Grid-search-and-box-search-assisted coordinate descent methodology for practical retrofit of the existing distillation columns to dividing wall columns

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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd

Grid-search-and-box-search-assisted coordinate descent methodology for practical retrofit of the existing distillation columns to dividing wall columns Nguyen Van Duc Long a,b , Le Quang Minh b , Moonyong Lee b,∗ a

Department for Management of Science and Technology Development & Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam b School of Chemical Engineering, Yeungnam University, Gyeongsan 712-749, South Korea

a r t i c l e

i n f o

a b s t r a c t

Article history:

A dividing-wall column (DWC) leading to savings in terms of substantial investment and

Received 25 July 2017

operating costs, and a significant reduction in CO2 emission constitutes an optimal solution

Received in revised form 27 October

for distillation process intensification. Recently, industrial applications of the DWC gradually

2017

increased although the need for an efficient, practical, and simple to implement optimiza-

Accepted 13 November 2017

tion methodology persists. This study proposes a practical method that employs coordinate

Available online xxx

descent methodology, which is assisted by a grid search to avoid local optimal points and box

Keywords:

columns to DWCs. The optimal DWC structure and operating conditions are determined in

Box search

a practical and effective manner that is simple to implement and requires minimal simu-

searches to seek a more promising solution to optimize the retrofit of existing distillation

Coordinate descent methodology

lation runs, which is suitable for industrial uses. The proposed method is examined in the

Dividing wall column

optimal retrofit of a side stream column and a conventional two-column sequence that are

Energy efficiency improvement

widely used in the chemical process industry. The results show that the grid-search-and-

Grid search

box-search-assisted coordinate descent methodology combining mathematical programing

Retrofit

techniques and statistical methods effectively avoids local optimal points but also corresponds to a more promising solution, and thus, it is competitive to coordinate descent methodology and response surface methodology that are popularly used in optimization processes in the chemical process industry. The retrofitted DWC systems lead to a substantial decrease in operating costs while effectively removing the bottleneck problem and mitigating CO2 emission as well. Notably, operating costs are reduced to a maximum of 33.8% and 43.3% in retrofit of side stream columns and conventional two-column sequences, respectively. Both structural and operating variables are effectively and simultaneously optimized. It allows for the identification of interactions between design variables. Furthermore, the carbon dioxide emission is calculated and evaluated when retrofitting to the DWC. © 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

1.

Introduction

Distillation is an extremely common process in several chemical process industries such as oil and gas, petrochemical, chemical, biofuel,

and biochemical industries. However, it leads to high operating costs and requires massive investment costs (Rong, 2011). Various process intensification techniques were proposed and applied to enhance distillation performance. These include a dividing wall column (DWC), as shown in Fig. 1, and this is one of the best proven configurations in distillation intensification (Halvorsen et al., 2013; Kiss, 2014; Long et al., 2016a). The main targets of most retrofit projects involve reduc-

∗

Corresponding author. E-mail addresses: [email protected] (N. Van Duc Long), [email protected] (M. Lee). https://doi.org/10.1016/j.cherd.2017.11.020 0263-8762/© 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Please cite this article in press as: Van Duc Long, N., et al., Grid-search-and-box-search-assisted coordinate descent methodology for practical retrofit of the existing distillation columns to dividing wall columns. Chem. Eng. Res. Des. (2017), https://doi.org/10.1016/j.cherd.2017.11.020

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proposed with the objectives of reducing the energy requirement and total annual cost (Bravo-Bravo et al., 2010). GA is like a black art and fine tuning of all the parameters often depend on trial and error searching. Furthermore, a sequential quadratic programming (SQP) method that was implemented in Aspen PlusTM was proposed (Kiss and Suszwalak, 2012). This methodology is only guaranteed to find a local solution. These methods are based on mathematical programing techniques while a response surface methodology (RSM) based on statistical methods to build an empirical polynomial model was developed to optimize the structure of DWCs (Long and Lee, 2012). RSM is quite powerful, however, a polynomial model is unlikely to be a reasonable approximation of the true functional relationship over the entire space of independent variables. Coordinate decent methodology (CDM) solves optimization problems by sequentially performing approximate minimization along coordinate directions (Wright, 2015). It corresponds to an iterative method in which each iterate is obtained by setting most components of the variable vector x at their values from the current iteration and approximately minimizing the objective with respect to the remaining components. The main advantages of the CDM include the simplicity of each iteration, simple implementation, and high efficiency (Long et al., 2016b). This methodology is suitable for the optimization of a highly

Fig. 1 – A simplified flow sheet illustrating the DWC.

nonlinear and complex system. However, this methodology, like SQP, can get stuck in local optimum.

ing energy requirement and/or increasing capacity, and thus a DWC is

Thus, there is a need of a new optimization methodology, which should be not only simple, efficient, and practical but also can overcome some above problems related to mathematical and statis-

considered as a primarily attractive solution (Long and Lee, 2014). The concept of a DWC involves azeotropic and extractive distillation as well as reactive distillation without any large modifications to the column internals (Olujic et al., 2003; Yildirim et al., 2011; Kiss, 2013; Long

tical approaches. That methodology should utilize the advantages of mathematical and statistical approaches, while eliminating their disadvantages by supporting each other. This study involved employing

and Lee, 2014). Two important DWC devices correspond to an internal reflux splitter and a vapor splitter that are used to split liquid and vapor approaching from the column top and bottom, respectively, into sec-

a simple, efficient, and practical methodology to optimize DWCs by using CDM that is assisted by grid search (GS) to avoid the local optimal points and box search (BS) to overlook a more promising solution for

tions divided by a wall (Lee et al., 2016). The energy performance of a DWC is deviated by slight fluctuations in the internal flows (Shin et al.,

optimal retrofit of existing distillation columns to DWCs. This method-

2013; Long and Lee, 2014; Lee et al., 2016). In most existing DWCs, only a liquid split is controlled during operation while it is not possible to arbitrarily adjust a vapor split once the column is fabricated (Lee et al., 2016). This leads to a few operability and controllability issues associated with the limitation of vapor split control during operation. Most recently, a novel active vapor distributor (AVD) was proposed to address the need for vapor split control during DWC design and operation (Kang et al., 2017). In the proposed AVD, vapor splitting was implemented by a modified chimney tray with a specially designed cap. The liquid level of the chimney tray on each end side of the dividing wall section was adjusted to control the vapor flow split. The proposed AVD efficiently

ology was termed as a grid-search-and-box-search-assisted coordinate descent (GSBSCD) methodology. The proposed methodology that combines a mathematical programing technique and a statistical method was implemented in the MS Visual Basic application and connected to the Hysys model via the MS Excel platform. Excel worksheets and Excel Macro were employed to interface and calculate the objectives and to implement the optimization algorithm. Two case studies including the retrofit of a side stream column (SSC) and a two-column sequence, which are widely used in chemical process industry, were employed to validate its application.

adjusted the friction of the vapor flow path without any mechanical moving parts, and thus it realized a more reliable operation of a DWC. Thus, the DWC can constitute a standard column that is considered in

2.

Design and optimization methodology

separation and purification steps without any critical issues.

2.1.

Design

A number of DWCs were introduced in the retrofit of existing distillation columns (Kolbe and Wenzel, 2004; Spencer and Plana Ruiz, 2005; Slade et al., 2006; Parkinson, 2007; Premkumar and Rangaiah, 2009; Long et al., 2010; Long and Lee, 2011, 2013). Recently, a suitable candidate for the first industrial application of a fully thermally coupled four-product DWC was suggested (Jansen et al., 2016). The results from the fore-mentioned retrofit projects suggest that the employment of DWC was identified as a good solution with lower capital and operating costs when compared with other conventional methods given that it may achieve higher product purity. Conversely, a few practical difficulties occur in the execution of conceptual design, detailed design, and implementation steps. Specifically, DWC optimization is very important during retrofit projects because it significantly affects the final results of those projects and can constitute a challenge due to the large number of design variables and their interactions. Various optimization methodologies of DWC were proposed. An external optimization routine based on an evolutionary algorithm that links with the Aspen PlusTM software was suggested (Wenzel and Rohm, 2003). Additionally, a constrained stochastic multiobjective optimization technique based on the use of genetic algorithms (GA) was

The initial design of a DWC structure and operating conditions is easily investigated by using a shortcut design procedure, which is constructed by using a conventional column configuration as shown in Fig. 2 (Long et al., 2010; Lee et al., 2016). Subsequently, as shown in Fig. 3, a rigorous simulation of a DWC based on a configuration including two columns with two recycle loops is implemented. The prefractionator column (Pre) without a reboiler and a condenser is modeled by using an absorber column. To solve the Pre, a recycled vapor stream and recycled liquid stream to the prefractionator are initially specified (Lee et al., 2016). It is necessary to supply five specifications while simulating the Main column because it includes five degrees of freedom. It should be noted that this procedure solves the Pre first and then the Main column. Another method includes first solving the Main column by specifying two inlet streams including Vapor pre out and Liquid pre out that are based on the shortcut design results. Next, the Pre is simulated with

Please cite this article in press as: Van Duc Long, N., et al., Grid-search-and-box-search-assisted coordinate descent methodology for practical retrofit of the existing distillation columns to dividing wall columns. Chem. Eng. Res. Des. (2017), https://doi.org/10.1016/j.cherd.2017.11.020

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(as shown in Fig. 1). The DWC optimization is a considerably complex and challenging process due to the presence of several variables including both structure and operating variables and their interaction. Note that the objective is reboiler duty, while keeping purity and recovery of main components as constants are constraints. The proposed methodology is based on the core idea that each iterate is obtained by setting most components of the variable vector x at their values from the current iteration and approximately minimizing the objective with respect to the remaining components (Wright, 2015). This can lead to a local optimum, and thus a grid search is first utilized to generate several starting points to avoiding sticking to a local optimum. In this study, multiple starting points were generated based on the grid search methodology using Minitab. With respect to



T

each starting point X0 = x10 , x20 , ..., xn0 , the values of structure and operating variables are determined and then Hysys will run to get the value of objective (reboiler duty). Because Hysys and Excel are interfaced and exchanged information each other, Excel can get value from Hysys, and then carry out search procedure, which was programmed. Cyclical iterations are individually performed through each coordinate by minimizing the objective function with respect to the individual coordinate direction. If xk is given, then the ith coordinate of xik+1 is given by Eq. (1) as follows: Fig. 2 – A schematic diagram of the three-column distillation system for initial structure design. two recycle blocks located in the Vapor pre out and Liquid pre out streams.

2.2.

Optimization

After setting the initial DWC structure and operating conditions, it is necessary to optimize the key design variables including the vapor split tray location (N1), liquid split tray location (N2), side tray location (N3), feed tray location (N4), internal vapor (FV), and liquid (FL) flows to the prefractionator

k+1 k xik+1 = arg min fy ∈ R (xik+1 , − − −, xi−1 , y, xi+1 , − − −, xnk )

(1)

The search continues to the second coordinate after obtaining the minimum for the first coordinate. The iterations in all different directions or coordinates are sequentially performed cyclically to determine the descent direction. Normally, the CDM stops the computations at some point near the optimum point rather than trying to find the precise optimum point (Rao, 2009). Thus, after obtaining a new candidate solution, Xmin , following a search on all coordinates, the coordinate descent search is then performed over the narrow space or the so-called box space with a smaller step size around Xmin to determine more promising solutions

Fig. 3 – A schematic diagram of two-column system for rigorous simulation of the DWC. Please cite this article in press as: Van Duc Long, N., et al., Grid-search-and-box-search-assisted coordinate descent methodology for practical retrofit of the existing distillation columns to dividing wall columns. Chem. Eng. Res. Des. (2017), https://doi.org/10.1016/j.cherd.2017.11.020

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Table 1 – Feed conditions for the EDC case. Feed conditions Component

Liquid stream (mol%)

Vapor stream (mol%)

Ethylene Carbon tetrachloride 1,1-Dichloroethane 1,2-Dichloroethane Trichloroethylene 1,1,2-Trichloroethane 3,4-Dichloro-1-butene

0.06 0.28 0.29 98.74 0.25 0.06 0.32

2.07 0.37 0.01 97.18 0.09 0.23 0.05

Temperature (◦ C) Pressure (bar) Mass flow (kg/h)

80 1.8 67,636

115 2.5 116,455

Table 2 – Column hydraulics, energy performance, and product specifications of the existing SSC. SSC Number of trays Tray type Column diameter (m) Number of flow paths Tray spacing (mm) Maximum flooding (%) Condenser duty (kW) Reboiler duty (kW)

45 Valve 3.8 1 609.6 84.5 20,980 11,381 Purity (mol%)

Fig. 4 – Optimization algorithm for the GSBSCD approach.

in the immediate vicinity of Xmin . An imaginary space of given dimensions is formed around Xmin and is explored when a previous search overlooks a few of the potential solutions to ensure the optimum within the box space with a given step size. During a search procedure, Excel always generates the values of variables so that Hysys can utilize to run, obtain the value of objective, and then send back to Excel. Again, Excel uses the value to compare with previous value and search next point. This procedure is iterated and finally can reach to local optimum. The best local optimum can be selected among several local optimums, which can be found with multiple starting points. The working flowchart of GSBSCD is shown in Fig. 4. The proposed GSBSCD methodology is implemented in the MS Visual Basic application and connected to the Hysys model via the MS Excel platform. MINITAB software is used not only to design a grid search but also to obtain interactions between variables.

3.

Case study

3.1.

Retrofit of side stream column

3.1.1.

Process description

The use of SSCs is widespread and increasingly popular because they are considered as a cost-effective alternative for ternary mixture separation (Papastathopoulou and Luyben, 1991; Long et al., 2015). Specifically, SSCs present attractive alternatives at particular feed compositions and product specifications (Smith, 2005). They are generally used when the middle product is dominant in the feed or when the side stream contains trace amounts of middle boiling components or when the columns act as prefractionators (Long et al., 2015).

EDC

99.6

In contrast, restricted purity of the side product is a common issue while using SSCs. Thus, a high-purity side product requires a large number of stages and high reflux ratios leading to significant energy requirements (Rooks et al., 1996), which lead to high CO2 emissions. Therefore, the growing cost of energy and tightening environment regulations motivated the industry to generate enhanced SSC substitutes to improve the performance (Long et al., 2015). Vinyl chloride monomer (VCM) that is used as a raw material in polyvinyl chloride production is generally manufactured by a thermal reaction of ethylene dichloride (EDC), which is produced from ethylene, oxygen, and chlorine through oxychlorination and direct chlorination (Porscha, 2001; Dimian and Bildea, 2008; Long et al., 2015). In the EDC purification process, an SSC presented in Fig. 5a is used for the removal of light and heavy impurities to obtain a high purity of EDC in the side stream to prevent side reactions leading to fouling in the pyrolysis tubes and to achieve a high-quality VCM (Long et al., 2015). Table 1 lists the feed composition, temperature, pressure, and flow rate. Table 2 presents the hydraulics, energy performance, and product specifications of the existing SSC. Aspen HYSYS 9.0 was used to perform all simulations, where the NRTL property method was chosen to predict the vapor–liquid equilibrium (VLE) (Long et al., 2015).

3.1.2.

Proposed configuration

As previously mentioned, the current SSC that requires high operating costs is needed to carry out a retrofit project to enhance energy efficiency. The key to a successful retrofit involves maximizing the utilization of the existing equipment while minimizing the new hardware to reduce the capital costs (Amminudin and Smith, 2001; Long et al., 2010). The retrofit of SSCs to DWCs includes removing existing trays and adding

Please cite this article in press as: Van Duc Long, N., et al., Grid-search-and-box-search-assisted coordinate descent methodology for practical retrofit of the existing distillation columns to dividing wall columns. Chem. Eng. Res. Des. (2017), https://doi.org/10.1016/j.cherd.2017.11.020

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Fig. 5 – Simplified flow sheet illustrating the (a) existing SSC and (b) retrofitted DWC.

Fig. 6 – Simplified flow sheet illustrating the process modification from the existing SSC to DWC. new trays or packing (if necessary) as well as a new dividing wall into the middle section (as shown in Fig. 6a) (Long and Lee, 2013). This may be followed by cutting the existing column shell into three pieces, which are subsequently welded in the new prefabricated column section (as shown in Fig. 6b) (Kolbe and Wenzel, 2004). Another approach involves cutting the existing column shell into two pieces (top and bottom sections) and then welding in the prefabricated new middle

section, which increases the total number of trays (as shown in Fig. 6c) (Lee et al., 2016). This approach enhances energy efficiency due to the effects of DWC as well as the effect of an increase in the number of trays. In this study, the side column is modified by adding a wall in the middle section while maintaining the same number of trays. A few variables are varied to optimize the structure and operating conditions of the proposed sequence. The GSB-

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Table 3 – Coded levels of the factors. Case

Table 5 – Feed conditions for the BTX case.

Factor

EDC

BTX

Levels

Feed conditions

−1

1

Component

Mole fraction (%)

N1 N2 N3 N4 FV FL

7 25 12 9 72,000 22,000

11 29 16 13 74,000 24,000

Benzene Toluene p-Xylene

33.0 33.0 34.0

Temperature (◦ C) Pressure (bar) Mole flow (kmol/h)

211.2 10.1 200

N1 N2 N3 N4 FV FL

10 29 20 5 4200 4800

14 33 24 9 4600 5200

SCD is implemented in the MS Visual basic application and connected to the Hysys model via the MS Excel platform to examine the effects on the operating cost of the retrofitted DWC. Excel worksheets and macros are employed to interface and calculate the objectives as well as implement the optimization algorithm. The factors and levels used in the case study are listed in Table 3. A 2-level fractional factorial design under the GS is first generated by using MINITAB. Table 4 lists the reboiler duty and minimal reboiler duty at each trial of grid search. The optimal point is then determined by employing a fine search to locate a more promising solution by using a box search. Fig. 7 presents plots of the effects of interactions between design variables N1, N2, N3, N4, FV, and FL. As shown in the figure, the interaction effects between N2–N4, N3–N4, N3–FV, and N4–FV are low. As a result, the minimum reboiler duty is obtained at N1, N2, N3, N4, FV, and FL corresponding to 10 kg/h, 26 kg/h, 13 kg/h, 10 kg/h, 13 kg/h, 72,200 kg/h, and 22,200 kg/h respectively. The column grand composite curve (CGCC) profile shown in Fig. 8 of the main column in the retrofitted DWC is shifted to the left side when compared with that of the existing SSC. This implies that the energy reboiler requirement is reduced while retrofitting current SSC to the DWC. The savings in reboiler duty and operating costs obtained from the retrofitted DWC are calculated as 34.5% and 33.8%, respectively, when compared to those of the current SSC. The prices of cooling water and low-pressure steam used in this study correspond to 0.35 $/GJ and 13.28 $/GJ, respectively (Turton et al., 2012). Fig. 5b presents a simplified flow chart that illustrates the proposed DWC. The results indicate that the utilization of grid search can avoid the local optimal point (7656 kW) when using CDM. It should be noted that maximum reboiler duty saving of 33.0% is achieved while using RSM for DWC optimization (Long et al., 2015).

The developed methodology can determine the effect of each variable as well as interactions on the performance of the objective using Minitab. In optimization of retrofit using DWC with six variables, the proposed methodology can handle well, there is no need to reduce the number of variables. In other optimization problems with many more variables, the variables with small effect as well as the interactions with small parameters can be ignored. This is another advance of the developed methodology. The expected cost savings by the proposed arrangement correspond to 12.5 m USD after 8 years. The payback period for the configuration installation is estimated as 3 months. Interestingly, the maximum flooding decreases from 84.5% to 69.0% and leads to a potential to increase the plant production throughput to a maximum of 15%.

3.2.

Retrofit of the two-column sequence

3.2.1.

Process description

Benzene, toluene, and p-xylene (BTX) were separated by using a conventional distillation column sequence (Premkumar and Rangaiah, 2009; Rangaiah et al., 2009). This study set the operating pressure as 9.15 bar or 10.13 bar, which caused high heating and cooling duties. This also required a more expensive heating source. Therefore, in this study, the operating pressure of a conventional distillation sequence is reduced to 1.01 bar, as shown in Fig. 9a. Table 5 lists the feed composition, temperature, pressure, and flow rates for the BTX case. The Peng–Robinson equation of state, which supports the widest range of operating conditions and the widest variety of systems, is used to predict the vapor–liquid equilibrium of the simulations (Long and Lee, 2015). The energy requirement of the current C-101 and C-202 correspond to 1527 kW and 1394 kW, respectively (as given in Table 6). Due to the increasing demand, it is necessary for the capacity to increase by 30% over the normal operational capability. However, the current columns already function with the maximum performance internals. Thus, it is impossible to utilize the current columns as they are bottlenecked when the input

Table 4 – Reboiler duty and minimal reboiler duty at each trial of the grid search. Trial no.

1 2 3 4 5 6 7 8

Coded variables Bottom section

Top section

Side product location

Feed location

FV

FL

−1 −1 −1 −1 1 1 1 1

−1 −1 1 1 −1 −1 1 1

−1 1 1 −1 1 −1 −1 1

1 1 −1 −1 −1 −1 1 1

1 −1 −1 1 1 −1 −1 1

1 −1 1 −1 −1 1 −1 1

Reboiler duty (kW)

Minimal reboiler duty (kW)

7678 7786 7875 7780 7686 8098 7785 7570

7530 7656 7656 7530 7656 7656 7530 7530

Please cite this article in press as: Van Duc Long, N., et al., Grid-search-and-box-search-assisted coordinate descent methodology for practical retrofit of the existing distillation columns to dividing wall columns. Chem. Eng. Res. Des. (2017), https://doi.org/10.1016/j.cherd.2017.11.020

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Fig. 7 – Effect of the interactions of main design variables on reboiler duty for the EDC case.

Fig. 8 – CGCC profile of the existing SSC and retrofitted DWC. is enlarged. The identification and removal of these bottlenecks is essential and challenging. The debottlenecking of a current sequence constitutes an attractive solution given the requirements of least cost and especially when compared with the implementation of an additional facility (Schneider, 1997; Liu and Jobson, 2004; Long et al., 2010).

3.2.2.

Proposed configuration

As shown in Fig. 10, there is a remixing phenomenon in both top and bottom sections of C-101, and thus the present twocolumn sequence is considered to retrofit to DWCs. The DWC is utilized in this retrofit to remove the bottleneck problem and satisfy the increased productivity while retaining the desired recovery and purity of products. With respect to the retrofitting of a two-column sequence to a DWC, Premkumar and Rangaiah (2009) proposed a solution in which a selected

existing column is modified by the addition of a middle section that houses the dividing wall. This is cut on-site into two portions to form the top and bottom sections of the retrofitted DWC. The middle section of the retrofitted DWC is shop fabricated and available prior to the commencement of the actual on-site retrofit. This section is first welded to the top of the bottom section, and the removed top portion is then welded to the top of the middle section to complete the column. However, a column is not utilized in the proposed solution. Hence, in this study, the dividing wall is added into two columns for the purpose of complete utilization and arranged in a parallel sequence (as shown in Fig. 9b) (Long and Lee, 2014, 2017). The main design parameters of the existing columns are checked to retrofit the two-column sequence to two parallel DWCs. The retrofit is performed with no change in the diameter or the total number of stages of each column to highlight

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Fig. 9 – Simplified flow sheet illustrating the (a) existing two-column sequence and (b) retrofitted 2-DWC sequence.

Fig. 10 – Composition profile of toluene in the existing sequence. the optimal utilization of the current columns. Furthermore, the current reboilers and condensers are checked for reusability with minimal modifications. There are two parallel DWCs, and thus the feed requires splitting. Following the optimization of the DWCs structure and operating conditions, the feed ratio is optimized to maximize the energy savings. Typically, a retrofitted DWC with a higher number of trays requires less energy when compared with a retrofitted DWC with a lower number of trays. Therefore, the fore-mentioned column

receives the maximum feed flow rate, and the remaining feed is handled by another retrofitted DWC. Specifically, the DWC retrofitted from C-102 is considered to exhibit a higher feed flow rate. The feed is first assumed as split with a ratio of 1:1.6 for an initial estimation of the sequence structure. A shortcut design method is used to estimate the initial DWC structure and operating condition. From this shortcut model, the number of stages for the bottom, middle, and top sections of the retrofitted DWC are determined as 7, 18 and 15,

Please cite this article in press as: Van Duc Long, N., et al., Grid-search-and-box-search-assisted coordinate descent methodology for practical retrofit of the existing distillation columns to dividing wall columns. Chem. Eng. Res. Des. (2017), https://doi.org/10.1016/j.cherd.2017.11.020

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Fig. 11 – Effect of the interactions of main design variables on reboiler duty for the BTX case.

Table 6 – Column hydraulics, energy performance, and product specifications of the existing conventional two-column sequence.

Number of trays Tray type Column diameter (m) Number of flow paths Tray spacing (mm) Maximum flooding (%) Condenser duty (kW) Reboiler duty (kW)

C-101

C-102

31 Sieve 1.34 1 609.6 83.4 2605 1527

40 Sieve 0.95 1 609.6 85.0 1333 1394 Purity (mol%)

Benzene Toluene p-Xylene

99.5 91.0 92.0

respectively. The number of stages of C-101 and C-102 correspond to 31 and 40, respectively, and thus only the number of stages for each section in the DWC retrofitted from C-101 are adjusted. Additionally, the DWC retrofitted from C-102 is rigorously simulated to obtain accurate results. The approaches for a rigorous simulation involve fewer assumptions that are more realistic when compared with the FUG equations (Premkumar and Rangaiah, 2009; Lee et al., 2016). The rigorous simulation used in the case study is based on the equilibrium-stage model. Following the design by using a shortcut and rigorous simulation, the main design variables associated with the column structure and operating conditions are optimized by the GSBSCD. It is necessary to determine the preliminary ranges of the variables (shown in Table 3) by single-factor testing. Eight simulations under a grid search are executed to optimize the six parameters associated with the DWC structure and operating conditions. Although the grid search itself is inefficient with respect to the function evaluations, it provides a good starting point for another method. This method constitutes a statistical method that allows the analysis of experimen-

tal or simulation data and building of empirical models to obtain the most accurate representation of the physical situation (Edgar et al., 2001; Rao, 2009). Subsequently, the CDM is applied to optimize the structure and operating conditions of the retrofitted DWC in eight starting points generated by GS. The optimal case is selected, and a local search is performed for fine tuning. The box search is implemented by restricting the search domain around the solution in CDM. A new step size corresponding to 10% of the original step size is used. The results show that minimum reboiler duty in the DWC retrofitted from C-102 corresponds to 755 kW. Note that, the retrofitted DWC from rigorous simulation without optimization requires 995 kW (Long and Lee, 2017). Thus, performance improvement contributed by DWC itself and optimization methodology are 66% and 34%, respectively. The optimal DWC structure and operating conditions are determined in a practical and effective manner, are simple to implement, and require minimal simulation runs. Theoretically this method can be applied to find the minimum of any function that possesses continuous derivatives. However, the optimization cannot work well when the objective function is discontinuous or Hysys model has a convergence problem during optimization. The more variables the optimization problem has, the more starting points it needs to generate. This can lead to more effort to accomplish the optimization problem. It also cannot guarantee to converge to the global optimal solution when there are so many local optimal points. As shown in Fig. 11, in this case, the interactions of N1–N2 and FV–FL are significant and considerably influence the reboiler duty while the interactions of N1–N3; N1–FV, N2–N3; N2–FL; and N4–FV are relatively insignificant. As previously mentioned, the exiting conventional column sequence is retrofitted to the configuration shown in Fig. 9b, which includes two parallel DWCs. The DWC retrofitted from C-102 includes a higher number of trays (40 trays) when compared to the DWC retrofitted from C-101 (31 trays), and thus it receives the maximum feed flow rate. To ensure a rigorous simulation, the maximum flooding in the DWC retrofitted from C-102 corresponds to 84.1% with a feed split ratio of 1:1.6. Therefore,

Please cite this article in press as: Van Duc Long, N., et al., Grid-search-and-box-search-assisted coordinate descent methodology for practical retrofit of the existing distillation columns to dividing wall columns. Chem. Eng. Res. Des. (2017), https://doi.org/10.1016/j.cherd.2017.11.020

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the remaining 160 kgmol/h of feed is separated in the DWC retrofitted from C-101. The structure of the DWC retrofitted from C-101 is derived proportionally from the structure of DWC, which is retrofitted from C-102. The optimization results from the GSBSCD methodology indicate a reboiler duty saving of 43.7% when compared to the existing sequence. It should be noted that maximum reboiler duty saving of 43.0% is achieved while using the DWC with 68 trays, which is much higher than that in the proposed sequence (Premkumar and Rangaiah, 2009). As a result, the use of the modified sequence results in an improvement of 43.3% in operating costs. In this case, all existing condensers and reboilers are utilized. With the proposed sequence, the simple payback period corresponds to 3.7 months. This payback period is economically attractive because of high energy costs saving and the re-use of most of the existing equipment. Furthermore, the maximum flooding in retrofitted DWC from C-102 corresponds to 84.1% while that in the retrofitted DWC from C-101 decreased from 83.0% to 73.9% through a retrofit to the DWCs. The implementation of DWCs from an existing SSC and/or conventional two-column sequence incurs plant downtime (Long et al., 2010). Although downtime corresponds to an extremely important economic factor (Amminudin and Smith, 2001), the production loss is ignored during the retrofit project (Lee et al., 2016). The reason is because chemical/petrochemical plants generally include an annual maintenance period of 10–14 days (Premkumar and Rangaiah, 2009) in which the retrofit project mentioned above is completed. The decrease in CO2 emissions that is linked to the lower energy requirement is another key advantage with respect to the retrofit of a SSC and conventional two-column sequence to DWCs. A method proposed by Gadalla et al. (2005) was employed to estimate the CO2 emissions. The CO2 emissions are substantially reduced when SSC and conventional twocolumn sequence are intensified by using a thermal coupling technique. Specifically, there are savings of 34.5% and 43.6% in the CO2 emission for the EDC and BTX processes, respectively. The value of the CO2 emission saving is slightly smaller than that of the reboiler duty saving because the higher temperature steam is needed in the DWC that is retrofitted from C-102.

4.

Conclusions

This study proposes a practical and effective method that employs CDM, which is assisted by GS to avoid local optimal points and BS to determine a more promising solution to optimize the retrofit of existing distillation columns to DWCs. The optimal DWC structure and operating conditions are determined in a practical and effective manner, are simple to implement, and require minimal simulation runs. This makes it suitable for industrial uses. The proposed method is confirmed in the optimal retrofit of SSC and the conventional two-column sequence, which are widely used in the chemical process industry. The results show that the proposed GSBSCD methodology that combines mathematical programing techniques and statistical methods effectively avoids the local optimal points and determines a more promising solution such that it is competitive to popular methods used in optimization processes in the chemical process industry such as CDM and RSM. The retrofitted DWC systems allows

lower substantial operating costs while effectively removing the bottleneck problem and mitigating CO2 emission. Notably, operating costs are reduced to a maximum of 33.8% and 43.3% in retrofit of SSC and a conventional two-column sequence, respectively. Both structural and operating variables are effectively and simultaneously optimized. Furthermore, it identifies the effect of each variable as well as the interactions between the design variables. In other optimization problems with many more variables, the variables with small effect as well as the interactions with small parameters can be ignored. This can simplify the optimization problem.

Acknowledgments This study was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1D1A3A01015621). This work was also supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A6A1031189).

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Please cite this article in press as: Van Duc Long, N., et al., Grid-search-and-box-search-assisted coordinate descent methodology for practical retrofit of the existing distillation columns to dividing wall columns. Chem. Eng. Res. Des. (2017), https://doi.org/10.1016/j.cherd.2017.11.020