erxn H j rj

(11)

j 1

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where Qr is the reboiler duty and Qc is the condenser duty. The heat of the reactive is represented by Erxn. When the value of Erxn is less than zero, the reactive is exothermic reaction. On the contrary, the reactive is endothermic reaction. 2.2.2 Stripping Section Balances The component material and enthalpy balances for a generic stripping tray n are represented as followed.

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The material balance: 0  x( n 1), i 

Sn 1 y n ,i  x B ,i  Sn  1 Sn  1

i = 1...c-1

n  H  Da  F    k      i  T xn 1,i   j  j  f j  j 1  H 0  k 0   S n  1  B  

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where the reboil ratio on the tray n is defined as Sn. The enthalpy balance:

  HH n

j 1



 k j     f j   Erxn  T E2Ls 0  k 0   j



 k1     f1  0  k 0   

1



(13)

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2.2.3 Rectifying Section Balances

 HH

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

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0  S n  1EnLs1  S1 E1Vs  S1  1E2Ls  S n EnVs   F  Da   Erxn  T EnLs1  B  

(12)

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The component material and enthalpy balances for a generic rectifying tray m are represented as follow:

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The material balance:

 F  y  xF ,i   B  xB ,i  ym,i  0  x( m 1), i  ym,i    m,i     D  Rm 1   D  Rm 1 

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 N s  H j  k j   m  H j  k j     F   T ym,i  i       f j       f j   ( Da )       D R H k H   m 1   j 1  0  0   j 1  0  k0   

i = 1...c-1

(14)

where the reflux ratio on the tray m is defined as follow: Rm  Lm / D

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(15)

The enthalpy balance:













F B 0  Rm 1 EmVr  EmLr1    EFV  q , F  EmVr    EmVr  S1 E1Vs  S1  1E2Ls  D D    H j  k j      f j   1   s Erxn    Ns   H 0  k0   F  Ls Vr   Da T E2  s  Em   N m  H D   j 1 s  H j  k j   j  k j    Vr   f j    T Em  Erxn     f j      H k H j  1 j  1  0  0    0  k0    









9

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(16) where the variable

is the amount of reaction which is completed in the reboiler. In

this work, εS is chosen as zero because of assuming a column with a non-reactive

EFV  EF

(17)

F

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q, 

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reboiler. q, is the dimensionless feed enthalpy, which is defined as the follow.

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where λF is the latent heat of the vaporization at the overall feed composition as discussed by Doherty and Malone (2001). And EF is the feed stream enthalpy.

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2.2.4 Feasibility conditions

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A necessary condition for column feasibility is that the end of the rectifying composition profile is the specified transformed distillate composition. This condition

i = 1...c-2

(18)

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Ym,i  X D ,i

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can be represented by the following equation.

The other condition is that the design result must fulfill the total material balance. The checkout equation can be achieved from the transformed total masterial balance,

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which is represented as follow.

 H j  k j    D   xDi   B   xBi  xFi   Da i=any component   f j           j 1  0  k0    F    i   F    i   i 

NT

  H

(19)

Since the vapor-liquid equilibrium is obtained, the vapor composition can be calculated by the liquid composition using the following phase equilibrium equation. Py i   i xi pis

i = 1...c-1

(20)

where γi is the liquid activity coefficient of the component i, and pis is the saturated 10

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vapor pressure of component i. The Eq. (20) supplements the previous equations to accomplish the calculation of the total reactive distillation column. Through this design methods, the values of the parameters can be achieved such

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as operating conditions (reflux and reboil), number of (non-)reactive stages, location feed staged. These parameters can directly influence the performances of the reactive

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distillation column.

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Because of the limitation of the inherent graphical nature, the fixed point

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method could only be used to the reaction systems with three components. Many of the reaction systems belong to  A A  B B   C C  D D and  i A  j B   k C

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with the inert component D. Therefore, it becomes necessary to extend the applicable

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field of the fixed point method to reaction systems with four components. After stage-to-stage calculation, the four compositions of the each stage are transformed by

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the element concept. The variation trend of every substance is visually achieved on the graph. Furthermore, the fixed point design method can be modified to apply to the reaction systems with four compositions.

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However, the element concept has an inherent disadvantage. On the graph, we

could only acquire the three element compositions. However, Four unknown cannot be figured out by three equations. In order to solve this defect, we introduce the Z axis for temperature, in which the information of each point contains the element compositions and the temperature of the each trays. According to the temperature on the each stage, there is not only three element 11

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fraction equations, but also four phase equilibrium equations and a limit equation (  yi  1 ). Defining the pressure of the stage, only eight parameters are unknown which are four liquid compositions and four vapor compositions. Using those eight

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equations, these parameters can be calculated. Design Algorithm for four components system:

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(1) Specify the operating pressure, the Damkohler number (Buzad and Doherty, 1994),

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feed composition and quality (Eq.(17)), bottoms compositions and one distillate

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specification.

(2) Analysis the fixed points (both the rectifying and stripping sections) and choose a

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suitable reboil ratio.

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(3) Achieve D/B, F/D and F/B through Eq. (7), Eq. (8) and Eq. (9). (4) Acquire the phase equilibrium temperature of bottoms (i.e. the reference

ce pt

temperature) by Eq. (18). And calculate the reference reactive rate constant. (5) Specify the ratio between the stage holdup and the reference stage holdup (H/H0) of the rectifying section and H/H0 of the stripping section respectively (Melles et

Ac

al., 2000).

(6) Calculate the stage-to-stage stripping profile using Eq. (12) and Eq. (13), and compute the element compositions and the phase equilibrium temperature of each stage on the stripping section. (7) Confirm the suitable feed stage. (8) Calculate the stage-to-stage rectifying profile using Eq. (14) and Eq. (16), and 12

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compute the element compositions and the phase equilibrium temperature of each stage on the stripping section. (9) Calculate the checkout equations (Eq. (18) and Eq. (19)). If the design results

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fulfill the checkout equation, this results are feasible. Whereas change the ratio (H/H0) and repeat step (6) to (8).

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(10) Compute the temperature of the condenser.

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(11) Draw the graph of the design results using the element compositions and the

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stage temperature (including condenser).

The modified fixed point method can be used to the reactive distillation of four

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components. Using this method, some important parameters can be achieved such as

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stage numbers, reactive zone, feed location, operating conditions and actual stage compositions. The material balances of this method use reaction rate equation and

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reactive tray holdup, which make the design result close to the actual situation. This is another important advantage of the modified fixed point method. However, this design method only can be used to one feed stream because of the limitation of the

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design equations. Conventional graphical techniques (Guo et al., 2004; Kang et al., 2014; Lee, 2002) has been developed to the double feed streams and reactive extractive distillation, which is the next research point of the modified fixed point method.

3. Case Studies In this section, we will discuss three different reaction systems with four 13

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compositions, such as Amyl acetate, MTBE, and TAME. All of these examples take heat effects, non-ideal vapor-liquid equilibrium, and the placement of reactive and nonreactive zones into account. Especially, the influences of the temperature are

ip t

considered on the whole design procedure. During the calculation of each stage, the temperature of the phase equilibrium is used rather than the average temperature of

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the column.

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3.1. Amyl acetate reaction system

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Amyl acetate has been used in industries as the solvent, the extracting agent, and the polishing agent, etc. The esterification reaction of Acetic acid and 1-Amyl alcohol

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to product Amyl acetate and Water is a reversible, endothermic reaction with a

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stoichiometry given in Eq. (21). The heat of the reaction is approximately 7.33 kJ/mol (Mu, 2008).

(21)

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Acetic acid(AA)  1 - Amylalcohol(AmOH)  Amylacetateol(AmA)  Water

Based on the element concept, the molecule fraction (CH)2O is element A, the chemical substance AmOH and water are element B and C, respectively. These

Ac

elements are located at each vertex of the triangle. The product AmA is combining element with A and B, like the reactant AA which is connecting with element A and C. According the formula matrix of this reaction system, the element fraction equations can be acquired, which is shown in Table 2. In recent years, some kinds of the catalysts have been presented to accelerate the reaction rate of Amyl acetate production. The strong acidic cation exchange resin 14

Page 15 of 54

(Aldrich Chemical Co) is chosen to the catalyst of the reaction (Lee et al., 1999). Because this catalyst has some advantages such as mild reactive condition, good selectivity, the simple post processing of the product, and the continuous production.

ip t

The operating condition of this reactive distillation is chosen at atmospheric (Chiang et al., 2002). The reaction rate can be expressed as following Eq. (22) from Wu (2014).

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The vapor-liquid equilibrium was calculated from the NRTL equation using the

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coefficients from Lee and Liang (1998), and Lee et al. (2000). Physical property data

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is given in Table 3.

(22)

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 C AmACH 2O   r  k f  C AAC AmOH    K eq  

where kf is the forward reaction rate constant given by (23)

ed

50193   1 k f  exp  7.6593   min RT  

ce pt

and the equilibrium constant as follow: 1006.68   K eq  exp  4.00233   T  

T K 

(24)

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In the Amyl acetate reaction system, some design conditions (the pressure, the Damkohler number, the feed composition and flux, the bottoms composition and one distillate specification and the operating reboil ratio) must be specified, which are shown as Table 4. Through these design conditions, the design results, fulfilling the feasibility conditions, can be achieved using the modified fixed point method. This design results for Amyl acetate reaction system are shown in Fig. 2. Specially, the

15

Page 16 of 54

feed stage is the most sensitive stage in the column. Based on the characteristic of the distillation, the stage compositions have a remarkable change on the feed stage. Therefore, when the calculated result of the stage compositions encounters above

ip t

situation, we should give up this stage composition. Furthermore, the computational formula is transformed from the stripping section equations to the rectifying section

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equations, as shown in the Fig. 3. The last stage in the stripping section is the feed

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stage, so the feed location of AmA production system is on the stage 4. According to

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the result of the reaction rate, the reaction zone can been judged. From Fig. 4, the reaction rates on the stage 1 to 4 are positive, while the reaction rate on the stage 5 is

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negative. So the reactive zone is from stage 1 to stage 4, and the feed location is at the

ed

top of the reactive zone.

In AmA production system, ternary azeotropies were found in the mixture of

ce pt

1-Amyl alcohol-amyl acetate-water (Lee et al., 2000; Lee et al., 1999). This might lead to the difficulties in downstream separation when the conventional recycle structure is employed (Chiang et al., 2002). Compared with above situation, the

Ac

reactive distillation could be effective in overcoming these difficulties, as displayed in Fig. 2. According to the design method, we can observe the exceeding 97 mol% for the production that is achieved by only five theoretical stages (without condenser).

3.2. MTBE Reaction System The C4 hydrocarbon mixture is the by-product of the oil refining and oil chemical production. Because of the approximate boiling point of the C4 mixture 16

Page 17 of 54

compositions, saving energy has become the research emphasis for the separation of these components. In recent years, the reactive distillation MTBE (methyl tert-butyl ether) is considered a new separation method of C4 mixtures. It is synthesized from a

ip t

catalyzed reaction between isobutene and methanol, typically in the presence of the inert C4’s (e.g. n-butane or 1-butene). The inerts and the reaction product MTBE are

cr

separated by distillation process (DeGarmo et al., 1992). After acquiring the pure

us

MTBE, isobutene can be produced by the decomposition of MTBE. Therefore, it is

an

necessary to research the reactive distillation design of MTBE production with inerts. A theoretical analysis of the phase behavior and reactive separation for this system

M

without inerts is given by Doherty and Buzad (1992), and the design of MTBE

ed

production without inerts has been presented. In this part, MTBE reaction system with the inerts will be considered, and n-butane is chosen as inert to be designed and

ce pt

analyzed with the reactants and a product.

The reaction of MTBE production is shown as Eq. (25). Isobutene(IB)  Methanol(MOH)  MTBE with n - butane(n - B)

(25)

Ac

Here, isobutene is the element A, methanol is the element B and the inert

n-butane is the element C. In this reaction system, A, B and C are components while the product MTBE is represented by combining AB. In contrast, the reaction for producing Amyl acetate includes a molecule fraction as element A. The formula matrix and the element fraction equations for this reaction system are shown in Table 5. 17

Page 18 of 54

The pressure of this reaction system is chosen as 11 atm (Almeida-Rivera and Grievink, 2004). At this pressure, the system has non-ideal vapor-liquid equilibrium and an exothermal reaction (approximately -36.5kJ/mol) (Ancillotti, 1976). For the

ip t

phase equilibrium, Wilson activity coefficient equation is used due to its accuracy for modeling multi-component mixtures that do not form two liquids (Kooijman and

cr

Taylor, 2000). Pure component vapor pressures are expressed as a function of

us

temperature by means of the Antoine’s equation. Wilson interaction parameters and

an

model parameters of the Antoine’s equation for MTBE reaction system are listed in Table 6 (Ung and Doherty, 1995b; Güttinger, 1998).

M

A kinetic rate expression for this reaction system is shown in Eq. (26) (Venimadhavan et al., 1994). The temperature-dependent rate as follow:   

ce pt

ed

 a r  k f (T )  aIB aMeOH  MTBE  K eq 

(26)

where kf is the temperature dependence of the reaction rate constant.

k f  74.40e3187.0 T

T K 

(27)

Ac

Venimadhavan et al. (1994) formulated the following temperature dependence of equilibrium constant Keq

ln( Keq ) 

6820.0  16.33 T

T [K ]

(28)

According to these equations of the reactive parameters, the reaction rate constant increase as temperature in Fig. 5. However, the line of the equilibrium constant has opposite trend, which is shown as Fig. 6.

18

Page 19 of 54

In this reaction system, the pure components IB, MOH and n-B are located at each vertex of the triangle, and MTBE is represented on the middle of the line that connects with IB and MOH based on the element concept. The design conditions of

ip t

MTBE reaction system are listed in Table 7. According to this conditions, a feasible reactive distillation design yielding MTBE as product is shown in the Fig. 7 using the

cr

same design method with the AmA reaction system. It can be observed from Fig. 7 (b)

us

that 8 reactive stages (without condenser) are required to achieve the product

an

specifications, and that the feed is located at stage 5. Every point of the stage compositions is on the one side of separation boundary (Song et al., 1997), which

M

conforms to the reactive azeotrope and separation principle (Ung and Doherty,

ed

1995a).

3.3 . TAME reaction system

ce pt

Because of the difficult degradation of methyl tert-butyl ether (MTBE), the production technology for reformulated gasoline must be changed. The better oxygenates should be found out and researched. Methyl tert-amyl ether (TAME) is

Ac

considered as a suitable alternative candidate for producing oxygenates with methyl tert-butyl ether (MTBE). In recent years, scientists pay attention to the research of TAME production system. The energy consumption of TAME production system is researched by Plesu et al. (2008), Gao et al. (2014). Therefore, it is very necessary to discuss the design of the reactive distillation column of TAME synthesis. In case of TAME, the fuel ether is formed from methanol and two isomers 19

Page 20 of 54

2-methyl-1-butene (2M1B) and 2-methyl-2-butene (2M2B). The latter two components simultaneously isomerize, forming a reaction triangle with the two TAME synthesis reactions (Oost and Hoffmann, 1996). The reaction scheme is

2 - methyl-1 - butene(2M1B)  methanol(MOH)  TAME

cr

2 - methyl- 2 - butene(2M2B)  methanol(MOH)  TAME

ip t

written as Eq. (29), Eq. (30) and Eq. (31).

us

2 - methyl -1- butene(2M1B)  2 - methyl -2- butene(2M2B)

(29)

(30)

(31)

an

In this reaction system, 2-methyl-1-butene (2M1B) and 2-methyl-2-butene (2M2B) respectively react with methanol to product TAME. According to the element

M

concept, A, B and C are three reactants and TAME is regarded as two different

ed

productions AB (TAME1) and BC (TAME2), which come from different reactants 2M1B and 2M2B. This reaction system can be treat as five compositions, though only

ce pt

four components exist in the reactive distillation. The formula matrix and the element fraction equations for this reaction system are shown in Table 8. The heat of TAME synthesis reaction in liquid-phase is -32.8 kJ/mol for TAME

Ac

synthesis from 2M1B, and -25.6 kJ/mol from 2M2B (Oost et al., 1995). The heat of the isomerisation is -7.2 kJ/mol from 2M1B. The kinetics of these reactions, which quoted by Al-Arfaj and Luyben (2004), are obtained from the Krause’s research group.

r1  1.3263 108 e 76.1037/ RmT x2 M 1B xMeOH  2.3535 1011e 110.541/ RmT xTAME

(32)

20

Page 21 of 54

r2  1.3718 1011 e98.2302/ RmT x2 M 2 B xMeOH  1.5414

(33)

1014 e124.994/ RmT xTAME

r3  2.7187 1010 e96.5226/ RmT x2 M 1B  4.2933

(34)

1010 e104.196/ RmT x2 M 2 B

ip t

In the reaction system, the vapor-liquid equilibrium is non-ideal, and the activity coefficient methods are often used for the simulation of the etherification reaction

cr

systems, including UNIQUAC (Baur and Krishna, 2002) and Wilson method

us

(Sundmacher et al., 1999; Mohl et al., 1999). The reactants can be predicted to form a

an

homogeneous mixture of methanol with the C5 hydrocarbons. The UNIQUAC model predicts the phase splitting, therefore it is not an adequate model for the TAME

M

system. In contrast, the Wilson method can describe the compound activities very

ed

well in this mixture (Mao et al., 2008). So the phase equilibrium is calculated by the Wilson method. Table 9 displays the model parameters of TAME production system.

ce pt

The pressure of this reactive distillation is selected as 5 atm (Sundmacher et al., 1999). All the design conditions, must be specified, are revealed in the Table 10. Feasible design results for this reaction system at 5 atm are shown in Fig. 8, which

Ac

fulfill the feasibility conditions. For this reaction system, reverse reactions have been considered in the reaction zone in order to break distillation boundary and achieve high purity product. The reaction-separation can be accomplished, yielding relatively pure products in about 9 reactive stages (without condenser) and the location of feed is stage 5. All of the stages are reaction stages. From the stereogram, we can achieve the temperature on the each stage, which is a very important factor in the researching 21

Page 22 of 54

of energy analysis.

4. Conclusions In this paper, we discuss the modified fixed point design method used in the

ip t

design of reactive distillation process with four compositions, based on the element concept. By transforming the four compositions in terms of the element, we can break

cr

the limitation of the inherent graphical nature and achieve the chart for the reaction

us

systems with four components. Through introducing Z axis for temperature, we also

an

solve the shortcoming of the element concept that the actual stage composition of four components cannot be obtained from the information of graph. After the calculation

M

used by the modified fixed point design method, the detailed design result with four

ed

compositions from the chart could be achieved, such as stage numbers, reactive zone, feed location, operating conditions and actual stage compositions.

ce pt

By comparing the design results of the three reaction systems (Amyl acetate, MTBE, TAME), the modified fixed point design method has been proved feasible and effective. This design method can be used to the multi-component reactive distillation

Ac

systems.

Acknowledgements The authors are grateful for the financial support from the National High Technology Research and Development Program of China (No. 2015AA030501), and the National Natural Science Foundation of China (No. 21336007).

Notation 22

Page 23 of 54

name of element

M

number of element

B

bottoms molar flow rate [mol/time]

c

number of components

D

distillate molar flow rate [mol/time]

Da

Damkohler number

E

enthalpy [kJ/mol]

Erxn

heat of reaction [kJ/mol]

f

composition-dependent term of the rate expression

F

feed molar flow rate [mol/time]

H

liquid reactive holdup on a tray [mol]

H0

reference reactive holdup on a tray [mol]

Hrxn

heat of reaction [kJ/mol]

k

rate constant [time-1]

Keq

reaction equilibrium constant

L

molar liquid flow rate [mol/time]

Ac

ce pt

ed

M

an

us

cr

ip t

A,B,C

NR

total number of rectifying stages

NS

total number of stripping stages

NT

total number of stages in the column

P

pressure [kPa]

Ps

saturated vapor pressure [kPa] 23

Page 24 of 54

feed quality as defined by Doherty and Malone

Qc

condenser duty [W]

Qr

reboiler duty [W]

R

reflux ratio

r

reaction rate [time-1]

S

reboil ratio

T

temperature [K]

V

molar vapor flow rate [mol/time]

x

liquid mole fraction

y

vapor mole fraction

Greek Letters

ed

M

an

us

cr

ip t

q

amount of reaction in the reboiler

γ

activity coefficient

λ

heat of vaporization [kJ/mol]

υ

stoichiometric coefficient of ith component

Ac

υ

ce pt

εs

summation of stoichiometric coefficients

X

transformed liquid composition variable

Y

transformed vapor composition variable

Subscripts 24

Page 25 of 54

bottoms

D

distillate

F

feed

f

forward

i

ith component

j

jth stage

k

reference component

m

rectifying section tray number

n

stripping section tray number

r

rectifying section

s

stripping section

V

vapor

us an

M

Ac

ce pt

liquid

ed

Superscripts L

cr

ip t

B

References

Abufares, A. A., Douglas, P. L. (1995). Mathematical modelling and simulation of an MTBE catalytic distillation process using SPEEDUP and ASPENPLUS. Chemical engineering research & design, 73(1), 3-12. Agreda, V. H., Lilly, R. D. (1990). U.S. Patent No. 4,939,294. Washington, DC: U.S. 25

Page 26 of 54

Patent and Trademark Office. Almeida-Rivera, C., Grievink, J. (2004). Feasibility of equilibrium-controlled reactive distillation process: application of residue curve mapping. Computers &

ip t

chemical engineering, 28(1), 17-25. Almeida-Rivera, C. P., Swinkels, P. L. J., Grievink, J. (2004). Designing reactive

cr

distillation processes: Present and future. Computers & chemical engineering,

us

28(10), 1997-2020.

an

Al-Arfaj, M. A., Luyben, W. L. (2004). Plantwide control for TAME production using reactive distillation. AIChE journal, 50(7), 1462-1473.

M

Ancillotti, F., Oriani, G., Pescarollo, E. (1976). U.S. Patent No. 3,979,461.

ed

Washington, DC: U.S. Patent and Trademark Office. Baur, R., Krishna, R. (2002). Hardware selection and design aspects for reactive

ce pt

distillation columns. A case study on synthesis of TAME. Chemical Engineering and Processing: Process Intensification, 41(5), 445-462. Buzad, G., Doherty, M. F. (1994). Design of three-component kinetically controlled

Ac

reactive distillation columns using fixed-points methods. Chemical Engineering Science, 49(12), 1947-1963.

Chiang, S. F., Kuo, C. L., Yu, C. C., Wong, D. S. (2002). Design alternatives for the amyl acetate process: coupled reactor/column and reactive distillation. Industrial & engineering chemistry research, 41(13), 3233-3246. Daza, O. S., Pérez-Cisneros, E. S., Bek-Pedersen, E., Gani, R. (2003). Graphical and 26

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stage-to-stage methods for reactive distillation column design. AIChE journal, 49(11), 2822-2841. DeGarmo, J. L., Parulekar, V. N., Pinjala, V. (1992). Consider reactive distillation.

ip t

Chemical Engineering Progress, 88(3), 43-50. Doherty, M. F., Buzad, G. (1992). Reactive distillation by design. Chemical

cr

engineering research & design, 70(A5), 448-458.

an

McGraw-Hill Science/Engineering/Math.

us

Doherty, M. F., Malone, M. F. (2001). Conceptual design of distillation systems.

Feinberg, M. (1999). Recent results in optimal reactor synthesis via attainable region

M

theory. Chemical engineering science, 54(13), 2535-2543.

ed

Gao, X., Wang, F., Li, H., Li, X. (2014). Heat-integrated reactive distillation process for TAME synthesis. Separation and Purification Technology, 132, 468-478.

ce pt

Guo, Z., Chin, J., Lee, J. W. (2004). Feasibility of continuous reactive distillation with azeotropic mixtures. Industrial & engineering chemistry research, 43(14), 3758-3769.

Ac

Güttinger, T. E. (1998). Multiple steady states in azeotropic and reactive distillation (Doctoral dissertation, Diss. Techn. Wiss. ETH Zürich, Nr. 12720, 1998. Ref.: Manfred Morari; Korref.: Sigurd Skogestad; Korref.: Massimo Morbidelli). Jacobs, R., Krishna, R. (1993). Multiple solutions in reactive distillation for methyl tert-butyl ether synthesis. Industrial & engineering chemistry research, 32(8), 1706-1709. 27

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Jakkula, J. J., Ignatius, J., Järvelin, H. (1995). Increase Oxygenates & Lower Olefins in Gasoline. Fuel Reformulation, 5(1), 46-54. Kang, D., Lee, K., Lee, J. W. (2014). Feasibility Evaluation of Quinary

ip t

Heterogeneous Reactive Extractive Distillation. Industrial & Engineering Chemistry Research, 53(31), 12387-12398.

cr

Kooijman, H. A., Taylor, R. (2000). The ChemSep book. Norderstedt, Germany:

us

Books on Demand.

an

Lee, L. S., Liang, S. J. (1998). Phase and reaction equilibria of acetic acid–1-pentanol–water– n-amyl acetate system at 760 mm Hg. Fluid Phase

M

Equilibria, 149(1), 57-74.

ed

Lee, M. J., Chen, S. L., Kang, C. H., Lin, H. M. (2000). Simultaneous chemical and phase equilibria for mixtures of acetic acid, amyl alcohol, amyl acetate, and

ce pt

water. Industrial & engineering chemistry research, 39(11), 4383-4391. Lee, M. J., Wu, H. T., Kang, C. H., Lin, H. M. (1999). Kinetic behavior of amyl acetate synthesis catalyzed by acidic cation exchange resin. Journal of the

Ac

Chinese Institute of Chemical Engineers, 30(2), 117-122.

Lee, J. W. (2002). Feasibility studies on quaternary reactive distillation systems. Industrial & engineering chemistry research, 41(18), 4632-4642. Lee, J. W., Hauan, S., Lien, K. M., Westerberg, A. (2000a). A graphical method for designing reactive distillation columns. I. The Ponchon–Savarit method. Proceedings of the Royal Society of London Series A: Mathematical Physical 28

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and Engineering Sciences, 456(2000), 1953–1964. Lee, J. W., Hauan, S., Lien, K. M., Westerberg, A. (2000b). A graphical method for designing reactive distillation columns. II. The McCabe–Thiele method.

and Engineering Sciences, 456(2000), 1965–1978.

ip t

Proceedings of the Royal Society of London Series A: Mathematical Physical

us

Chemistry Research, 39(11), 3953-3957.

cr

Malone, M. F., Doherty, M. F. (2000). Reactive distillation. Industrial & Engineering

an

Mao, W., Wang, X., Wang, H., Chang, H., Zhang, X., Han, J. (2008). Thermodynamic and kinetic study of tert-amyl methyl ether (TAME) synthesis.

M

Chemical Engineering and Processing: Process Intensification, 47(5), 761-769.

ed

Melles, S., Grievink, J., Schrans, S. M. (2000). Optimisation of the conceptual design of reactive distillation columns. Chemical Engineering Science, 55(11),

ce pt

2089-2097.

Mohl, K. D., Kienle, A., Gilles, E. D., Rapmund, P., Sundmacher, K., Hoffmann, U. (1999). Steady-state multiplicities in reactive distillation columns for the

Ac

production of fuel ethers MTBE and TAME: theoretical analysis and experimental verification. Chemical Engineering Science, 54(8), 1029-1043.

Mu, R. N. (2008). Synthesis of N-amyl acetate catalyzed by Keggin-type heteropolyacids. Master dissertation, Lanzhou University of Technology, Lanzhou, China. Nisoli, A., Malone, M. F., Doherty, M. F. (1997). Attainable regions for reaction with 29

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separation. AIChE journal, 43(2), 374-387. Okasinski, M. J., Doherty, M. F. (1998). Design method for kinetically controlled, staged reactive distillation columns. Industrial & engineering chemistry research,

ip t

37(7), 2821-2834. Oost, C., Sundmacher, K., Hoffmann, U. (1995). Synthesis of tertiary amyl methyl

cr

ether (TAME): Equilibrium of the multiple reactions. Chemical engineering &

us

technology, 18(2), 110-117.

an

Oost, C., Hoffmann, U. (1996). The synthesis of tertiary amyl methyl ether (TAME): microkinetics of the reactions. Chemical engineering science, 51(3), 329-340.

M

Serafimov, L. A., Pisarenko, Y. A., & Kardona, K. A. (1999). Optimization of

33(5), 455–463

ed

reactive distillation processes.Theoretical Foundations of Chemical Engineering,

ce pt

Pérez Cisneros, E. S., Gani, R., Michelsen, M. L. (1997). Reactive separation systems—I. Computation of physical and chemical equilibrium. Chemical Engineering Science, 52(4), 527-543.

Ac

Pérez Cisneros, E. S. (1998) Modeling, design and analysis of reactive separation process. Doctoral dissertation, Technical University of Denmark.

Plesu, A. E., Bonet, J., Plesu, V., Bozga, G., Galan, M. I. (2008). Residue curves map analysis for tert-amyl methyl ether synthesis by reactive distillation in kinetically controlled conditions with energy-saving evaluation. Energy, 33(10), 1572-1589. Song, W., Huss, R. S., Doherty, M. F., Malone, M. F. (1997). Discovery of a reactive 30

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azeotrope. Nature, 388(6642), 561-563. Siirola, J. J. (1996). Industrial applications of chemical process synthesis. Advances in chemical engineering, 23, 1-62.

ip t

Sundmacher, K., Uhde, G., Hoffmann, U. (1999). Multiple reactions in catalytic distillation processes for the production of the fuel oxygenates MTBE and

us

Engineering Science, 54(13), 2839-2847.

cr

TAME: Analysis by rigorous model and experimental validation. Chemical

an

Ung, S., Doherty, M. F. (1995). Synthesis of reactive distillation systems with multiple equilibrium chemical reactions. Industrial & engineering chemistry

M

research, 34(8), 2555-2565.

ed

Ung, S., Doherty, M. F. (1995). Vapor-liquid phase equilibrium in systems with multiple chemical reactions. Chemical Engineering Science, 50(1), 23-48.

ce pt

Venimadhavan, G., Buzad, G., Doherty, M. F., Malone, M. F. (1994). Effect of kinetics on residue curve maps for reactive distillation. AIChE journal, 40(11), 1814-1824.

Ac

Wu, Y., (2014). The research of Reaction Kinetics for the amyl acetate synthesis. Bachelor dissertation, Tianjin University, Tianjin, China.

31

Page 32 of 54

Figure captions

Figure Captions Fig. 1. Schematic representation of a reactive distillation column

Fig. 2. Feasible design for Amly acetate reation system. The solid line represents the column

ip t

profile. The stages are marked by +. (a) three dimentional stereogram, (b) vertical view, (c) side

cr

view.

us

Fig. 3. The calculation result of stripping section, the red point is abandoned

an

Fig. 4. The reaction rate of each stage in the stripping section

M

Fig. 5. Evolution of the equilibrium constant Keq versus the temperature

Fig. 6. Evolution of the reaction rate constant kf versus the temperature

ed

Fig. 7. Feasible design for MTBE reation system. The solid line represents the column profile. The stages are marked by + . (a) three dimentional stereogram, (b) vertical view, (c) side view.

Ac

ce pt

Fig. 8. Feasible design for TAME reation system. The solid line represents the column profile. The stages are marked by + . (a) three dimentional stereogram, (b) vertical view, (c) side view.

Page 33 of 54

ce pt

ed

M

an

us

cr

ip t

Figure 1

Ac

Fig. 1. Schematic representation of a reactive distillation column

Page 34 of 54

Ac

ce pt

ed

M

(a)

an

us

cr

ip t

Figure 2

(b)

Page 35 of 54

ip t cr us an

M

(c)

ed

Fig. 2. Feasible design for Amly acetate reation system. The solid line represents the column profile. The stages are marked by +. (a) three dimentional stereogram, (b) vertical view, (c) side

Ac

ce pt

view.

Page 36 of 54

an

us

cr

ip t

Figure 3

Ac

ce pt

ed

M

Fig. 3. The calculation result of stripping section, the red point is abandoned

Page 37 of 54

M

an

us

cr

ip t

Figure 4

Ac

ce pt

ed

Fig. 4. The reaction rate of each stage in the stripping section

Page 38 of 54

M

an

us

cr

ip t

Figure 5

Ac

ce pt

ed

Fig. 5. Evolution of the equilibrium constant Keq versus the temperature

Page 39 of 54

M

an

us

cr

ip t

Figure 6

Ac

ce pt

ed

Fig. 6. Evolution of the reaction rate constant kf versus the temperature

Page 40 of 54

Ac

ce pt

ed

M

(a)

an

us

cr

ip t

Figure 7

(b)

Page 41 of 54

ip t cr us an

M

(c)

Fig. 7. Feasible design for MTBE reation system. The solid line represents the column profile. The

Ac

ce pt

ed

stages are marked by + . (a) three dimentional stereogram, (b) vertical view, (c) side view.

Page 42 of 54

Ac

ce pt

ed

M

(a)

an

us

cr

ip t

Figure 8

(b)

Page 43 of 54

ip t cr us an

Ac

ce pt

ed

M

(c) Fig. 8. Feasible design for TAME reation system. The solid line represents the column profile. The stages are marked by + . (a) three dimentional stereogram, (b) vertical view, (c) side view.

Page 44 of 54

Table 1

Table 1. Formula matrix of methyl acetate Element

Component Acetic acid

methanol

water

Methyl acetate

A

1

0

0

1

B

1

1

0

0

C

0

0

1

1

Ac

ce pt

ed

M

an

us

cr

ip t

amyl acetate

Page 45 of 54

Table 2

Table 2. Amly acetate reaction system AA = (CH)2O(H2O),

AmOH= C5H12O,

AmA = (CH)2O(C5H12O),

Water = H2O

(CH)2O(H2O)+C5H12O↔H2O+(CH)2O(C5H12O) Element definition: (CH)2O =A, C5H12O = B, H2O = C Element reaction: AC+B↔C+AB Formula matrix AmOH(2)

Water (3)

A

1

0

0

B

0

1

0

C

1

0

1

1

cr

1 0

us

x1  x3 x2  x4 x1  x4 , WB  , WC  1  x1  x4 1  x1  x4 1  x1  x4

Ac

ce pt

ed

M

an

Element fractions: WA 

AmA (4)

ip t

AA(1)

Page 46 of 54

Table 3

Table 3. Thermodynamic Data for the Amly acetate system Antoine Coefficients A

B

C

AA AmOH AmA Water NRTL Parameters (i,j) (1,2) (1,3) (1,4) (2,3) (2,4) (3,4)

6.5729 6.3975 7.356 7.074056

1572.32 1337.613 2258.3 1657.459

-46.777 -106.567 0 -46.13

Aij(K) -316.8 -37.943 -110.57 -144.8 100.1 254.47

Aji(K) 178.3 214.55 424.018 320.6521 1447.5 2221.5

αij 0.1695 0.2000 0.2987 0.3009 0.2980 0.2000

ln  i 

 j 1 m

ji

G ji x j

G k 1

x

ki k

cr us

p s Pa , T K 

  m   rjGrj xr  x j Gij   m  ij   r 1m   j 1 Gkj xk    Gkj xk  k 1  k 1  m

M

m

B T C

an

lg p s  A 

ip t

component

     

where

ed

Gij  exp   ij ij  ,

G ji  exp   ij ji 

Ac

ce pt

 ij  Aij T ,  ji  Aji T , and  ii   jj  0

Page 47 of 54

Table 4

Table 4. Specific design conditions for the Amyl acetate reaction system Parameters

Input number

Feed compositions AA/AmOH/AmA/Water Bottoms compositions AA/AmOH/AmA/Water Distillate compositions AA/AmOH/AmA/Water The ratio between distillate flow rate (D) and bottoms flow rate (B) /(D/B) The ratio between feed flow rate (F) and distillate flow rate (D) /(F/D) The ratio between feed flow rate (F) and bottoms flow rate (B) /(F/B) Feed quality / q 

0.5/0.5/0/0

1.7766 2.2877

us

cr

1 0.5 2.5 0.001246

ip t

1.2877

1.7350

an

Da number Reboil ratio /s The reference kinetic rate constant /k0 The ratio between stage holdup and the reference stage holdup /(H/H0) Pressure /P(atm)

0.0055/0.0245/0.97/ 1  108 0.02933/0.01457/0.1014/0.8547

Ac

ce pt

ed

M

1

Page 48 of 54

Table 5

Table 5. MTBE reaction system IB = C4H8,

MOH = CH4O,

MTBE = C5H12O,

n-B = C4H10

C4H8+CH4O↔C5H12O with the inert C4H10 Element definition: C4H8 =A, CH4O = B, C4H10 = C Element reaction: A + B ↔ AB with the inert C Formula matrix MOH (2)

n-B (3)

A

1

0

0

B

0

1

0

C

0

0

1

1

cr

1 0

us

x3 x1  x4 x  x4 , WB  2 , WC  1  x4 1  x4 1  x4

Ac

ce pt

ed

M

an

Element fractions: WA 

MTBE (4)

ip t

IB (1)

Page 49 of 54

Table 6

Table 6. Thermodynamic Data for the MTBE reaction system Antoine Coefficients component

A

B

C

IB MOH MTBE n-B Wilson Parameters aij (-) IB MOH MTBE n-B bij (K) IB MOH MTBE n-B

6.27428 7.23029 6.0911 6.574609

1095.288 1595.671 1171.54 1349.115

-9.441 -32.245 -41.542 24.7281

MOH -0.742 0 -0.9833 -0.81492

MTBE 0.2413 0.9833 0 0

0 -1296.719 -136.6574 0

85.5447 0 204.5029 -192.4019

30.2477 -746.3971 0 0

C

ed

0 -1149.28 0 0

p s Pa , T K 

    x ln  i  1  ln   x j  ij     C k ki  j 1  k 1   x j  kj   j 1 C

cr

us

an

B T C

M

lg p s  A 

n-B 0 0.81492 0 0

ip t

IB 0 0.742 -0.2413 0

     

where

 ij  1 Implies ideality

Ac

ce pt

ln ij   aij  bij T

Page 50 of 54

Table 7

Table 7. Specific design conditions for the MTBE reaction system Parameters

Input number

Feed compositions IB/MOH/MTBE/n-B Bottoms compositions IB/MOH/MTBE/n-B Distillate compositions IB/MOH/MTBE/n-B The ratio between distillate flow rate (D) and bottoms flow rate (B) /(D/B) The ratio between feed flow rate (F) and distillate flow rate (D) /(F/D) The ratio between feed flow rate (F) and bottoms flow rate (B) /(F/B) Feed quality / q 

0.4/0.4/0/0.2 0.04/0.129/0.85/0.02 0.2184/0.0105/0.0022/0.7689

2.4671

us

cr

1 10 20 0.04660

ip t

4.0069

5.6897

an

Da number Reboil ratio /s The reference kinetic rate constant /k0 The ratio between stage holdup and the reference stage holdup /(H/H0) Pressure /P(atm)

0.6157

Ac

ce pt

ed

M

11

Page 51 of 54

Table 8

Table 8. TAME reaction system 2M1B = CH2C(CH3)C2H5,

2M2B = (CH3)2CCHCH3,

MOH = CH4O,

TAME1/2 = C6H14O CH2C(CH3)C2H5+CH4O↔C6H14O; (CH3)2CCHCH3+CH4O↔C6H14O Element definition: CH2C(CH3)C2H5 =A, CH4O = B,(CH3)2CCHCH3= C Element reaction: A + B ↔ AB C + B ↔ BC

ip t

Formula matrix 7.

2M1B (1)

MOH (2)

2M2B (3)

TAME1(4)/TAME2(5)

A

1

0

0

1

B

0

1

0

C

0

0

1

cr 1

0

1

us

1

x  x4  x5 x1  x4 x3  x5 , WB  2 , WC  1  x4  x5 1  x4  x5 1  x4  x5

Ac

ce pt

ed

M

an

Element fractions: WA 

0

Page 52 of 54

Table 9

Table 9. Thermodynamic Data for the TAME reaction system Antoine Coefficients A

B

C

Vi (cm3/mol)

MOH 2M1B 2M2B TAME* Wilson Parameters Aij (-) MOH 2M1B 2M2B TAME*

7.23029 6.09149 6.04808 9.1556

1595.671 1124.33 1099.054 2782.4

-32.245 -36.52 -39.836 -55.243

6.62 7.2827 7.3708 1.2987

MOH 0 1.3765 0.96881 -0.177

2M1B 9.7723 0 -0.47794 0.95133

2M2B 10.147 0.4788 0 0.71233

TAME 4.8263 -0.61175 -0.38604 0

p s bar , T K 

B T C

an

TAME: ln p s  A 

cr

p s Pa , T K 

B T C

us

lg p s  A 

ip t

component

    x ln  i  1  ln   x j  ij     C k ki  j 1  k 1   x j  kj   j 1 C

M

C

     

where

 Aij exp  Vi  RT

ed  ij 

Vj

  

Ac

ce pt

Aii  0  ii  1 implies ideality

Page 53 of 54

Table 10

Table 10. Specific design conditions for the TAME system Parameters

Input number

Feed compositions 2M1B/2M2B/MOH/TAME Bottoms compositions 2M1B/2M2B/MOH/TAME Distillate compositions 2M1B/2M2B/MOH/TAME The ratio between distillate flow rate (D) and bottoms flow rate (B) /(D/B) The ratio between feed flow rate (F) and distillate flow rate (D) /(F/D) The ratio between feed flow rate (F) and bottoms flow rate (B) /(F/B) Feed quality / q 

0.16/0.34/0.5/0 0.02/0.014/0.034/0.95 0.1971/0.6935/0.1076/0.0018

1.9730

ip t

85.8268

us

cr

1 5 5 0.06 0.01(stripping section) /4.43027(rectifying section) 5

Ac

ce pt

ed

M

an

Da number Reboil ratio /s The reference kinetic rate constant /k0 The ratio between stage holdup and the reference stage holdup /(H/H0) Pressure /P(atm)

0.0229885

Page 54 of 54