Batch Reactive Distillation with Off-Cut Recycling - American Chemical

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Batch Reactive Distillation with Off-Cut Recycling Yu-Lung Kao and Jeffrey D. Ward* Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan ABSTRACT: Off-cut recycling in batch reactive distillation (BREAD) processes is studied. The strategy is to recycle off-cut to the next batch as a part of the initial feed. This transforms the operation problem from a single-batch problem into a batch-tobatch problem. The pseudo-steady-state concept is applied to BREAD processes to simplify the optimization problem. Optimization based on maximizing batch capacity (CAP) for the batch-to-batch problem is demonstrated using three real chemistry processes. The results show that the optimal operating recipe and CAP when off-cut is recycled are similar to those in the case when off-cut is collected but not recycled and that the CAP is on average almost twice (93.3% more) the maximum that can be achieved when off-cut is not used. Therefore, recycling off-cut may not only save the trouble of processing the off-cut but also make the process more economical. beginning. Miladi and Mujtaba8 investigated an off-cut recycle problem with fixed product demand. Bonny et al.9 and Bonny10 proposed a superstructure model considering all the possible alternatives of handling off-cut, which leads to a nonlinear programming problem. The production campaign of batch distillation processes was optimized. In later contributions they considered improved operating policies in which offcuts collected during the previous batch were introduced at different times during the batch and a varying reflux ratio was empolyed.11,12 Off-cut collection has also been shown to be beneficial in terms of batch capacity (CAP) for quaternary BREAD processes if both products have purity specifications, especially when the separation task is difficult, e.g., the purity specification is high, the reaction equilibrium constant is small, etc.13 Figure 1 shows

1. INTRODUCTION Distillation is a vital technique for liquid separation in chemical industries. Batch distillation is suitable for low-volume production, and it is widely used to produce high value added fine and specialty chemicals. Integrating reaction and distillation in a single unit (reactive distillation) has been shown to be advantageous in many literature reports.1 This intensified process can overcome the reaction equilibrium limitations and azeotropes, save energy, and reduce capital and operating costs. Batch-wise operation of reactive distillation is called batch reactive distillation (BREAD). As the demand for fine and specialty chemicals has increased, BREAD processes have attracted more attention. For batch distillation, off-cut (slop cut or waste cut) collection is a common operation to improve the process efficiency. Off-cut is material that is collected during the operation that does not meet any product purity specification. The collection usually begins when further addition of distillate or bottom product to the product receiver will cause the purity of the product to fall below the specification and ends when the composition of distillate or bottom achieves the specification of the next product cut. Off-cut must be either disposed of safely, recycled to the next batch, or collected for further processing in a separate batch. Therefore, recycling of off-cut has been studied by different researchers for nonreacting systems. One chapter in the book by Mujtaba2 discusses the off-cut recycle problem. The off-cut recycling problem was first studied in a binary system in which off-cut was recycled to the next batch.3,4 Later, the problem was extend to multicomponent systems. Luyben5 used the capacity factor, which is defined as the total amount of product on specification divided by total batch time, to study ternary mixture separation with off-cut recycling. The two off-cuts collected were recycled to the next batch, and a pseudosteady state was optimized.3−5 Luyben and Quintero-Marmol6 proposed different off-cut recycling alternatives, and comparison was made with their previous work. Mujtaba and Macchietto7 decomposed the overall multicomponent system into a sequence of optimal binary problems with off-cut recycle. Off-cuts collected were recycled to the reboiler at suitable times during the batch instead of only at the © XXXX American Chemical Society

Figure 1. Variation of CAP and percent of off-cut as product period length changes for methyl lactate system. Received: October 31, 2014 Revised: January 7, 2015 Accepted: January 29, 2015

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DOI: 10.1021/ie5042929 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

subroutine of Aspen Properties is interfaced with MATLAB to calculate the vapor−liquid equilibrium (VLE) on each tray and in the reboiler at each integration step. The benefits of employing the flash calculation subroutine are that different VLE models and the thermodynamic data bank in Aspen can be directly used and the VLE can be calculated quickly and accurately. 2.2. Case Studies. In our previous work,15 improved operating policies for batch reactive distillation with off-cut were demonstrated for three real chemical systems: hydrolysis of methyl lactate, esterification of formic acid, and production of dimethylacetal. The results of the improved policies show that the process efficiency in terms of batch capacity is improved significantly compared to conventional operation (CBD/IBD with neat design) in which it is difficult or impossible to remove unconsumed reactants by distillation. However, the amount of off-cut collected during each batch also increased. Therefore, in this work the optimization of these processes including off-cut recycle is considered. The thermodynamics and kinetics models for the three systems are given in the Appendix. 2.2.1. Hydrolysis of Methyl Lactate. The hydrolysis reaction is water + methyl lactate ⇔ methanol + lactic acid, which is an important step in the purification of lactic acid (LAC) by esterification and hydrolysis. The boiling point ranking of this system including an azeotrope is listed in Table 1. A CBD

the CAP variation as the length of product period (one of the two products is withdrawn from the column and collected in this period) increases for the hydrolysis of methyl lactate system. The length of the product period affects the amount of off-cut collected. The off-cut period is used to purify the other product accumulating in the reboiler. The longer the product period, the less off-cut is collected because the reaction can achieve a higher conversion; therefore, there is less unconsumed reactant to be collected as an off-cut. For the maximum CAP design, the off-cut is about 50% of the initial feed. Therefore, the off-cut recycling problem must be considered for BREAD processes. However, compared with batch distillation processes, less attention has been paid to the off-cut recycling problem in BREAD processes in the literature. We are aware of only one report considering a batch reactive distillation campaign with off-cut recycling.14 However, the off-cut recycling strategy and the optimization discussed in that work are relatively complex. Therefore, in this work a more general and simpler recycle strategy is used. Batchto-batch operation with off-cut recycling is optimized and compared with the optimal single-batch operation. The remainder of this article is organized as follows. In section 2, the process model and three chemistry systems with realistic reaction kinetics and vapor−liquid equilibrium that are used to illustrate off-cut recycling method are described. In section 3, the off-cut recycling strategy is presented and a nonconvergence problem in the batch-to-batch operation is discussed and solved. In section 4, optimization results of batch-to-batch operation with off-cut recycling are shown and compared with single-batch operation. section 5 presents the conclusions.

Table 1. Boiling Point Rankings with Composition in Mole Fraction for Different Reaction Systems Hydrolysis of Methyl Lactate temp (K)

2. MODEL AND CASE STUDY 2.1. BREAD Column Model. The dynamic model for the BREAD processes used in this work is the same as that in our previous work,13,15 in which the detailed mathematical model equations can be found. The main assumptions of the model are (a) constant molar liquid holdup on trays; (b) negligible vapor holdup; (c) reaction takes place only in the feed drum, not on the trays; and (d) trays have constant molar overflow. Three column configurations are used in this work: conventional batch distillation column (CBD), inverted batch distillation column (IBD), and middle-vessel column (MVC). When modeling a batch reactive distillation operation, it is assumed that the process first reaches steady state under total reflux with no reaction. This point corresponds to t = 0 for all simulations. At this point the reaction begins and simultaneously the total reflux period (or product period if no total reflux period is required) begins. This assumption is common when modeling batch reactive distillation and is employed to avoid the complexities associated with modeling the start-up of the process starting with a dry column. In practice it is unlikely that the catalyst would be removed from the reaction vessel after each batch and reintroduced after steady state under total reflux was achieved. However, it is also unlikely that this assumption significantly affects the results presented in this work. If the reaction proceeded during startup from a dry column, then the total reflux period could be made somewhat shorter (or the initial reflux ratio could be somewhat smaller if no total reflux period was required). However, the results would not be substantially affected. The differential algebraic equations (DAEs) describing the model are coded in MATLAB and solved with the built-in ordinary differential equations solver ode15s. The flash calculation

337.68 373.16 373.17 417.99 489.78

water

methyl lactate

methanol

0 0 0.9909 0.0091 1 0 0 1 0 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

1 0 0 0 0

0 0 0 0 1

methyl formate

0 0 0 1 0.5434 Synthesis of DMA

lactic acid

1 0 0 0 0

water 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

column can be used because the lighter product methanol is the lightest boiler. Because off-cut removal is effective for this system (both unconsumed reactants are the next two volatile boilers after the collection of the lighter product methanol), a conventional design, CBD with stoichiometric feed, is used in this work. 2.2.2. Esterification of Formic Acid. The esterification reaction is methanol + formic acid ⇔ methyl formate + water. Methyl formate (MF) can be used to manufacture products including formamide, dimethylformamide, methyl acrylate, etc., and can also be used as an insecticide. According to the boiling B


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period. Unlike our previous work, a constraint on the amount of off-cut collected is not required when off-cut is recycled to the next batch. Therefore, the only constraints applied in this work are purity constraints for both products. The product period is divided into four periods of equal length based on our previous work13 which showed that the process improvement from increasing the number of periods becomes relatively small after four periods. The simulated annealing method is applied to find the optimal relux/boilup ratio in these four periods as well as the optimal relux/boilup ratio in the off-cut period. The length of the product period is optimized separately because it is easier for the reflux/boilup ratio profile to converge to a global optimum under a fixed product period. Determination of the maximum CAP is easier for a singlebatch process because it is not necessary to simulate the column operation repeatedly to achieve a pseudosteady state for each objective function evaluation. The optimization procedure for single-batch operation is shown in Figure 2. On the other hand,

point ranking listed in Table 1, a CBD column can be used because methyl formate is the lightest boiler. However, the boiling point of the heavier product water is between the two reactants, which means that only one of the two unconsumed reactant species can be removed by distillation in the off-cut period in a conventional design. The use of excess methanol and a CBD column was shown to be advantageous15 for this process and will be studied in this work. 2.2.3. Production of Dimethylacetal. The main route for the production of 1,1-dimethoxyethane (or dimethylacetal, DMA) is acetalization of methanol with acetaldehyde (CH3CHO, abbreviated as MeCHO) and the reaction is acetaldehyde + 2 methanol ⇔ DMA + water. DMA is an intermediate for specialty chemicals and pharmaceutical compounds. The boiling point of the lighter product DMA is between the two reactants according to the boiling point ranking (Table 1). However, the distillation boundary formed because of the MeOH−DMA azeotrope means that the next species to be distilled from the column after water is DMA when an IBD column is used. Thus, neither unconsumed reactant can be removed by distillation. A modified design with excess methanol reactant and an MVC was shown to be advantageous15 for this process and will be studied in this work.

3. BATCH-TO-BATCH OPERATION AND OPTIMIZATION 3.1. Off-Cut Recycling Strategy. In this work, the recycling policy employed is to recycle all the off-cut collected to the next batch because a large amount of unconsumed reactant is collected in the off-cut. The recycled off-cut is combined with makeup fresh feed and fed to the next batch as the initial charge. For batch-to-batch operation, if the operating recipe (reboiler duty and reflux/boilup ratio) is kept the same for a few batch cycles, the system may reach a pseudosteady state. Once the pseudosteady state is established, the amount and composition of the off-cut is almost identical from batch to batch. According to Luyben,5 batch distillation processes without reaction require about three batch cycles to achieve a pseudosteady state. The advantage of this recycling policy is that it is simple and can be applied to many different chemical systems. Furthermore, only the operating recipe at pseudosteady state must be determined because identical operation is applied for all batches. 3.2. Problem Formulation. Following our previous work,13,15 the optimal reflux/boilup ratio profile (Rr(t)/Br(t)) and the length of product period (tp) are optimized to maximize the batch capacity (CAP). A piecewise constant trajectory for the reflux/boilup ratio is used in the product period to improve performance. On the other hand, a constant value is used in the off-cut period (toff) because the off-cut does not have a purity specification. The length of the off-cut period and its corresponding reflux/boilup ratio are not independent; the off-cut period ends when the accumulated product achieves the purity specification. 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. A vector is used to denote the reflux ratio profile in this work, for example, Rr = [1; 0.87; 0.89; 0.91; 0.93; 0.9 ]. The first entry 1 is for the total reflux period (tt); the next four values are for the product period, and the last value is for the off-cut

Figure 2. Optimization procedure flowsheet for single operation.

batch-to-batch operation requires more simulations to obtain a CAP depending on how many batch cycles are needed to reach a pseudosteady state. Therefore, the computational load is greater for batch-to-batch optimization. 3.3. Achieving Convergence in Batch-to-Batch Operation. Preliminary tests were performed to determine whether BREAD processes would converge to a pseudosteady state when off-cut is recycled from batch-to-batch. The optimal operating recipe for single-batch operation was applied batch-to-batch with off-cut recycle to determine whether BREAD batch-tobatch operation will also reach a pseudosteady state and approximately how many batches would be required. Hydrolysis of C


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Industrial & Engineering Chemistry Research methyl lactate was studied first. An equimolar mixture (total 5000 mol) of fresh reactants was loaded for the first batch. The CBD column contains 10 trays including a reboiler and a total condenser. The vapor rate was specified to be 2500 mol/h. An initial charge of 100 mol was distributed as total liquid holdup on trays, and another 100 mol of initial charge was placed in the condenser during the start-up period. It is assumed that the column is operated under total reflux without the reaction taking place during the start-up period. The start-up period ends when a steady state is achieved, and this state is also the initial condition for the simulation for a BREAD single-batch cycle. Figure 3 shows the off-cut amount and its corresponding composition for a batch-to-batch operation from the first batch

initial charge amount (see Figure 1). When the amount of offcut is small, the system can reach a pseudosteady state in a few batch cycles. In this work, the pseudosteady state is considered to be reached when the deviation of amount and composition of the off-cut between the current batch and the previous batch is less than 3%. On the other hand, when the off-cut is large, the system will not reach a pseudosteady state. The nonconvergence is caused by the quantity and composition of the off-cut. In all cases, the composition of the off-cut at pseudosteady state is primarily water because this is the species that must be removed in the offcut period to achieve the desired composition of lactic acid in the reactive reboiler. This off-cut is then combined with a fresh mixture having the stoichiometric (1:1) composition. If the quantity of off-cut is small (such as in our case study in which off-cut is less than 20% of total mixed charge), a pseudosteady state can be achieved. However, as the quantity of off-cut increases, the composition of the off-cut begins to dominate the overall feed composition. The result is that each batch has more water in the feed than the previous batch, and also as a consequence, each batch has more total off-cut than the previous batch. The off-cut composition and quantity run away and pseudosteady state is never achieved. The situation is analogous to that of a continuous process with two reactants and recycle. If the flow rate of both reactant streams is fixed, one reactant may accumulate in the process until it becomes inoperable. The solution to the nonconvergence problem is to adjust the ratio of raw materials in the fresh makeup so that the ratio of reactants in the total initial charge is some desired value (1:1 in this case). Table 2 shows the properties of off-cut, makeup feed, and mixed charge of batch cycle for the maximal CAP case after the modification. The process reaches a pseudosteady state in four batches under the same operating recipe. This simple modification solves the nonconvergence problem and also reduces the number of batches required to reach pseudosteady state. This reduces the computational load for optimization. Therefore, the modification will be applied for all batch-to-batch operations. 3.4. Starting the Batch-to-Batch Optimization from the Second Batch. Next, optimizing a batch-to-batch operation from the first batch is attempted. A CBD column with the same column specification mentioned in section 3.3 and equimolar reactant design are used. The initial feed condition is the same as the single-batch operation where only reactants are loaded in the charge. The off-cut collected from the first batch is recycled to the next batch. The composition of the fresh makeup feed is adjusted so that the ratio of the two reactants in the mixed charge for the second batch is the same as that of the first batch. In this case, a stoichiometric reactant composition is used. Likewise, the off-cut collected from the second batch is recycled to the third batch along with the adjusted makeup feed. The same recycling operation with a fixed operating recipe repeats until the system reaches a pseudosteady state. The objective is to maximize the batch capacity at pseudosteady state. The optimization procedure for batch-tobatch operation is shown in Figure 4. The optimal operating recipe which gives the highest CAP for batch-to-batch operation is shown in the middle row in the upper part of Table 3. This table gives the process initial condition, CAP, total reflux period (tt), product period (tp), off-cut period (toff), total batch time (tb), and the reflux ratio profile (Rr) of the optimal design. For comparison, the optimal operating recipe for single-batch operation is also shown in the first row in the upper part of

Figure 3. Off-cut amount and its corresponding composition for a batch-to-batch operation from initially only fresh feed to the 15th batch for different operating recipe depending on the off-cut amount collected in the 1st batch.

(with only fresh feed) to the 15th batch. The operating policy is kept the same for each batch except for the length of the off-cut period. The batch ends when the purity of the accumulated product reaches the purity specification. Therefore, the off-cut period may be different from batch-to-batch. The recycling strategy is to recycle all the off-cut to the next batch. Three different operating recipes, in which the reflux ratio profile is optimized under a fixed product period, corresponding to three different off-cut amounts, are shown. They are 10%, 20%, and 47.6% (which corresponds the maximal CAP case) compared to D


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Table 2. Properties of Off-Cut, Makeup Feed, and Mixed Charge of Batch Cycle with the Modification of Makeup Feed for MeLC System ⟨Water, MeLC, MeOH, LAC⟩ batch

off-cut from the previous batch (mol)

fresh/makeup feed (mol)

1 2 3 4 5 6

2287.7 ⟨0.464, 2424.1 ⟨0.461, 2464.1 ⟨0.458, 2481.9 ⟨0.456, 2488.1 ⟨0.455,

5000 ⟨0.500, 2712.3 ⟨0.482, 2575.9 ⟨0.473, 2535.9 ⟨0.471, 2518.1 ⟨0.471, 2511.9 ⟨0.471,

0.422, 0.113, 0.002⟩ 0.403, 0.135, 0.001⟩ 0.398, 0.144, 0.000⟩ 0.397, 0.147, 0.000⟩ 0.397, 0.148, 0.000⟩

0.500, 0.000, 0.000⟩ 0.518, 0.000, 0.000⟩ 0.527, 0.000, 0.000⟩ 0.529, 0.000, 0.000⟩ 0.529, 0.000, 0.000⟩ 0.529, 0.000, 0.000⟩

mixed charge (mol) 5000 ⟨0.500, 5000 ⟨0.474, 5000 ⟨0.467, 5000 ⟨0.465, 5000 ⟨0.464, 5000 ⟨0.463,

0.500, 0.000, 0.000⟩ 0.474, 0.052, 0.001⟩ 0.467, 0.066, 0.000⟩ 0.465, 0.071, 0.000⟩ 0.464, 0.073, 0.000⟩ 0.463, 0.073, 0.000⟩

Table 3. Compared with the single-batch operation, the optimal CAP and the corresponding operating recipe for batch-to-batch operation do not differ too much. The optimal CAP of the process with batch-to-batch operation is 5.3% less than that of the optimal single-batch design, and operational variables including the length of each period and the values of reflux ratio differ by between 0.1% and 21.1%. In addition, the cut properties including the amount and composition of both product cuts and off-cut of optimal design for both operations are listed in the upper part of Table 4. The methanol purity is much higher than the specification (98.5% compared to the specification of 95 mol %) for batch-to-batch operation. The composition profiles in the reflux drum and reboiler and the reflux ratio profile for both operations are shown in Figure 5. The reason that the methanol product purity exceeds the specification is that in the optimization the operating policy is required to meet the product purity specification for the first batch (which has no offcut recycle mixed into the feed). In fact, the first batch is more difficult than subsequent batches because the recycled off-cut contains a small amount of product. Thus, the first batch requires a total reflux period before any product can be collected, whereas the second and later batches do not. Optimizing the batch-to-batch operation subject to the unnecessary constraint that the operating policy must meet the product purity specifications for the first batch results in an operating policy which produces product that exceeds the specifications and has a batch capacity smaller than necessary. To improve the results of the optimization, an initial charge condition closer to the mixed charge condition at the pseudosteady state is desired. Because the optimal single-batch operating policies have already been determined, we start the optimization of the batch-to-batch process using the quantity and composition of off-cut determined from the single-batch optimization. This results in a feed composition much closer to the pseudosteady state that is eventually achieved than if the optimization were started using only fresh feeds. We call this strategy “starting from the second batch”, and it is shown schematically in Figure 6.

4. OPTIMIZATION RESULTS In section 3, the pseudosteady state for a BREAD process was found and the nonconvergence problem was solved. Moreover, the optimization for batch-to-batch operation from the second batch was proposed to improve the design at the pseudosteady state. In this section, the optimization results of three case

Figure 4. Optimization procedure flowsheet for batch-to-batch operation starting from the first batch. E


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Industrial & Engineering Chemistry Research Table 3. Optimal Operating Recipe for MeLC System operation

CAP (mol/h)

tt (h)

tp (h)

toff (h)

tb (h)

Rr

from first batch (only reactants)

initial conditions single with off-cut b-to-b single without off-cut

487.91 461.92 195.44

0.56 0.56 0.56

3 3.5 24

1.582 1.372 0

initial conditions

5.142 5.432 24.56

[1.000; 0.798; 0.849; 0.881; 0.842; 0.421] [1.000; 0.821; 0.846; 0.882; 0.858; 0.332] [1.000; 0.908; 0.961; 0.986; 0.985; (−) ]

from second batch (contains off-cut)

single with off-cut b-to-b

539.08 540.05

0 0

3 3

1.456 1.499

4.456 4.477

[ (−); 0.826; 0.815; 0.850; 0.832; 0.342] [ (−); 0.828; 0.813; 0.854; 0.827; 0.355]

Table 4. Cut Properties for Optimal Results for MeLC System operation

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


initial conditions single with off-cut b-to-b single without off-cut

1181.3 1297.2 2400.0

(4.92; 0.00; 95.03; 0.00) (1.50; 0.00; 98.50; 0.00) (4.86; 0.08; 95.06; 0.00)

initial conditions single with off-cut b-to-b

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

1327.6 1211.8 2400.0

(0.00; 4.87; 0.00; 95.13) (0.00; 4.96; 0.00; 95.04) (0.00; 4.46; 0.00; 95.54)

2291.1 2291.0 0

(46.30 ; 42.21; 11.26; 0.23) (46.08; 41.32; 11.42; 1.18) (−)

2397.6 2382.1

(45.15; 42.55; 11.46; 0.84) (45.48; 42.38; 11.54; 0.60)

from second batch (contains off-cut) 1269.3 1271.3

(4.98; 0.00; 95.02; 0.00) (4.61; 0.01; 95.38; 0.00)

1133.1 1146.6

(0.00; 4.77; 0.00; 95.23) (0.00; 4.92; 0.00; 95.08)

Figure 5. Reflux ratio profile and composition profile of optimal operating policy for single-batch operation for the first batch (left) and batch-to-batch operation optimized from the first batch (right) for methyl lactate system.

and the other product lactic acid accumulates in the reboiler. For the process design described in section 3.3 and the optimization procedure shown in Figure 6, the optimal results are shown in the second row in the lower part of Tables 3 and 4, including the optimal operating recipe and properties. The optimal CAP for

studies for batch-to-batch operation are shown and compared with optimal single-batch operation without off-cut. 4.1. Hydrolysis of Methyl Lactate. When a CBD column is used for the hydrolysis of the methyl lactate system, the lighter product methanol can be withdrawn from the top of the column F


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recipe close to the optimal one can reduce the computational effort required for optimization. The optimal batch-to-batch operation design is also compared with the optimal single-batch design without off-cut collection (the third row in the upper part of Tables 3 and 4) to illustrate the benefit from including an off-cut collection. For these two operations, all collected cuts from the batch are either products or recycled to the next batch. That is, no cuts remain unprocessed. For the design without off-cut collection, the reaction must achieve a certain conversion so that the accumulated product can achieve the purity specification after the collection of the withdrawn product. As a result, the optimal product period without off-cut collection (24 h) is much longer than the optimal product time of batch-to-batch operation with off-cut collection (3 h). Although all feed converts to valuable products, the optimal CAP without off-cut collection is much smaller. The CAP improvement by including an off-cut collection is 176.3%. 4.2. Esterification of Formic Acid. For the esterification of formic acid BREAD process, a CBD column is used because product methyl formate is the lightest species. The other product, water, accumulates in the reboiler. The boiling point of water is between that of the two reactants, which makes the withdrawal of the heavier unconsumed reactant formic acid as off-cut impossible. Operation with excess methanol can force almost complete conversion of formic acid, which overcomes the off-cut removal difficulty and improves the CAP significantly. The same column specification as in MeLC processes (total 10 plates and constant boilup rate of 2500 mol/h) is used here. In addition to the operating recipe, the ratio of excess reactant is also optimized. For batch-to-batch operation, the operation is optimized from the second batch, and the initial mixed charge is composed of fresh makeup feed and the off-cut obtained from the optimal single-batch design. The composition of fresh makeup feed for each batch is adjusted so that the overall ratio of reactants remains the same. Figure 8 shows the maximal CAP for different methanol excess ratios employed for different operations including singlebatch design for the first and second batch, and the batch-tobatch operation. The excess ratio is defined as the ratio of the moles of methanol to moles of formic acid in the feed. The optimal methanol excess ratio for all three operations is 1.10. The optimization results including the optimal operating recipes and cut properties for these three operations are shown in Tables 5 and 6 (the first row in the upper part of the table shows the single operation from the first batch, and the lower part of the table shows the single and batch-to-batch operation from the second batch). Similar to the hydrolysis of methyl lactate system, compared with that of optimal single-batch design, optimal batch-to-batch operation has a higher CAP because the total reflux period is omitted. Thus, the total batch time is reduced. Moreover, compared with that of the optimal singlebatch design for the second batch, the optimal operating recipe for batch-to-batch operation is very similar. Figure 9 shows the operating recipe and composition profile of these two operations. The composition profile in the reflux drum shows that only the lighter unconsumed reactant, MeOH, can be removed by distillation in the off-cut period, confirming the effectiveness of the excess design. To conclude, not only the optimal operating recipe but also the optimal excess reactant ratio of the single-batch optimization result for the second batch is very close to the results for the optimization of the batch-tobatch operation. Compared with that of batch-to-batch operation, the optimal CAP is only 0.17% different, and the average

Figure 6. Optimization procedure flowsheet for batch-to-batch operation starting from the second batch.

batch-to-batch operation when starting from the second batch is higher than when starting from the first batch. The total reflux period is omitted because the methanol purity is high enough for collection after the startup period. This operation reduces the total batch time and increases the optimal CAP. For comparison, the single-batch operation with the initial condition of the second batch is also optimized. The results are also shown in the first row in the lower part of Tables 3 and 4. When these two optimal results are compared, both the operating recipes and the cut properties are very similar. The composition profiles in the reflux drum and reboiler and the reflux ratio profile for both operations are shown in Figure 7. The similar operating recipes (the difference of operation variables including the length of each period and the values of reflux ratio is 1.22% on average) suggest that the optimal operating recipe obtained for the single-batch operation can be a very good initial guess for optimization of batch-to-batch operation. This is good because optimization of batch-to-batch operation is more time-consuming. An initial guess of operating G


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Figure 7. Reflux ratio profile and composition profile of optimal operating policy for single-batch operation for the second batch (left) and batch-tobatch operation optimized from the second batch (right) for methyl lactate system.

deviation of operational variables, including the length of each period and the values of reflux ratio, is 1.48%. Similar to methyl lactate process, the optimal single-batch design without off-cut collection is also shown in the second row in the upper part of Tables 5 and 6 to show the benefit from collecting an off-cut (batch-to-batch operation with off-cut). Because off-cut is not collected, neat design is used in this case. Excess methanol will just make the purity constraint of the accumulated product more difficult or impossible to achieve. The optimal CAP can be improved by 44.9% if excess reactant design is used and off-cut is collected and recycled in batch-tobatch operation. 4.3. Production of 1,1-Dimethoxyethane (DMA). For the production of DMA process, one of the products, water, is the heaviest boiler. An IBD column can be used to withdraw one of the products so as to force the reaction completion. However, neither unconsumed reactant can be removed from the bottom of the column. Off-cut removal is ineffective for process

Figure 8. Maximal CAP under different methanol excess ratios for different operations.

Table 5. Optimal Operating Recipe for MF System operation

MeOH excess ratio

CAP (mol/h)

tt (h)

single with off-cut single without off-cut

1.1 1.0

1368.41 985.53

0.37 0.37


tp (h)

toff (h)

tb (h)

Rr


initial conditions

2.5 4.5

0.625 0

3.495 4.87

[1.000; 0.478; 0.515; 0.653; 0.853; 0.829] [1.000; 0.605; 0.653; 0.943; 0.969; (−) ]


1430.67 1428.24

0 0

2.75 2.75

H

0.605 0.598

3.355 3.348

[ (−); 0.622; 0.481; 0.629; 0.852; 0.835] [ (−); 0.616; 0.495; 0.617; 0.860; 0.821]


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Industrial & Engineering Chemistry Research Table 6. Cut Properties for Optimal Results for MF System operation

amount of product MF (mol)

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

amount of product water (mol)

2345.5 2334.4

(4.99; 0.00; 95.00; 0.01) (3.56; 0.00; 96.43; 0.01)


amount of off-cut (mol)

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

267.3 0

(46.38; 0.00; 53.40; 0.22) (−)

249.7 267.8

(44.87; 0.00; 54.86; 0.27) (45.27; 0.00; 54.31; 0.42)


initial conditions single with off-cut single without off-cut

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

2437.2 2465.6

(0.58; 4.41; 0.01; 95.00) (0.22; 4.74; 0.01; 95.04)


(4.99; 0.00; 95.00; 0.01) (4.97; 0.00; 95.02; 0.01)

2366.4 2355.3

(0.57; 4.41; 0.01; 95.01) (0.54; 4.45; 0.01; 95.00)

Figure 9. Reflux ratio profile and composition profile of optimal operating policy for single-batch operation for the second batch (left) and batch-tobatch operation optimized from the second batch (right) for formic acid system.

Table 7. Optimal Operating Recipe for DMA System operation

MeCHO excess ratio

CAP (mol/h)

tt (h)

tp (h)

toff (h)

tb (h)

single with off-cut

1.18

162.01

0.34

12

3.098

15.438

single without off-cut (IBD)

1.00

91.83

0.40

34

0

34.40

initial conditions

[1.000; 1.000; 1.000; 1.000; 1.000; 0.865]a [1.000; 0.907; 0.946; 0.973; 0.978; 1.000]b [1.000; 0.936; 0.994; 0.998; 1.000; (−) ]b

from second batch (contains off-cut)

single with off-cut

1.24

148.89

0.38

14

4.185

18.565

b-to-b

1.18

145.80

0.38

13

4.786

18.166

a

Rr/Br


initial conditions

[1.000; 1.000; 1.000; 1.000; 1.000; 0.903]a [1.000; 0.924; 0.959; 0.977; 0.985; 1.000]b [1.000; 1.000; 1.000; 1.000; 1.000; 0.897]a [1.000; 0.923; 0.956; 0.978; 0.983; 1.000]b

Reflux ratio. bBoilup ratio.

improvement. Therefore, an MVC with 15 plates and a constant boilup rate (2500 mol/h) is employed to overcome this

difficulty, and a reactant ratio with an excess of acetaldehyde is also used to improve the CAP. The excess ratio is defined as the I


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Industrial & Engineering Chemistry Research Table 8. Cut Properties for Optimal Results for DMA System operation

amount of composition of product DMA amount of composition of product water amount of product DMA (MeCHO; MeOH; DMA; water) product water (MeCHO; MeOH; DMA; water) off-cut (mol) (mol %) (mol) (mol %) (mol) from first batch (only reactants)

initial conditions single with off-cut single without off-cut (IBD)

927.1 1535.1

(0.69; 4.25; 95.03; 0.03) (1.65; 3.31; 95.00; 0.04)


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

1574.0 1623.8

(0.00; 0.26; 4.66; 95.08) (0.00; 0.00; 4.38; 95.62)

1046.1 0

(36.11; 19.02; 44.87; 0.00) (−)

1015.4 1118.2

(47.41; 16.80; 35.79; 0.00) (34.68; 24.25; 41.07; 0.00)


(0.63; 4.33; 95.01; 0.03) (0.53; 4.42; 95.02; 0.02)

1433.0 1375.1

(0.00; 0.16; 4.67; 95.17) (0.00; 0.21; 4.61; 95.18)

Figure 10. Reflux/boilup ratio profile and composition profiles of optimal operating policy for single-batch operation for the second batch (left) and batch-to-batch operation optimized from the second batch (right) for DMA system.

total reflux period is longer for the mixed charge with off-cut recycled because the existence of products suppress the reaction rate. Tables 7 and 8 show optimal results of single second batch design with off-cut (in the first row in the lower part of the table) and batch-to-batch operation design (in the second row in the lower part of the table). As was observed for the other processes, the optimal batch-tobatch operating policy is quite similar to the optimal single second batch. The optimal CAP of the single second batch is 2.1% more than that of the process with batch-to-batch operation, and the differences in operational variables including the excess ratio, length of each period, and the values of reflux ratio is 3.21% on average. The operating recipe and composition profile for these two operations are shown in Figure 10.

amount of acetaldehyde for excess design/the stoichiometric amount. The feed contains 5000 mol of reactants, and the ratio of MeOH to acetaldehyde is the stoichiometric ratio, 2. During the product period, water is withdrawn from the bottom, and in the off-cut period, unconsumed reactants are removed at the top of the column. Unlike the previous two case studies, the product cut and offcut for the DMA process are collected at different locations. Although the off-cut is collected after the water product cut, there is hardly any water in the off-cut (less than 0.0004 mol %). Therefore, when the off-cut is recycled to the next batch, there is almost no water at the beginning of the process. A total reflux period is required for the production of water until the bottom stream achieves the water purity specification for collection. The J


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Industrial & Engineering Chemistry Research 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 System16 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

it is difficult to find an operating recipe leading to a feasible design (one which satisfies the purity specifications) for every batch if the optimization starts from the first batch because the initial conditions of the first batch and the later batches are very different. The optimization results for the second single batch are very similar to the optimal operating recipe for batch-tobatch operation for all three cases. The average deviation of operational variables for the methyl lactate system, formic acid system, and DMA system case studies are 1.22%, 1.48%, and 3.21%, respectively. This understanding can reduce the difficulty of batch-to-batch optimization. The optimal designs of batch-to-batch operation are also compared with the optimal designs of single-batch operation without off-cut collection to evaluate the benefit of off-cut collection and recycle. The optimal designs without off-cut collection have the same number of stages and reboiler vapor flow rate as the batch-to-batch optimal design. Conventional designs (CBD/IBD with neat operation) are employed because modified designs are beneficial only if off-cut is collected. The design with off-cut collection improves the CAP by 176.3% for methyl lactate system, 44.9% for formic acid system, and 58.8% for DMA system. These significant improvements mainly come from the reduced product period length. The unconsumed reactants in the charge drum (the impurity of the accumulated product) can be removed more efficiently by off-cut collection. Therefore, a long reaction time to achieve a certain reaction conversion is not required.

Although both unconsumed reactants can be removed by distillation at the top during the off-cut period, a certain amount of accumulated product DMA is also withdrawn because of the DMA−MeOH azeotrope. Excess of acetaldehyde can force more consumption of MeOH, which can reduce the loss of DMA in the off-cut. To show the improvement by including an off-cut collection, the optimal single-batch design without off-cut is also shown in the second row in the upper part of Tables 7 and 8. For the design without off-cut, an IBD column with neat design is used because the modified design (MVC with excess reactant) facilitates only the operation with off-cut collection where the product cut and the off-cut are collected from different locations. The IBD column used has the same number of stages and reboiler vapor flow rate. Compared with the optimal design without offcut, the optimal CAP can be improved by 58.8% when off-cut collection is employed for modified DMA process design. 4.4. Discussion. The optimization of batch-to-batch BREAD operation with off-cut recycling has been illustrated using three case studies. The optimal design based on maximizing CAP at the pseudosteady state is obtained. When the composition of makeup feed is adjusted, all three processes reach a pseudosteady state in three or four batch cycles. For hydrolysis of methyl lactate and esterification of formic acid systems, off-cut contains the withdrawn product species which facilitates the next batch cycle. The total reflux period can be omitted because the high-purity product can be withdrawn after the start-up period. Starting the batch-to-batch operation optimization from the second batch improves the optimization results. For some cases, K


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5. CONCLUSION Optimization of a batch campaign with off-cut recycled from batch-to-batch has been studied for batch reactive distillation processes. The recycling policy studied is to recycle all off-cut collected in the current batch to the next batch because the offcut contains a large amount of unconsumed reactants. If the operating recipe and the off-cut recycling operation are kept the same for a few batch cycles, the batch-to-batch operation will achieve a pseudosteady state. In other words, the recycled off-cut properties will be identical for every batch, so every batch will be the same. For BREAD processes, reaction and distillation are interactive. Therefore, the reactant composition in the makeup feed is adjusted to solve the problem of nonconvergence. The optimal operating recipe based on maximizing batch capacity at the pseudosteady state is determined. Three processes with realistic vapor−liquid equilibrium models and reaction kinetics and different design configurations are investigated for illustration. The batch-to-batch optimization results show that starting the optimization from the second batch is more favorable than starting from the first batch because the second batch already includes some off-cut and therefore is much more similar to a batch at pseudosteady state. Compared with the optimal operating recipe of the second batch, the optimal operating recipe of batch-tobatch operation optimized from the second batch is very similar. This suggests that the more easily obtained optimal recipe of the second batch can be a good initial guess for the more complicated batch-tobatch optimization problem. Furthermore, BREAD processes with off-cut collection show significant CAP improvements, from 45% to more than 175%, compared with the processes without off-cut collection. The improvements are due to the fact that off-cut collection can avoid the requirement of high reaction conversion.

■

weight in grams (g), R (J/mol/K) the ideal gas constant, T the reaction temperature in K, and ai the activity.17 It is assumed that there is 3000 g of catalyst in the reactive reboiler. Esterification of Formic Acid. ⎡ ⎤ k ̅′ exp( −Ea((Ea′/Ea) − 1)z /R )C FA ⎥ ri = ke̅ −EaZ / R ⎢1 + ⎣ ⎦ k̅ ⎛ 1 ⎞ × ⎜ C FACMeOH − CMFCwater ⎟ ⎝ KC ⎠

where z = (1/T − 1/T̅ ) (K−1); k̅ = 0.026 (kg/mol/min); k̅′ = 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. The kinetics model was adapted from an expression presented for the hydrolysis of methyl formate by Jogunola et al.18 Because the process we study is for esterification rather than hydrolysis, we use an expression for the net rate of the reverse reaction. Synthesis of DMA

⎛ ⎞ a a ri = kc⎜⎜aaldehydeaMeOH − DME water ⎟⎟ KeqaMeOH ⎠ ⎝ ⎡ − 5853.8 ⎤ kc = 7.59 × 108 exp⎢ ⎥ ⎣ T (K) ⎦ ⎡ 2103.3 ⎤ Keq = 0.0173 exp⎢ ⎥ ⎣ T (K) ⎦

Details of Thermodynamics and Reaction Kinetics

The reaction rate r and the kinetics parameter kc have the units of mole per minute per gram catalyst (mol/g/min); ai is the activity, and Keq is the reaction equilibrium constant.19 It is assumed that 150 g of catalyst is loaded in the reactive vessel.

Thermodynamics. The nonrandom two-liquid (NRTL) model is used to describe the vapor−liquid equilibrium, and the model is as follows:

Notes

APPENDIX

nc

ln ri =

∑ j = 1 τjiGjixj nc

∑k = 1 Gkixk

nc

+

∑ j=1

■

The authors declare no competing financial interest.

nc ⎡ ∑m = 1 xmτmGmj ⎤ ⎢ ⎥ τ − ij nc nc ∑k = 1 Gkjxk ⎥⎦ ∑k = 1 Gkjxk ⎢⎣

■

xjGij

Gij = exp( −αijτij),

τij = aij +

cij = cji = αij ,

αii = αjj = 0

bij T (K)

,

ACKNOWLEDGMENTS The authors express their gratitude to the National Science Counsel of Taiwan for funding under Project 101-2221-E-002159-MY2.

τii = τjj = 0,

■

τij =

Aij RT

,

REFERENCES

(1) Luyben, W. L., Yu, C. C. Reactive Distillation Design and Control. Wiley: Hoboken, NJ, 2008. (2) Mujtaba, I. M. Batch Distillation: Design and Operation; Imperial College Press: London, 2004. (3) Mayur, D. N.; May, R. A.; Jackson, R. The Time-Optimal in Binary Batch Distillation with a Recycled Waste-Cut. Chem. Eng. J. (Amsterdam, Neth.) 1970, 1, 15. (4) Christensen, F. M.; Jorgensen, S. B. Optimal-Control of Binary Batch Distillation with Recycled Waste Cut. Chem. Eng. J. (Amsterdam, Neth.) 1987, 34, 57. (5) Luyben, W. L. Multicomponent Batch Distillation. 1. TernarySystems with Slop Recycle. Ind. Eng. Chem. Res. 1988, 27, 642. (6) Quintero-Marmol, E.; Luyben, W. L. Multicomponent Batch Distillation. 2. Comparison of Alternative Slop Handling and Operating Strategies. Ind. Eng. Chem. Res. 1990, 29, 1915. (7) Mujtaba, I. M.; Macchietto, S. An Optimal Recycle Policy for Multicomponent Batch Distillation. Comput. Chem. Eng. 1992, 16, S273.

or Gij = exp( −αijτij),

AUTHOR INFORMATION

τii = τjj = 0,

αii = αjj = 0

The parameters of the NRTL model of each system are listed in Tables 9−11. ⎛ ⎛ −50910 ⎞ ⎟a ri = mcat ⎜1.65 × 105 exp⎜ a ⎝ RT ⎠ water MeLC ⎝ ⎞ ⎛ −48520 ⎞ ⎟a a ⎟ − 1.16 × 106 exp⎜ ⎝ RT ⎠ MeOH LAC⎠

Kinetics. Hydrolysis of Methyl Lactate. The reaction rate (r) has the units of mole per minute (mol/min); mcat is the catalyst L


Article

Industrial & Engineering Chemistry Research (8) Miladi, M. M.; Mujtaba, I. M. Optimisation of Design and Operation Policies of Binary Batch Distillation with Fixed Product Demand. Comput. Chem. Eng. 2004, 28, 2377. (9) Bonny, L.; Domenech, S.; Floquet, P.; Pibouleau, L. Strategies for Slop Cut Recycling in Multicomponent Batch Distillation. Chem. Eng. Process. 1994, 33, 23. (10) Bonny, L. Strategies for Handling Mixtures in Multicomponent Batch Distillations with Slop Recycle. Chem. Eng. Process. 1995, 34, 401. (11) Bonny, L. Multicomponent batch distillations campaign: Control variables and optimal recycling policy. Ind. Eng. Chem. Res. 2006, 45, 8998. (12) Bonny, L. Multicomponent Batch Distillations Campaign: Control Variables and Optimal Recycling Policy. A Further Note. Ind. Eng. Chem. Res. 2013, 52, 2190. (13) Kao, Y. L.; Ward, J. D. Design and Optimization of Batch Reactive Distillation Processes with Off-Cut. J. Taiwan Inst. Chem. Eng. 2014, 45, 411. (14) Wajge, R. M.; Reklaitis, G. V. An Optimal Campaign Structure for Multicomponent Batch Distillation with Reversible Reaction. Ind. Eng. Chem. Res. 1998, 37, 1910. (15) Kao, Y. L.; Ward, J. D. Improving Batch Reactive Distillation Processes with Off-Cut. Ind. Eng. Chem. Res. 2014, 53, 8528. (16) Qi, W. Synthesis, Design and Operating Strategies for Batch Reactive Distillation. Ph.D. dissertation, University of Massachusetts Amherst, Amherst, MA, 2010. (17) 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. (18) 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. (19) 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.

M


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