Mixed-Integer dynamic optimization of conventional and vapor recompressed batch distillation for economic and environmental objectives

Journal Pre-proof Mixed-Integer Dynamic Optimization of Conventional and Vapor Recompressed Batch Distillation for Economic and Environmental Objectives Sidharth Sankar Parhi, Gade Pandu Rangaiah, Amiya K. Jana

PII:

S0263-8762(19)30573-8

DOI:

https://doi.org/10.1016/j.cherd.2019.12.006

Reference:

CHERD 3929

To appear in:

Chemical Engineering Research and Design

Received Date:

31 October 2019

Accepted Date:

2 December 2019

Please cite this article as: Sankar Parhi S, Pandu Rangaiah G, Jana AK, Mixed-Integer Dynamic Optimization of Conventional and Vapor Recompressed Batch Distillation for Economic and Environmental Objectives, Chemical Engineering Research and Design (2019), doi: https://doi.org/10.1016/j.cherd.2019.12.006

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Mixed-Integer Dynamic Optimization of Conventional and Vapor Recompressed Batch Distillation for Economic and Environmental Objectives Sidharth Sankar Parhia, Gade Pandu Rangaiahb,c and Amiya K. Janaa* a

Energy and Process Engineering Laboratory, Department of Chemical Engineering, Indian Institute of Technology, Kharagpur, India 721302

b

Department of Chemical and Biomolecular Engineering, National University of Singapore,

c

School of Chemical Engineering, VIT, Vellore, India 632014

Corresponding author. Tel.: +91-3222-283918; fax: +91-3222-282250.

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E-mail address: [email protected] (A. K. Jana).

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*

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Singapore 117585

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Highlights

● Direct vapor recompression employed for thermal integration in batch distillation

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● Elitist non-dominated sorting genetic algorithm for multi-objective optimization (MOO)

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

● Unique MOO problem for maximizing production and minimizing CO2 emission

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● 10 Pareto selection methods for multi-criteria decision making



● Illustrated by a binary wide boiling mixture separation

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

Abstract

In this contribution, a unique multi-objective mixed-integer dynamic optimization problem considering two conflicting objectives, namely, maximization of amount of product per dollar while minimizing CO2 emission is formulated and solved using the elitist non-dominated

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genetic algorithm for both conventional batch distillation (CBD) and vapor recompressed batch distillation (VRBD) operating at constant reflux mode. Here, selection of an optimal solution from the Pareto-optimal front is performed by 10 Pareto ranking methods along with entropy weighting. A wide boiling separating system (i.e., acetone and water) is adopted for illustrating the proposed multi-objective optimization of batch distillation. Two separate optimization studies for CBD and VRBD are conducted with the target of either improving an existing plant or setting up a new plant. Results obtained show that most of the popular Pareto ranking methods select same optimal solution for each of these problems. Finally, a comparative analysis is performed to find the benefits of vapor recompression over the

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conventional scheme. Keywords: Batch distillation with constant reflux ratio; vapor recompression; amount of

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product per dollar; CO2 emission; multi-objective optimization; Pareto ranking methods

1. Introduction

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Energy demand continues to increase for one reason or other. It is projected that there will be a 48% increase in energy requirements in the year 2040 with reference to the year 2012.1

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Today, around 86% (of which, 32% oil, 30% coal and 24% natural gas) of the total global energy demand is fulfilled by the combustion of fossil fuels.2 The dreadful consequences of using fossil fuels as an energy source have reflected in the form of global warming,

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environmental pollution and climate change. To address this concern, attention needs to be paid in improving the energy efficiency of industrial processes. In this light, all attempts

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should be made in generating internal heat sources, so that utility consumption gets reduced. For further advancement, one should optimize process performance in terms of both energy consumption and cost. It is with this intention that the present work was undertaken. Domination of the distillation process for separation of liquid mixtures in the chemical

industry is well known; it accounts for approximately 95% of all fluid separations.3 It is solely responsible for more than 50% of plant operating costs4 and accounts for roughly 3% of the World’s energy consumption.3 As most of the distillation units use steam produced by the energy generated from the combustion of fossil fuels, emission of CO2 to the atmosphere 2

is inevitable. CO2 has been globally recognized as the major greenhouse gas, whose reduction has become a challenge to researchers and practitioners. Although distillation is the most extensively used technology across the World, it has low overall efficiency of around 11%.5 This makes distillation as the most suitable candidate for process optimization and intensification for curbing CO2 emission to the atmosphere. Recently, small scale food and pharmaceuticals industries have bloomed across the globe; they require separation of small quantities of material having diverse composition with the help of batch distillation (BD). The major benefit of BD includes its flexibility to handle, in a single column, a wide range of feed compositions along with numerous components having

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various degrees of separation difficulty. Despite relatively higher energy and capital cost of BD, large volume continuous plants are unable to substitute batch processes for highly specific commodity chemicals due to an increase in associated costs.

The loss of energy in the distillation is caused by irreversible separation process due to differences in temperature, pressure and concentration. Here, there is a large driving force for

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mass and heat transfer between the top and bottom of the column contributing to a large loss of energy. This eventually leads to lower thermodynamic efficiency of conventional

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distillation. Under this scenario, any contribution to reduce energy consumption with the help of energy-efficient technologies will not only improve the economics but also socio-

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environmental welfare. With this impulsion, various heat integrated schemes have been formulated and studied; they include dividing wall column6-10, thermally coupled distillation sequence10,11, heat pump assisted distillation12-15, double-effect distillation16, and internally

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heat-integrated distillation column17-19 and thermally integrated double-column batch stripper.20 In recent years, the use of heat pump for external heat integration21 is increasing; it is configured either by closed-cycle heat pump13 or direct vapor recompression.22-24 Reactive

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distillation25-29 is receiving renewed attention in recent years, where the concept of dividing wall25 and novel reflux splitting26 is adopted.

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With increased environmental and economic compulsions, optimization becomes more

and more important as any improper selection will lead to high cost and energy penalties. Because of stringent environmental laws across the globe, designing and optimizing any batch process has become critical. It raises the following questions. What are the bestoperating conditions for a given system to have minimal impact on the environment? What are the optimal working conditions from the point of process economics and production? Answers to these queries are often conflicting in nature, and are discussed for BD in this article. 3

Process optimization for two or more objectives related to production, economics, environmental impact, control and/or safety has recently received significant interest.30 Although several multi-objective optimization (MOO) problems have been formulated and solved for BD in the literature, no studies reported MOO of BD for production, economic and environmental objectives. The present study addresses this research gap. This apart, to the best of our knowledge, there is no optimization study addressing the use of the elitist nondominated sorting genetic algorithm (NSGA-II) and multiple Pareto ranking methods for selecting one optimal solution from the Pareto-optimal front in case of both conventional BD (CBD) and vapor recompressed BD (VRBD).

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In this contribution, we propose and study the design optimization of both CBD and VRBD for production, economic and environmental objectives. This complex design process is segmented into three phases. The first phase is the MOO problem formulation, where objectives of interest are developed, dominating (significant) variables are selected as decision variables, and applicable bounds and constraints are specified. The second phase

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deals with the solution of the formulated MOO problem using NSGA-II in conjunction with BD simulator. This phase gives many non-dominated solutions, formally known as Pareto-

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optimal front. In the last and third phase, one of Pareto-optimal solutions is selected using many Pareto ranking methods. Ultimately, environmental and economic analysis of

2. Batch distillation

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conventional and vapor recompressed BD columns is conducted.

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2.1. Conventional batch distillation (CBD)

With reference to Fig. 1a, CBD process is briefly described. The batch operation begins

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with the heating up of the charge to its boiling point in the reboiler, that is initially loaded with a liquid mixture of given composition, to gradually fill up the column trays by

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condensation of vapor from the trays below and reboiler. Initially the column is operated under total reflux mode to attain the steady-state. With the progression of distillation, steadystate is reached, where the lighter component composition at the overhead condenser reaches its maximum. Subsequently, the production phase commences with drawing out distillate (top product) and continues as long as the product withdrawn is at or above a pre-specified composition. Modelling of a typical nth tray in BD is presented in Section S1 (in the supplementary file).

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Fig. 1. Schematic diagram of CBD (plot a on left side) and VRBD (plot b on right side).

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2.2. Vapor recompressed batch distillation (VRBD) In VRBD shown in Fig. 1b, vapor from the top tray (at

T NT

) of the distillation column is

liquid (i.e., cold stream at

TB

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compressed in such a way that it acts as a hot stream, which is condensed against reboiler ). This vaporizes some of the contents in the still pot throughout

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BD operation, and the generated vapor moves up into the column. The overhead stream leaving the reboiler as condensate is at a higher pressure, and so its pressure is reduced in a throttling valve before returning it to reflux drum. Thus, latent heat of condensation is

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recovered from the top section and employed in the reboiler at a higher temperature, to reduce the hot utility requirement and increase overall thermodynamic efficiency of the

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system. However, this requires some energy for compression. Reboiler duty may not be met completely by condensation of compressed overhead stream; in such a situation, external

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utility will be required to supply part of reboiler duty. The theoretical power required for compressions (i.e., compressor duty in kJ/h) can be

computed by the following equation: Q Comp 

Here,

V



 1

NT

V NT

  PC   Pi     Pi    

 1 

  1  

(1)

(in kmol/h) refers to vapor inflow rate to the compressor and

the pressure (outlet pressure,

PC

P

(in atm) refers to

and inlet pressure, P ). The temperature dependent polytropic i

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coefficient of species j (  ) having mole fraction ( y ) in the vapor stream are used to j

j

calculate  from: C

1

 1



 j 1

y

j

(2)

 j1

For VRBD scheme, three additional manipulated variables are identified, i.e.,

V

,

NT

external heat input to the reboiler ( Q E ) and compression ratio (CR = PC/Pi). The first operating criterion of VRBD is the driving force, here,

T T

( T

NTC

T

B

) of 15ºC for heat transfer;

is the compressed overhead vapor temperature. This criterion is satisfied by

T NTC

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employing a variable speed compressor to vary CR as follows: 

 T B   TT CR    T NT 

   1   

(3)

Here, TNT is the overhead vapor temperature.

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The second operating criterion of VRBD is providing constant

QR

to the reboiler. For

VRBD, part of this heat input is generated internally by condensation of compressed Q CV   V

NT

where  is the latent heat of condensation of overhead vapor)

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overhead vapor ( 

and the rest (QE) is provided by external utility (usually, steam) according to:

Owing to the variation of

V

(4)

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Q R  Q E  Q CV

NT

in BD, Q CV

varies accordingly; this gives rise to two

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scenarios, i.e., Q CV  Q R (Scenario 1) and Q CV  Q R (Scenario 2). Scenario 1

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When the heat released by condensation of compressed top vapor is more than the heat needed for liquid reboiling, then the extra heat input does not improve the column

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performance if it is operating at optimal conditions. It unnecessarily lengthens the start-up operation because of vaporization of the heavier component by the extra heat (i.e., Q CV  Q R ). This necessitates the splitting of overhead vapor ( V generation of Q R and V

NTC



Q

NTI

) into two fractions:

V

NTC

for the

directly flows to the condenser. (5)

R

 (at T

V

NT

NTC

)

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It is interesting to note here that this scenario never requires hot utility (steam) in the reboiler, and also requires a smaller sized condenser with a reduced coolant flow rate. Scenario 2 This scenario comes into play when heat from the internal sources (i.e., from the compressed top vapor stream) is inadequate. Then, external source (i.e., hot utility) is required as per the requirement (Eq. 4). m S  S  Q E  Q R  Q CV

(6)

Here, ms is the amount of steam required and  Ts .

is the latent heat of steam at its saturation

In this scenario, overhead condenser is not needed and required steam

quantity is reduced as compared to the conventional column.

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temperature,

S

Still, a dubiety arises with the installation of the additional compressor, which usually runs by electrical energy. Is there significant savings in energy and cost by VRBD? Is there a

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substantial reduction in CO2 emission achieved or not by VRBD? To answer these queries, quantitative analysis is needed.

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3. Performance Measures

With the growing pressures related to environmental impact and economics, we propose

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two criteria to assess the performance of CBD and VRBD schemes. They are the amount of product per dollar (PPD) and CO2 emission per annum, for the optimization of CBD and VRBD schemes. In addition, total annual cost (TAC) and total annual production (TAP),

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described in Section S2 (in the supplementary file), are calculated (Table S1) and presented. For a fair comparison of CBD and VRBD, every effort is made to operate the two schemes

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with closely matching dynamics, if not same. For this, feed specifications (given in Section 5) and heat input to reboiler ( Q ) are maintained identical to obtain the same product R

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specification in terms of quantity and quality.

3.1 Product per dollar (PPD) The PPD is computed by the ratio of annual production to that of cost (including both

capital and operating costs) incurred for the process. It is given by: PPD (kg/$)



T pr  M OPEX

w

 T bc

 CAPEX

(7) / t pb

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Here,

T pr

,

M

w

,

T bc

and

t pb

respectively denote the total product recovered (kmol) per batch,

molecular weight of the lighter component, total number of batch cycles performed per annum, and payback period (assumed to be 5 years in this study). OPEX ($/a) is the operating expenditure, which includes costs of steam, cooling water and electricity. CAPEX ($) is the capital investment for the column shell, trays, heat exchangers for both reboiler and condenser, and compressor. Details on these cost calculations are provided in Section S2 (in the supplementary file). 3.2 CO2 emission model

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Production of greenhouse gases including CO2 is more prominent in two utility systems (i.e., steam boiler and gas turbine) as compared to core processes such as distillation.31 In a steam boiler, energy is supplied to vaporize water to steam, while a gas turbine is used to produce electricity. Generally, steam is used in CBD for liquid reboiling, while both steam

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and electricity are required for VRBD column.

In this study, CO2 emission is estimated assuming use of natural gas as the fuel for the utility devices mentioned above. The following stoichiometric equation is utilized for the

m

m    n   O 2  nCO 4  



2

m 2

H 2O

(8)

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C nH

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calculation of CO2 emission, which is related to the quantity of fuel combusted:

The complete combustion is assumed for this stoichiometric equation, which is ensured by supplying an excess amount of air and with proper burner design, periodic maintenance and

2

flow rate (kg/hr)

Here,



Q Fuel

NHV

Q Fuel



C%



(9)

100

refers to the heat duty of combusted fuel (kJ/h), C% the percentage of carbon

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CO

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adequate control. CO2 liberation rate in a utility unit can be computed as follows:

mass in fuel, NHV the net heating value (kJ/kg) and



(=3.67) the ratio of the molar mass of

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CO2 to the molar mass of carbon. NHV and C% of natural gas are taken as

5 . 16  10

4

kJ/kg

and 75.38% respectively.31 Steam is often employed for heating in the reboiler in the distillation system. The boiler

produces steam from the combustion of fuel. In this boiler, the theoretical flame temperature ( T FT

) and the stack temperature ( T Stack ) are considered as 1800ºC and 160ºC respectively. The

Q Fuel

can be computed from the following expression:

8

Q Fuel 

Q



process process

 (H

process where Q and

process



process

 H

water

 T FT  T A )   T FT  T Stack

   

(10)

denote the process heat duty (kW) and latent heat of vaporization

given to the process (kW) respectively. The enthalpy of steam delivered to the process and feed water are referred by

H

process

(kJ/kg) and

H

water

(= 419 kJ/kg of boiler feed water at

100ºC) respectively while T A is the ambient temperature taken as 25ºC. The above expression is obtained by simple energy balance around the boiler to supply the necessary process heat duty, Q to the process/reboiler via steam produced by burning the required amount

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of fuel.

CO2 emission of a compressor operating by the electric power is considered as 51.1 kg CO2/GJ of electricity, i.e., 184 kg CO2/h for 1000 kW power.32

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4. Optimization layout

Optimization complexity increases for the case of BD due to the process unsteady

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operation. First, we propose an optimum configuration for CBD column, and then we endeavour to retrofit the optimal column to VRBD for the existing plant scenario. Besides this, we design an optimal VRBD column for setting up a new plant. For these, the batch

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simulator is developed in the MatLab platform (version 2015a) using the rigorous model, which is more accurate than that of the shortcut model. The simulator of CBD and VRBD is

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designed for constant reflux mode operation.

To optimize any process, a comprehensive strategy is highly recommended. It should consider not only the significant decision variables but also provide the global optimum for

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the process. Fig. S2 (in the supplementary file) represents the entire MOO procedure, which consists of three steps. The first step is the “formulation”, where the decision variables, their

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bounds, constraints and objectives are chosen to formulate the optimization problem. The second step is the solution of the formulated optimization problem; for this, the elitist nondominated sorting genetic algorithm (NSGA-II)33 is used for the optimization of both CBD and VRBD. This step gives a cluster of non-dominated solutions, formally known as “Paretooptimal front”. The third and final step is the selection of one optimal solution from Paretooptimal front using suitable Pareto ranking methods. Here, the selection method program developed by Wang and Rangaiah,34 is employed to choose one optimal solution from the Pareto-optimal front. This program comprises of 10 methods, namely, technique for order of 9

preference by similarity to ideal solution (TOPSIS), linear programming technique for multidimensional analysis of preference (LINMAP), gray relational analysis (GRA), multiplicative exponent weighting (MEW), elimination and choice translating priority II (ELECTRE II), elimination and choice translating priority III (ELECTRE III), net flow method (NFM), simple additive weighting (SAW), Viekriterijumsko Kompromisno Rangiranje (VIKOR) and Faire Un Choix Adéquat (FUCA). All these methods are employed along with weighting based on entropy information, for selecting one of the Pareto-optimal solutions. Each of these methods may choose a different optimal solution. In the present study, the optimal solution chosen by most of the Pareto ranking methods is selected.

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4.1 Full-factorial design methodology

The foremost step of the optimization process deals with studying the effect of all process variables (i.e., logical, design and operational variables) on relevant objectives. Here, process variables and their ranges are selected based on knowledge about BD and industrial practice.

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Reboiler heat duty ( Q ) and reflux ratio (RR) are considered as the operational variables. R

Number of trays ( N ) and weir height ( WH ) are considered as design and logical variables T

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respectively. To study the effect of these input variables, a few output responses (steady-state purity, x D , PPD and CO2 emissions) are considered and a total of 256 simulated experiments

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according to the full factorial design of experiments are performed. Note that the number of trays refers to the number of theoretical trays or ideal stages, and

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the reflux ratio is defined as RR = L/D. The pressure drop of the column can be kept constant, which results in nearly constant reboiler duty, and hence constant reboiler duty is considered here. This assumption is made in several studies in the literature35,36 as well. The lower and

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upper bounds of number of trays, reboiler heat duty (kJ/min), reflux ratio and weir height (inch) are assumed as 4 to 30, 2000 to 12000, 0.01 to 9 and 1 to 4 (25.4 to 101.6 mm)

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respectively. The detailed levels and ranges of decision variables are given in Table S2 (in the supplementary file). The main effect plots are presented later to finalize the dominating variables.

4.2 Solution of the optimization problem The optimization of BD can be performed using either a deterministic or a stochastic optimization method. For finding the global optimum of a non-convex mixed-integer nonlinear programming problem, stochastic search methods are simpler and better over 10

deterministic methods. This apart, when dealing with real-world problems including optimization of BD, we encounter several conflicting objectives and require MOO. It has been concluded by a comparative analysis of deterministic and stochastic techniques that the latter are better for efficient and robust optimization of continuous distillation columns.37 For solving MOO problems, elitist non-dominated sorting genetic algorithm (NSGA-II) was proposed by Deb and co-workers.33 This particular algorithm has been used for solving many optimization problems in chemical engineering.30 For the present study, NSGA-II program in MatLab platform (version 2015a) is used, and its parameters are adopted from the literature.24,38 Note that the batch distillation simulator is also developed in the same MatLab

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platform. 4.3 Selection strategy

Once different Pareto-optimal sets are obtained by solving the MOO problem several times, then all the sets obtained are combined and subjected to non-dominated sorting to find

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true Pareto-optimal front.39 Subsequently, one optimal solution from many alternate solutions in the true Pareto-optimal front is generally selected by decision-makers (i.e., senior

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managers/engineers). To aid this decision-making process, a Pareto ranking procedure with prior predilection of objective functions should be utilized for selecting one optimal solution.

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For the prior predilection, entropy information can be employed for the weighting of objectives.40 Many multi-criteria decision-making (MCDM) methods have been suggested for ranking optimal solutions.34 As mentioned earlier, TOPSIS, LINMAP, PROMETHEE II,

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GRA, MEW, ELECTRE II, ELECTRE III, NFM, SAW, VIKOR, and FUCA are employed for selecting an optimal solution. These methods are briefly described below; their algorithms are available in Wang and Rangaiah.34

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In TOPSIS, the selected optimal solution has the smallest Euclidean distance from the positive ideal solution (PIS) and the largest Euclidean distance from the negative ideal

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solution (NIS). The PIS is comprised of the best value of each objective in the given optimal solutions, while the NIS is a combination of the worst value of each objective in the given optimal solutions. Unlike TOPSIS, which selects an optimal solution based on the distances from both PIS and NIS, LINMAP selects an optimal solution based on the distance from PIS only. The basic idea of SAW is to find the weighted sum of performance of each alternative (i.e., Pareto-optimal solution) overall criteria (i.e., objectives). The rating score is computed for each alternative by multiplication of its normalized value of the criterion (objective) with 11

the weight of relative importance of that criterion chosen by the decision-maker (or entropy information used in the current study) followed by adding up these products for all criteria. The chosen solution has the highest (best) value of this sum among all alternatives. The benefit of this methodology is that it is a proportional linear transformation of the raw data, which implies that the relative order of the magnitude of the normalized scores remains unchanged. The algorithm of MEW is similar to that of SAW with a difference in the estimation of a weighted normalized objective matrix. One limitation of MEW is that it cannot be applied to the objective matrix having negative values. In the current study, the objective matrix has all positive values confirming the applicability of MEW.

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The GRA basically consists of three steps: data normalization, determining the ideal solution and estimation of gray relational coefficient (GRC). The GRC is employed to quantify the similarity between objective values of each optimal solution and an ideal solution made by choosing the best value of each objective (i.e., PIS). It is important to mention here that GRA does not require prior allocation of weights or any other input from

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the decision maker.

ELECTRE II and ELECTRE III are formulated specifically to address the ranking

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problems, where the extent of one objective surpassing other objectives is ranked, and the solution is selected based on the rank values. Compared to ELECTRE II, ELECTRE III uses

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a different set of equations to compute the concordance and discordance matrix elements. In NFM, which is formulated from the principle of ELECTRE methods, ranking the difference of the extent of one objective outranking other objectives and the extent of other objectives

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outranking this objective is performed.

VIKOR is primarily suited for those cases where the quantitative criteria are prevalent. It was formulated based on the elements of compromise programming. Here, the chosen

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solution has the smallest selection value that represents the shortest distance to PIS. Apart from weighting information of each objective, this method needs a balancing factor, whose

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value is assumed to be 0.5 in the current study. In FUCA, values of each objective are ranked (starting from 1 for the best, 2 for the second-best etc.), the weighted sum of ranks is calculated for each Pareto-optimal solution and then the optimal solution with the lowest rank is chosen. Each of the above methods may give a different optimal solution. In the present study, the optimal solution chosen by most of the Pareto ranking methods is selected. 5. A case study: separation of a wide-boiling binary mixture 12

A wide-boiling separation41-43 (i.e., acetone and water) is chosen for the implementation of the proposed MOO. Although this separation by continuous distillation is viable, the employment of VRC or bottoms flashing is not economical for wide-boiling mixtures. However, CBD and VRBD never achieve high purity in the top reflux and still pot simultaneously as in case of continuous distillation; this reduces the required CR and enhances the energy and cost savings. Experimental investigation44 shows that this example system exhibits a pressure-sensitive binary azeotrope45 at 100 psi (6.8 atm) and higher pressure. Since the column operates at around 1 atm (14.7 psi) and thus, there is no chance of azeotrope formation. As the purpose of this study is to find the impact of vapor

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recompression on production, cost and environment aspects of BD, vapor recompression will be attractive for close-boiling mixtures as well if it succeeds for a wide-boiling mixture. The column feed in total is taken to be 100 kmol having an equal molar composition of acetone and water. The liquid holdup at the beginning (time t = 0), condenser holdup are assumed as 0.03 kmol and 1 kmol, respectively, and tray efficiency of 80% is assumed for the case study.

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Integration time interval for solving differential equations is 0.005 min.

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5.1 Factorial design approach

The first step of the optimization is the determination of dominating variables and the

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formulation of the optimization problem. The dominating variables are determined according to the full factorial simulated design approach. The dominancy of a variable can be estimated

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from the degree of deviation from the horizontal mean line in the main effects plot (Fig. 2). Higher the deflexion from the horizontal mean line, more considerable is the dominancy of the variable. To study the impact of variables, three output responses (i.e., x D , PPD and CO2

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emission) are considered. The main effect plots (Fig. 2) shows that weir height does not have significant deviation from the horizontal line for all three outputs, which indicates that the

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impact of weir height on the output responses is negligible as compared to other process variables. Hence, the optimization problem is formulated excluding the (effect of) weir height.

The change in feed composition affects the time for attaining the steady-state of a batch

operation (i.e., start-up period), which in turn affects the total product recovered per batch. This can be seen in Table S3 (in the supplementary file), which shows that the start-up period reduces with the increase of acetone in the fresh feed. Hence, if there is any change in feed composition, then the total product recovered per batch should be tracked and computed 13

separately for each batch operation. This will lead to different sets of an optimization problem, which will unnecessarily increase the computational effort as additional constraints have to be incorporated in the optimization problem. Because the cost analysis is performed on an annual basis, production-related parameters are considered on a yearly basis. Therefore, the current study can be perceived as an average computation of product

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recovered per dollar.

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Fig. 2. Main effects of potential decision variables on steady-state purity under total reflux (plot a), on PPD (plot b) and on CO2 emission (plot c)

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5.2 MOO problem formulation

The design space of CBD and VRBD is kept comparable for optimization studies. Here,

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number of trays, reboiler heat duty and reflux ratio are perceived as dominating decision variables to be optimized. Over the years, several multi-objective mixed-integer dynamic optimization (MO-MIDO) problems are proposed for the optimization of BD. These include simultaneous minimization of investment cost and operating cost46 and concurrent minimization of capital investment and energy consumption rate during the batch process.43 Recently, our group has identified the conflicting behaviour of TAP and TAC and proposed optimization for TAP maximization while minimizing TAC.23,24,38

14

Here, we have identified two other conflicting objectives, i.e., PPD and CO2 emission. Maximization of PPD while minimizing CO2 emission for BD is the primary purpose of the current study. Optimization becomes more tedious with an increased number of objectives. Combining production and cost (i.e., two criteria) into a single performance criterion not only reduces the complicacy in the optimization but also enhances the possibility of better optimal solutions. In addition, due to the growing environmental concern, an emission-related objective is highly recommended. The use of PPD and CO2 emission gives not only the opportunity to find the best-operating conditions from the industry point of view but also enables the reduction of harmful greenhouse gas emissions to the atmosphere.

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It is true that PPD and CO2 emission are not totally independent. But, PPD involves the amount of coolant, steam and electricity used for the estimation of OPEX, whereas CO2 emission involves the amount of steam and electricity used. That makes the considered objectives not “totally dependent”. According to several works published by Mujtaba and coauthors,25,26,42 the length period for each interval (i.e. batch time) is also an optimization

this issue as well. The numerator in Eq. 7 includes

-p

variable. However, in our considered objective function, PPD (product per dollar) addresses T bc

(i.e., the total number of batch cycles

The optimizer is indirectly maximizing

T bc

re

performed per annum), whose calculation of this term is given in the supplementary material. along with

T pr

(the total product recovered per

lP

batch) while minimizing OPEX and capital expenditure CAPEX simultaneously. Maximizing the total number of batches per year means indirectly minimizing the total batch time if batch

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setup time is kept constant after each batch cycle.

In the following MO-MIDO optimization problem, the number of trays is a discrete/integer type decision variable, and reboiler heat duty and reflux ratio are the

ur

continuous decision variables. Additionally, steady-state purity related constraint is included to avoid producing lower-grade products. The formulated MOO problem (P1) is as follows: PPD  f 1 ( u dv )

Jo

max min

CO

2

emission

 f 2 ( u dv )

(11) (12)

Subject to:

u dv  u dv  u dv

(13)

x d  99 . 9

(14)

l

u

s

avg

xd

 99 . 9

(15)

15

Here,

f1

and

comprising of

f2

are the objective functions.

NT

,

QR

u dv

denotes the vector of decision variables,

and RR; lower and upper bounds of these decision variables are

respectively 4 to 30, 2000 to 12000 kJ/min, and 0.01 to 10. Note that reboiler duty is closely related to reboiler vapor rate and condenser vapor load.

s

xd

in Eq. 14 is the purity related

constraint during startup operation of the batch column operating under total reflux mode. Eq. 15 is the constraint to ensure the desired purity of the product (on average during batch production). As suggested in the literature, to avoid encountering hydraulic limitations during a batch separation, constant reboiler duty may be employed. Although, a high reboiler duty

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may be required for optimal capacity, but high rates of entrainment encountered close to the flood point may decrease the profitability of the separation.47 Use of reboiler duty as a decision variable with an upper bound (i.e., a constraint) is also motivated by the published articles.35,36 To achieve the desired purity, multi-control interval policy leads to provide better

-p

performance (in terms of total batch time and energy consumption) than single-control interval policy.25 This is because varied reflux ratio based multi-control policy gets updated

re

frequently whereas the single-control policy works with a fixed reflux ratio.

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6. CBD Optimization

As stated, the modelling of a typical nth tray is described in Section S1 (supplementary file), and it can be extended to the whole distillation column. The BD column studied here

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operates at a condenser pressure of 101.325 kPa and a constant tray pressure drop of 0.3 kPa. The development of an optimal CBD column using the stated MOO strategy is presented in this section.

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6.1 Analysis of MOO outcomes

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The MOO problem (P1) is solved by employing the NSGA-II optimizer and CBD simulator. Then, non-dominated sorting is performed on results from 5 runs, using a program from the literature.39 The obtained true “Pareto-optimal front” has 201 non-dominated solutions, which are shown in the objective space and decision variable space in Figs. 3 and 4 respectively. The Pareto-optimal solution recommended by TOPSIS and 6 other methods (i.e., the same solution was chosen by these methods) is identified by a filled circle in these figures. Fig. 3a depicts the Pareto-optimal front consisting of non-dominated solutions over a

16

range of PPD from 35.7 to 42 kg/$ with respective CO2 emission of 110 t/a to 209 t/a. Thus, CO2 emission increases significantly with PPD. Fig 3b shows the conflicting behaviour of TAP and TAC for all non-dominated solutions, which cover a wide range of TAP from 33272 to 66543 kmol/a and TAC of 52952 to 92032 $/a. Fig. 3c demonstrates other conflicting nature of OPEX and CAPEX, which vary linearly but with a significantly different scattering as compared to objective design space. Note that the points in this plot are not all non-dominated because OPEX and CAPEX are not the objectives used in the MOO problem solved. This comment applies to other plots where one or both quantities are not objectives in the MOO problem. Fig. 3d depicts the response of

The decision variable space of inputs (i.e., N T ,

QR

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CO2 emission with respect to TAP; here, CO2 emission increases with TAP. and RR) with objective functions is

shown in Fig. 4. The disconnected segments in Figs. 4a and 4b can be attributed to integer type decision variable (i.e.,

NT

); most of the non-dominated solutions are having QR

in the

shows a similar response with PPD

-p

range 19 to 26. Just like the objective space (Fig. 4a),

NT

(Fig. 4c). It is observed from Figs. 4c and 4d that values of objective functions increase with the increment of reboiler heat duty ( Q ); optimal

QR

is between 3904 kJ/min to 7365 kJ/min.

re

R

Figs. 4e and 4f show that most of the non-dominated solutions have RR between 0.667 and 0.98395 and that, with the decrement of RR, values of objective functions increase.

lP

The minimization of TAC can be performed for a specific product demand. However, single-objective optimization (SOO) of TAC cannot address the conflicting behavior of TAC

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with the total annual production (TAP). On the other hand, the use of PPD as one objective accounts for both TAC and TAP. In general, we recommend MOO followed by a selection of one of the Pareto-optimal solutions although there is some uncertainty in this selection. For

ur

the application studied here, non-dominated solutions have the lowest and highest PPD of 35.7 and 42 kg/$ with respective CO2 emission of 110 t/a to 209 t/a. For the lowest PPD

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value, optimal values of decision variables are 24 trays (excluding reboiler and total condenser), reboiler heat duty of 3904 kJ/min throughout the operation with a constant reflux ratio of 0.875. Similarly, the highest PPD corresponds to 25 trays, reboiler heat duty of 7365 kJ/min with a constant reflux ratio of 0.67. Thus, although the optimal number of trays is comparable, optimal values of reboiler duty and reflux ratio are very different. Hence, MOO is better than SOO despite some uncertainty in choosing one of the non-dominated solutions.

17

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Fig. 3. Objective space for CBD showing the trade-off between the two objectives (plot 3a),

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TAC with TAP (plot 3b), OPEX with CAPEX (plot 3c), and CO2 emission with TAP (plot 3d) of the non-dominated solutions found by MOO. The filled circle corresponds to the

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chosen optimal solution by TOPSIS and six other methods. 6.2 Construction of optimal CBD

As described earlier the optimum CBD is selected based on 10 Pareto ranking methods.

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The optimal CBD (selected by TOPSIS and 6 other methods) is constructed with a total of 24 trays (excluding reboiler and total condenser), reboiler heat duty of 3904 kJ/min throughout

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the operation with a constant reflux ratio of 0.875. The corresponding top product composition profile for optimal CBD is given in Fig. 5a. The temperature difference profile is shown in Fig. 5b. Other plots in Fig. 5 are discussed later. The steady-state is achieved in 1.9 h (114 min.) with a product purity of 99.9864 mol%.

Then, the production phase is continued till 10.14 h (608.3 min.), and the obtained product has an average purity of 99.9%. Consequently, there will be a total of 751 batches yearly. This implies total operating hours are 7624.5 h/a (= 8000 h/a – 751 batch cycles/a × 0.5 h/batch cycle) excluding batch setup time of 0.5 h for each batch (or 375.5 h/a). According to 18

Douglas,48 a batch column can be operated around 7500 hours per annum, which is eventually close to our computed values. The reduction in the operating hours (OH) leads to decrease PPD as the total number of batches per annum will be lower. The effect of OH on the conclusions of this study can be investigated, and it is quite straightforward. However, this requires the optimization of all systems studied for 3 to 4 values of OH for meaningful conclusions, and the manuscript becomes much longer. Hence, we feel this is not necessary,

ur

na

lP

re

-p

ro of

particularly since we are using a reasonable value for OH.

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Fig. 4. Decision variable space showing the variation of number of trays (NT) with PPD (plot 4a), NT with CO2 emission (plot 4b), reboiler heat duty ( Q R ) with PPD (plot 4c), Q R with CO2 emission (plot 4d), reflux ratio (RR) with PPD (plot 4e), and RR with CO2 emission (plot 4f) of the non-dominated solutions obtained by MOO (shown in Fig. 4a). 6.3 Retrofitting of optimal CBD The optimal CBD is retrofitted externally by adding vapor recompression set up to produce retrofitted VRBD. The yearly operating hours are equal (7624.5 h/a) for optimal 19

CBD and its retrofitted VRBD counterpart due to the same dynamics. As mentioned earlier, the retrofitted VRBD column is constructed based on two operating criteria (i.e., and

QR

 T T  15 º C

= 3904 kJ/min). By employing a variable speed compressor that operates according to

the CR profile (Fig. 5c), the first criterion is fulfilled. The second criterion requires a fixed QR

supply. It is noticed from the

scenario (i.e., Q

 QR

CV

according to the

QE

Q CV

profile (Fig. 5d) that for retrofitted VRBD, the second

) is prevalent during start-up necessitating the external makeup heat

profile (Fig. 5e). The first scenario ( Q

CV

 QR

) is dominated during the

production period, requiring the splitting of overhead vapor in accordance with

V 24 C

profile

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ur

na

lP

re

-p

ro of

(Fig. 5f).

Fig. 5. Dynamic profiles of optimal CBD (Figs. 5a and 5b) and retrofitted VRBD (Figs. 5c5f): distillate composition (plot 5a), temperature difference profile (plot 5b), compression ratio, CR (plot 5c), QE

Q CV

and

QR

profiles of retrofitted VRBD (plot 5d), external heat supply,

(plot 5e) and overhead vapor split ( V

24 C

) (plot 5f). 20

7. VRBD Optimization This particular study is conducted mainly for evaluating VRBD for setting up a new plant. Note that the same MOO problem (P1) is adopted for this VRBD optimization. The respective design space is given in Subsection 5.2. 7.1 MOO results of VRBD studies The MOO problem (P1) is solved using the VRBD simulator and NSGA-II optimizer. The non-dominated sorting is conducted on the 500 optimal solutions from 5 runs, to find true “Pareto-optimal front”, comprised of 228 non-dominated solutions. Results are presented in

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the objective space (Fig. 6) and decision variable space (Fig. 7). The chosen solution by TOPSIS and six other method(s), which recommended the same solution, is shown as a filled circle in these figures. The objective space in Fig. 6a has PPD from 40.3 to 48.9 kg/$, which is slightly higher compared to the objective space of CBD (Fig. 6a). The corresponding CO2

-p

emission range is reduced drastically to 26 to 68 t/a in comparison to that for CBD (110 to 209 t/a) due to the use of vapor recompression heat pump. In general, trends of plots in Figs.

Jo

ur

na

lP

re

7 and 8 are similar to those in Figs. 3 and 4, and hence their further discussion is not repeated.

Graph22

Fig. 6. Objective space VRBD showing the trade-off between the two objectives (plot 6a), 21

TAP with TAC (plot 6b), OPEX with CAPEX (plot 6c), and CO2 emission with TAP (plot 6d) of the non-dominated solutions found by MOO. The filled circle corresponds to the chosen optimal solution by TOPSIS and 5 other methods. 7.2 Optimal VRBD development The optimal VRBD column is constructed from the MOO results. For the optimal solution recommended by the TOPSIS and 5 other Pareto ranking methods, the design conditions are as follows: 16 trays (excluding reboiler and condenser), constant reboiler duty of 3798 kJ/min and a constant reflux ratio of 0.99. The steady state for the batch process is achieved at 117

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min (1.95 h) with acetone purity of 99.9861%. Afterward, the product is withdrawn until 485 min (8.09 h), when the average purity of acetone decreased to just below 99.9%. A total of 930 batches can be performed, owing to reduction in total operating hours to 7535 h/a (= 8000 h/a – 930 batch cycles/a × 0.5 h/batch cycle = 7535 h/a). The related composition and temperature difference profiles are given in Figs. 8a and 8b, respectively. For maintaining the

-p

thermal driving force, CR is varied as shown in Fig. 8c. For the operation of vapor recompression, period of external heat input is shown in Fig. 8d and provided accordingly as

Jo

ur

na

lP

re

in Fig. 8e. The variation of overhead vapor splitting is presented in Fig. 8f.

22

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Fig. 7. Decision variable space showing the variation of number of trays (NT) with PPD (plot

na

7a), NT with CO2 emission (plot 7b), reboiler heat duty ( Q R ) with PPD (plot 7c), Q R with CO2 emission (plot 7d), reflux ratio (RR) with PPD (plot 7e), and RR with CO2 emission

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ur

(plot 7f) of the non-dominated solutions obtained by MOO for VRBD.

23

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Fig. 8. Dynamic profiles of optimal VRBD: distillate composition (plot 8a), temperature

ur

difference (plot 8b), compression ratio, CR (plot 8c), 8d), external heat supply,

QE

Q CV

and

QR

(plot 8e) and overhead vapor split ( V

16 C

of optimal VRBD (plot ) (plot 8f).

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8. Comparative performance analysis As stated earlier, 10 Pareto ranking methods are used to find out one optimal solution. As

shown in Fig. 9, these 10 methods chose four different optimal operating solutions for CBD and also VRBD. From Fig. 9a for CBD, it is observed that 7 Pareto ranking methods, i.e., TOPSIS, LINMAP, VIKOR, FUCA, SAW, MEW and ELECTRE II chose the same optimal solution (due to large weight of ~0.93 for CO2 emission compared to ~0.07 for PPD as per entropy weighting), while GRA, ELECTRE III and NFM select different optimal solutions. 24

The chosen optimal solutions have PPD between 35.7 to 37.1 (kg/$) and CO2 emission between 110 to 122 (t/a) (Fig. 9a). Going by the majority of Pareto ranking methods, we have considered their recommended solution as the final optimal solution. Similarly, for the case of VRBD (Fig. 9b), 6 out of 10 Pareto ranking methods (i.e., TOPSIS, LINMAP, VIKOR, FUCA, SAW and MEW) chose the same optimal solution (for the same reason stated earlier for CBD) whereas GRA, ELECTRE II, ELECTRE III and NFM selected different optimal solutions. These optimal solutions have PPD between 40.3 to 48.9 (kg/$) and CO2 emission between 26 to 67 (t/a). The final optimal solution for VRBD is again selected on the basis of

na

lP

re

-p

ro of

the majority of Pareto ranking methods.

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Fig. 9. Objective values of the optimal solutions chosen by the 10 Pareto ranking methods for

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CBD (plot 9a) and VRBD (plot 9b). After choosing the optimal solutions, various performance measures are considered to

quantify and compare the improvements; they include PPD, CO2 emission, TAC savings and operating cost savings/kg of product. In Table 1, the optimal operating configurations are given for CBD, retrofitted VRBD and new plant with VRBD. The CAPEX for VRBD is bound to increase as compared to CBD due to the installation of the compressor. However, from Table 2, it can be seen that there is a substantial reduction in CO2 emission for retrofitted VRBD (71.8%) and optimal VRBD (76.36%) as compared to optimal CBD, for 25

better environmental sustainability. Although CAPEX/kg of product/a is increased for both the retrofitted VRBD and optimal VRBD, OPEX/kg of product is reduced significantly and almost equally for both retrofitted VRBD (72.6 %) and optimal VRBD (by 71.4%). CO2 emission per kg of product for optimal CBD and VRBD is 0.055 kg and 0.0156 kg, respectively. In other words, vapor recompression substantially reduces CO2 emission per kg of product, i.e., 72% for retrofitted VRBD and 71.6% for optimal VRBD as compared to optimal CBD. Another advantage of retrofitted VRBD and optimal VRBD is the significant increment in PPD, i.e., 10% for the former system and 13% for the later system. From the physical

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viewpoint, between optimal CBD and VRBD, there is a significant change in number of trays, which leads to 30.8% reduction in the cost of the column for optimal VRBD. But, the installation space requirement is definitely more in the case of VRBD due to the installation of extra equipment (i.e., compressor). For the retrofitted VRBD, apart from similar dynamics of column and reboiler, the condenser size is smaller as compared to optimal CBD. For the

-p

optimal VRBD, both condenser and reboiler are smaller due to a reduction in the amount to be condensed and smaller external heat input as compared to optimal CBD. From the process

re

intensification point of view, external energy requirement for optimal VRBD is reduced substantially as compared to optimal CBD. From the standpoint of plant operation, optimal

lP

VRBD requires lesser amount of coolant and steam as compared to CBD to operate, but the former requires electrical energy to run the compressor, which is not present in case of CBD.

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Table 1. Optimal design and operating conditions for the separation of acetone-water mixture Optimal CBD

Retrofitted VRBD

Optimal VRBD

24

24

16

3904 (65.1)

3904 (65.1)

3798 (63.3)

Reflux ratio (initial)

0.875

0.875

0.99

Steady-state purity

0.9999

0.9999

0.9999

No of trays

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ur

Reboiler heat duty, kJ/min (kW)

Table 2. Comparative performance analysis of optimal CBD, retrofitted VRBD and optimal VRBD

Performance Measure

Optimal CBD

Retrofitted VRBD

Optimal VRBD

110225

110225

76280

CAPEX ($) Column shell

26

Trays

5492

5492

3452

Reboiler

36445

36445

35802

Condenser

45154

16417

14670

Compressor

-

64328

57164

197316

232907

187368

Coolant

2480

523

440

Steam

14424

102

125

-

3977

3444

Total

16904

4602

4009

TAC $/a

56367

51183

41483

-

9.2*

26.4*

34695

34695

28788

CO2 emission (t/a)

110

31

26

PPD (kg/$)

35.7

CO2 emission/kg of

0.055

Total

TAP kmol/a

product

OPEX/kg of product

0.098

lP

CAPEX/kg of product/a

-p

TAC savings %

39.3

40.3

0.0154

0.0156

re

Electricity

ro of

OPEX ($/a)

0.0084

0.116

0.112

0.0023

0.0024

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* with reference to optimal CBD

Finally, from production, economic and environmental points of view, optimal VRBD scheme proves to be superior as compared to optimal CBD, due to higher PPD, lower TAC

ur

and lesser CO2 emission to the environment. These advantages of vapor recompression studied here for a wide-boiling mixture will be even more for the separation of close-boiling

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mixtures due to less compressor work required.

9. Conclusions

This work deals with the formulation and solution of an MO-MIDO problem for the

optimization of both CBD and VRBD, considering both the existing and new plant scenarios, for economic and environmental objectives. A MOO strategy, comprised of three steps, is adopted; the first step deals with the formulation of MO-MIDO problem using the dominated variables confirmed by full-factorial analysis. The solution of the formulated optimization 27

problem for the CBD and VRBD systems by NSGA-II forms the second step. Finally, the selection of one optimal solution from the “true” Pareto-optimal front is performed by 10 Pareto ranking methods with weighting using entropy information. A wide-boiling system of acetone-water separation with three decision variables is considered for illustration. The selection of an optimal solution from the true Pareto-optimal front became easier with the employment of 10 Pareto ranking methods; this is because the same optimal solution was selected by many ranking methods (7 in case of CBD and 6 in case of VRBD). From the aspect of system performance, compared to the optimal CBD, the addition of vapor recompression substantially reduces CO2 emission by 72% and also improves PPD by at least

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10%, for both retrofitted VRBD and optimal VRBD. This apart, TAC savings of 9.2% and 26.4% are achieved for retrofitted VRBD and optimal VRBD, respectively, for separation of a wide-boiling mixture. All these improvements are expected to be even more for separation

-p

of closer-boiling mixtures by BD.

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Declaration of interests

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☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Nomenclature

CAPEX

Capital expenditure

Conventional batch distillation

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CBD

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Abbreviations

ELECTRE II Eliminating and Choice Translating Priority II ELECTRE III Eliminating and Choice Translating Priority III FUCA

Faire Un Choix Adéquat

GRA

Gray Relational Analysis

LINMAP

Linear Programming Technique for Multidimensional Analysis of Preference

M & S

Marshall and Swift cost index

MEW

Multiplicative Exponent Weighting 28

Multi-objective optimization

NFM

Net Flow Method

NSGA-II

Elitist Non-Dominated Sorting Genetic Algorithm

OPEX

Operating expenditure ($/a)

PPD

Product per dollar

RR

Reflux ratio

SAW

Simple Additive Weighting

TAC

Total annual cost ($/a)

TAP

Total annual production (kmol/a)

TOPSIS

Technique for Order of Preference by Similarity to Ideal Solution

VIKOR

Viekriterijumsko Kompromisno Rangiranje

VRBD

Vapor recompressed batch distillation

Annum

A

Area of heat exchanger (m2)

C

Heat capacity (kJ/kg.K)

p

Column diameter (m)

L

Liquid flow rate (gmol/min)

LC

Height of column (m)

m

Liquid holdup on tray (gmol)

ms

Steam flow rate (kg/min)

Pi

Inlet pressure (atm)

PC

Outlet pressure (atm)

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Reboiler heat duty (kJ/min)

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QR

lP

Dc

re

a

-p

Symbols

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MOO

t

Tonne

T

Temperature (K)

V

Vapor flow rate (gmol/min)

x

Liquid phase composition (mole fraction)

y

Vapor phase composition (mole fraction)



Latent heat (J/gmol)

Subscripts 29

Condenser

con

i

Component index

n

Tray index

R

Reboiler

s

Steam

Superscripts L

Liquid phase

V

Vapor phase

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References 1. U.S. Energy Information Administration, (EIA). International Energy Outlook 2016. http://www.eia.gov/outlooks/ieo/pdf/0484 (2016).pdf (accessed December 2018).

2. British Petroleum, (BP). BP Energy Outlook 2014. https://www. bp.com/content/dam/bp/

-p

pdf/energy-economics/energy-outlook-2014/bp-energy-outlook-2014.pdf (accessed April 2019).

3. Hewitt G., Quarini J., Morrell M., More efficient distillation. Chem. Eng. 1999, 16–19.

re

4. Kiss A.A., Landaeta S.J.F., Ferreira C.A.I., Towards energy efficient distillation technologies − Making the right choice. Energy 2012, 47, 531−542.

lP

5. Humphrey J.L., Separation process technology. McGraw-Hill (Canada) 1997. 6. Dejanovic I., Matijasevic L., Olujic Z., Dividing Wall Column-a Breakthrough towards Sustainable Distilling. Chem. Eng. Process. 2010, 49, 559-580.

na

7. Premkumar R., Rangaiah G.P., Retrofitting conventional column systems to dividing-wall columns. Chem. Eng. Res. Des. 2009, 87, 47−60.

ur

8. Dejanovic I., Matijasevic L.J., Halvorsen I.J., Skogestad S., Jansen H., Kaibel B., Olujic Z., Designing four-product dividing wall columns for separation of a multicomponent aromatics mixture. Chem. Eng. Res. Des. 2011, 89, 1155−1167.

Jo

9. Modla G., Energy saving methods for the separation of a minimum boiling point azeotrope using an intermediate entrainer. Energy 2013, 50, 103-109.

10. Long N.V.D., Lee M., Review of retrofitting distillation columns using thermally coupled distillation sequences and dividing wall columns to improve energy efficiency. J. Chem. Eng. Jpn. 2014, 47 (2), 87−108. 11. Wang C., Chao G., Yue C., Chen W., Zhishan Z., Compared novel thermally coupled extractive

distillation

sequences

for

separating

multi-azeotropic

mixture

of 30

acetonitrile/benzene/methanol. Chem. Eng. Res. Des. 2018,136,513-528. 12. Jana A.K., Mane A., A Heat Pump Assisted Reactive Distillation: Wide Boiling Mixture, AIChE J. 2011, 57, 3233-3237. 13. Reddy C.C.S., Fang Y., Rangaiah G.P., Improving Energy Efficiency of Distillation Using Heat Pump Assisted Columns, Asia-Pac. J. Chem. Eng. 2014, 9, 905-928. 14. Qian, X., Huang, K., Chen, H., Yuan, Y., Zhang, L. and Wang, S., Intensifying Kaibel dividing-wall column via vapor recompression heat pump. Chem. Eng. Res. Des. 2019, 142, 195-203. 15. Modla G., Lang P., Heat pump systems with mechanical compression for batch

ro of

distillation. Energy 2013, 62, 403 −417. 16. Cui C., Sun J., Li X., A hybrid design combining double-effect thermal integration and heat pump to the methanol distillation process for improving energy efficiency. Chem. Eng. Process. 2017, 119, 81–92.

17. Cui C., Sun J., Coupling design of inter unit heat integration in an industrial crude

-p

distillation plant using pinch analysis. Appl. Therm. Eng. 2017, 117, 145−154.

18. Nakaiwa M., Huang K., Endo A., Ohmori T., Akiya T., Takamatsu T., Internally heat-

re

integrated distillation columns: a review. Chem. Eng. Res. Des. 2003, 81(1), 162-177. 19. Wakabayashi, T., Yoshitani, K., Takahashi, H., Hasebe, S., Verification of energy

lP

conservation for discretely heat integrated distillation column through commercial operation. Chem. Eng. Res. Des., 2019, 142, 1-12. 20. Modla G., Lang P., Separation of an acetone− methanol mixture by pressure-swing batch

na

distillation in a double-column system with and without thermal integration. Ind. Eng. Chem. Res. 2010, 49(8), 3785-3793. 21. Modla G., Lang P., Vapor compression for batch distillation: comparison of different

ur

working fluids. Ind. Eng. Chem. Res. 2015, 54(3), 1081-1092. 22. Babu G.U.B., Pal E.K., Jana A.K., An adaptive vapor recompression scheme for a ternary

Jo

batch distillation with a side withdrawal. Ind. Eng. Chem. Res. 2012, 51(13), 4990-4997.

23. Parhi S.S., Rangaiah G.P., Jana A.K., Optimizing reboiler duty and reflux profiles of vapor recompressed batch distillation, Sep. Purif. Technol. 2019, 213, 553-570.

24. Parhi S.S., Rangaiah G.P., Jana A.K., Multi-objective optimization of vapor recompressed distillation column in batch processing: improving energy and cost savings. Appl. Therm. Eng. 2019, 150, 1273 – 1296. 25. Aqar D.Y., Rahmanian N., Mujtaba I.M., Feasibility of novel integrated dividing-wall batch reactive distillation processes for the synthesis of methyl decanoate. Sep. Purif. 31

Technol. 2018, 202, 200-215. 26. Aqar D.Y., Rahmanian N., Mujtaba I.M., A novel split-reflux policy in batch reactive distillation for the optimum synthesis of a number of methyl esters. Sep. Purif. Technol. 2019, 221, 363-377. 27. Aqar D.Y., Rahmanian N., Mujtaba I.M., Methyl lactate synthesis using batch reactive distillation: operational challenges and strategy for enhanced performance, Sep. Purif. Technol. 2016, 158, 193–203. 28. Marquez-Ruiz, A., Méndez-Blanco, C.S., Özkan, L., Modeling of reactive batch distillation processes for control. Comput. Chem. Eng., 2019, 121, 86-98.

ro of

29. Reddy, P.S., Rani, K.Y., Patwardhan, S.C., Multi-objective optimization of a reactive batch distillation process using reduced-order model. Comput. Chem. Eng., 2017, 106, 40-56.

30. Rangaiah G.P., Sharma S., Sreepathi B.K., Multi-objective Optimization for the Design and Operation of Energy Efficient Chemical Processes and Power Generation, Curr.

-p

Opin. Chem. Eng. 2015, 10, 49-62.

31. Gadalla M.A., Olujic Z., Jansens P.J., Jobson M., Smith, R., Reducing CO2 emissions and

re

energy consumption of heat-integrated distillation systems, Environ. Sci. Technol. 2005, 39, 6860-6870.

lP

32. You X., Rodriguez-Donis I., Gerbaud V., Reducing process cost and CO2 emissions for extractive distillation by double-effect heat integration and mechanical heat pump. Appl. Energy 2016, 166, 128-140.

na

33. Deb K., Pratap A., Agarwal S., Meyarivan T., A fast and elitist multi-objective genetic algorithm: NSGA-II, IEEE Tran. Evol. Comput. 2002, 6, 182–197. 34. Wang Z., Rangaiah G.P., Application and Analysis of Methods for Selecting an Optimal

ur

Solution from the Pareto-Optimal Front obtained by Multiobjective Optimization, Ind. Eng. Chem. Res. 2017, 56, 560-574.

Jo

35. Furlonge, H.I., Pantelides, C.C., Sørensen, E., 1999. Optimal operation of multivessel batch distillation columns. AIChE J., 45(4), 781-801.

36. Low, K.H., Sørensen, E., 2002. Optimal operation of extractive distillation in different batch configurations. AIChE J. 48 (5), 1034–1050. 37. Segovia-Hernandez J.G., Hernandez S., Petriciolet A.B., Reactive distillation: a review of optimal design using deterministic and stochastic techniques. Chem. Eng. Process. 2015, 97, 134–143. 38. Parhi S.S., Rangaiah G.P., Jana, A.K., Vapor recompressed batch distillation: Optimizing 32

reflux ratio at variable mode. Comput. Chem. Eng. 2019, 124, 184-196. 39. Sharma S., Rangaiah G.P., Maréchal F., Multi-objective optimization programs and their application to amine absorption process design for natural gas sweetening, in: G.P. Rangaiah (Ed.), Multi-Objective Optimization: Techniques and Applications in Chemical Engineering, second ed., World Scientific, Singapore, 2017. 40. Sianaki O. A., Intelligent Decision Support System for Energy Management in Demand Response Programs and Residential and Industrial Sectors of the Smart Grid, PhD thesis, Curtin University, Curtin University Library, 2015. 41. Barakat T.M., Sørensen E., Simultaneous optimal synthesis, design and operation of

ro of

batch and continuous hybrid separation processes. Chem. Eng. Res. Des., 2008, 86(3), 279-298.

42. Miladi M.M., Mujtaba I.M., Optimization of Design and Operation Policies of Binary Batch Distillation with Fixed Product Demand, Comput. Chem. Eng. 2004, 28, 2377– 2390.

-p

43. Barakat T.M.M., Fraga E.S., Sorensen E., Multi-objective optimization of batch separation processes, Chem. Eng. Process. 2008, 47, 2303–2314.

re

44. Othmer D.F., Chudgar M.M., Levy S.L., Binary and ternary systems of acetone, methyl ethyl ketone, and water. Ind. Eng. Chem. Res. 1952, 44(8), 1872-1881.

lP

45. Knapp J.P., Doherty M.F., A new pressure-swing distillation process for separating homogeneous azeotropic mixtures. Ind. Eng. Chem. Res 1992, 31, 346–357. 46. Leipold M., Gruetzmann S., Fieg G., An evolutionary approach for multi–objective

na

dynamic optimization applied to middle vessel batch distillation, Comput. Chem. Eng. 2009, 33, 857–870.

47. Tomazi, K. G., Limitations and Dynamics Imposed on Multicomponent Batch Distillation

ur

by Tray Hydraulics, Ind. Eng. Chem. Res., 36, 4273 (1997). 48. Douglas J. M., Conceptual Design of Chemical Processes. First ed., McGraw-Hill, New

Jo

York, 1988.

33

34

ro of

-p

re

lP

na

ur

Jo