Improving Batch Reactive Distillation Processes with Off-Cut

Article pubs.acs.org/IECR

Improving Batch Reactive Distillation Processes with Off-Cut Yu-Lung Kao and Jeffrey D. Ward* Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan ABSTRACT: Methods for improving the operation of batch reactive distillation with off-cut are presented and discussed. Although off-cut can improve the operation of batch reactive distillation, its usefulness is limited in some cases due to the relative volatility ranking of reactants and products. In these cases, performance can be improved by using a middle vessel column or by using an excess of one reactant. These methods are demonstrated with case studies of three processes with realistic reaction kinetics and vapor−liquid equilibrium models: hydrolysis of methyl lactate, esterification of formic acid, and production of 1,1dimethoxyethane. Batch capacity can be improved on average 41.9% if the appropriate method is employed.

1. INTRODUCTION Reactive distillation has been shown to be advantageous compared with conventional processes in many literature reports and has been applied successfully in many existing commercial processes.1 It can reduce the capital cost and the energy consumption, overcome the reaction equilibrium limitation and azeotropes, and improve the conversion and selectivity. Reactive distillation can also be conducted batch-wise and such a process is called batch reactive distillation (BREAD). Compared with continuous distillation, the operating flexibility of batch distillation makes it preferable for the production of low-volume products or products with seasonal demand. Cuille and Reklaitis,2 Wajge et al.,3 Bollyn and Wright,4 and Brüggemann et al.5 discuss the development and numerical solution of dynamic models for BREAD systems. The feasibility of BREAD processes is investigated by Lee and co-workers6−8 using RCMs and Steger et al.9 using a graphical method. Venimadhaven et al.,10 Fernholz et al.,11 Edreder et al.,12 and Qi and Malone13 discuss the design and operation of BREAD processes for different chemical systems. A common operation to improve the performance of batch distillation processes is the collection of off-cut (waste-cut).14,15 Off-cut is material that does not meet any product purity specifications and must be either disposed of safely, recycled to the next batch, or collected for further processing in a separate batch. The off-cut is usually collected between two successive valuable product cuts. However, only a few articles discuss off-cut collection in BREAD processes10,16 because most researchers consider collecting only one single valuable product, let alone the optimization of BREAD processes with off-cut.17−19 In our previous work,20 an ideal quaternary reactive system A + B ↔ C + D which has 6 distinct boiling point rankings was investigated for the design and optimization of BREAD processes including off-cut collection. Two basic column configurations, conventional batch distillation (CBD) and inverted batch distillation (IBD), with neat design (equal molar feed) were considered (see Figure 1). Both products were assumed valuable and have a purity specification, so off-cut may be used between two product cuts. The results show that including an off-cut collection period improves the process performance in terms of batch capacity (CAP),21 especially when both reactant species in the chemistry can be withdrawn as an off-cut. Because © 2014 American Chemical Society

unconsumed reactants are impurities in the accumulated product after the collection of the withdrawn product, effectively removing them by distillation can help the accumulated product achieve the purity specification in a shorter time. However, for many systems, off-cut removal is limited by the column configuration. In a CBD, only components lighter than the accumulated product can be removed. On the other hand, in an IBD only components heavier than the accumulated component can be removed. This limitation results in two unfavorable scenarios for some quaternary systems: 1. Only one unconsumed reactant species can be removed by distillation during the off-cut period. 2. No unconsumed reactant species can be removed by distillation during the off-cut period. For these two scenarios, the CAP improvement from including an off-cut period is not significant. Therefore, in this work we propose two design alternatives to overcome this limitation. The first one is to use a composite column configuration, middle-vessel column (MVC) which is depicted in Figure 1. An MVC can be seen as a combination of a CBD and an IBD column. Feed (reactants) is loaded in the middle-vessel (feed drum), and products or off-cuts can be withdrawn either form the top or the bottom of the column. By adjusting the reflux ratio and the boilup ratio, product cuts and off-cuts can be collected only at the top (operated as a CBD with total boilup), at the bottom (operated as an IBD with total reflux), or both the top and bottom simultaneously during the batch depending on which species should be collected. Therefore, an MVC can remove components either lighter or heavier than the accumulated product. The second design alternative is to use excess reactant. The limiting reactant is expected to be almost completely consumed so that only one reactant species (the excess reactant) remains in the accumulated product must be withdrawn as an off-cut. The first design alternative can be applied to both unfavorable scenarios mentioned previously, whereas the second method can only apply to the first scenario. Received: Revised: Accepted: Published: 8528

December 17, 2013 March 26, 2014 April 23, 2014 April 23, 2014 dx.doi.org/10.1021/ie404229w | Ind. Eng. Chem. Res. 2014, 53, 8528−8542

Industrial & Engineering Chemistry Research

Article

Figure 1. Conventional batch distillation (CBD), inverted batch distillation, and middle-vessel column (MVC) diagram.

IBD is feasible. The feasibility of the quaternary system for CBD, IBD and MVC are summarized in Table 1. In our previous work, a BREAD process with total batch time tb is divided into three periods: total reflux/boilup period, product period, and off-cut period, and the reaction takes place in the feed drum (reaction vessel) during the whole batch. In the total reflux/boilup period tt, the column is operated under total reflux or total boilup until high purity product can be withdrawn. In the product period tp, distillate or bottom flow is withdrawn and collected in the accumulator as a product cut. In most cases, this period ends when adding any further distillate or bottom flow to the accumulator will cause the product purity in the product cut to fall below the specification. In the off-cut period toff, distillate or bottom flow is diverted to another accumulator as an off-cut until the product accumulating in the reactive vessel reaches the specification. This is also the end of the batch. Similarly, an MVC process is also divided into three periods in this work except for the type Ip system in which both products are withdrawn from the column at the same time. This will be discussed further in the MVC collection policy in section 3.2. 2.2. Case Studies. Modified designs are demonstrated for three chemical systems with realistic reaction and vapor−liquid equilibrium models: hydrolysis of methyl lactate,12 esterification of formic acid,23 and synthesis of 1,1-dimethoxyethane (DMA).24 We found that the feasibility of these three real systems with azeotropes is consistent with the criteria proposed by Gao et al.: at least one of the products is a stable node or an unstable node lying in a reachable distillation region.6 For each system, it is shown that off-cut collection can be made more practical and efficient with modifications to the operating policy. These three systems represent three possible off-cut removal scenarios (zero, one or two unconsumed reactants can be removed effectively by distillation) that may be encountered in the design of BREAD processes for quaternary reactions. 2.2.1. Hydrolysis of Methyl Lactate. The hydrolysis of methyl lactate is an important step in the purification of lactic acid (LAC). The reaction is water + methyl lactate ↔ methanol + lactic acid. The vapor liquid equilibrium is described by the NRTL model, and the boiling point raking of this system including an azeotrope is listed in Table 2. According to the classification, it belongs to type Ip system. 2.2.2. Esterification of Formic Acid. The second chemistry system is the esterification of formic acid (FA) to produce methyl formate (MF). MF is the simplest ester, and can be used in agriculture such as insecticide, fungicide, crops fumigant, fruit desiccants among other uses. The reaction is methanol + formic acid ↔ methyl formate + water. The vapor liquid equilibrium is described by the NRTL model, and the dimerization of formic acid in the vapor phase is considered. A maximum-boiling

The remainder of this article is organized as follows. First, the classification of quaternary systems and their feasibility is shown, and three real chemistry systems which are used to illustrate these methods are presented. In section 3, challenges associated with the use of off-cut removal for conventional designs (CBD/ IBD neat design) are reviewed, and the two proposed methods for improving process performance with off-cut are discussed. Next, the formulation of the optimization problem is described. Then, optimization results of conventional designs and modified designs are given and compared. Suggested design configurations for quaternary BREAD process with off-cut are summarized in the discussion subsection. Finally, conclusions are drawn. The BREAD process model and the thermodynamic and kinetic models for three systems are given in the Appendix.

2. BREAD PROCESS DESCRIPTION 2.1. Reactive System Classification and Feasibility. According to Tung and Yu’s classification,22 an ideal quaternary reaction system A + B ↔ C + D can be divided into 6 (4!/2!/2!) distinct types depending on the boiling point ranking among the reactants and products if two reactants and two products are interchangeable (Table 1). LLK (lighter-than-light key), LK Table 1. Classification and Feasibility of a Quaternary System feasibilitya type

chemistry A + B ↔ C + D

CBD

Ip Ir IIp IIr IIIp IIIr

LK + HK ↔ LLK + HHK LLK + HHK ↔ LK + HK HK + HHK ↔ LLK + LK LLK + LK ↔ HK + HHK LK + HHK ↔ LLK + HK LLK + HK ↔ LK + HHK

O X O X O X

b

IBDc

MVCd

O X X O X O

O X O O O O

a

O: feasible; X: infeasible. bConventional batch distillation. cInverted batch distillation. dMiddle-vessel distillation column.

(light key), HK (heavy key), and HHK (heavier-than-heavy key) are used to denote each component in the system from the most volatile species to the least volatile species. Therefore, the boiling points from low to high are Tb,LLK < Tb,LK < Tb,HK < Tb,HHK. These 6 types represent all possible rankings for an A + B ↔ C + D reaction system without azeotropes. The feasibility of BREAD processes with azeotropes was studied by Guo et al.6 For the ideal reactive system mentioned, a BREAD processes is feasible if and only if one of the product species is the lightest boiler (CBD is feasible) or the heaviest boiler (IBD is feasible). Because an MVC can be operated as either a CBD or an IBD, an MVC is feasible if either a CBD or an 8529

dx.doi.org/10.1021/ie404229w | Ind. Eng. Chem. Res. 2014, 53, 8528−8542


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abbreviated as MeCHO) and the reaction is acetaldehyde +2 methanol ↔ DMA + water. The NRTL model is also used to describe the vapor−liquid equilibrium, and the boiling point ranking of pure components and an azeotrope is listed in Table 2. Based only on the boiling point ranking, this process appears to be a type IIIr system. However, a distillation boundary is formed due to the azeotrope (the residue curve map is shown in the Appendix) which makes DMA the next species withdrawn from an IBD column after the collection of the heaviest boiler, water. Therefore, the DMA system in fact behaves as a type IIr process where the two products are close boilers.

Table 2. Boiling Point Rankings for Different Reaction Systems hydrolysis of methyl lactate temp (K)

water

methyl lactate

337.68 373.16 373.17 417.99 489.78

0 0.9909 1 0 0

0 0.0091 0 1 0 esterification of formic acid

temp (K)

methanol

304.94 337.68 373.17 373.7 379.96

0 1 0 0 0

formic acid

methanol 1 0 0 0 0

methyl formate

0 0 0 1 0.5434 synthesis of DMA

1 0 0 0 0

lactic acid 0 0 0 0 1 water

3. OFF-CUT REMOVAL 3.1. Challenges in Off-Cut Removal. After the product period, off-cut removal assists the purification of the accumulated product in the reaction vessel by distillation. At this time, the species that must be removed in the off-cut are unconsumed reactants. Because the composition in the reaction vessel is not favorable for the reaction, using distillation and off-cut collection to reduce the concentration of unconsumed reactant is likely to be more efficient than using reaction. However, off-cut removal is not always effective for conventional designs depending on the boiling point ranking of the reactants and products.20 If a CBD is used, only reactants lighter than the accumulated product can be removed by distillation as off-cut. For CBD Ip process, off-cut removal is effective because both reactants (LK and HK) are lighter than the accumulated product (HHK). The hydrolysis of the methyl lactate system is an example of this type. Residual amounts of both water and methyl lactate, the two reactants, can be removed in an off-cut. However, for CBD IIIp process, the accumulated product is the HK and the two reactants are the LK and HHK. One is lighter and the other one is heavier than the accumulated product. Consequently one reactant species (LK) can be removed in an off-cut. For example, in the esterification of formic acid, only methanol can be removed

0 0 1 0 0.4566

temp (K)

acetaldehyde

methanol

DMA

water

294.21 332.23 337.45 337.68 373.17

1 0 0 0 0

0 0.5265 0 1 0

0 0.4735 1 0 0

0 0 0 0 1

azeotrope exists between formic acid and water. The boiling point raking of this system is listed in Table 2. According to the classification, it is a type IIIp system. 2.2.3. Production of Dimethylacetal. The third chemistry is to produce 1, 1-Dimethoxyethane (or dimethylacetal, DMA) which is an intermediate for specialty chemicals such as alkyl vinyl ethers, and a raw material in consumer chemicals and pharmaceutical chemicals.24 The main synthesis route is through acetalization of methanol with acetaldehyde (CH3CHO,

Figure 2. Collecting policy of MVC design. 8530



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in the esterification of formic acid, methanol should be the excess reactant because it can be removed by distillation in an off-cut. Excess reactant design can also be applied to CBD Ip process, and the more easily removed reactant is chosen as the excess reactant. LK is excess for CBD Ip and HK is excess for IBD Ip. For example, in the hydrolysis of methyl lactate, if a CBD column is employed water should be the excess reactant because it is more volatile than the other reactant methyl lactate and therefore easier to separate from the product lactic acid that will accumulate in the reaction vessel at the bottom of the column. Conversely, if an IBD column is employed the excess reactant should be methyl lactate because it is heavier than water and therefore easier to separate from the methanol that will accumulate in the reaction vessel at the top of the column.

as an off-cut. Furthermore, for CBD IIp processes in which both of the reactants are heavier (HK and HHK) than the accumulated product (LK), no reactant species can be removed in an off-cut. Synthesis of DMA system is an example of a system in which neither reactant species (acetaldehyde or methanol) can be effectively removed using an off-cut in a conventional column. These limitations impose a reaction conversion constraint depending on the product purity specification for the product that accumulates in the reaction vessel for type IIp and type IIIp processes. Because IBD Ip, IBD IIr, and IBD IIIr are mirror images of CBD Ip, CBD IIp, and CBD IIIp, they have analogous constraints. For IBD processes, only reactants heavier than the accumulated product can be removed by off-cut; therefore, both reactants species (LK and HK), one reactant species (HK), and no reactant species can be removed as off-cut for type Ip, type IIIr, and type IIr, respectively. In this work, two modified designs, MVC design and excess reactant design are proposed to overcome the off-cut removal limitation in conventional processes. MVC columns offer greater flexibility for the collection of products and off-cuts. Where and when to collect product and off-cut is discussed in section 3.2 depending on the boiling point rankings. Operation of a conventional or inverted column with excess reactant is similar to regular operation: a product cut is withdrawn followed by an off-cut. Only which reactant is the excess reactant must be determined, and this is discussed in section 3.3. 3.2. Improving Off-Cut Removal with MVC. Because both light and heavy components can be withdrawn from an MVC, the difficulties of off-cut removal discussed previously can be overcome with proper operation. When an MVC is employed, it is important to consider the collection policy which determines where and when product cuts and off-cuts are withdrawn from the column and collected. The collection policy in the off-cut period is straightforward: If the species to be removed is lighter, off-cut is withdrawn from the top. Conversely, if the species to be removed is heavier, off-cut is withdrawn from the bottom. Figure 2 shows the proper collection policy for all 5 feasible boiling point rankings for MVC processes. For type IIp and type IIIp, the MVC is operated under total boilup as a CBD in the product period, and the product LLK is collected at the top. Conversely, for type IIr and type IIIr the MVC is operated under total reflux as an IBD, and the product HHK is collected at the bottom. Although there is no difficulty of off-cut removal for type Ip, MVC provides another possible operation. Because the two products are the lightest and heaviest components, the product LLK and HHK can be collected simultaneously at the top and bottom during the product period. An off-cut period is not required because no product accumulates in the middle-vessel. However, if any material remains in the middle-vessel at the end of the process, it can be regarded as an off-cut of the process. 3.3. Improving Off-Cut Removal with Excess Reactant Design. The idea of using excess reactant design to overcome the difficulty of off-cut removal is to use the excess reactant to consume almost all of the limiting reactant so that the amount of limiting reactant left in the reaction drum is very small and does not need to be removed from the column as an off-cut. However, the excess reactant will constitute an impurity in the accumulated product and must still be removed by distillation as an off-cut. Therefore, excess design is only appropriate for CBD IIIp and IBD IIIr processes in which one reactant species can be removed as off-cut. The excess reactant should be the one that can be removed by distillation. Thus, the LK is the excess reactant for CBD IIIp and HK is the excess reactant for IBD IIIr. For example,

4. OPTIMIZATION PROBLEM FORMULATION In this work, optimization is employed to determine the best process design with and without the improvements described in this article. The optimization problem formulation for the processes is similar to our previous work.20 The same model assumptions and the same algorithm of optimization are used. The main assumptions of the model include constant molar holdup on the stage, no reaction on the stage, and constant molar overflow. Details about the model assumptions and model equations of MVC are given in the Appendix. Batch capacity (CAP) is chosen as the objective function, and it is defined as the total moles of on-spec products collected divided by the total batch time.21 Since the number of column stages and reboiler size are fixed, the optimization variables are the reflux ratio Rr(t) for CBD, the boilup ratio Br(t) for IBD, and both Rr(t) and Br(t) for MVC as well as the length of the product collection period tp. For batch distillation, the reflux ratio is usually defined as L/(L+D) in which L denotes reflux flow rate and D denotes distillation flow rate. Similarly, the boilup ratio is defined as V/(V+B) in which V denotes vapor flow rate leaving the reboiler and B denotes bottom flow rate. The value of reflux/ boilup ratio is between 0 and 1, and 1 represents total reflux or total boilup. The reactant feed ratio is also optimized for excess reactant designs. During the product period, the composition of reactants and products changes significantly in the reaction vessel. Thus, a piecewise constant reflux/boilup profile is used to improve the process performance. The product period is divided into four time periods based on our previous work,20 which showed that the improvement in CAP from increasing the number of periods becomes relatively small after 4 periods. A constant reflux/boilup ratio in each time interval is determined by optimization. For the off-cut period a constant reflux/boilup ratio for the entire period is determined by optimization. The length of the off-cut period is not an optimization variable because the off-cut period ends when the accumulated product reaches the product purity specification. Therefore, the reflux/ boilup ratio and length of off-cut period are not independent variables. A vector is used to denote the reflux or boilup ratio profile in this work, for example, Rr = [1; 0.87; 0.89; 0.91; 0.93; 0.9 ]. The first entry is always 1 (representing the total reflux period), the next four values are for the product period, and the last value is for the off-cut period. Two constraints are applied to the optimization problem: the total amount of product obtained and the purity of both products at the end of the batch. The product amount is specified as 90% of theoretical total conversion of the initial feed amount remaining in the reaction vessel after the start-up period. That is, the holdup amount in the reboiler/condenser and on the trays 8531



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Figure 3. Variation of CAP and % of product as product period length changes for conventional BREAD design (left column) and MVC design (right column) for (a) methyl lactate system, (b) methyl formate system, and (c) DMA system.

is excluded from the theoretical yield. (For excess reactant design, the excess amount is not included in the initial feed calculation. That is, the product yield requirement is the same as neat design.) The purity specification is set at 95 mol % for both products. The minimum total amount of product is specified to prevent the optimization from suggesting an impractically large amount of off-cut because only single-batch operation is considered. However, if batch-to-batch operation is considered, off-cut collected during the batch can usually be recycled to next batch as part of the feed. The differential algebraic equations describing the model is built in Matlab and solved by a built-in ode solver ode15s. The simulated annealing (SA) method is used to find the optimal reflux/boilup ratio profile.20,25 Details about parameters used for optimization are listed in the Appendix. For each chemistry, different designs are compared. In order to make a fair comparison, the column specification for different configurations (stage number = 20, 10, and 15 for MeLC, MF, and DMA system, respectively, holdup on trays and in the condenser/reboiler, and the boilup rate = 2500 mol/h) and

initial feed condition are set the same. For an MVC, the same total number of trays is employed with half of the trays above the reaction vessel and half of the trays below the reaction vessel. The initial charge of the limiting reactant is always 2500 mol. If an excess reactant is employed, the amount of the excess reactant is determined by optimization. The total holdup on trays is 100 mol, and the holdup in the condenser for a CBD, reboiler for an IBD or the combined holdups of the condenser and the reboiler for an MVC (50 mol each) is also 100 mol. Therefore, 4800 mol are contained in the feed drum (reaction vessel) after start-up period for the neat design. The modeling of the start-up period from a dry column is not considered in the work. Instead, the initial condition for the simulations reported in this work (the end of the start-up period) is calculated by the following procedure. First, the appropriate quantity of feed mixture is distributed to the trays and reboiler/condenser/middle vessel depending on the column configuration. Then the column is operated under total reflux/boilup without reaction until a steady-state is achieved. This steady-state is the end of the start8532



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Table 3. Optimal Operating Recipe for Conventional Design, MVC Design, and Excess Reactant Design (Excess Ratio = 1.12) for Methyl Lactate Hydrolysis Process CAP (mol/h)

tt (h)

tp (h)

toff (h)

CBD

293.01

0.51

13

1.319

MVC

382.96

0.93

11

CBD excess

304.09

0.53

12

configuration

Rr(*) Br(+)

tb (h) 14.829 11.930

1.858

14.388

[1.000; 0.860; 0.942; 0.973; 0.956; 0.862]* [1.000; 0.907; 0.915; 0.924; 0.920; (−) ]* [1.000; 0.936; 0.924; 0.923; 0.912; (−) ]+ [1.000; 0.858; 0.938; 0.962; 0.949; 0.844]*

Table 4. Optimal Results for Methyl Lactate Hydrolysis Process: Properties of Products and Off-Cut

configuration

amount of product MeOH (mol)

composition of product MeOH (water; MeLC; MeOH; LAC) (mol %)

CBD MVC CBD Excess

2185.6 2296.2 2197.5

(4.89; 0.02; 95.09; 0.00) (4.65; 0.00; 95.35; 0.00) (4.97; 0.02; 95.01; 0.00)

amount of product LAC (mol)

composition of product D (water; MeLC; MeOH; LAC) (mol %)

amount of offcut (mol)

composition of off-cut (water; MeLC; MeOH; LAC) (mol %)

2159.4 2272.5 2177.7

(0.00; 4.99; 0.00; 95.01) (0.00; 4.56; 0.00; 95.44) (0.00; 4.98; 0.00; 95.02)

455.0 231.3 724.8

(57.63; 32.94; 9.43; 0.00) (34.79; 37.08; 9.11; 19.02) (71.60; 18.41; 9.92; 0.07)

Figure 4. Reflux/boilup ratio profile and composition profile of optimal operating policy for CBD neat, MVC, and CBD excess (water = 2800 mol) design for methyl lactate system.

removal efficacy. Optimal designs based on maximizing CAP are presented and compared between modified and conventional design. Design guidelines for different boiling rankings are addressed in the Discussion section. 5.1. Hydrolysis of Methyl Lactate. The hydrolysis of methyl lactate is a type Ip system; thus, CBD and IBD are both feasible for the process because the two products are the lightest and the heaviest boiler. For off-cut removal, type Ip is the most favorable because both reactants can be removed by distillation.

up period and also the initial condition for simulations presented in this work.

5. OPTIMIZATION RESULTS AND DISCUSSIONS In this section, modified processes are designed and optimized for three real chemical systems, hydrolysis of methyl lactate, esterification of formic acid, and synthesis of 1,1-dimethoxyethane (DMA) to demonstrate the improvement in the off-cut 8533



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higher reaction conversion can be achieved. During the product period, the reflux ratio increase to maintain the product purity because the reaction rate in the reboiler decreases as the concentration of two reactants decreases. The product period ends when collecting additional distillate in the product receiver will result in the total concentration of the product cut falling below the product purity specification. At this time, the distillate is diverted into the off-cut receiver and the off-cut period starts. During the off-cut period, unconsumed reactants are the major impurities in the product LAC and they can be removed effectively by distillation because they are the next two most volatile boilers after methanol. Water is removed first, followed by methyl lactate. When the concentration of LAC in the reboiler achieves the specification, the batch process ends. For the MVC process reactants are charged in the middlevessel initially. According to the collection policy discussed in section 3.1, the column is operated under total reflux and total boilup until the concentrations of methanol and lactic acid achieve specification at the reflux drum and reboiler, respectively. Methanol and LAC are withdrawn from the column simultaneously in the product period. The optimization result shows that reflux ratio and the boilup ratio are kept in a certain range because the concentration profile does not vary too much in the product period. Reactants are consumed by reaction, and products are removed by distillation. Because no product accumulates in the middle vessel, an off-cut period is not required for purification. The process ends when any distillate or bottom flow added to the product cuts will cause the product purity to fall below the specification. A small amount of material remains in the reactive middle vessel. Compared with the CBD design, MVC design has a higher CAP because it can remove both products from the reaction vessel which favors the reaction during the whole batch. Therefore, it can be expected that MVC design is especially favorable when the reaction equilibrium is small and the production constraint is high. The maximal CAP of the CBD design not subject to the product yield constraint is comparable to the optimal MVC design which meets the product yield constraint. However, the high CAP of the CBD design results from a short product period with small product amount and a large amount of off-cut (which is why it does not satisfy the product yield constraint). That is, the process only produces methanol in the early part of the process during which the LAC concentration is still low in the reboiler and the reaction is still favorable. When the reaction is not favorable due to the accumulation of LAC, the process stops collecting methanol and begins the off-cut period so that the process can end in a shorter time. Therefore, for this system MVC design is an attractive alternative. Excess reactant design is also tested for this chemistry for the CBD column configuration. Figure 5a shows the CAP of optimal design and its corresponding batch time distribution for different excess ratios. The excess ratio is defined as the total amount of excess reactant divided by the total amount of one reactant in the neat design. In this case the excess reactant is the more volatile reactant water. As the excess ratio increases, the optimal product period can be reduced (from 13 to 12 h) and CAP can be improved because the excess reactant can force the reaction to achieve a certain conversion (depending on the production constraint) in a shorter time. However, there is an optimal excess ratio (excess ratio = 1.12) because increasing the excess ratio results in a longer off-cut time required for removing the excess reactant in the off-cut period. The optimal CAP and operating

Although there is no limitation on off-cut collection for Ip systems, MVC and excess design are applied to see if they can improve the batch capacity. For type Ip systems, CBD usually has a higher CAP than IBD because the temperature of the reaction vessel is greater for CBD (because the heavy product accumulates in the reaction vessel).20 Therefore, only CBD processes are considered for the optimization. In the conventional design, methanol is withdrawn from the top of the column and LAC accumulates in the reboiler. On the other hand, according to the collection policy of MVC type Ip, methanol and LAC are withdrawn from the top and the bottom of the column simultaneously. The effect of the product period length on the objective function CAP and the percentage of product obtained compared to the total amount of feed for CBD neat design and MVC design is shown in Figure 3a. For each product period, an optimal reflux/boilup profile satisfying only the purity constraint is determined to maximize the CAP. (The optimal CAP satisfying both purity and product amount constraints can be found from the figure by identifying the column with the greatest CAP for which the product yield is greater than 90%.) For both designs, it can be noted that the product amount collected at the end of the batch increases as product period increases. In other words, the process has a higher product yield and less off-cut (holdup left in the middle-vessel at the end of the batch for the MVC design is regarded as off-cut) if the process runs for a longer batch time. Off-cut amount decreases progressively as product period increases. This is straightforward for a batch process because the reaction and the separation require time. However, the product yield is not the only concern for the process design. The longer batch time causes more energy consumption. The objective function CAP used in this work considers the product yield as well as the operating time, and it determines the maximal production rate under a given separation ability of the distillation column, e.g. fixed total number of stages and the reboiler specification. The result shows that the design of the maximum CAP for the MVC satisfies the production constraint, but the optimal CBD neat design does not. Therefore, the optimal feasible design for the conventional process has a lower CAP than the maximum theoretical value without the constraint. The optimal CAP and operating recipes including the optimal reflux/boilup ratio profile and the optimal duration of the total reflux period, product period, off-cut period, and total batch time for both designs are listed in the first and second row of Table 3. Compared with the conventional design, the CAP is improved by 30.7%. Table 4 shows the corresponding properties of the products and off-cut collected for the optimal design. The left and middle column of Figure 4 shows the reflux/ boilup ratio profile and the composition profile at different locations in the process for the optimal CBD neat design and MVC design. For the CBD process, reactants are loaded in the reboiler initially. As the batch process begins, the reaction takes place in the reboiler and products are produced. Since product methanol is the lightest boiler in the system, its concentration becomes richer and richer at the top (see the reflux drum profile). When the concentration reaches the product specification (t = 0.51 h), the reflux ratio is lowered so that methanol can be withdrawn from the column and collected in the product cut receiver. This is also the end of the total reflux period and the beginning of the product period. During the product period, the other product LAC accumulates in the reboiler. Because product methanol is continuously removed from the reactive reboiler, the reaction will not be limited by the reaction equilibrium, and a 8534



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removal, because the accumulated product lies in between the two reactants in the boiling point ranking, only the lighter unconsumed reactant can be removed by distillation in the offcut period. Therefore, MVC design and excess design are both applied to improve the off-cut removal and seek possible improvement in the CAP. For the conventional design, similar to the methyl lactate process the lighter product MF is withdrawn at the top and the heavier product water accumulates in the reboiler. For the MVC design, MF is also withdrawn from the column at the top. Water accumulates in the middle-vessel and is purified by two off-cuts withdrawn from the top and bottom of the column in the off-cut period. The effect of the product period length on the CAP and the percentage of product obtained for CBD neat design and MVC design is shown in Figure 3b. For each product period, an optimal reflux profile is determined to maximize the CAP satisfying the purity constraint. Unlike the methyl lactate process where both unconsumed reactants can be removed effectively in a single off-cut, the off-cut amount for the conventional design for the methyl formate process is small even for a short product period. Methanol must be kept in the reboiler and to react with formic acid until the amount of unconsumed formic acid remaining is smaller than the impurity constraint for the water. In other words, if too much methanol is removed with the MF in the product period or removed too early as an off-cut, the product water will contain too much FA and will never achieve the purity specification. Therefore, when a shorter length of product period is used, the process will have a very high reflux ratio in the off-cut period so that methanol can still be refluxed back to the reboiler for the further reaction. The small amount of offcut collected in this case has a very high concentration of MF (Table 5) which meets the product purity specification and therefore should be combined with the MF product (in practice, no off-cut should be collected). In other words, the optimization result indicates that including an off-cut period does not improve the process for neat CBD process. By contrast, the optimal MVC process has a trend similar to the methyl lactate process in which both unconsumed reactants can be removed effectively. However, for the methyl formate process, MVC design does not give a better CAP than the conventional process even though the difficulty of removing unconsumed reactants is overcome. The CAP and corresponding operating policy of optimal design for these two designs are listed in Table 6. MVC has a much lower CAP than the conventional process because there are only half as many trays available for separating MF in the product period. A higher reflux ratio and a longer product period are required for the MVC design. Moreover, the heavier reactant forms a maximum-boiling azeotrope with the accumulated product water which makes the bottom off-cut removal impractical. For these two reasons, MVC is not a good process alternative for MF process. Excess reactant design provides another way of overcoming the difficulty of off-cut removal. With an excess of the lighter reactant methanol, the reaction conversion of lactic acid is expected to be achieved more easily, and the problem of depleting the system of methanol too early is mitigated. The optimal CAP and the batch time distribution for different excess ratios is shown in Figure 5b. The optimal operating recipe for each excess ratio is also listed in Table 6 for reference. The CAP increases significantly when small excess ratio is applied, and a maximal CAP is achieved when excess ratio equals 1.1 (MeOH = 2750 mol) with 34.6% CAP improvement. The significant CAP improvement comes from the reduced optimal product period

Figure 5. CAP and batch time distribution of optimal design for different excess ratios (a) methyl lactate system, (b) methyl formate system, and (c) DMA system.

recipe and the properties of the products and off-cut collected are also listed in Table 3 and Table 4 respectively along with CBD neat and MVC design. Compared with the neat design, the CAP improvement is less significant (3.8%). The composition profile for excess optimal design is shown in the right column of Figure 4. 5.2. Esterification of Formic Acid. The esterification of formic acid (FA) to produce methyl formate (MF) is a type IIIp system, thus a CBD column is feasible for the process. For off-cut 8535



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Table 5. Optimal Results for Esterification of Formic Acid Process: Properties of Products and Off-Cut amount of feed MeOH (mol)

amount of product MF (mol)

MF product composition (MeOH; FA; MF; water) (mol %)

2500

2295.0

(3.92; 0.00; 96.07; 0.01)

2500

2345.0

(4.81; 0.00; 95.08; 0.11)

2550 2600 2650 2700 2750 2800 2850

2321.7 2313.4 2354.6 2326.6 2345.5 2356.3 2361.1

(4.88; 0.00; 95.10; 0.02) (4.97; 0.00; 95.01; 0.02) (4.98; 0.00; 95.00; 0.01) (4.99; 0.00; 95.00; 0.01) (4.99; 0.00; 95.00; 0.01) (4.98; 0.00; 95.01; 0.01) (4.99; 0.00; 95.00; 0.01)

amount of product water (mol) CBD neat 2455.5 MVC 1977.3 CBD excess 2452.3 2444.9 2434.4 2444.1 2437.2 2429.1 2420.2

composition of product water (MeOH; FA; MF; water) (mol %)


composition of off-cut (MeOH; FA; MF; water) (mol %)

(0.18; 4.82; 0.00; 95.00)

49.4

(2.41; 0.00; 97.57; 0.02)a

(0.41; 4.47; 0.12; 95.00)

477.7

(8.31; 17.67; 14.13; 59.89)

(0.28; 4.72; 0.00; 95.00) (0.30; 4.69; 0.00; 95.01) (0.40; 4.58; 0.01; 95.01) (0.51; 4.45; 0.01; 95.03) (0.58; 4.41; 0.01; 95.00) (0.64; 4.32; 0.01; 95.03) (0.78; 4.19; 0.01; 95.02)

76.0 141.7 161.0 229.3 267.3 314.6 368.7

(4.27; 0.00; 95.70; 0.03)a (12.67; 0.00; 87.27; 0.06) (30.50; 0.00; 69.32; 0.18) (35.49; 0.00; 64.39; 0.12) (46.38; 0.00; 53.40; 0.22) (54.19; 0.00; 45.43; 0.38) (60.84; 0.00; 38.58; 0.58)

The cut collected during the off-cut period satisfies the MF product specification, and will be combined with the MF product cut to form the final MF product cut obtained. a

Table 6. Optimal Operating Recipe for Conventional Design, MVC Design, and Different Amount of Excess Reactant Design for Esterification of Formic Acid Process amount of feed MeOH (mol)

CAP (mol/h)

tt (h)

tp (h)

2500

1026.96

0.37

2500

260.17

2550 2600 2650 2700 2750 2800 2850

1221.97 1296.60 1339.04 1355.15 1368.41 1367.59 1361.78

Rr(*) Br(+)

toff (h)

tb (h)

4.0

CBD 0.304 MVC

4.674

[1.000; 0.583; 0.603; 0.911; 0.985; 0.935]*

0.42

14

2.194

16.614

[1.000; 0.858; 0.926; 0.964; 0.984; 0.979]* [1.000; 1.000; 1.000; 1.000; 1.000; 0.938]+

0.37 0.37 0.37 0.37 0.37 0.37 0.37

3.25 2.75 2.75 2.5 2.5 2.5 2.5

CBD excess 0.349 0.550 0.456 0.650 0.625 0.629 0.641

3.969 3.670 3.576 3.520 3.495 3.499 3.511

[1.000; 0.479; 0.542; 0.864; 0.972; 0.913]* [1.000; 0.468; 0.510; 0.736; 0.940; 0.897]* [1.000; 0.476; 0.499; 0.748; 0.907; 0.859]* [1.000; 0.499; 0.483; 0.660; 0.869; 0.859]* [1.000; 0.478; 0.515; 0.653; 0.853; 0.829]* [1.000; 0.497; 0.498; 0.658; 0.839; 0.800]* [1.000; 0.487; 0.517; 0.660; 0.825; 0.770]*

purity to the constraint and can be removed effectively in the offcut period. 5.3. Synthesis of 1,1-Dimethoxyethane (DMA). The DMA system behaves as a type IIr process, thus an IBD column is feasible for the process, but the off-cut removal has the least favorable scenario: no unconsumed reactants can be removed by distillation. Since the stoichiometry for the reaction is not 1:1, the feed contains 1666.7 mol of MeCHO and 3333.3 mol of methanol. For conventional design, an IBD column is feasible because one of the products is the heaviest boiler. Water is withdrawn from the bottom of the column and DMA accumulates in the feed drum. On the other hand, for MVC design water is also withdrawn from the bottom of the column, and DMA accumulates in the middle-vessel and is purified by an off-cut withdrawn at the top in the off-cut period. The effect of product period length on CAP and product percentage for conventional design and MVC design is shown in Figure 3c. For each product period, an optimal reflux/boilup profile is determined to maximize the CAP satisfying the purity constraint. The figure shows that for conventional design no off-cut is withdrawn (total boilup in the off-cut period) from the column except for tp = 8 h because unconsumed MeCHO and methanol tend to stay in the top of the column. Neither of the unconsumed reactants can be removed from the column by distillation. They can only be

(4h to 2.5h). For neat design, an unusually high product purity of MF is obtained, 96.10% (including the cut collected in the off-cut period) compared to the minimum requirement 95.0%, from the optimization result (see Table 5) which results in a higher reflux ratio and a longer optimal batch time. This can be understood as follows. The major impurity in the product cut is methanol that is withdrawn along with the methyl formate in the product period. Keeping more methanol in the column allows the formic acid (which cannot be removed by distillation) to reach the necessary reaction conversion. Therefore, when excess methanol is employed, more methanol can be withdrawn along with MF. The product purity of MF returns to the constraint value (from 96.10% for neat, 95.12% for 2550 MeOH used, to almost 95.00% for more MeOH used), and a lower reflux ratio and shorter batch time can be used. However, when too much excess methanol is used, a longer off-cut period is required to separate it from the water in the reboiler during the off-cut period. The reflux/boilup profile and composition profile of optimal conventional, MVC and excess design are shown in Figure 6. The arguments presented above are borne out by the figure. Only a small amount of methanol is removed in the conventional design. In the MVC design, both unconsumed reactants can be removed by off-cut, but a large amount of accumulated product water is lost with the bottom off-cut. Excess methanol lowers the withdrawn product 8536



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Figure 6. Reflux/boilup ratio profile and composition profile of optimal operating policy for CBD neat, MVC, and CBD excess (MeOH = 2750 mol) design for methyl formate system.

Although excess reactant design is not suitable for the IBD process because neither reactant can be removed by distillation, it can be applied to the MVC process. The lighter reactant MeCHO is chosen as the excess reactant because it is easier to remove in the off-cut period. Furthermore, according to the reaction stoichiometry, one mole of MeCHO reacts with two moles of methanol. Therefore, excess MeCHO is more effective in driving the reaction forward. Figure 5c shows the optimal CAP and batch time distribution for different excess ratios. Similar to the excess design of the methyl formate process, the optimal product period can be reduced significantly when small amount of excess is used because excess MeCHO drives the reaction forward, especially toward the end of the batch as the production constraint is approached. It can be seen in Figure 3c which shows the product percentage versus the length of product period, that in order to increase the product amount from about 80% to 90%, product period increases from 20h to 40h. Similarly, there is an optimal excess ratio because too large excess ratio will increase the effort required for removal of the excess reactant. The optimal excess ratio for this design is 1.18 (1966.7 mol of MeCHO) and there is a significant improvement in the CAP of 60.4%. The optimal operating recipe and properties of collected products and off-cut are listed in Table 7 and Table 8. MVC operation helps to reduce the off-cut period, and excess reactant design helps to reduce the product period. 5.4. Discussion. The modifications discussed earlier have been applied to three different systems which represent three

reduced by the reaction until the sum of their amount is less than what the product DMA can contain. The function of the off-cut period is to remove any water produced in the feed drum in order to drive the reaction forward. Total boilup operation allows water to accumulate in the reboiler, and does not result in the loss of DMA in an off-cut (see reboiler composition profile in the left column of Figure 7). For tp = 8 h, a small amount of off-cut is withdrawn because water produced in the off-cut period exceeds the capacity of the reboiler. The optimal design given in the first row of Table 7 has a very long off-cut period because the reaction is very slow when a large amount of DMA is present. On the other hand, MVC design can remove both unconsumed reactants in an off-cut at the top of the column, thus the off-cut period can be reduced significantly and the product yield increases as the product period increases. The maximal CAP of MVC design is 145.61 mol/h when tp = 11 h which is about 44.4% higher than the optimal conventional design. However, this design does not meet the production constraint. The CAP of the optimal design that satisfies the production constraint requires tp = 42 h which results in a worse CAP than the conventional optimal design (see Table 7). Because only half of the total stages are used for separating water in the product period, a longer time is required to produce enough products that satisfy the constraint. Although unconsumed reactants are removed effectively in the product period (see the reflux drum composition profile in the middle column of Figure 7), MVC design is not a good process alternative. 8537



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Figure 7. Reflux/boilup ratio profile and composition profile of optimal operating policy for IBD neat design, MVC design, and MVC excess (acetaldehyde = 1966.7 mol) design for DMA system.

Table 7. Optimal Operating Recipe for Conventional Design, MVC Design, and MVC Excess Reactant Design (Excess Ratio = 1.18) for DMA Process CAP (mol/h)

tt (h)

tp (h)

toff (h)

tb (h)

IBD

100.81

0.40

10

20.939

31.339

MVC

65.09

0.34

42

2.093

44.433

MVC Excess

161.72

0.34

12

3.109

15.449

configuration

Rr(*) Br(+) [1.000; 0.865; 0.944; 0.980; 0.980; 1.000]+ [1.000; 1.000; 1.000; 1.000; 1.000; 0.937]* [1.000; 0.956; 0.989; 0.997; 0.998; 1.000]+ [1.000; 1.000; 1.000; 1.000; 1.000; 0.865]* [1.000; 0.907; 0.946; 0.973; 0.978; 1.000]+

Table 8. Optimal Results for Synthesis of DMA Process: Properties of Products and Off-Cut

configuration

amount of product DMA (mol)

composition of product DMA (MeCHO; MeOH; DMA; water) (mol %)

IBD MVC MVC excess

1558.0 1260.6 1262.2

(1.65; 3.31; 95.00; 0.04) (0.13; 4.85; 95.02; 0.01) (0.66; 4.29; 95.03; 0.03)

amount of product water (mol)

composition of product D (MeCHO; MeOH; DMA; water) (mol %)


composition of off-cut (MeCHO; MeOH; DMA; water) (mol %)

1601.3 1631.7 1633.1

(0.00; 0.01; 4.99; 95.00) (0.00; 0.05; 4.72; 95.23) (0.00; 0.11; 4.71; 95.18)

0 329.9 606.4

(25.98; 28.03; 45.98; 0.00) (54.11; 14.76; 31.13; 0.00)

different possible scenarios for quaternary systems with off-cut removal. The hydrolysis of methyl lactate represents type Ip system. MVC design is preferred because it can remove both products simultaneously. The esterification of formic acid is a type III system. Type IIIp and type IIIr are mirror image, and they can be understood using the same logic. Excess reactant design with a CBD or an IBD is preferred because excess reactant can

solve the off-cut removal difficulty and all distillation stages are used for separation during the product period for CBD and IBD operation. The synthesis of DMA represents type II system. Type IIp and type IIr are also analogous. MVC configuration is preferred for type II because the off-cut period can be reduced significantly. Moreover, both unconsumed reactants are withdrawn from the same side of the column, so the loss of the 8538



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accumulated product in the off-cut period is smaller compared to MVC type III processes. However, for the DMA system neat MVC design does not improve the optimal CAP due to the production constraint. Therefore, excess reactant design is employed, and a significant CAP improvement is achieved. The presence of azeotropes would make the classification of processes more difficult and some systems with azeotropes would not behave like any of those considered by Tung and Yu. However, the modified designs illustrated in this work can still be applied to improve the process performance. For example, if the lightest product forms an azeotrope with the lighter reactant, and the azeotrope is a saddle lying in the same distillation as the lightest product, then an excess of the heavier reactant can be used to consume the reactant that forms the azeotrope, and an MVC configuration can be used to remove the unconsumed excess reactant from the bottom to purify the accumulated product. Excess design can eliminate or reduce reactant species which is undesired in the distillate/bottom or not removable for a CBD or an IBD. MVC design can remove either the lightest or the heaviest species in the mixture at any point in the batch. Similarly, the ideas of these two modifications can be extend to systems with different number of components depending on the boiling point ranking, residue curve maps, reaction stoichiometry, and the collecting policy. For the three systems studied here, the purity requirements of both products are the same. However, it can be expected that the suggested modified designs will be especially preferable when the purity specification on the accumulated product is higher because off-cut removal is most useful in this case. Conversely, if the purity of the withdrawn product is the only concern, off-cut removal is not required. Thus, the modified designs are not recommended. In practice, batch operations are usually conducted repeatedly. In this case off-cut can be recycled to the next batch, in which case the expense and complication associated with collecting off-cut are minimal. For the case of the design of a batch campaign at quasi-steady-state, an objective function can be formulated based on minimizing total cost and in this case it is not necessary to include a constraint on the minimal amount of product collected from a given batch. This may result in an even greater improvement in process performance.

batch capacity is improved by 60.4% compared to a neat IBD process.

■

APPENDIX

Model

A set of differential and algebraic equations (DAEs) can be used to describe a BREAD process. Time dependent differential equations correspond to the mass balance and energy balance during the batch. Algebraic equations correspond to physical properties such as the stage temperature, vapor-liquid equilibrium, reaction rate, holdup volume, liquid and vapor flow rate, etc. A simplified model modified from Cuille is adopted in this study.2 Main assumptions include: (1) Vapor−phase holdups are negligible. (2) Energy balance is neglected. (3) Constant molar overflow. (4) Constant molar holdup on each stage. (5) The liquid flow leaving the stage reaches phase equilibrium with the vapor flow leaving the stage. (6) The initial condition is the steady-state under total reflux without reaction. (7) The reaction takes place only in the reaction vessel. The model equation of CBD and IBD can be referred to Kao and Ward,20 and the model equations of an MVC are present here. An MVC can be divided into three sections shown in Figure A1: Rectifying Section

Component i Mole Balance, i = A, B, C, and D. Condenser: A0

dX 0, i

= V1·Y1, i − L0 ·X 0, i − D·X 0, i

dt

(1)

Stage j, 1 ≤ j ≤ Nf-1 (Nf: feed stage): Aj

dX j , i dt

= Vj + 1·Yj + 1, i + Lj − 1·Xj − 1, i − Vj·Yj , i − Lj ·Xj , i

(2)

Feed Section

Total Mole Balance. Middle-vessel: NC

dAM = LNf − LM + AM ·∑ RM , i dt i=1

6. CONCLUSION Although off-cut can improve the performance of batch reactive distillation, the benefit is limited in some cases. In such cases, performance can usually be improved by employing one or both of the methods discussed in this article, namely middle vessel column design and excess reactant design. The middle vessel column design gives the flexibility to remove unconsumed reactant from either the top or bottom of the column as necessary, and excess reactant can allow for the near-total consumption by reaction of a reactant that is difficult to remove. These methods have been demonstrated for three case studies of real reacting systems. For the hydrolysis of methyl lactate, the best process is an MVC design in which both products are withdrawn at the same time. The batch capacity is improved by 30.7% compared to a conventional CBD process. For the esterification of formic acid, the best process is an excess CBD design where the methanol excess ratio is 1.1. The batch capacity is improved by 34.6% compared to a neat CBD process. For the production of 1,1-dimethoxyethane, the best process is an excess MVC design where the acetaldehyde excess ratio is 1.18. The

(3)

Component i Mole Balance, i = A, B, C, and D. Middlevessel: dAM ·XM , i dt

= LNf ·XNf , i − LM ·XM , i + RM , i·AM , i

(4)

Feed tray: ANf

dXNf , i dt

= VNf + 1·YNf + 1, i + LNf − 1·XNf − 1, i + LM ·XM , i − VNf ·YNf , i − L′Nf ·XNf , i − LNf ·XNf , i

(5)

Stripping Section

Component i Mole Balance, i = A, B, C, and D. Stage j, Nf+1 ≤ j ≤ n: Aj

dX j , i dt

= Vj + 1·Yj + 1, i + L′ j − 1 ·Xj − 1, i − Vj·Yj , i − L′ j ·Xj , i (6)

Reboiler: 8539



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Figure A1. Schematic diagram for the three sections of an MVC.

Table 9. NRTL Binary Parameters for Hydrolysis of Methyl Lactate Systema component i

component j

aij

aji

bij

bji

cij

water water water methyl lactate methyl lactate methanol

methyl lactate methanol lactic acid methanol lactic acid lactic acid

0 2.732 0 0 0 0

0 −0.693 0 0 0 0

1016.067 −617.269 823.797 −243.325 −371.074 1120.780

−315.277 172.987 −363.348 298.865 489.665 −660.681

0.3 0.3 0.3 0.3 0.3 0.3

a

The NRTL parameters for the methanol−water pair were taken from the Aspen Plus database, and other pairs were estimated using UNIFAC in Aspen Plus.

Table 10. NRTL Binary Parameters for Esterification of Formic Acid Systema component i

component j

aij

aji

bij

bji

cij

methanol methanol methanol formic acid formic acid methyl formate

formic acid methyl formate water methyl formate water water

0 0 −0.693 0 4.516 0

0 0 2.732 0 −2.586 0

−288.109 199.014 172.987 −132.564 −1432.084 317.399

457.264 217.046 −617.269 415.184 725.017 652.312

0.3 0.3 0.3 0.3 0.3 0.3

a

The NRTL parameters for the methanol-formic acid and methyl formate-water pairs were estimated using UNIFAC in Aspen Plus, and other pairs were taken from the Aspen Plus database.

Table 11. NRTL Binary Parameters for Synthesis of DMA System24

Ab

component i

component j

Aij (cal/mol)

Aji (cal/mol)

αij

αji

acetaldehyde acetaldehyde acetaldehyde methanol methanol dimethylacetal

methanol dimethylacetal water dimethylacetal water water

−568.3023 1107.7748 1034.0769 786.5994 −253.8802 −543.5079

14.6398 −565.8342 310.5491 −125.2404 845.2062 2231.1877

0.3 0.3 0.2878 0.3 0.2994 0.3

0.3 0.3 0.2878 0.3 0.2994 0.3

dX b , i dt

= L′n ·X n , i − Vb·Yb , i − B ·Xb , i

Gij = exp( −αijτij),

(7)

τii = τjj = 0,

τij = aij + cij = cji = αij ,

bij , T (K ) αii = αjj = 0

Details of Thermodynamics and Reaction Kinetics

Thermodynamics. NRTL model is used to describe the

or

vapor−liquid equilibrium, and the model is as follows: nc

ln ri =

∑ j = 1 τjiGjixj nc

∑k = 1 Gkixk

nc

+

∑ j=1

Gij = exp( −αijτij),

nc ∑ xmτmGmj ⎤ xjGij ⎡ ⎢τij − m =nc1 ⎥ nc ∑k = 1 Gkjxk ⎢⎣ ∑k = 1 Gkjxk ⎥⎦

τij =

Aij RT

,

τii = τjj = 0,

αii = αjj = 0 8540



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Synthesis of DMA

The parameters of NRTL model of each system are listed in Tables 9−11. The dimerization of formic acid in the vapor phase is considered, and the dimerization constant is log10(KD) = − 10.743 +

⎛ ⎞ a a ri = kc ⎜⎜aaldehydeaMeOH − DME water ⎟⎟ KeqaMeOH ⎠ ⎝

3083 T

⎡ − 5853.8 ⎤ kc = 7.59 × 108 exp⎢ ⎥ ⎣ T (K ) ⎦

where KD in mmHg and T in K.26 The ternary residue curve map for the system consisting of acetaldehyde (CH3CHO, or MeCHO), methanol (CH3OH), and 1,1-dimethoxyethane (or dimethylacetal, abbreviated as DMA) is shown in Figure A2. The distillation boundary is noted.

⎡ 2103.3 ⎤ Keq = 0.0173 exp⎢ ⎥ ⎣ T (K) ⎦

The reaction rate r and the kinetic parameter kc have the unit of mole per minute per gram catalyst (mol/g/min), ai is the activity, and Keq is the reaction equilibrium constant.29 It is assumed that 150 g of catalyst are loaded in the reactive vessel. Parameters for Simulated Annealing

Following our previous work, the parameters used for simulated annealing method is listed in Table 12, and the revolution of the Table 12. Parameters for SA Optimization20 initial temperature

temperature decrement factor

number of iteration as an indication of equilibrium

number of temperature decrement

50

0.9

15

150

objective function CAP to the annealing temperature can be found in our previous work.20 The neighborhood moves for the optimization variables has a random value ranging from −0.01 to +0.01 with minimum discrete value 0.001. Although there can be no guarantee that SA will find the global optimum, the results are reasonable and always converge to near the same point from different initial conditions.

Figure A2. Ternary residue curve map for acetaldehyde−MeOH−DMA system.

Kinetics

Notation

⎛ ⎛ − 50910 ⎞ ⎟a ri = mcat⎜1.65 × 105 exp⎜ a ⎝ RT ⎠ Water MeLC ⎝ ⎞ ⎛ − 48520 ⎞ ⎟a − 1.16 × 106 exp⎜ a ⎟ ⎝ RT ⎠ MeOH LAC⎠

Hydrolysis of Methyl Lactate. The reaction rate r has the unit of mole per minute (mol/min), mcat is the catalyst weight in gram (g), R (J/mol/K) is the ideal gas constant, T is the reaction temperature in K, and ai is the activity.27 It is assumed that there are 3000 g of catalyst in the reactive reboiler. Esterification of Formic Acid. The kinetics of the reverse reaction, hydrolysis of methyl formate is studied by Jogunola et al.28 and is shown below: ⎡ ⎤ k ̅′ ri = k ̅ e−EaZ / R ⎢1 + e−Ea((Ea ′ / Ea) − 1)z / R C FA ⎥ ⎣ ⎦ k̅ ⎛ ⎞ 1 × ⎜CMFCwater − C FACMeOH⎟ KC ⎝ ⎠

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where Z = (1/T) − (1/T̅ ) (K−1), k̅ = 0.026 (kg/mol/min), k ̅′ = 0.12 (kg2/mol2/min), KC = 0.17, Ea = 88.2 (kJ/mol), E′a = 66.4 (kJ/mol), r (mol/kg/min) is the reaction rate, and C (mol/kg) is the component concentration in liquid phase. We use the reverse kinetics for our esterification reaction.

Aj = liquid holdup on stage j (mol) B = bottom flow rate (mol/h) Br = boilup ratio D = distillate flow rate (mol/h) HHK = heavier than heavy key HK = heavy key Lj = liquid flow rate from stage j (mol/h) LK = light key LLK = lighter than light key NC = number of components Nf = feed stage Rr = reflux ratio Ri = reaction rate of component i (kmol/s) tb = length of total batch time (h) toff = length of off-cut period (h) tp = length of product period (h) tt = length of total reflux period (h) Vj = vapor flow rate from stage j (mol/h) Xj,i = composition of component i in liquid phase at stage j Yj,i = composition of component i in vapor phase on stage j

AUTHOR INFORMATION

Corresponding Author

*Tel.: +886-2-2366-3037. Fax: +886-2-2369-1314. E-mail: jeff[email protected]. Notes

The authors declare no competing financial interest. 8541



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Article

(24) Qi, W. Synthesis, Design and Operating Strategies for Batch Reactive Distillation. Ph.D. dissertation; University of Massachusetts: Amherst, MA, 2010. (25) Hanke, M.; Li, P. Simulated Annealing for the Optimization of Batch Distillation Processes. Comput. Chem. Eng. 2000, 24, 1. (26) Tamir, A.; Wisniak, J. Vapor Equilibrium in Associating Systems (Water-Formic-Acid Propionic Acid). Ind. Eng. Chem. Fundam. 1976, 15, 274. (27) Sanz, M. T.; Murga, R.; Beltran, S.; Cabezas, J. L.; Coca, J. Kinetic Study for the Reactive System of Lactic Acid Esterification with Methanol: Methyl Lactate Hydrolysis Reaction. Ind. Eng. Chem. Res. 2004, 43, 2049. (28) Jogunola, O.; Salmi, T.; Eranen, K.; Warna, J.; Kangas, M.; Mikkola, J. P. Reversible Autocatalytic Hydrolysis of Alkyl Formate: Kinetic and Reactor Modeling. Ind. Eng. Chem. Res. 2010, 49, 4099. (29) Gandi, G. K.; Silva, V. M. T. M.; Rodrigues, A. E. Acetaldehyde Dimethylacetal Synthesis with Smopex 101 Fibres as Catalyst/ Adsorbent. Chem. Eng. Sci. 2007, 62, 907.

ACKNOWLEDGMENTS The authors wish to express their gratitude to the National Science Counsel of Taiwan for funding under Project No. 1012221-E-002-159-MY2.

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REFERENCES

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Improving Batch Reactive Distillation Processes with Off-Cut

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