Short-Cut Methods versus Rigorous Methods for Performance

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Short-cut Methods versus Rigorous Methods for Performance-evaluation of Distillation Configurations Gautham Madenoor Ramapriya, Ajiththaa Selvarajah, Luis Eduardo Jiménez Cucaita, Joshua Huff, Mohit Tawarmalani, and Rakesh Agrawal Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b05214 • Publication Date (Web): 17 May 2018 Downloaded from http://pubs.acs.org on May 17, 2018

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Industrial & Engineering Chemistry Research

Short-cut Methods versus Rigorous Methods for Performanceevaluation of Distillation Configurations Gautham Madenoor Ramapriya,1 Ajiththaa Selvarajah,1 Luis Eduardo Jimenez Cucaita,1 Joshua Huff,1 Mohit Tawarmalani,2 and Rakesh Agrawal1* 1

2

School of Chemical Engineering, Purdue University, West Lafayette, IN 47907

Krannert School of Management, Purdue University, West Lafayette, IN 47907

*Corresponding author: [email protected] Abstract This study demonstrates the efficacy of a short-cut method such as the Global Minimization Algorithm (GMA) 1,2, that uses assumptions of ideal mixtures, constant molar overflow (CMO) and pinched columns, in pruning the search-space of distillation column configurations for zeotropic multicomponent separation, to provide a small subset of attractive configurations with low minimum heat duties. The short-cut method, due to its simplifying assumptions, is computationally efficient, yet reliable in identifying the small subset of useful configurations for further detailed process evaluation. This two-tier approach allows expedient search of the configuration space containing hundreds to thousands of candidate configurations for a given application. Keywords: multicomponent distillation, global optimization, short-cut methods

Introduction Several distillation configurations can be used to separate a given feed-mixture into a desired set of product streams. Many methods have been presented in the literature to synthesize

1 ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 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

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the possible distillation configurations.3-14 The step-wise and easy to use method of Shah and Agrawal14 synthesizes configurations containing (n-1) distillation columns to separate an ncomponent mixture. For example, the method provides us with a set of 152 and 6128 configurations respectively for the distillation of 4-component and 5-component mixtures. Upon obtaining the list of all feasible configurations, referred to as the distillation configuration search-space, it is then useful to prune the large search-space by reliably identifying the arrangements that are likely to be attractive for performing the given separation. One way of achieving the task is by using a commercial process simulator like ASPEN Plus to rigorously simulate each distillation configuration for performance-evaluation. However, since such simulators perform stage-by-stage calculations using rigorous thermodynamic models, exploring the large search-space using such an approach is computationally prohibitive. There is a need for a reliable short-cut method that can quickly prune the search-space in a short time to identify a handful of promising configuration candidates which can then be evaluated rigorously using commercial process simulators. Note that it is important that the short-cut method be reliable in pruning the large search-space. A short-cut method based on pinched columns that estimates vapor duty using the Underwood’s equations15 presents an opportunity for devising a reliable scheme to narrow the search-space.16-22,6,8,12,1,2 The Underwood’s equations assume that liquid and vapor flowrates in rectifying (resp. stripping) sections are constant (CMO), and feed mixtures are ideal. With these assumptions, using the Underwood’s equations allows bypassing stage-by-stage calculations, thereby significantly reducing the computation-time. Agrawal and Herron, for several binary mixtures, used these simplifying assumptions for quick estimation of thermodynamic efficiencies and showed very good agreement with the corresponding thermodynamic efficiency values calculated using detailed Aspen simulations.23 Similarly, with


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these assumptions, thermodynamic efficiencies were estimated for all ternary configurations including thermally linked columns for a ternary air mixture (N2, Ar, O2) to quickly demonstrate why a side stripper configuration has historically provided the highest product recoveries.24 However, in the distillation community, some doubt and skepticism has persisted about the magnitude of impact these simplifying assumptions have on real world applications, and whether the results obtained from the short-cut methods that use these assumptions are trustworthy. In this work, we carry out extensive simulations for a set of four-component configurations and, rank-list the results using the two approaches: (a) the short-cut approach and (b) the rigorous simulation based approach. Then, we show that the short-cut method is a reasonable tool to prune the search-space. Procedure In this section, we present the set-up of a case study that compares the rank-lists of simulated distillation configurations from two approaches: the short-cut method and the rigorous stage-by-stage method. Although rank-lists can be prepared by comparing many different criteria (e.g., overall cost, exergy loss, etc.), we shall use the overall minimum heat duty requirement of a configuration as the basis for comparison. As a first approximation, the overall minimum heat duty requirement of a configuration is a good indicator of the configuration’s onsite operating and capital costs. For short-cut calculation of total minimum heat duty requirement of configurations, we use the Global Minimization Algorithm (GMA) proposed by Nallasivam et al.1,2 GMA is an optimization model that determines the global total minimum heat duty requirement of all distillation configurations in the search-space. Since GMA uses Underwood’s equations for calculations, it inherits the following critical underlying assumptions of the latter:



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1)

Pinched Columns

2)

Constant relative volatility between each pair of components (Ideal feed mixture)

3)

Constant molar overflow

To determine minimum heat duty requirement of configurations through the rigorous stage-by-stage simulation procedure, we use the ASPEN Plus software. Since the goal of this work is to test the applicability of the assumptions 2 and 3 listed above to model real systems, in order to make assumption 1 a non-factor in the comparative study, and maintain uniformity across ASPEN Plus simulations, we introduce excess stages in each section of all configurations. The minimum heat duty of each studied configuration from ASPEN Plus is obtained through a combination of extensive sensitivity analyses and optimization. Since this exercise is extremely time-consuming, it is not practical to use ASPEN Plus to obtain minimum heat duty results for the entire search-space, which contains hundreds to thousands of distillation configurations. So, we limit our search-space for this comparative study to the eighteen four-component basic configurations, which are shown in Figure 1. In this figure, filled ovals denote condensers, while unfilled ovals denote reboilers. Further, alphabets denote components, and the volatility decreases in alphabetical order. In all the configurations of the figure, submixtures associated with reboilers and condensers are respectively assumed to be in the saturated liquid and vapor phase. All products, and the BC submixture stream are withdrawn from the intermediate location of a distillation column (configurations ‘j’, ‘o’, ‘q’ and ‘r’ in Figure 1) are saturated liquids. The feed to be separated, as in Kim and Wankat,25 is a saturated liquid mixture of alkanes at 3 atm. The details of the composition of the components in the feed are shown in Table 1. The feed composition and relative volatilities between components are the only inputs to GMA. To 4 ACS Paragon Plus Environment

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determine the relative volatility values, we obtain the K-values from ASPEN Plus at the feed conditions (Peng-Robinson equation of state is used to model the thermodynamics of this system). The relative volatility of each component in the feed is shown in Table 1. For the ASPEN Plus simulations, all columns are operated at a constant pressure of 3 atm., and each product stream is required to have a purity of 99.9% in the respective component (which is close to the 100% purity of products assumed in GMA). Results Using each of the methods, for the given feed, configuration ‘r’ provides the lowest minimum heat duty value. Table 2 shows the minimum heat duties from the GMA method and using ASPEN Plus simulations. The heat duties are normalized with respect to the minimum heat duty of configuration ‘r’ within each method. The heat duty results from each approach are sorted in increasing order down the table. For easy interpretation, we divide the set of configurations into three bands: ‘attractive (I)’ (within 10% of the minimum), ‘border-line (II)’ and ‘unattractive (III)’ (more than 15% of the minimum). The critical observation to be made from the table is that both the approaches put the same set of configurations in each band. So, the GMA approach neither misplaces a configuration that is attractive into the other bands nor does it wrongly identify an unattractive configuration as attractive. Secondly, there is a close overlap between the rank-lists generated by the two approaches. In the ‘attractive’ band, with only the exception of the position of configuration ‘o’, the rest of the configurations in the band follow the same order in the two approaches, while in the ‘border-line’ band, there is very little to differentiate between configurations ‘g’ and ‘k’ in terms of heat duty. In the ‘unattractive’ band, except the configurations ‘m’ and ‘j’, the rest follow the same ranking order in both the approaches. The above results make a strong case for the applicability of the GMA method as a 5 ACS Paragon Plus Environment


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screening tool for identifying configurations which have low heat duty, and pruning out those that don’t, even though GMA makes simplifying assumptions that ASPEN Plus does not. In Figure 2, we perform a simple regression analysis to relate the GMA heat duty to that estimated using ASPEN Plus. The correlation between these data series is 0.956. The scatter plot shows the quality of fit and the corresponding p-value for significance is 6.25×10-10. This shows that GMA heat duty has a good predictive power for the corresponding heat duty obtained using ASPEN Plus simulations. We provide additional information in Table 3. In the table, as an example, the relative volatility values at the top and bottom stage of the first column of configuration ‘r’ from the ASPEN Plus simulation are shown. This gives a sample of the actual variation of the relative volatilities across stages of a given configuration. Despite this variation, the extent of matching in Table 2 between the results obtained from GMA, which uses a single relative volatility set at the feed location, and ASPEN is quite remarkable. The greatest benefit of using a short-cut method for evaluating distillation configurations over a rigorous approach is the time taken for evaluation. For our case study, we obtained the minimum heat duty requirements for the eighteen configurations using GMA in less than 1 minute. Using ASPEN Plus, to obtain the same results, we adopted a combination of optimization and an extensive, time-consuming sensitivity analysis for each distillation flowsheet, which took us months of effort to complete. It should be pointed out that while each simulation run in ASPEN Plus is computationally efficient and reliable, the sequential quadratic programming (SQP) it uses does not guarantee global optimality of the calculated heat duty. As a result, for each configuration, through sensitivity analysis, we had to perform a large number of runs with systematic parameter variation to ensure global optimality of the calculated heat duty, and the parameters that were varied simultaneously for each of the eighteen configurations are 6 ACS Paragon Plus Environment

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detailed in Table 4. Such an exercise was essential for proper comparison with the GMA, which guarantees global optimality within its set of assumptions. In practice, even when only estimates of minimum heat duty requirements without the guarantee of global optimality are sufficient, using rigorous, stage-by-stage methods to span the entire search-space of available fourcomponent (152 in number) or five-component (6128 in number) configurations would be an immensely time-consuming exercise, and hence impractical. In contrast, a shortcut GMA approach makes the evaluation of each configuration quick, and, as shown here, with reasonable accuracy, for practical use. These key features of the short-cut approach enable a systematic, complete and reliable evaluation of the entire search-space of distillation configurations. Conclusions The goal of this work was to test the applicability of short-cut performance-evaluation methods and their underlying assumptions to model distillation configurations. To verify this, minimum heat duty results from two approaches: the short-cut approach (GMA) and the rigorous stage-by-stage approach (ASPEN Plus) were obtained and compared for eighteen fourcomponent basic configurations. The configurations identified as attractive (unattractive) by the short-cut GMA method were also found to be attractive (unattractive) using ASPEN Plus simulations. The rank-listing of the studied configurations from the two approaches was very similar. However, while the short-cut evaluation of all eighteen configurations took us less than a minute, obtaining minimum heat duty results from ASPEN Plus with guaranteed global optimality was significantly more time consuming. These observations highlight the importance and relevance of the short-cut method (GMA), despite its underlying assumptions, as a computationally efficient and reliable alternative to expediently prune the entire search-space and identify a few distillation configurations with low heat duty requirements. In the next step, 7 ACS Paragon Plus Environment


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the identified subset can be further evaluated using rigorous process simulators to choose the final configuration for implementation. This work also provides a reliable basis for extending the short-cut procedures using assumptions similar to that in GMA, to prune the search space based on exergy loss or overall cost of distillation configurations.

Acknowledgement The information, data, or work presented herein was funded in part by the Office of Energy Efficiency and Renewable Energy (EERE), U.S. Department of Energy, under Award Number DE- EE0005768. We would also like to thank Dr. Anirudh Shenvi for his inputs in the early stages of this project.

Disclaimer ·

The information, data, or work presented herein was funded in part by an agency of the

United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The


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views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

References (1). Nallasivam, U.; Shah, V. H.; Shenvi, A. A.; Tawarmalani, M.; Agrawal, R. Global Optimization of Multicomponent Distillation Configurations: 1. Need for a Global Minimization Algorithm. AIChE J. 2013, 59, 971. (2). Nallasivam, U.; Shah, V. H.; Shenvi, A. A.; Tawarmalani, M.; Agrawal, R. Global Optimization of Multicomponent Distillation Configurations: 2. Enumeration based global minimization algorithm. AIChE J. 2016, 62, 2071. (3). Petlyuk, F. B.; Platonov, V. M.; Slavinskii, D. M. Thermodynamically Optimal Method for Separating Multicomponent Mixtures. Int. Chem. Eng. 1965, 5, 555. (4). Sargent, R. W. H.; Gaminibandara, K. Optimum Design of Plate Distillation Columns. In: Optimization in Action; Dixon LCW, Ed., New York: Academic Press, 1976, 267. (5). Agrawal, R. Synthesis of Distillation Column Configurations for a Multicomponent Separation. Ind. Eng. Chem. Res. 1996, 35, 1059. (6). Caballero, J. A.; Grossmann, I. E. Generalized Disjunctive Programming Model for the Optimal Synthesis of Thermally Linked Distillation Columns. Ind. Eng. Chem. Res. 2001, 40, 2260. (7). Agrawal, R. Synthesis of Multicomponent Distillation Column Configurations. AIChE J. 2003, 49, 379. (8). Caballero, J. A.; Grossmann I. E. Design of Distillation Sequences: From Conventional to Fully Thermally Coupled Distillation Systems. Comp. Chem. Eng. 2004, 28, 2307.



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(9). Rong, B.; Kraslawski, A.; Turunen, I. Synthesis of Functionally Distinct Thermally Coupled Configurations for Quaternary Distillation. Ind. Eng. Chem. Res. 2003, 42, 1204. (10). Fidkowski, Z. T. Distillation Configurations and their Energy Requirements. AIChE J. 2006, 52, 2098. (11). Ivakpour, J.; Kasiri, N. Synthesis of Distillation Column Sequences for Nonsharp Separations. Ind. Eng. Chem. Res. 2009, 48, 8635. (12). Giridhar, A. V.; Agrawal, R. Synthesis of Distillation Configurations: I. Characteristics of a Good Search Space. Comp. Chem. Eng. 2010, 34, 73. (13). Giridhar, A. V.; Agrawal, R. Synthesis of Distillation Configurations: II. A Search Formulation for Basic Configurations. Comp. Chem. Eng. 2010, 34, 84. (14). Shah, V. H.; Agrawal, R. A Matrix Method for Multicomponent Distillation Sequences. AIChE J. 2010, 56, 1759. (15). Underwood, A. J. V. Fractional Distillation of Multicomponent Mixtures. Chem. Eng. Prog. 1948, 44, 603. (16). Glinos, K.; Malone, M. F. Minimum vapor flows in a distillation column with a sidestream stripper. Ind. Eng. Chem. Res. 1985, 24, 1087. (17). Fidkowski, Z. T.; Krolikowski, L. Thermally coupled system of distillation columns: optimization procedure. AIChE J. 1986, 32, 537. (18). Carlberg, N. A.; Westerberg, A. W. Temperature-heat diagrams for complex columns. 2. Underwood's method for side strippers and enrichers. Ind. Eng. Chem. Res. 1989, 28, 1379. (19). Carlberg, N. A.; Westerberg, A. W. Temperature–Heat Diagram for Complex Columns. 3. Underwood's Method for Petlyuk Configuration. Ind. Eng. Chem. Res. 1989, 28, 1386.


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(20). Fidkowski, Z. T.; Krolikowski, L. Energy requirements of nonconventional distillation systems. AIChE J. 1990, 36, 1275. (21). Fidkowski, Z. T.; Agrawal, R. Multicomponent thermally coupled systems of distillation columns at minimum reflux. AIChE J. 2001, 47, 2713. (22). Adiche, C.; Ait Aissa, B. Generalized Approach for the Conceptual Design of Distillation Columns with Complex Configurations. Chem. Eng. Res. Des. 2016, 109, 150. (23). Agrawal, R.; Herron, D. M. Optimal Thermodynamic Feed Conditions for Distillation of Ideal Binary Mixtures. AIChE J. 1997, 43, 2984. (24). Agrawal, R.; Fidkowski, Z. T. Are Thermally Coupled Distillation Columns Always Thermodynamically More Efficient for Ternary Distillations? Ind. Eng. Chem. Res. 1998, 37, 3444. (25). Kim, J.; Wankat, P. C. Quaternary Distillation Systems with Less than N − 1 Columns. Ind. Eng. Chem. Res. 2004, 43, 3838.



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Figures

Figure 1: All basic configurations for separating a four-component feed mixture7,12


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GMA Vs. ASPEN Plus 1.9 1.8

y = 1.0572x - 0.0138

1.7 1.6

GMA

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


1.5 1.4 1.3 1.2 1.1 1 1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

ASPEN Plus

Figure 2: Plot of normalized heat duty values (also appearing in Table 2) from ASPEN Plus versus GMA along with the trend line.



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Table 1: Feed data

Feed Mole Fraction

Relative Volatility w.r.t. D (ASPEN Plus)

A N-butane

0.3

46.21

B N-pentane

0.4

17.40

C N-heptane

0.25

2.65

D N-octane

0.05

1

Component


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Table 2: Minimum heat duty results from ASPEN Plus and GMA for the configurations in Figure 1 ASPEN Plus Results

GMA Results

Configuration

Normalised Heat Duty

Configuration

Normalised Heat Duty

1

r

1.000

r

1.000

2

o

1.013

n

1.036

n

1.021

l

1.036

4

l

1.024

p

1.058

5

p

1.068

o

1.085

k

1.107

g

1.101

7

g

1.109

k

1.103

8

q

1.188

q

1.242

9

i

1.199

i

1.361

10

m

1.203

f

1.364

11

f

1.226

h

1.372

12

h

1.302

m

1.422

c

1.352

j

1.431

14

a

1.374

c

1.439

15

j

1.385

a

1.442

16

b

1.424

b

1.450

17

e

1.438

e

1.455

18

d

1.708

d

1.763

Rank

3

Band

I

6 II

13

III



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Table 3: Relative volatilities at the top and bottom stage of the main feed-column in configuration ‘r’

Relative Volatility Relative Volatility w.r.t. w.r.t. D (top stage) D (bottom stage) Component A

N-butane

43.12

26.79

B

N-pentane

16.13

11.21

C

N-heptane

2.62

2.29

D

N-octane

1

1


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Table 4: Parameters of each configuration of Figure 1 that are systematically/concurrently varied for the sensitivity analysis are indicated in the below table with a ‘×’ symbol Configuration (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) (q) (r)

Reflux Ratio Column 1 × × × × × × × × × × × × × × × × × ×



Distillate Flow Column 1

Distillate Flow Column 2

Sidedraw (BC) Flow Column 2

× × × × × × × × × × × × ×

× × × × ×

×



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Short-Cut Methods versus Rigorous Methods for Performance

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