Simultaneous Optimization of the Design and Operation of Batch

Subscriber access provided by UNIV OF NEBRASKA - LINCOLN

Article

Simultaneous Optimization of the Design and Operation of Batch Reactive Distillation Processes Yu-Lung Kao, and Jeffrey Daniel Ward Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b03170 • Publication Date (Web): 09 Dec 2015 Downloaded from http://pubs.acs.org on December 11, 2015

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Industrial & Engineering Chemistry Research is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

Simultaneous Optimization of the Design and Operation of Batch Reactive Distillation Processes Yu-Lung Kao and Jeffrey D. Ward* Department of Chemical Engineering National Taiwan University Taipei 10617, Taiwan

Abstract Simultaneous optimization of equipment design and process operation for batch reactive distillation processes is studied in this work. The minimal total annual cost problem is illustrated with two realistic chemical systems: hydrolysis of methyl lactate and esterification of formic acid. The effect of design and operating variables on total annual cost is investigated. The optimization results suggest that a reflux policy which maintains constant distillate composition can provide nearly optimal operation. The column should be designed with an adequate number of stages so that the batch capacity improvement by further increasing the number of stages is insignificant. Vapor boilup rate should be specified to make the best use of the available operating time, and the optimal vapor boilup rate is primarily affected by the catalyst loading. The insight into the effect of process design variables on design performance is used to develop an efficient algorithm for determining simultaneously the optimal column design and operating policy.

Keywords: batch reactive distillation, design, optimization, total annual cost

*

Tel.: +886-2-2366-3037 Fax: +886-2-2369-1314 email: [email protected] 1

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1. Introduction Batch distillation is a widely used technique for liquid-liquid separation in chemical processes. In a conventional chemical plant, reaction and distillation usually take place in a separate units. However, the drive to reduce costs and energy consumption has motivated the study of more efficient alternatives. Combining batch reaction and batch distillation into a single operation unit, batch reactive distillation (BREAD), has the potential to overcome reaction equilibrium and azeotropes and to reduce capital and operating costs. Compared with its counterpart, continuous reactive distillation, batch-wise operation is more flexible and suitable for small scale production, such as for specialty chemicals, fine chemicals and pharmaceuticals. Many researchers have studied the optimal operation of non-reactive batch distillation with a fixed column design. This is reasonable because batch distillation processes are flexible, and different separation tasks can be achieved using existing batch distillation column equipment. Therefore, much less attention has been paid to the optimal column design problem. However, because the demand for flexible, integrated process alternatives is increasing, simultaneous optimization of design and operation of batch distillation and batch reactive distillation is also of interest.1 Because of the inherently dynamic nature of batch processes, optimal design of

2


Page 2 of 45

Page 3 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


non-reactive batch distillation has been studied by short-cut methods to avoid large computational time. Some researchers decomposed the more complex mixed integer dynamic optimization (MIDO) problem into a nonlinear programming problem (NLP) and solved the maximal profit problem for simultaneous optimal design and operation.1, 2

Mujtaba and Macchietto3 proposed a two-loop optimization method where operating

control variables (reflux ratio and times) were determined in the inner loop4 while batch properties (recovery amount and composition) as well as tray number, which was treated as a continuous variable and rounded off in the NLP, were solved in the outer loop by sequential quadratic programming. This method can be applied to both simple and rigorous dynamic models, and problems with both a single separation duty and multiple separation duties were investigated. In all cases, the objective function was to maximize the profit. Sharif et al.5 also studied the simultaneous optimal design and control problem as a finite dimensional mixed integer nonlinear problem (MINLP), and illustrated the algorithm with an integrated batch distillation process (two batch distillation columns). In the research described previously, the optimization problems were solved by gradient-based sequential methods. However, a disadvantage of this optimization technique is that the optimization may converge to a local optimum. To avoid this drawback, stochastic optimization methods have also applied to solve the simultaneous optimal design and 3



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

operation problem. A genetic algorithm was applied to optimize batch distillation process models of varying complexity by Low and Sørensen.6, 7 The maximal profit problem was investigated to find optimal tray number, vapor boilup rate as well as the optimal operation. The method was further extended to find the optimal column configuration simultaneously.7 In addition to using the profit as the objective function, Al-Tuwaim and Luyben8 fixed the production rate and minimized the total annual cost. For each fixed column size, the operation was optimized based on maximizing the batch capacity (CAP). Exhaustive gridding of column design space was employed to find the optimal design. The advantage of this objective function is that the costs of products and feed are not required for the calculation. Various aspects of BREAD processes have been studied by several authors in the past decade due to the observed potential benefits of integrated processes.9 However, compared with batch distillation without reaction, much less research has been conducted on the optimization of BREAD processes,10–15 let alone the determination of optimal column designs. In all of these reports the optimal operation problem was studied for a fixed column design, e.g. fixed total number of stages and catalyst loading. In most studies, the reboiler specification (vapor boilup rate or heat duty) was considered to be a design variable (constant value) because it is interdependent with the reflux ratio. 10–14 On the other hand, the boilup ratio profile was optimized in the work 4


Page 4 of 45

Page 5 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of Giessler et al.15 Mujtaba and Macchietto10 proposed an efficient optimization framework by using polynomial fitting techniques to find the reflux profile in a fixed batch time that maximizes the reaction conversion. Kao and Ward11,12 considered optimal operation with off-cut collection (multiple collection periods) for different column configurations (conventional distillation, inverted batch distillation and middle-vessel batch distillation column) as well as excess reactant design. The problem of optimal operation of batch-to-batch operation with off-cut recycling was also studied and solved.13,14 Giessler et al. 15 investigated different aspects of optimization (number of time intervals, model complexity, objective function etc.) separately for a column with a fixed number of stages. However, to the best of our knowledge, there is no open literature considering the simultaneous optimal design and operation problem for BREAD processes. If new equipment is to be purchased, it is important to consider the number of trays and column diameter as well as the operating policy. Therefore, the simultaneous optimization of design and operation is investigated in this work. The minimal total annual cost problem is formulated and solved. Exhaustive gridding of the column design space is used for the optimization. That is, the optimal operation is determined for all possible batch column designs and the one giving the best result is chosen as the optimal design. Although this method is more time consuming, a more comprehensive 5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

understanding of the process can be obtained. The remainder of this article is organized as follows. In Section 2, two realistic chemistry systems used for illustration and the process model used in this work are briefly introduced. The equations for total annual cost calculations are also presented. In Section 3, the effects of design and operating variables on the process economics is discussed in detail and an efficient optimization procedure is proposed. In Section 4, optimization results for the two case study systems are shown. Finally, in Section 5, conclusions are drawn.

2. BREAD Process and Model 2.1. Case study Two real chemistry systems are used for illustration in this work. Hydrolysis of methyl lactate: water + methyl lactate methanol + lactic acid (MeLC system) and esterification of formic acid: methanol + formic acid methyl formate + water (MF system). The vapor liquid equilibrium is described by the NRTL model, and the boiling point rakings of these systems including an azeotropes are listed in Table 1. The details of thermodynamic and kinetic models can be found in our previous work.12 Conventional batch distillation is used for both systems because for both systems one of the products is the lightest component and it can be withdrawn from the 6


Page 6 of 45

Page 7 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


top of the column. For the hydrolysis of methyl lactate, the light product methanol can be collected at the top to drive the reaction forward while the heavier product lactic acid accumulates in the reboiler and is purified later by off-cut removal. Similarly, in the esterification of formic acid, methyl formate is collected at the top while water accumulates in the reboiler. In this process, excess methanol design is used to improve the process performance.12 The operation of both BREAD process studied can be divided into three sub-periods as follows: (1) total reflux period: total reflux is employed until the composition of the lighter product in the distillate is pure enough for collection; (2) product period: the lighter product is collected at the top; (3) off-cut period: the heavier product accumulates in the reboiler and is purified by off-cut removal.

2.2. Process Model Following our previous work, the BREAD model used in this work is based on the following assumptions: (a) liquid holdup on trays and in the condenser is constant; (b) vapor holdup is negligible; (c) molar overflow between trays is constant; (d) reaction takes place only in the reboiler; (e) vapor and liquid achieve equilibrium on trays; (f) vapor boilup rate is constant during the batch; (g) column pressure is constant. The differential-algebraic equations (DAEs) describing the model are coded in MATLAB™ and solved with the built-in ordinary differential equations solver ode15s. 7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Details of the model equations can be found in our previous work.15 As stated in the list of assumptions, it is assumed in this work that reaction takes place only in the reboiler. Early in this work, the possibility of allowing reaction to take place on the stages as well was investigated. However it was observed that relatively little reaction occurred on the trays because the holdup on the trays is small compared to the holdup in the reactive reboiler and furthermore it was often the undesired reverse reaction that occurred on the stages because the concentration of products is enriched on the stages. These findings were consistent with those of Giessler et al.15 Therefore the decision was made not to consider the possibility of allowing reaction on the stages in the process design and optimization work.

2.3. Economic Calculation The objective function, total annual cost (TAC), is minimized with respect to both design and operating variables. This method of problem formulation is similar to that of Al-Tuwaim and Luyben, but also different in some respects.8 Similar to their work, for a given set of column design variables (e.g., total number of stages, vapor boilup rate) the operation is optimized based on maximizing the batch capacity (CAP) which is defined as the total product on specification divided by the total batch time plus a 0.5 hour set-up time between batches:

8


Page 8 of 45

Page 9 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Np

∑P i

CAP =

i =1

tb + 0.5

In their problem formulation, the hourly production rate was fixed for each column design. Because CAP is proportional to the vapor boilup rate for non-reactive batch distillation processes, the optimal CAP obtained under a fixed vapor boilup rate can be rescaled to meet the fixed hourly production rate by changing the vapor boilup rate. Therefore, with the adjusted vapor boilup rate each column design can meet the specified hourly production rate. In other words, each column design with different number of stages and vapor boilup rates produces the same CAP. Then, the corresponding TAC can be calculated for each column design. However, for BREAD processes the reaction rate affects the distillate composition and is also affected by the distillate rate. The optimal CAP can not be rescaled only by changing the vapor boilup rate. As a result, the annual production rate is fixed in our work, which can be achieved by conducting different numbers of batches (different total operating times) for each column design. Again, the corresponding total annual cost can also be calculated. Then, the operation of columns with different values of design variables is simulated repeatedly to find the optimal design for the process. The cost equations are taken from Al-Tuwaim and Luyben8 and can be found in the Appendix. 9


(1)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3. Effect of Variables on Economics In this section, the effect of reflux policy and design variables including total number of stages (N), vapor boilup rate (V), and catalyst loading (Wc) on the process economics is studied individually. Based on this investigation, an algorithm for simultaneous optimization of design and operation of BREAD processes is proposed. As each of these variables is changed, the values of the product period length and reflux ratio during the offcut period that maximize the batch capacity are determined. Finally, in Subsection 3.5, an optimization algorithm is proposed for determining the optimal values of the number of stages, vapor boilup rate and catalyst loading while at each stage in the optimization the values of the product period length and offcut reflux ratio that maximize the batch capacity are determined.

3.1. Reflux Policy Reflux ratio is a very important variable for batch distillation operation. In order to improve the BREAD process efficiency, it is recommended that a variable reflux ratio be employed during the product period instead of a constant ratio.15 In our previous work, a piecewise constant reflux ratio policy was used. However, it is computationally intensive to find the optimal reflux ratio profile because there are thousands of possible combinations of reflux ratios depending on how many intervals are used. It would be

10


Page 10 of 45

Page 11 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


even more time consuming if the operation is optimized for different column designs. Therefore, in this work a constant distillate composition reflux policy is applied in the product period. At each point in time, the minimal reflux ratio which keeps the distillate composition equal to or slightly larger than the purity constraint is implemented. The length of the product period is determined by optimization. On the other hand, a constant reflux ratio is adequate in the off-cut because there is no purity specification on the off-cut collected. The reflux ratio in the off-cut is an optimization variable and the length of the off-cut period is determined so that the accumulated product achieves the purity specification at the end of the batch. In order to investigate the effect of using a constant distillation composition reflux policy, an optimal operating policy based on maximizing the CAP is determined for both a piecewise constant reflux policy and a constant distillate composition reflux policy for the MeLC system using the same column design. The purity constraint is 95 mol% on both products. Figure 1 shows the results including the optimal reflux profile and composition profiles in the reflux drum and reboiler. The biggest difference between the two reflux policies is that the optimal piecewise constant policy collects distillate purity higher than the constraint during most of the product period and lower than the constraint near the end of the product period. By contrast, the constant distillate composition policy collects distillate almost at the specified purity during the whole 11



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

product period. The CAP of the process with the piecewise constant policy is only 1.18% more than that of the constant composition policy. In addition, the two reflux policies are also optimized and compared for the MF system. Detailed results are not presented due to space limitations, but it was found that the CAP of the more computationally intensive piecewise constant policy is only 5.46% larger than constant distillate composition policy. Therefore, we conclude that using constant distillate composition is sufficient to achieve nearly optimal operation for a given column design, and this method is used in this work.

3.2. Total Number of Stages A specified separation objective can be achieved by a larger column with a shorter operating time or a smaller column with a longer operating time. Therefore, understanding the effect of total number of stages on the process is important. First, the effect of changing the total number of stages on CAP under a fixed vapor boilup rate for batch reactive distillation processes is investigated. Both the MeLC system and the MF system are used for illustration. The vapor boilup rate and feed conditions are listed in Table 2. A constant holdup of 0.125 kmol on each tray and 1 kmol in the condenser is assumed. Three different product purity specifications, 90 mol% 95 mol% and 99 mol% for both products are applied for the process. Constant distillate composition reflux policy is employed in the product period. The operation variables optimized are 12


Page 12 of 45

Page 13 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the length of product period and the reflux ratio in the off-cut period. Figure 2 shows the optimization results for both systems. A similar trend can be observed in both figures. For a given product purity specification, the CAP increases as the number of stages increases because having more stages improves the separation efficiency. However, the CAP improvement becomes insignificant after a certain number of stages. Furthermore, this certain number of stages increases as the product purity specification increases. Take the MeLC system as an example, this certain number of stages is 9, 10, and 12 for 90 mol%, 95mol% and 99 mol% purity specification respectively. For the MF system, an excess of methanol is employed and the excess ratio is defined as the ratio of the moles of methanol to moles of formic acid in the feed. The optimal value of the excess ratio is determined for a fixed total number of stages for different purity specifications (N=10 for 90 mol% and 95 mol%; N=15 for 99 mol%). The result shows that the higher the purity specification, the larger the optimal excess ratio is (Figure 2b) because the excess of methanol is very important for the purification of water in the reboiler. Because the excess ratio is not re-optimized each time the number of stages is changed, the change in CAP as the total number of stages is changed is not as smooth and strictly increasing as for the MeLC system. However, it is unlikely that the results would change significantly if the excess ratio was re-determined for each value of the total number of stages. In addition, it is worth 13



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

noting that when the total number of stages is large, more methanol (the lighter reactant) will be distributed in the holdup of higher stages which causes the excess ratio in the rebolier to be smaller than the optimal ratio found for the initial value of the total number of stages. This results in a decrease in CAP and may even make the process infeasible. For the MeLC system, the number of stages beyond which the CAP improvement by adding stages is insignificant differs only a little bit among the three purity specifications studied (Figure 2a, N=9, 10 and 12 for spec.=90, 95 and 99 mol% respectively). By contrast, the number of stages beyond which the CAP improvement by adding stages is insignificant differs significantly among the three purity specifications studied for MF system (Figure 2b, N=8, 13, and 18 for spec.=90, 95 and 99 mol%). This is because the separation is more difficult in the MF system. Therefore, a larger increase in the number of stages is required to handle the purity specification changes. Next, the annual production rate (both products combined) is specified and the optimal number of stage that minimize the total annual cost is found. The process parameters of both systems including the annual production rate, total operating time available, feed amount (reboiler capacity), vapor boilup rate, and catalyst loading for the base case are also listed in Table 2. 14


Page 14 of 45

Page 15 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3a shows the operating cost, capital cost, and total annual cost (payback period=3 years) for different numbers of stages for the MeLC system with a 95 mol% product purity constraint. The steam requirement for the reboiler accounts for most of the operating cost, and the capital cost includes the cost of the column, reboiler and condenser. The capital cost increases gradually as the number of stages increases. On the other hand, the operating cost decreases drastically when the number of stages increases from 5 to 10, then the reduction becomes small as the number of stages increases. This trend reflects the trend of CAP improvement by increasing the number of stages. For the case studied, the operating cost is about 2.5 times the capital cost divided by the payback year, and it dominants the total annual cost. The minimal total annual cost (51800 $/year) happens when the number of stages is 10. Compared with the smallest and largest number of stages investigated (6 and 40), the total annual cost is reduced by about 20% and 10% respectively. The optimization is flat around the neighborhood of the optimal number of stages, especially in the direction of increasing the number of stages. For the three purities considered, the optimal number of stages and operation are listed in Table 3. In addition, the corresponding cost details are also listed in Table 4. The total annual cost calculation for the MF process with 95 mol% product purity constraint is also shown in Figure 3b. Similar trends of operating cost, capital cost and 15



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

total annual cost can be observed as in the MeLC system. The minimal total annual cost (27,450 $/year) is located at N=13. Compared with the smallest and largest total number of stages investigated (6 and 20), the total annual cost is reduced by about 22% and 3% respectively. Compared with the MeLC system, the fraction of total cost attributable to operating cost is smaller. Therefore, the total annual cost rises more rapidly as the total number of stages increases beyond the optimal value. However, the objective function is still flat around the optimum point (N=10 to 20). The optimal operation results and corresponding cost details including the optimal number of stages are listed in Table 5 and Table 6 for different purity specifications. For the 99 mol% purity case, the design is not feasible because the total required operating time exceeds the time available in one year (8400h). Therefore this operating policy could not be implemented in practice. The production is too slow which may be caused by slow reaction rate or small vapor boilup rate. This will be discussed and resolved in the later sections. To conclude, a similar tradeoff is observed for both systems as the number of stages in the column is changed. It is important not to design the column so that the total number of stages is located in the region where CAP improvement by adding more stages is significant. This will cause an unnecessarily high operating cost.

16


Page 16 of 45

Page 17 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.3. Vapor Boilup Rate In Section 3.2, it is found that when the annual production rate, reboiler capacity, vapor boilup rate and catalyst loading (process parameters listed in Table 2) are specified, the total number of stages does not strongly affect the TAC as long as the total number of stages is located in the region where CAP improvement by adding more stages is insignificant. Therefore, in this section the vapor boilup rate is investigated with the fixed optimal number of stages found in Section 3.2. Other process parameters are also fixed as listed in Table 2. Unlike the non-reactive case, the operating recipe must be re-optimized for each value of the vapor rate because the ability of separation is changed while the ability of reaction remains the same. First, the effect of vapor boilup rate on the CAP is studied. Figure 4 shows the result of the MeLC system with a 95 mol% product purity constraint and ten stages. As can be expected, the CAP increases as the vapor boilup rate increases because more distillate can be collected under the same reflux ratio if a higher vapor boilup rate is used. However, the trend is unlike batch distillation without reaction for which CAP is proportional to the vapor boilup rate. The marginal improvement in CAP decreases as the vapor boilup rate increases because the ability of reaction rate remains the same. That is, the process approaches the situation where the reaction rate is limiting. It is difficult to further increase the process efficiency only by increasing the ability of separation. Therefore, when a very 17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

high vapor boilup rate is required to achieve the required production rate, increasing the reaction rate by adding more catalyst is an alternative. However, the decision still depends on the total annual cost. Next, Figure 5 shows the cost results when the vapor boilup rate decreases from 25 kmol/h to 16 kmol/h for the same conditions just mentioned. The operating cost and capital cost decreases as the vapor boilup rate decreases, as does the total annual cost. However, the expense of reducing the vapor boilup rate for lower total annual costs is the increase of total operating time in order to achieve the specified annual production rate. That is, the total operating hours increase as the vapor boilup rate decreases (right axis in Figure 5). Because there are a limited number of operating hours in one year, there is a minimum vapor boilup rate which gives a feasible operation. Assuming that the maximum number of operating hours per year is 8400 hours (24 hours a day, 7 days a week, and 50 weeks a year), the minimal feasible vapor boilup rate in this case is 19 kmol/h. Compared with the base case in which vapor boilup rate is 25 kmol/h, the total annual cost is reduced by 7% and the number of operating hours per year is increased from 6797 hour to 8276. For such a vapor boilup rate, the operation of the process makes the best use of the time available. Similarly, if the production needs to be completed in half a year or in one month, the optimal vapor boilup rate can be determined in the same way so that the equipment is 18


Page 18 of 45

Page 19 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


not idle in the available time. Similarly, the vapor boilup rate is optimized to make the best use of operating time for all cases. The optimal results are listed in Table 7 which shows the optimal vapor boilup rate, corresponding TAC, and the TAC reduction compared with the base case in which V=25 kmol/h. As expected, more effort is required for a higher product purity specification. Both the optimal number of stages and vapor boilup rate increase as the product purity specification increases, as does the total annual cost. For the MF system with 99 mol% product purity, instead of reducing the vapor boilup rate from 25 kmol/h which was previously shown to be infeasible (requiring 13,588 hours of operation per year), vapor boilup rate is increased to 94 kmol/h so that the production can be complete in 8400 hours. In order to reduce the operating time by about 38%, a 376% increase in the vapor boilup rate is required which results in a very high total annual cost of 157,979 $/year. This is like the case where the process is limited by the reaction rate. If the reaction rate could be increased, the total annual cost could be reduced. However, the MF process has a homogeneous uncatalyzed reaction. An alternative is to purchase an additional batch distillation column with the same reboiler capacity, and then each column only needs to produce half of the specified production rate. The optimization result (in Table 7) shows that only 16 kmol/h of vapor boilup rate is required for each column and the combined total annual cost is only 110,900 $/year, a 19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

savings of about 30%. With the optimal vapor boilup obtained, the total number of stages is optimized again to verify that the optimal number of stages is not strongly dependent on boilup rate and to seek the possibility of further reducing the TAC. Figure 6 shows the TAC in the neighborhood of the optimal total number of stages found with fixed V=25 kmol/h. The TACs are flat for all cases investigated. Improvement in TAC by re-optimizing the total number of stages can only be found in two cases, MeLC 99% and MF 95% , and the optimal number of stages change from 12 to 13 and 13 to 12 respectively. The TAC reductions are only 0.39% and 0.14%. This shows that the optimal total number of stages is not sensitive to the vapor boilup rate. In summary, the vapor boilup rate should be designed to make the best use of the available operating time. If the vapor boilup rate is too small, the production will not be completed in the available time. On the other hand, if the vapor boilup rate is too large, the operating cost will be high and the equipment will be idled some of the time. Because the total operating hours is expected to be the total operating hours available for the optimal design, the problem is equivalent to fix the hourly production rate (which is the same as the batch capacity). The slight difference between the problem formulation in this work and fixing the hourly production rate is that the effect of using more or fewer batches to achieve the same annual production rate on 20


Page 20 of 45

Page 21 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the process economics is also considered. In addition, the optimal number of stages is found not to be sensitive to the value of the vapor boilup rate.

3.4. Catalyst Loading Finally, the catalyst loading in the reactive reboiler is studied for the MeLC system. The hydrolysis of methyl lactate is a heterogeneous catalytic reaction and the reaction rate is proportional to the catalyst weight. The MF system is not considered in this section because it has an uncatalyzed reaction. The effect of catalyst loading on the optimal vapor boilup rate and TAC is illustrated using the MeLC process with a 95% product purity constraint. The number of stages is fixed at ten. Different catalyst loadings are applied and the optimal vapor boilup rate which makes the best use of operating time is determined. To begin with, the cost of catalyst is not considered in the total annual cost calculation and Figure 7 shows the optimization result. As the catalyst loading increases from 10kg to 70kg, the total annual cost and optimal vapor boilup rate both decrease because the energy consumption contributes a large portion to the total annual cost. This also indicates that when the reaction is faster, the vapor boilup rate required to achieve the same separation task is smaller. The increase of the catalyst loading from 10kg to 20kg significantly reduces the total annual cost by about 40%. After that, the reduction of total annual cost for every 21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

additional 10kg of catalyst becomes smaller and smaller. This indicates that at least a certain amount of catalyst loading (20kg) is required for a good process design. If the reaction rate is too slow, an unnecessarily large vapor boilup rate is required to achieve the specified rate by removing more product from the reboiler to increase the reaction rate. Moreover, it can be expected that there should be an optimal catalyst loading that minimizes the total annual cost if catalyst cost is considered. The optimal catalyst loading is the tradeoff between the reduction in vapor boilup rate that can be achieved and the cost of catalyst used. The optimization algorithm presented in Section 3.5 includes catalyst cost in the calculations and so the results shown in Section 4 show this tradeoff and an optimal catalyst loading is identified. Note that if the catalyst loading is large the catalyst in the reboiler may not all be covered by the liquid holdup during the whole batch (liquid holdup in the reboiler decreases as the process proceeds). For such a case, the reaction rate calculation needs to be modified or less catalyst should be used to avoid inefficient use of the catalyst.

3.5. Summary and Optimization Algorithm Based on the results discussed in Section 3.1–3.4, an optimization algorithm was developed for BREAD processes. For a fixed annual production rate problem, a procedure for simultaneous optimization of design and operation of a catalytic BREAD 22


Page 22 of 45

Page 23 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


process is proposed in Figure 8. For each set of process design variables specified in steps 4–6, operating variables (tp and Rr) are also optimized to maximize the batch capacity. That is, for each value of the catalyst loading, number of stages and vapor rate, the values of the product collection period and the reflux ratio during the offcut collection period that maximize the batch capacity are determined. Following the procedure, the optimal total number of stages, vapor boilup rate and catalyst loading can be found to minimize the total annual cost. Because the total number of stages has only a minor effect on the process economics as long as it is located in the region where CAP improvement by adding more stages is insignificant, the total number of stages need not be optimized for each catalyst loading in step 4 of the procedure. Instead, a total number of stages determined for an initial guess of the catalyst loading can be used. In the end, the optimal total number of stages will be determined in step 7. In addition, if the reaction is uncatalyzed (such as the MF system), steps 3 and 8 should be omitted, and the optimal total number of stages and vapor boilup rate can be found by following the same procedure. The proposed algorithm is a sequential optimization algorithm. Other methods for multivariable optimization could also be applied to this problem but the proposed method is straightforward and was found to be effective for all of the cases studied. Therefore other optimization algorithms were not considered in this work. 23



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

4. Optimization Results In this section, the optimization results are presented. For the hydrolysis of methyl lactate system, in order to find the optimal catalyst loading, the cost of the catalyst is assigned and included in the total annual cost calculation. The price of the catalyst used (Amberlyst 15) is set 3.5 $/lb based on Tang et al.16 It is assumed that the catalyst must be replaced every 3 months, so that the annual catalyst cost is 30.8 $/(kg·year). The optimization procedure proposed in Figure 8 was applied to both processes, and the results are summarized in Table 8. For the MeLC system, the total annual cost for different catalyst loadings (step 3 to step 8 in Figure 8) are shown in Figure 9. Because the catalyst cost is relatively small compared to the TAC, the TAC trend is similar to the trend of TAC in Figure 7 where the catalyst cost is not included. The optimal catalyst loading can be read from the figure. As the purity constraint increases from 90 mol%, 95 mol% to 99 mol%, the optimal catalyst loadings also increase from 50kg, 60kg, to 80kg. Compared with the base case in which 30kg of catalyst is used, the TAC reduction is about 3.0%, 5.5% and 7.5% respectively. On the other hand, for the MF system, the values of the optimal design variables are the same as those presented in Section 3.4. The operation results and cost details for the optimal designs are also provided in

24


Page 24 of 45

Page 25 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Tables 9 and 10. It is interesting to note that the optimal CAPs for different product purity specifications in each system are similar after the optimization because the minimal TAC problem is formulated for a fixed annual production rate and a fixed available operating hours in one year (fixed total annual production rate). The optimization also shows that more batches with less product produced by a single batch is preferred when the product purity specification is higher. In addition, as expected, as the product purity specification increases, the operating cost and capital cost increase as well.

5. Conclusion The optimal operation of batch reactive distillation (BREAD) processes has been studied in the past decade. For most studies, a fixed column design is given for the operational optimization. However, if a new process is going to build, the column design must be considered. The simultaneous optimization of design and operation is studied for BREAD processes in this work. Design by minimization of the total annual cost is illustrated with two real chemistry system, hydrolysis of methyl lactate and esterification of formic acid. The optimal design is obtained by exhaustive gridding of the column design space. Although this method is time consuming, the results provide information than merely the optimal design and operating variables. 25



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

For the minimal total annual cost problem, the annual production rate is specified and operation is optimized based on maximizing the batch capacity. Process design variables including the total number of stages, vapor boilup rate, and catalyst loading are investigated. The optimization results suggest that the column should be designed with adequate number of stages beyond which the CAP improvement by increasing the number of stages is insignificant. Vapor boilup rate should be designed to make the best use of the available operating time, and the optimal vapor boilup rate is primarily affected by the catalyst loading. With the understandings of the effect of these process design variables, an optimization procedure for simultaneous determination of column design and operation is proposed. Following the optimization procedure, the optimal operating recipe, number of stages, vapor boilup rate and catalyst loading can be found for both case studies. Results show that as the product purity increases, the operating cost and capital cost also increase because a higher reflux ratio profile, greater number of stages, larger vapor boilup rate and more catalyst loading are required to achieve the same annual production rate.

26


Page 26 of 45

Page 27 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Appendix: Cost Equations for TAC Calculation The cost equations are taken from Al-Tuwaim and Luyben.8 Equations used are listed as follows: Calculate column diameter DIA(ft):

 (MW)V  DIA = 2    ρ V πVm 

1

2

(1)

where MW ≡ vapor molecular weight; V ≡ vapor boilup rate (lb mol/h); ρV ≡ vapor density (lb/ft3); Vm ≡ maximum allowable superficial vapor velocity (ft/s).

 ρ -ρ  Vm = K V  L V   ρV 

1

2

(2)

where Kv ≡ empirical constant for tray spacing = 0.3 ft/s; ρL ≡ liquid density (lb/ft3). The energy consumption Q (Btu/h):

Q =VHV

(3)

where H V ≡ molal heat of vaporization of the liquid in the reboiler (Btu/lbmol). The steam flow rate W (lb/h):

W = Q / Hv' ' where H v ≡ molal heat of vaporization of steam = 915.5 Btu/lb.

27


(4)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 45

Calculate the condenser heat transfer area Ac (ft2):

AC = q U∆T

(5)

where q= VHV ; U ≡ overall heat transfer coefficient = 100 Btu/(h ft2 ℉); ∆T ≡ temperature difference = 20 °F. The reboiler heat transfer area is similarly calculated except that U = 50 Btu/(h ft2 °F); ∆T = 50 °F. The column cost Ct ($):

Ct = Cb FM + NCbt FTM FTT FNT + Cpl

(6)

where Cb ≡ cost of the shell as a function of shell weight, height and diameter; FM ≡ material construction factor (shell) = 2.1 for stainless steel; N ≡ total number of stage; Cbt ≡ cost of trays as a function of diameter; FTM ≡ material construction factor (trays) = 1.189+0.0577(DIA) for stainless steel; FTT ≡ cost factor of tray type = 1 for valve tray; FNT ≡ cost factor for total tray number; Cpl ≡ platform and ladder cost as a function of diameter.

Cbt = 278.38exp(0.1739(DIA))

(7)

C b = exp  6.329 + 0.18255(ln Ws ) + 0.02297(ln Ws ) 2 

(8)

If N < 40

28


Page 29 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


C pl = 182.50(DIA)0.73960 L0.70684

(9)

C b = exp  6.823 + 0.14178(ln Ws ) + 0.02468(ln Ws ) 2 

(10)

C pl = 151.81(DIA)0.63316 L0.80161

(11)

If N ≥ 40

where Ws shell weight (lbs); L tangent to tangent length (ft) and assume tray spacing = 8 inch. If N < 20

FNT = 2.25 (1.0414)N

(12)

FNT =1.0

(13)

condenser cost (or reboiler cost) = 103 (0.73 + 0.064A0.65 )FEX

(14)

Otherwise

Condenser and reboiler cost:

where A ≡ condenser or reboiler heat transfer area (ft2); FEX condenser or reboiler material construction factor = 3.35 for stainless steel. Finally the operating cost OC ($/year):

29



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

operating cost=WT (SC)

Page 30 of 45

(15)

where T ≡ operation time (h) which can be calculated by the total number of batch required to produce the specified total product rtae multiples the single batch time; SC ≡ steam cost per 1000 lb = 5 $. Capital cost CC ($) is calculated by adding the column cost, condenser cost and reboiler cost. Then, total annual cost TAC ($/year) can be obtained:

TAC = OC + CC

payback year

30


(16)

Page 31 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


References (1 ) Logsdon, J. S.; Diwekar, U. M.; Biegler, L. T., On the Simultaneous Optimal-Design and Operation of Batch Distillation-Columns. Chem. Eng. Res

Des. 1990, 68, 434. (2) Diwekar, U. M.; Madhavan, K. P.; Swaney, R. E., Optimization of Multicomponent Batch Distillation-Columns. Ind. Eng. Chem. Res. 1989, 28, 1011. (3) Mujtaba, I. M.; Macchietto, S., Simultaneous Optimization of Design and Operation of Multicomponent Batch Distillation Column - Single and Multiple Separation Duties. J. PROCESS CONTR. 1996, 6, 27. (4) Mujtaba, I. M.; Macchietto, S., Optimal Operation of Multicomponent Batch Distillation Multiperiod Formulation and Solution. Comput. Chem. Eng. 1993, 17, 1191. (5) Sharif, M.; Shah, N.; Pantelides, C. C., On the Design of Multicomponent Batch Distillation Columns. Comput. Chem. Eng. 1998, 22, S69. (6) Low, K. H.; Sorensen, E., Simultaneous Optimal Design and Operation of Multipurpose Batch Distillation Columns. Chem. Eng. and Process. 2004, 43, 273. (7) Low, K. H.; Sorensen, E., Simultaneous Optimal Configuration, Design and Operation of Batch Distillation. AIChE J. 2005, 51, 1700. (8) Altuwaim, M. S.; Luyben, W. L., Multicomponent Batch Distillation .3. Shortcut Design of Batch Distillation-Columns. Ind. Eng. Chem. Res. 1991, 30, 507. (9) Mujtaba, I. M. Batch Distillation: Design and Operation. Imperial College Press: London, 2004. (10) Mujtaba IM, Macchietto S. Efficient Optimization of Batch Distillation with 31



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemical Reaction Using Polynomial Curve Fitting Techniques. Ind. Eng. Chem.

Res. 1997, 36, 2287. (11) 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 (12) Kao, Y. L.; Ward, J. D., Improving Batch Reactive Distillation Processes with Off-Cut. Ind. Eng. Chem. Res. 2014, 53, 8528. (13) Wajge, R. M.; Reklaitis, G. V., An Optimal Campaign Structure for Multicomponent Batch Distillation with Reversible Reaction. Ind. Eng. Chem.

Res. 1998, 37, 1910. (14) Kao, Y. L.; Ward, J. D., Batch Reactive Distillation with Off-Cut Recycling. Ind. Eng. Chem. Res. 2015, 54, 2188. (15) Giessler S, Hasebe S, Hashimoto I. Optimization Aspects for Reactive Batch Distillation. J. Chem. Eng. Jpn. 2001, 34, 312. (16) Tang, Y. T.; Chen, Y. W.; Huang, H. P.; Yu, C. C.; Hung, S. B.; Lee, M. J., Design of Reactive Distillations for Acetic Acid Esterification. AIChE J. 2005, 51, 1683.

32


Page 32 of 45

Page 33 of 45

Figures

Constant distillate composition reflux policy

1

1

0.8

0.8

0.6

reflux ratio

reflux ratio

Piecewise constant reflux policy

tp

0.4

0.6

tp

0.4 0

1

2

3

4

5

0

1

Reflux Drum

0.4

mole fraction

mole fraction

H2O ML MeOH LAC

0.6

0.2 0

1

2

3

4

4

5

4

5

4

5

H2O ML MeOH LAC

0.8 0.6 0.4 0.2 0 0

5

1

2

Reboiler 1

0.6

mole fraction

H2O ML MeOH LAC

0.8

0.4 0.2 0

1

2

3 time(h)

3 Reboiler

1

0

3

1

0.8

0

2

Reflux Drum

1

mole fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4

0.8 0.6 0.4 0.2 0 0

5

H2O ML MeOH LAC

1

2

3 time(h)

Figure 1. Reflux ratio profile and composition profile of optimal piecewise constant reflux policy (left) and constant distillate composition reflux policy for MeLC system.

33



(a) MeLC system 5.5 5.0

CAP (kmol/h)

4.5 4.0 3.5 3.0 2.5

spec=90 mol% spec=95 mol% spec=99 mol%

2.0 1.5 5

10

15

20

25

30

35

40

45

Total number of stage

(b) MF system 18 17 16 15 14 13

CAP (kmol/h)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 45

12 11 10 9

spec=90 mol%, excess ratio=1.06 spec=95 mol%, excess ratio=1.1 spec=99 mol%, excess ratio=1.22

8 7 6 5 4 3 2 5

10

15

20

25

30


Figure 2. CAP versus total number of stages for (a) MeLC system, (b) MF system.

34


Page 35 of 45

Operating cost ($/year)

(a) MeLC system 6.5x10

4

6.0x10

4

5.5x10

4

5.0x10

4

4.5x10

4

4.0x10

4

3.5x10

4

3.0x10

4

2.5x10

4

2.0x10

4

1.5x10

4

1.0x10

4

Operating cost Capital cost/payback year Total annual cost

5

10

15

20

25

30

35

40

45


(b) MF system

Operating cost ($/year)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.5x10

4

3.0x10

4

2.5x10

4

2.0x10

4

1.5x10

4

1.0x10

4

5.0x10

3

Operating cost Capital cost/payback year Total annual cost

5

10

15

20

25


Figure 3. The operating cost, capital cost, and total annual cost versus total number of stages for (a) MeLC system with 95 mol% product specification, (b) MF system with 95 mol% product specification.

35



10

CAP

9 8

CAP (kmol/h)

7 6 5 4 3 0

20

40

60

80

100

120

Vapor boilup rate (kmol/h)

Figure 4. Optimal CAP as vapor boilup rate increases for MeLC system with 95 mol% purity specification and N=10.

Operating cost Capital cost Total annual cost

5.5x10

Operating time 10000

4

9500

4

9000

4

8500 8400

4

8000

4

7500

4

7000

4

6500

4

6000

4

5500

5.0x10 4.5x10 4.0x10 3.5x10 3.0x10 2.5x10 2.0x10 1.5x10 1.0x10

3

Operating time (h)

4

Cost ($/year)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 45

5000

5.0x10

15

16

17

18

19

20

21

22

23

24

25

26


Figure 5. The costs and operating time versus vapor boilup rate for MeLC system with 95 mol% purity specification and N=10. 36


Page 37 of 45

MeLC system 4

6.2x10

4

6.0x10

4

Total annual cost ($/year)

5.8x10

4

5.6x10

4

5.4x10

4

5.2x10

4

5.0x10

4

4.8x10

4

4.6x10


4

4.4x10

4

4.2x10

4

4.0x10

6

7

8

9

10

11

12

13

14

15


MF system 5

1.7x10


5

1.6x10


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5

1.5x10

5

1.4x10

4

4.0x10

4

3.0x10

4

2.0x10

4

1.0x10

0.0 5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21


Figure 6. Total annual cost in the neighborhood of the optimal number of stages found with fixed V=25 kmol/h.

37



45 4

4

8.0x10

Total annual cost

40

Vapor boilup rate

35

4

7.0x10

30

4

6.0x10

4

25

4

20

4

15

4

10

4

5

5.0x10 4.0x10 3.0x10 2.0x10

1.0x10

0.0


9.0x10


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 45

0 10

20

30

40

50

60

70

Catalyst loading (kg)

Figure 7. Catalyst loading V.S. total annual cost and optimal vapor boilup rate.

38


Page 39 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1. Given the total product yield and the reboiler capacity (throughput per single batch)

2. Specify a initial vapor boilup rate (V) (V is specified as about half of the total feed can be vaporized in one hour in this work)

3. Specify the catalyst loading (Wc)

4. Find the optimal total number of stages (N) which minimizes the total annual cost (TAC).

5. With the obtained N, find the minimal V which meets the total annual production rate and makes the best use of the available operating time

6. With the obtained V, change N

to minimize the (TAC).

7. N is changed

Yes No 8. Min. TAC among all Wc ?

No Yes 9. Optimal column design

Figure 8. Optimization procedure flowsheet for BREAD processes. At each step in the optimization, the values of the product period length and offcut period reflux ratio that maximize the batch capacity are determined.

39



5


1.4x10

5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 45

1.2x10

5

1.0x10

4

8.0x10

4

6.0x10

4

4.0x10

0

10

20

30

40

50

60

70

80

90

100

Catalyst loading (kg)

Figure 9. Total annual cost versus catalyst loading (catalyst price=30.8 $/(kg·year)).

40


Page 41 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Tables Table 1. Boiling point rankings for both reaction systems Hydrolysis of methyl lactate Temperature (K)

Water

Methyl lactate

Methanol

Lactic acid

337.68

0

0

1

0

373.16

0.9909

0.0091

0

0

373.17

1

0

0

0

417.99

0

1

0

0

489.78

0

0

0

1

Esterification of formic acid Temperature

Methyl

Methanol

Formic acid

304.94

0

0

1

0

337.68

1

0

0

0

373.17

0

0

0

1

373.7

0

1

0

0

379.96

0

0.5434

0

0.4566

(K)

Water

formate

Table 2. Process parameters for the base case for both reaction systems Annual

Total operating

Feed amount

Vapor boilup

Catalyst

production rate

time available

(reboiler capacity)

rate

loading

(kmol/year)

(h/year)

(kmol)

(kmol/h)

(kg)

25

30

25

(-)

MeLC system

30000

8400

Water: 25 Methyl lactate: 25 MF system

60000

8400

Methanol: 25*excess ratio Formic acid: 25

41



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 45

Table 3. Optimal operation results for the MeLC system Purity

Optimal

Total

Amount of

Amount of

Amount of

batch time

product MeOH

product LAC

product off-cut

(h)

(kmol)

(kmol)

(kmol)

CAP specification

number of (kmol/h)

(mol/%)

stages

90

8

4.930

5.092

12.95

14.62

20.68

95

10

4.415

5.462

12.50

13.82

21.68

99

12

3.741

6.320

12.72

12.79

22.24

Table 4. Cost details of the optimal design for the MeLC system Purity

Total

Operating

Column

Reboiler

Condenser

Capital

Total

Operating

cost

cost

Cost

cost

cost

annual cost

time (h)

($/year)

($)

($)

($)

($)

($/year)

Number spec. of batch (mol%) 90

1089

6089.5

3.387E+04

9.260E+03

1.378E+04

1.554E+04

3.858E+04

4.674E+04

95

1140

6796.6

3.845E+04

1.054E+04

1.386E+04

1.564E+04

4.003E+04

5.180E+04

99

1176

8020.1

4.674E+04

1.166E+04

1.399E+04

1.579E+04

4.144E+04

6.056E+04

Table 5. Optimal operation results for the MF system Purity

Optimal

Total

Amount of

Amount of

Amount of

batch time

product MeOH

product LAC

product

(h)

(kmol)

(kmol)

off-cut (kmol)

CAP specification

number of (kmol/h)

(mol%)

stages

90

6

16.174

2.489

23.59

24.76

1.65

95

13

12.270

3.385

23.24

24.43

2.45

99

19

4.426

10.01

22.74

23.78

5.85

42


Page 43 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 6. Cost details of the optimal design for the MF system Purity

Total

Operating

Column

Reboiler

Condenser

Capital

Total

Operating

cost

cost

Cost

cost

cost

annual cost

time (h)

($/year)

($)

($)

($)

($)

($/year)

Number spec. of batch (mol%) 90

1242

3712.6

1.049E+04

7.124E+03

1.017E+04

1.138E+04

2.868E+04

2.005E+04

95

1259

4891.6

1.609E+04

1.132E+04

1.073E+04

1.202E+04

3.407E+04

2.745E+04

99

1290

13558.3b

5.613E+04

1.383E+04

1.153E+04

1.294E+04

3.830E+04

6.889E+04

b: exceed the total operating time available

Table 7. Optimal number of stages, vapor boilup rate and total annual cost Product

N

specification

(optimized under

(mol%)

fixed V=25 kmol/h)

Optimized V

TAC

Total annual cost

(kmol/h)

($/year)

reduced (%)

MeLC system 90

8

16

41502

11

95

10

19

48172

7

99

12

24

59836

1

MF system 90

6

8

15188

24

95

13

11

17861

22

19

94

157979

(-)

19a

16a

55453a

30b

99 a

: two identical columns design case, and here shows the result of the individual one b

: compared with one column design case

43



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 44 of 45

Table 8. Optimal values of design variables for different product purities for both processes Purity

Optimal number

specification

Optimal vapor

Optimal catalyst

boilup rate

loading

(kmol/h)

(kg)

of stages

(mol/%)

MeLC system 90

8

15

50

95

10

17

60

99

15

20.5

80

MF system 90

6

8

(-)

95

12

11

(-)

99

19

94

(-)

Table 9. Optimal single batch properties for different product purities for both processes Purity

Total batch

Amount of

Amount of

Amount of

time

product MeOH

product LAC

product off-cut

(h)

(kmol)

(kmol)

(kmol)

CAP specification (kmol/h) (mol/%)

MeLC system 90

3.588

6.860

12.77

13.61

21.62

95

3.620

6.653

12.30

13.59

22.11

99

3.645

6.235

12.27

12.28

23.45

MF system 90

7.176

6.268

23.30

25.27

0.93

95

7.201

6.127

23.19

24.53

4.78

99

7.165

6.063

22.71

24.31

8.48

44


Page 45 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 10. Cost details of optimal designs for different product purities for both processes Purity

No.

Total

Operating

Column

Reboiler

Condenser

Catalyst

Total

cost

annual cost

($/year)

($/year)

Capital cost spec.

of

Operating

cost

cost

Cost

cost ($)

(mol%)

batch

time (h)

($/year)

($)

($)

($)

MeLC system

90

1137

8368.4

2.926E+04

8.437E+03

1.070E+04

1.199E+04

3.112E+04

1.540+03

4.117E+04

95

1159

8290.8

3.317E+04

9.841E+03

1.146E+04

1.287E+04

3.418E+04

1.848+03

4.641E+04

99

1222

8230.4

4.030E+04

1.267E+04

1.276E+04

1.437E+04

3.980E+04

2.464E+03

5.603E+04

MF system

90

1236

8365.1

8.792E+03

6.118E+03

6.239E+03

6.831E+03

1.919E+04

(-)

1.519E+04

95

1258

8336.9

1.281E+04

9.912E+03

7.305E+03

8.064E+03

2.528E+04

(-)

2.123E+04

99

1276

8368.4

1.344E+05

1.754E+04

2.480E+04

2.829E+04

7.062E+04

(-)

1.580E+05

45


Simultaneous Optimization of the Design and Operation of Batch

Recommend Documents