Dynamic Controllability Comparison of Conventional Distillation ...

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Dynamic Controllability Comparison of Conventional Distillation Sequences and Dividing-Wall Columns with Upper and Lower Partitions Using the Desirability Function Janka A Tarjani, Andras Jozsef Toth, Tibor Nagy, Enikő Haaz, and Peter Mizsey* Department of Chemical and Environmental Process Engineering, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics P.O. Box 1521, Budafoki Street 8, H-1111, Budapest, Hungary ABSTRACT: The aim of this study is to compare the controllability properties of conventional distillation sequences and dividing-wall columns with upper and lower partitions (DWCs). The controllability analysis methodology uses the Control Design Interface (CDI) module of Aspen Dynamics to obtain the state space representation of the studied systems. The frequency dependent controllability indices are calculated by Matlab on the basis of the matrices of the transferred state space representation. The study includes the examination of the conventional direct and indirect sequences and two DWCs systematically generated from the corresponding conventional sequences. Case studies are completed using ternary alcohol mixtures with different eases of separation. Results show that conventional distillation sequences have more favorable controllability properties than those of the DWCs if direct separation and mixtures with symmetrical ease of separation are considered. In the cases of mixtures with nonsymmetrical ease of separation, the indirect separation, the DWCs with lower partition show practically similar controllability features than those of the corresponding conventional sequences. avoiding the remixing effect.2 In such a way both investment and operational costs can be reduced compared to that of the conventional sequences. Despite being a 30 years old technology there are only 40 operating DWCs now.17,18 Recent studies have investigated these complex arrangements, and the interest in DWCs has begun to increase. Several design methods19−23 and applications for azeotropic, extractive and reactive distillation are also developed.24 However, there are just a few articles about the controllability of such columns. Mizsey et al.25 studied the controllability features of heat integrated distillation schemes and FTCDCs and found stronger interactions in the case of the FTCDCs than that of the heat integrated ones. Abdul Mutalib et al.26,27 studied temperature control of a DWC on simulations and a pilot plant. Serra et al.28,29 compared different DWC designs and found that nonoptimal DWC designs may improve the controllability features. Segovia-Hernández et al.30 compared control properties of conventional distillation schemes and DWCs for the separation of ternary mixtures in the time domain. Wang and Wong31 studied the energy efficiency and controllability of DWCs and suggested a temperature and composition cascade control system for controlling a DWC. Gómez-Castro et al.32,33 studied the dynamic properties of DWCs with one and two walls inside. Ling and Luyben34 studied a differential control structure for DWCs in which four temperatures are controlled,

1. INTRODUCTION Distillation is the most widespread unit operation for separating liquid mixtures in the chemical process industries. Although distillation has several recognized advantages, its energy efficiency has been continuously improved with different developments. The operational cost of distillation is usually considered to be 40−50% of the entire plant.1,2 Nowadays it is a fundamental goal to design environmentally friendly and energy and cost efficient processes.3 To reduce both the energy and cost requirements there are several heat-integrated distillation column structures (e.g., refs 4−6). Heat-integrated structures are proven to be more economical in certain cases than conventional column sequences.7 An important alternative of the energy integration is the socalled fully thermally coupled distillation columns (FTCDC) introduced by Petlyuk et al. in 1965.8 Merging two thermally coupled columns into one is the most recognized and still upto-date energy-integrated distillation technology, that is, the dividing-wall column (DWC).9,10 Dividing-wall columns have a vertical partition inside the column and they are capable of separating multicomponent mixtures into relatively high purity products. This one column structure was first introduced in 1987 by Kaibel11 as a simpler solution of FTCDC with a partition in the middle part of the column. Annakou and Mizsey have shown that the FTCDC can be energetically competitive only in special cases.7 The most significant advantage of a DWC is the potential capital cost saving. Using a DWC can lead to cost saving up to 30%12−16 as it only requires one distillation column instead of two, considering the separation of a ternary mixture. On the other hand thermodynamic efficiency can be increased by © 2016 undefined

Received: Revised: Accepted: Published: 952

July 29, 2016 October 4, 2016 November 14, 2016 November 14, 2016 DOI: 10.1021/acs.iecr.6b02904 Ind. Eng. Chem. Res. 2017, 56, 952−959

Industrial & Engineering Chemistry Research

Article

and they achieved a good product quality control. Van Diggelen and Kiss et al.35 compared the control strategies of a DWC using a ternary benzene−toluene−xylene (BTX) mixture. Woinaroschy and Isopescu36 studied the time-optimal control for the startup of DWCs. Dohare et al.37 used MATLAB Simulink environment to study a model predictive control for DWCs which has been proven to be better than PI controllers. Model predictive control (MPC) strategies are considered suitable for controlling a DWC. Adrian et al.38 found that MPC shows a favorable control behavior than single loop PI controllers. Buck et al.39 developed a method for designing model predictive control (MPC) for DWCs. Kiss et al.40 studied multiloop PID control strategies and MPC and concluded that DWCs have good controllability properties. Rewagad and Kiss41 made a full-size nonlinear model of a DWC and studied the performance of a MPC. The conceptual design method of a chemical process has been determined by Douglas42 and other authors; for example, Mizsey43 and Emtir44 also call the attention to the complexity of the process design activity in which process design and control may mutually influence each other. Among the design steps the control structure design is a well-known subject matter.45,46 Although the design of an equipment item and its control structure can be considered incorrectly for two different subsequent tasks, it is necessary to complete such a design simultaneously as it is mentioned in the literature.47,48 Hence when studying a novel process, equipment, or technology it is vital to investigate its controllability properties as well. Therefore, the aim of this work is to investigate the controllability properties of dividing-wall columns with upper and lower partitions and compare them to those of the corresponding conventional column series. The comparison is completed in the frequency domain using the CDI module of Aspen Plus and the desirability function with special aim.

Figure 2. Conventional indirect sequence (CIS).

constructions of a DWC in the literature,50−52 but it is a common trend to investigate the properties of the original structure introduced by Kaibel11 with the partition in the middle (see, e.g., Wolff and Skogestad53). As a systematic approach54 suggests, there is a strong connection between the conventional sequences and the DWCs with upper (DWCU) and lower (DWCL) partitions (Figures 3, 4). Since there are

2. SYSTEMS STUDIED 2.1. Conventional Distillation Sequences. The separation of a zeotropic three component mixture (ABC) requires two conventional distillation columns since they have one feed and two products. The order of the separations defines the direct and the indirect structures (Figures 1 and 2). The selection between the two sequences is usually determined by the features of the mixture, physicochemical parameters, and composition.42,49 2.2. Dividing-Wall Columns. A dividing-wall column is capable of separating three component zeotropic mixtures since it has one feed and three products. There are numerous feasible

Figure 3. Dividing wall column with upper partition (DWCU).

only a few articles about the properties of these systems it is reasonable to study and compare the conventional sequences and the DWCs with upper and lower partitions. DWCU can be considered as an alternative of the conventional direct sequence

Figure 1. Conventional direct sequence (CDS).

Figure 4. Dividing wall column with lower partition (DWCL). 953

DOI: 10.1021/acs.iecr.6b02904 Ind. Eng. Chem. Res. 2017, 56, 952−959


Article

are listed in Table 1. The separation index (SI) for a ternary ABC mixture is calculated in the following way:7

(Figure 1) and DWLC as an alternative of the conventional indirect sequence (Figure 2).

3. CASE STUDIES 3.1. Process Design. First rigorous simulations of the studied systems are carried out using the RadFrac model of Aspen Plus software55,56 using the UNIQUAC thermodynamic model. Since the professional flowsheeting software tools miss the built in module of a dividing-wall column, the setup of an adequate model of a DWC should be completed. The thermodynamically equivalent systems are presented in Figures 5 and 6 generated from the conventional sequences applying thermal coupling.

SI =

αAB αBC

(1)

where αij is the relative volatility. The mixtures are so selected that in case 1 the separation index is around 1 which means that the ease of separation of A/ B is similar to that of the separation of B/C. In mixture 2 the separation of B/C is harder than the separation of A/B and in mixture 3 the separation of A/B is harder than that of the B/C. The feed is equimolar, it contains 33 kmol/h A, 34 kmol/h B, and 33 kmol/h C. Product purities are always 95 mol %. For the conventional distillation schemes the optimal design parameters (number of trays, feed tray locations, reflux ratio) are determined by parametric optimization in which the objective function is the total annual cost (TAC). During the optimization, the purity of the products is fixed through a design specification. The cost estimation is carried out with a user added subroutine in Aspen Plus. The calculations follow the philosophy of Douglas.42 Features of the DWCs are determined by those of the conventional alternatives as a systematic approach suggested by Rong.54 Parameters of each column in the conventional direct distillation schemes are listed in Table 2. Specifications of other constructions, DWCs, are determined according to these parameters. 3.2. Controllability Analysis. After obtaining the steady state models, dynamic simulations are carried out in Aspen Dynamics. PID controllers are used as it is suggested in the literature.57,58 The control variables are the three product compositions. Two groups of manipulated variables are selected following the heuristic rule of control structure design that for the control of any parameters the closest possible manipulated variable is selected. Finally, four groups of manipulated variables are considered (Table 3). The groups of the manipulated variables are so selected that they can be applied for both the conventional and the dividing wall column systems. This philosophy reduces the number of possible groups. In each group the first manipulated variable controls the composition of product A, the second one controls the composition of product B and the third one controls the composition of product C, respectively. Tuning is made according to the Ziegler-Nichols algorithm using the automatic tuning tool of Aspen Dynamics.56 Closed loop simulations are completed where the disturbances are in the feed flow rate, the feed composition, and the set points of the composition control loops to demonstrate the effectiveness of the control structure. On the basis of these load rejection investigations the process time constants are also determined. The controllability analysis methodology is based on calculating the frequency-dependent controllability indices. Several procedures are presented in the literature for such calculation30,59,60 but the fastest and simplest method has been introduced by Gabor and Mizsey.61 It can be successfully applied for the conventional and the thermally coupled

Figure 5. Partially coupled direct configuration.

Figure 6. Partially coupled indirect configuration.

Usually ideal, that is, hydrocarbon mixtures are selected for the study of new column configurations,18,42,50,57 but such calculations can be argued since the DWCs are frequently applied for the separation of nonideal mixtures. In our study three ternary alcohol mixtures are considered for the simulation work. These mixtures cannot be considered as ideal ones but they form zeotropic mixtures. The selected components, their relative volatilities, and the ease of separation for each mixture Table 1. Mixtures Examined mixture

A

B

C

αAC

αBC

αAB

SI

1 2 3

ethanol ethanol methanol

n-propanol n-propanol t-butanol

n-butanol i-butanol n-butanol

8.47 5.52 17.87

3.00 1.96 6.07

2.82 2.82 2.95

0.94 1.44 0.49

954



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Table 2. Optimal Parameters of the Designed Columns SI = 0.94 no. stages feed stream (kmol/h) reflux ratio

SI = 1.44

column 1

column 2

column 1

46

33

46

1.4

2.5

direct xA−xB−xC

indirect xA−xB−xC

R1−R2−Q2 L1−L2−Q2

R2−Q1−Q2 L2−Q1−Q2

1.3

column 2

85

38

26

4.5

2.0

1.0

of the controllability of each system. As an example Figures 7 and 8 show the controllability indices as a function of angular frequency for mixture 1.

distillation systems studied. It is important to note that this methodology that relies on frequency-dependent controllability indices is not capable of comparing different control structures of the same system62−66 but it is capable of comparing the controllability features of different processes/systems64,65 as it is applied for in our study. The procedure uses the Control Design Interface (CDI) module of Aspen Dynamics to obtain the state space representation of the dynamic system. To calculate the different matrices of the state space model a script is written in Aspen with the input and output variables and the proper functions of the system investigated. At this point it is vital that the input variables always have to be fixed and the output variables have to be free in the simulation. After reaching the steady state, the simulation has to be stopped and the script can be invoked. Five output files are generated that contain the basic information about the results and the different matrices of the state space model in a sparse matrix form. The frequencydependent controllability indices can be calculated by Matlab from the transferred matrices according to the procedure of Gabor and Mizsey.61 The first controllability index calculated is the Morari Resiliency Index (MRI). MRI is the smallest singular value of the open loop frequency function matrix of the process.45 It is favorable to have a large MRI value of the process as it means better controllability features. The second controllability index is the Condition Number (CN). CN is the ratio of the largest and smallest singular values of the open loop frequency function matrix of the process. The value of CN is generally acceptable in the range of 1 to 10. Systems with CN higher than 100 are usually considered to be ill-conditioned, and it usually indicates control problems and instability.67 The third controllability index is the Relative Gain Array Number (RGAno). Every G nonsingular square matrix has an RGA(G) square matrix defined as

Figure 7. Controllability indices for mixture M1 for the R1−R2−Q2 control group (CDS).

Figure 8. Controllability indices for mixture M1 for the R1−R2−Q2 control group (DWCU).

(2)

To get a comprehensive single number for each controllability index, it is reasonable to choose the value at the frequency determined on the basis of the typical time constant for each process. Time constants are obtained from load rejection studies, that is, the closed loop simulations of step changes in set point.45 To get the comprehensive single number typical for the controllability features of each system, the three controllability indices are aggregated using the desirability function.66 The desirability function is usually used in statistics to combine different criteria in one process indicator. This method allows making a direct comparison between the studied technologies.

where ⊗ donates the element by element multiplication. The RGA matrix represents the level of interactions in the system. To get a single number displaying the interactions, RGAno can be defined as RGAno = |RGA − I|sum

column 1

100

Table 3. Groups of Manipulated Variables of Composition Control Loops

RGA(G) = G ⊗ (G−1)T

SI = 0.49 column 2

(3)

where I is the unit matrix. Control systems with RGA close to unit matrix and low RGAno are considered to have weak interactions.45 These three controllability indices are calculated in a range of frequencies that gives an overview about the dynamic features 955



Article

Table 4. Results of Mixture 1 SI = 0.94 control structure technology

R1−R2−Q2 CDS

time constant (h) frequency MRI CN RGAno d(MRI) d(CN) d(RGA) D (m = 1)

0.5 3.49 0.13 5 3 7.27 9.65 7.40 8.04

DWCU

× 10−03

× × × ×

R2−Q1−Q2

10−01 10−01 10−01 10−01

0.25 6.98 × 5.00 × 5000 9 4.98 × 7.46 × 4.06 × 1.14 ×

10−03 10−04

10−03 10−16 10−01 10−06

CIS 1 1.75 × 0.025 90 22 2.21 × 5.34 × 1.10 × 2.35 ×

L1−L2−Q2

DWCL 0.38 4.59 × 1.00 × 1000 500 9.94 × 9.43 × 1.93 × 1.22 ×

10−03

10−01 10−01 10−01 10−01

CDS

10−03 10−03

10−03 10−04 10−22 10−09

0.5 3.49 0.12 25 15 6.98 8.40 2.23 5.07

DWCU

× 10−03

× × × ×

L2−Q1−Q2

10−01 10−01 10−01 10−01

0.25 6.98 5.00 5.00 95 4.98 5.35 7.49 2.71

× 10−03 × 10−04 × 1004 × × × ×

10−03 10−152 10−05 10−53

CIS 1 1.75 × 0.024 1500 110 2.13 × 2.89 × 1.67 × 4.69 ×

DWCL

10−03

10−01 10−05 10−05 10−04

0.38 4.59 1.00 1.00 200 9.94 5.56 2.06 2.25

× 10−03 × 10−03 × 1004 × × × ×

10−03 10−31 10−09 10−14

Table 5. Results of Mixture 2 SI = 1.44 control structure technology

R1−R2−Q2 CDS


0.4 4.36 5.00 18 9 3.93 8.82 4.06 5.20

DWCU

× 10−03 × 10−02

× × × ×

R2−Q1−Q2

10−01 10−01 10−01 10−01

0.6 2.91 × 1.50 × 1650 710 1.48 × 1.01 × 1.47 × 2.81 ×

10−03 10−03

10−02 10−05 10−31 10−13

CIS 0.2 8.73 2.50 80 12 2.21 5.72 3.01 3.36

DWCL 0.2 8.73 6.00 90 7 4.51 5.34 4.96 4.92

× 10−03 × 10−02

× × × ×

L1−L2−Q2

10−01 10−01 10−01 10−01

CDS

× 10−03 × 10−02

× × × ×

10−01 10−01 10−01 10−01

0.4 4.36 5.00 125 78 3.93 4.18 4.10 4.07

DWCU

× 10−03 × 10−02

× × × ×

L2−Q1−Q2

10−01 10−01 10−04 10−02

0.6 2.91 1.50 1.50 5.00 1.48 4.15 7.50 7.74

× × × × × × × ×

10−03 10−03 1004 1003 10−02 10−46 10−218 10−89

CIS 0.2 8.73 1.50 140 10 1.39 3.77 3.67 2.68

DWCL

× 10−03 × 10−02

× × × ×

10−01 10−01 10−01 10−01

0.2 8.73 4.00 350 24 3.29 8.73 9.07 1.37

× 10−03 × 10−02

× × × ×

10−01 10−02 10−02 10−01

Table 6. Results of Mixture 3 SI = 0.49 control structure

R1−R2−Q2

technology

CDS


1.03 × 4.00 ×

3.29 9.19 4.49 5.14

× × × ×

0.17 10−02 10−02 12 8 10−01 10−01 10−01 10−01

DWCU 0.5 3.49 × 10−03 5.00 × 10−03 2.00 × 1002 30 4.87 × 10−02 2.48 × 10−01 4.98 × 10−02 8.44 × 10−02

R2−Q1−Q2 CIS 3.49 ×

2.59 8.69 4.49 4.66

× × × ×

DWCL 0.05 10−02 0.03 20 8 10−01 10−01 10−01 10−01

3.49

1.64 8.40 4.96 4.09

dMRI = 1 − exp( −MRI·10)

(4)

dCN = exp(− (a + b·CN))

(5)

⎛ RGAno ⎞ ⎟ dRGAno = exp⎜ − ⎝ 10 ⎠

(6)

where a and b are suitable parameters. After obtaining the separate desirability functions the aggregated desirability function can be defined as the geometric average of the separate desirability functions with desired weight factors:

CDS 1.03 × 4.00 ×

3.29 7.05 2.23 3.73

× × × ×

0.17 10−02 10−02 50 15 10−01 10−01 10−01 10−01

DWCU 3.49 × 5.00 ×

4.87 6.63 3.35 2.21

× × × ×

0.5 10−03 10−03 7000 80 10−02 10−22 10−04 10−09

CIS 3.49 ×

2.59 1.75 4.98 1.31

× × × ×

DWCL 0.05 10−02 0.03 250 30 10−01 10−01 10−02 10−01

0.05 3.49 × 10−02 0.018 500 40 1.64 × 10−01 3.07 × 10−02 1.83 × 10−02 4.52 × 10−02

4. RESULTS Results of the controllability analysis of the studied systems are presented in Tables 4−6. Each Table refers to one of the ternary mixtures indicated with the corresponding separation index. The typical frequency range for the controllability indices is determined according to the load rejection behavior of the separation system studied.

m

D = (∏ di j)1/ ∑ mj i=1

0.05 × 10−02 0.018 25 7 × 10−01 × 10−01 × 10−01 × 10−01

L2−Q1−Q2

where k is the number of separate desirability functions and m is the weight factor. Now the weight factor is equal to 1 in all cases. Using the aggregated desirability function, the desirability values can be calculated for every system. These values represent the control properties in one number offering a way to make an easy and direct comparison of the different process alternatives. The systems of the desirability value close to 1 are preferred since such a situation indicates good controllability features.

First the different indices are transformed into separate desirability functions in the following way:66

k

L1−L2−Q2

(7) 956



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AUTHOR INFORMATION

In the case of mixture 1 (Table 4), with a similar ease of separation, there is a great difference in the desirability values of the studied systems since the D-values of conventional distillation sequences (CDS, CIS) are closer to 1 than any of the related DWCs (DWCU, DWCL). The differences between the conventional sequences and the dividing wall column alternatives are so significant that the conclusion is unambiguous; that is, the conventional sequences show much better controllability features than the DWCs. As for mixture 2 (Table 5), the ease of separation of A/B is easier than that of the separation of B/C, the D-values show great improvement in the case of the dividing wall columns corresponding to the indirect separation structures. In this cases, the D-values of the conventional and dividing wall columns (CIS, DWCL) are practically identical. Similar to that for the second mixture, the results of mixture 3 (Table 6), in which the separation of A/B is harder than that of the B/C, show improvement in the cases of both dividing wall column structures, but neither of them is able to reach the value of the corresponding conventional sequence; that is, the conventional sequence has better controllability features.

The authors would like to acknowledge the financial help of OTKA 112699 project.

5. CONCLUSION The controllability properties of conventional distillation sequences and the corresponding dividing-wall column systems are investigated on three alcohol mixtures with different eases of separation. Rigorous models are generated in Aspen Plus, and both steady state and dynamic simulations are carried out. The state space representations of the studied systems are obtained by using the Control Design Interface of Aspen Dynamics. Using the state space matrices controllability indices are calculated in the frequency domain by Matlab. The multiple control characteristics are aggregated into one representative so-called desirability value to perform an easy direct comparison. In conclusion, with regards to the desirability values of the 12 studied system pairs, three mixtures and four separation systems, in the case of direct separation sequences the conventional distillation sequences show better controllability features than those of the DWCs by far (CDS, DWCU). For mixture 1, showing a similar ease of separation, it is also true for the indirect separation sequences (CIS, DWCL). However, if the separation is nonsymmetrical, mixtures 2 and 3, the case of direct separation is clearly favored for the common sequences (CDS, CIS), but in the case of the indirect separation sequence the conventional and dividing wall structures show relatively similar controllability features according to the controllability indices aggregated in the desirability function. As a final conclusion, for the mixtures studied the newly developed dividing wall column systems show significantly worse controllability features than those of the common separation sequences if a direct separation sequence is considered. It is believed that the reason is the internal interconnection of the streams in the column. If a separate column body is applied, that is, conventional structures, such internal interconnections can be avoided. However, if indirect separation should be carried out, they show almost similar features, that is, the dividing wall column where the wall is in the lower partition seems to be more promising from a controllability point of view than that with the wall in the upper part.

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Corresponding Author

*E-mail: [email protected]. Tel.: 36 1 463 3196. Fax 36 1 463 3197. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

NOMENCLATURE CDS = conventional direct distillation sequence CIS = conventional indirect distillation sequence CN = condition number D = desirability function d = separate desirability function DWC = dividing-wall column DWCL = dividing-wall column with lower partition DWCU = dividing-wall column with upper partition L = reflux flow rate L1 = reflux flow rate of the first column L2 = reflux flow rate of the second column MRI = Morari resiliency index Q = reboiler duty Q1 = reboiler duty of the first column Q2 = reboiler duty of the second column R = reflux ratio R1 = reflux ratio of the first column R2 = reflux ratio of the second column RGA = relative gain array matrix RGAno = relative gain array number SI = separation index TAC = total annual cost x = mole fraction xA = mole fraction of component A xB = mole fraction of component B xC = mole fraction of component C α = relative volatility REFERENCES

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