Design, Optimization, and Retrofit of the Formic Acid Process I: Base

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Design, Optimization and Retrofit of the Formic Acid Process I: Base Case Design and Dividing-Wall Column Retrofit Sergio da Cunha, Gade Pandu Rangaiah, and Kus Hidajat Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00883 • Publication Date (Web): 26 Jun 2018 Downloaded from http://pubs.acs.org on July 7, 2018

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Industrial & Engineering Chemistry Research

Design, Optimization and Retrofit of the Formic Acid Process I: Base Case Design and Dividing-Wall Column Retrofit Sergio da Cunhaa, G. P. Rangaiaha*, Kus Hidajata a

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

Singapore 117585 *

Corresponding author. Email address: [email protected]

Abstract: Formic acid (FA) is an important chemical with many applications in the industry. Despite this, FA process has not received much attention in the open literature. In this work, FA process design and optimization are performed for the production of 98 wt% FA. Total annual cost (TAC) of the optimal base case process is 0.686 USD/kg. In addition, a recently developed methodology for process retrofit is applied, and retrofitting two distillation columns to a dividing-wall column (DWC) is investigated in detail. Results show that DWC retrofit is not attractive as it increases TAC of the process. The reasons for the increase in TAC are discussed. However, FA process with DWC is attractive for a new plant, with lower capital and operating costs compared to the optimized base case process with conventional distillation columns. Keywords: Formic Acid; Multi-Objective Optimization; Process Retrofitting, Process Revamping; Dividing-Wall Column

Nomenclature ACCR

Annual Capital Charge Ratio

Ci

Cooler index i

CO

Carbon Monoxide

COM

Cost of Manufacture (USD/kg)

CSTR

Continuous Stirred Tank Reactor

DIPE

Diisopropyl Ether

DV

Decision Variable

DWC

Dividing-Wall Column

FA

Formic Acid

FCI

Fixed Capital Investment ($)

HEN

Heat Exchanger Network 1 ACS Paragon Plus Environment

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

HETP

Height Equivalent to a Theoretical Plate

Hi

Heater index i

IMODE

Integrated Multi-Objective Differential Evolution

MA

Methanol (Methyl Alcohol)

MNG

Maximum Number of Generations

MOO

Multi-Objective Optimization

MF

Methyl Formate

PF

Pre-fractionator

PR

Production Rate (kg/y)

RD

Reactive Distillation

RDWC

Reactive Dividing-Wall Column

SOO

Single-Objective Optimization

TAC

Total Annual Cost (USD/kg)

UC

Utility cost (USD/kg)

1. Introduction Formic acid (FA) is an important chemical with many applications in the industry. This acid is commonly used in silage to prevent the growth of undesirable bacteria. It is also used for pretreatment of the hides (in tanning industry) and for the synthesis of a variety of pharmaceuticals.1 FA global production capacity has increased more than 10 times in 35 years, from 90,000 t/a in 1979 to 950,000 t/a in 2014.1,2 It is expected to increase further in the coming years, mainly due to its potential new applications in fuel cells technology.3 The rise in the global production of FA was possible, partly due to the developments and improvements in the FA manufacture process through the years. Until 1980, the main production routes for FA were: liquid phase oxidation of butane, hydrolysis of formamide and acidolysis of alkali formats.2 Nowadays, only the later process is still used in the industry, accounting for 19% of the world production capacity. The remaining 81% is obtained from hydrolysis of methyl formate (MF), a more contemporary route.1 Market price of 94 wt% FA drums, based on its value in 1998 (1.05 USD/kg) given by Sinnott4 and using the purchasing power index via FinanceRef/Alioth website,5 would have been 1.58 USD/kg. However, actual price of high-purity FA is expected to be smaller than this, due to the expected reduction in contract price for bulk orders and due to the developments in the process since 1998. The price of bulk quantities of FA 85 wt% is estimated as 0.78 USD/kg.6,7

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The MF route for FA production consists of two reactions: methanol (methyl alcohol, MA) carbonylation followed by hydrolysis of MF to produce FA as shown below. + →

+ → + Thus, MF is an intermediate, not required as a raw material and also not present in the overall reaction of CO and H2O to FA. Similarly, MA is absent in the overall reaction. However, small amount of MA may be necessary as make-up due to its loss in the production. The MF route is followed by a number of companies, mostly in three different ways:1 (i) Kemira has developed a process in which the downstream separation of MF, water, MA and FA is performed using four distillation columns1, (ii) BASF patented a process in which the downstream separation used a combination of distillation and liquid-liquid extraction8, and (iii) the former Soviet Union implemented a different process scheme in which the hydrolysis reaction is carried in a reactive distillation (RD) column; the upper section of this column is packed with catalyst, while the lower section performs auto-catalyzed reaction.9 Even though the above processes have been employed industrially, new technologies and knowledge still can improve them. In 2012, Kemira Chemicals patented a process in which a chromatographic reactor packed with an ion-exchange resin is used for the hydrolysis reaction.10 This process uses both the catalytic activity and the adsorbent properties of such resins to increase the speed of reaction and also shift the equilibrium towards the products. Wang11 and Huang et al.12 have investigated the RD process for MF hydrolysis leading to FA using an ion-exchange resin as catalyst. In this case, the product from the hydrolysis reaction has a smaller reactant-to-product ratio, resulting in easier separation steps in the downstream. Sahin et al.13 have investigated FA separation from aqueous solution by reactive extraction, while Jogunola et al.14 have studied the use of complexing agents in MF hydrolysis to shift the equilibrium towards the products. Novita et al.15 have studied the FA process intensification using reactive dividing wall column (RDWC) via simulation. They claimed that 85 wt% FA can be obtained from CO and water using only one continuous stirred tank reactor (CSTR) to perform carbonylation and two columns. The first distillation column separates part of MA for recycle to the CSTR, while the second column (RDWC) performs the hydrolysis reaction as well as product separation with 85 wt% FA leaving from the bottoms of this column and MA being withdrawn as the distillate of RDWC for recycle to the CSTR. A similar process leads to the 3 ACS Paragon Plus Environment


production of FA 99 wt%.12,16 However, the downstream separation is more energy-intensive, and an extra distillation unit is required to further purify the FA. Recently, Sharma et al.17 have investigated economics of adding vapor recompression to the RD and RDWC systems. It was found that this addition results in savings of ~ 16% in utility cost and ~ 6% in TAC compared to the original RDWC system. All the papers reviewed above investigated improvements for designing new FA processes, but none has tried to simulate current industrial processes. In other words, they did not study on how to improve the existing/operating plants. Such improvements are nevertheless imperative, as FA plants have been operating for more than 30 years. Indeed, the first attempt to study the FA process from retrofitting perspective was recently presented by da Cunha et al.18 However, it presents only the RD solution for retrofitting the conventional FA process prior to any optimization, and details of the results could not be included in the proceedings due to the page limit. The novelty and contribution of the present work are systematic simulation and optimization of the complete FA process using distillation and extraction for the downstream separation, as well as DWC retrofit option for FA process. The process developed here serves as basis for Part II of this work, where RD and RDWC retrofit configurations will be presented. RDWC is a cutting-edge technology with significant potential for industrial implementation. A process based on BASF manufacture route was developed and simulated in Aspen Plus V9.0, heat integration was performed and the process was rigorously optimized for two objectives (namely, capital and utility costs), for the first time. The recent methodology for retrofitting developed by Niu and Rangaiah19 was applied for improving the economics of the optimized process. Finally, the optimal results for the process after retrofitting with a DWC are presented and compared with the optimized base case. The rest of this paper is organized as follows. Section 2 describes the main features of the FA process development and simulation, which forms the base case process. Section 3 outlines the procedure to obtain the optimal design parameters for the base case process. Section 4 discusses the results of multi-objective optimization (MOO) described in Section 3. It also presents economics of the design selected from the Pareto-optimal front. Section 5 describes the retrofitting methodology used in this study, together with its application to the FA process. Section 6 discusses the DWC retrofit solution for the FA process. It presents MOO results as well as economic aspects of the retrofit configuration selected from the


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Pareto-optimal front. Section 7 compares the economics of the optimized base case and the retrofitted FA processes. Finally, Section 8 summarizes the main findings of this work.

2. Base Case Development In 2013, three companies held approximately 50% of the FA market share: BASF, Feicheng Acid Chemical and Shandong Liaocheng Luxi Chemical; among these, BASF led with 32.1% of FA market share.20 Due to the size and importance of this company in the global FA production, BASF process has been chosen for developing the base case process. In this section, this process is described briefly, and then development and simulation of FA process for the base case are described. As mentioned in the Introduction section, the BASF process is based on carbonylation of MA followed by hydrolysis of MF to produce FA. Figure 1 shows the main steps in this process.1 As shown in this figure, carbonylation reaction is carried in a CSTR (R1). The outlet stream of this reactor is sent to a distillation column (D1), which separates unreacted MA from MF (intermediate product). MA is recycled back to (R1), while the distillate is sent to the hydrolysis CSTR (R2). The outlet stream of this reactor goes to another distillation column (D2), where MF is separated at the top, MA is withdrawn as a side stream, and aqueous FA is obtained at the bottoms. MA and MF are recycled to (R1) and (R2), respectively. The aqueous FA is sent to an extraction column (E1), where a solvent (most likely a secondary amide) is used for liquid-liquid extraction. Solute (FA), solvent and water (small amount) are obtained at the top, while pure water is recycled from E1 bottoms back to R2. The subsequent dehydration column (D3) separates the remaining water from the ternary mixture. Finally, the last distillation column (D4) is operated under vacuum in order to obtain high-purity FA (up to 98 wt%) at the top. The bottoms of this column contains mostly solvent, which is recycled back to E1. In the BASF process, carbonylation reaction of MA is catalyzed by sodium methoxide, whereas MF hydrolysis is catalyzed by FA (autocatalysis). For more details on the process and operating conditions, see Wolf et al.8 and Hietala et al.1



Figure 1 – BASF process scheme1 For simulating the BASF process as our base case process, sufficient information were not available in the open literature. The first issue was the lack of data on catalyst decomposition and split ratio for removing catalyst decomposition product from the bottoms of D1 column (Figure 1). Another problem encountered was the lack of binary coefficients data for mixtures of secondary amides mentioned in Wolf et al.8 with water or FA. The third issue faced was the simulation of D2 column. Simulation results showed that the side withdrawal stream from this column contains water as impurity with a concentration of more than 3200 ppm. Without considering the unknown catalyst decomposition product flow rate from D1 column, this amount of water in the side draw of D2 column would cause accumulation of water in the R1-D1 recycle loop in Figure 1. Since the boiling point of water is much higher than those of both MF and MA, most of the water entering D1 column will leave in the bottoms of this column. If the catalyst decomposition stream is neglected, the small amount of water coming from D2 will be “trapped” in the R1-D1 loop. In the BASF process, water leaving in the catalyst decomposition stream is likely to keep water from accumulating indefinitely in the R1-D1 loop. Due to the importance of the BASF process in the FA industry, we decided to proceed with our study in spite of the above issues. To overcome them, we first neglected the purge stream for the catalyst decomposition product, since its flow rate is expected to be low. This assumption will result in lower MA make-up flowrate, as methanol is no longer purged from the D1 bottoms. Another consequence of this assumption is that heavy components such as water and FA may easily accumulate in the R1-D1 loop. Therefore, extra care is taken to avoid water/FA contamination in the MA recycle stream from D2. Further, we used diisopropyl ether (DIPE) as solvent and replaced D2 column in Figure 1 by a 2-column 6 ACS Paragon Plus Environment

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sequence. DIPE is also a suitable solvent for FA extraction process.8 However, unlike N,Ndibutylformamide and other suitable secondary amides, DIPE is more volatile than FA and water. As a result, products from columns D3 and D4 are different. As top/bottom products and relative volatilities are different from the original process, we also expect reboiler duties of these columns to be different. The 2-column sequence permits recycle of MA with higher purity (i.e., with water concentration of only 94 ppm). This concentration is low enough to avoid significant water accumulation in the R1-D1 loop. Finally, according to our simulation results, sum of reboiler duties of the two columns in the 2-column sequence is 22% lower than the reboiler duty of column D2 in Figure 1, for the same purities and recoveries of MF and MA. Nevertheless, capital cost for the plant is expected to increase when compared to the original process, as it is necessary to purchase an extra column. The base case process for FA 98 wt% simulated after applying the required changes is illustrated in Figure 2. Product purity was set based on the range of 90-98 wt% given by Hietala et al.1 for the BASF process. Further, the process was designed for a production capacity of 27,100 t/y, which requires CO feed similar to those reported in Novita et al.15 and Sharma et al.17 This was done in order to compare the RD/RDWC processes for 85 wt% FA reported in these references with the RD/RDWC retrofitted processes for FA 98 wt%, to be reported in Part II of our work. For the initial design (prior to any optimization), some of the design parameters are assumed based on heuristics and/or data available in the literature.1,8,15 These parameters are shown in Table 2, under the “Initial values” column. This table shows, for example, that DC2 operates at higher pressure, different from DC3 operating at atmospheric pressure. This difference in pressure allows for heat integration between condenser of DC2 and reboiler of DC3; the two columns are said to operate in a double-effect configuration. Heat integration of hot and cold process streams was performed using pinch analysis concepts and minimum temperature approach of 10°C, prior to design optimization. This heat integration results in ~33% savings in hot utility requirements. However, the developed heat exchanger network (HEN) is omitted in Figure 2 to keep the process flow diagram easy to follow; instead, a simpler diagram with heaters (H) and coolers (C) is shown. HEN details are given in Appendix A. The thermodynamic model used for simulation was UNIQUAC with Hayden O’Connell equation of state for vapor phase, which can account for the effects of FA dimerization in vapor phase. In addition, Henry law was used to calculate the amount of CO 7 ACS Paragon Plus Environment


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dissolved in liquid phase. This choice is common when the system temperature is well above the component’s critical temperature.21 Equations and parameters used for thermodynamic modeling as well as the thermodynamic model validation are summarized in the supporting information. Kinetics for the carbonylation reaction were taken from Bai et al.22 Concentration of sodium methoxide in CSTR1 was assumed to be 0.408 mol/L, which is the highest catalyst concentration considered in the experiments reported by Bai et al.22 This corresponds to 3 wt% in the reactor for our final simulation, comparable to 2 wt% reported in Aguilo and Horlenko.2 The overall reaction rate is:

70748 !"# 92059 2.507 10'( exp ) 1.419 10 exp

(1)

where r is given in mol/L×min, cat refers to the catalyst and the square brackets indicate liquid concentration in mol/L.

Figure 2 – Base case process developed in this study; data of streams corresponding to optimal conditions are in Tables S7 and S8 in the supporting information Kinetics for the MF hydrolysis were taken from Jogunola et al.23


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0.39+,- "./

01.2

exp 3

1 67800 5

1 6 "./ "=/ 368.15 7 " 89:;< "=. 0.18

(2)

Here, R is the reaction rate (mol/kg×min), Kd is the FA dissociation constant ( 1.8

10>? )24 and C refers to liquid concentration in mol/kg. The kinetics given by Jogunola et al.23

are given on the basis of per kg of mixture. Such a choice of kinetic basis is not a built-in option in Aspen Plus. Hence, a FORTRAN subroutine was used to declare the MF hydrolysis kinetics. It was compiled using the Customize Aspen Plus V9 tool. By using a subroutine, it is possible to write user-defined equation(s) to calculate the rate of reaction. Variables such as temperature, composition and density of reactor outlet stream can be accessed from the process simulation and used to calculate R in eq. (2). Temperature, composition and density of the reactor outlet stream are then updated, and a new R value is obtained in the next iteration. These steps are repeated until there are no significant changes in the reactor outlet stream. Note that this iterative procedure is a built-in procedure in Aspen Plus, and the FORTRAN statement written by the user should only contain the reaction rate equation (eq. 2). Instead of using a FORTRAN statement to declare the kinetics, certain density for the CSTR2 outlet mixture can be assumed, and use it to estimate kinetic parameters on a volume basis. In this approximate case, the kinetics can be entered directly into the Aspen Plus kinetic sheet. The developed process in Figure 2 was optimized for two objectives: capital and utility costs. This is discussed in the next section.

3. Multi-Objective Optimization In recent years, MOO has found many applications in chemical engineering, as can be seen from the reviews by Sharma and Rangaiah25 and Rangaiah et al.26 Similarities and differences between single-objective optimization (SOO) and MOO are also summarized in Rangaiah et al.26 Assuming some conflict between objectives, MOO gives many Paretooptimal solutions (also known as non-dominated solutions), from which quantitative trade-off between objectives can be obtained. MOO results provide deeper understanding of optimal results and help to choose an appropriate optimal solution. For example, suppose a company has limited budget for a new FA facility. Engineers can develop a design, which minimizes energy requirements or utility cost while respecting the budget constraint. In this case, SOO may solve the problem. However, the budget assigned for the project may change and/or higher budget may be 9 ACS Paragon Plus Environment


justified for better return on investment or reducing energy requirements. Then, SOO would have to be performed multiple times according to these changes. A better approach would be to define the objectives of interest at the beginning and then perform MOO. The Paretooptimal solutions (front) can then be used for quantitative assessment of the trade-off along with other factors not included in the objectives. For example, if MOO of FA plant is performed, Figure 3 given later can be used to assess the optimal solutions based on different budget constraints as well as optimal values of decision variables. Before performing MOO, the user needs to choose objective functions, decision variables and their bounds, and process constraints, if any. Then, it is necessary to select the algorithm and program for solving the formulated MOO problem. These steps are presented in the sections below.

3.1 Objective functions, decision variables and constraints There are many ways to evaluate the performance of a process. Some possible objective functions are: CO2 emissions, energy requirement, total annual cost and controllability. This paper evaluates economic aspects of FA process. Therefore, capital cost and annual utility cost (hereafter simply referred as utility cost) were chosen as the objective functions. Note that utility cost is directly related to CO2 emissions and also energy requirements. Capital cost was considered to be that of a new facility on an undeveloped site (i.e. grassroots cost). Its estimation followed the procedure described by Turton et al.27 Reactor sizing and distillation column diameter calculations were performed using Aspen Plus. Flash drum sizing was done following the procedure described in Wankat28, whereas decanter sizing method was taken from Frank et al.29, and diameter of the extraction column was obtained by scaling-up the experimental equipment reported in Wolf et al.8 Utility cost includes cost of steam (for heating), cooling water (for cooling), electricity (for pumps) and fuel oil (for compressor drive). The unit cost of each of these utilities was taken from Turton et al.27, and is given in Table 1. Table 1 – Unit cost of utilities27 Utility type

Cost ($/GJ)

Cooling water

0.244*

Chilled water

4.43

Low pressure steam

13.28

Medium pressure steam

14.19


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Fuel oil

14.2

Electricity

16.8

* The cited reference gives cost of cooling water for temperature change from 30oC to 40oC; here, we assumed this range to be from 30oC to 45oC, and updated the cost to $0.244/GJ proportionately. A priori, all the design parameters (e.g. no. of stages, feed stages, reactor temperatures and column specifications) affect the objective functions. However, setting all design parameters of the process as DVs would slow down the optimization significantly. Hence, DVs for MOO were chosen after sensitivity analysis of the process shown in Figure 2. The choice of DVs and their ranges were made based on two criteria: convergence of process simulation and objective function values. In other words, DV ranges have been restricted in order to provide reasonable (not too high) objective function values, while assuring convergence of process simulation. In addition, variables with narrow range (within 5%) were not included as DV. When performing sensitivity analysis for one DV, all the others were set to certain initial values, as mentioned in Section 2. Table 2 summarizes all DVs, their ranges and initial values as well as the selected optimal solution (discussed later). As shown in this table, MOO was solved with respect to 15 DVs, of which 5 are discrete (no. of stages of each column) and 10 are continuous variables. Note that the number of stages in distillation columns DC1, DC2, DC3, DC4 and DC5 refers to ideal stages, and the number of real trays for cost estimation is found using efficiencies of 49%, 50%, 53%, 54% and 43%, respectively. These efficiencies were calculated from the initial simulation results, using the O’Connor equation:28

@ 0.52782 0.27511 log'1+DE0 + 0.044923 log'1+DE 0(

(3)

Here, E is the column efficiency, and α and µ are respectively the relative volatility of the key components and the liquid viscosity of feed (in cP), both determined at average temperature and pressure of the column. Efficiency values did not change significantly during sensitivity analysis, and therefore they were assumed to be constant in the optimization stage. Besides DV bounds in Table 2, there are no other constraints in the MOO problem. Note that all the governing equations for FA process including product purities are satisfied as part of process simulation in Aspen Plus, for each set of DV values given by the MOO algorithm. The mathematical formulation of the problem, including objective functions and constraints, is shown below.



Minimize Minimize With respect to Subject to

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FCI+I0 UC+I0 I

KL ≤ I ≤ NL

Here, FCI and UC are respectively the fixed capital investment and utility cost of the process; each of them is a function of DVs. X is the vector of DVs, and LB and UB are the lower and upper bounds of this vector, as given in the second and third columns of Table 2. Maximum number of iterations to achieve convergence of tear streams in Aspen Plus was set to 1200, which was found necessary due to the number of recycle loops in FA process (Figure 2). For some trial solutions, Aspen Plus simulation did not converge within this maximum number of iterations; reasons for this include water accumulation in the CSTR1DC1 loop, oscillation of FA concentration in stream 46, unexpected errors in one or more distillation columns. In such non-converged situations, objective function values for trial solutions generated by the optimizer were set to a large pre-fixed number (1×1010). Since the objectives have to be minimized, the trial solutions resulting in non-converged simulations were discarded from the subsequent generations of optimization. Table 2 – DVs, their ranges, initial values and selected optimal solution for the base case process

54

Initial values 10

Selected optimal solution 16

0.0833

0.55

0.5

0.354

DC2 no. of stages

23

47

30

34

DC2 feed stage*

0.351

0.817

0.567

0.725

DC2 pressure (bar)

3.75

4.46

4.05

3.78

DC3 no of stages

16

42

16

38

DC3 feed stage*

0.345

0.969

0.938

0.821

DC3 vapor distillate fraction

0.00095

0.00105

0.001

0.00104

DC4 no. of stages

20

43

20

22

DC4 feed stage*

0.221

0.525

0.5

0.508

DC5 no of stages

5

50

6

8

CSTR1 residence time (h)

0.525

1.220

1.22

0.717

CSTR1 temperature (°C)**

60

110

80

102

DV

Lower bound

Upper bound

DC1 no. of stages

10

DC1 feed stage*


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CSTR1 pressure (bar)**

20

40

40

24

CSTR2 residence time (h)

0.179

0.231

0.201

0.202

* Feed stage is given as a fraction of the number of stages in the column. Integer value for it is obtained from round off (fraction × no of stages). ** Operational range taken from Bai et al. 22 Before proceeding to the solution of the optimization problem, it is important to study whether the HEN configuration is affected by values of DVs. The HEN configuration of this process was developed using the initial values in Table 2. Heat integration was assisted by pinch analysis, and the resulting HEN minimizes hot and cold utilities required. Nevertheless, the arrangement obtained for the initial values may or may not be optimal for other values of DVs. Indeed, by changing some of the design parameters in the process, stream temperatures and heating/cooling duties may change, altering pinch analysis results and consequently the optimal HEN. In the present process, sensitivity analysis showed that the HEN configuration developed before optimization is also optimal for other sets of DV values. Therefore, HEN arrangement was kept unchanged in the optimization stage, and only duties and temperatures were updated as required. In some simulations, extra heat exchangers were necessary to achieve the target temperatures of certain streams. For these cases, they were sized considering cooling/heating by utility. Other cases arose where some heat exchangers were no longer necessary or no longer feasible due to temperature approach constraint. Then, capital cost of these exchangers was taken as zero. For example, the vapor stream at the top of DC2 (high pressure) is partially condensed by the liquid stream at DC3 bottoms (atmospheric pressure). If the duty of DC3 reboiler is higher than the duty of DC2 condenser, one needs another reboiler for DC3, whereas if DC2 condenser duty is higher than reboiler duty of DC3, one needs an extra condenser. For the initial design, it was found that the process required an extra reboiler for DC3. However, the optimal solution presented in Section 4.2 requires an extra condenser for column DC2.

3.2 MOO algorithm and program Several methods are available to solve MOO problems. For example, an optimization tool implemented in CHEMASIM integrates process simulation and MOO.30 This tool allows the user to explore interactively the optimal sets of solutions during optimization, and it enables comparison of different process configurations during the optimization stage. In the present work, the Integrated Multi-Objective Differential Evolution (IMODE) developed and 13 ACS Paragon Plus Environment


used by our group31 was employed to find the Pareto-optimal front for the FA process. This algorithm is based on differential evolution with tabu list and self-adaptation of algorithm parameters, and includes two progress-based termination criteria besides maximum number of generations/iterations (MNG). Its performance was previously assessed using the CEC2009 constrained test problems,32,33 and results were compared with the best algorithm presented in the 2009 Congress on Evolutionary Computation for the same set of problems, namely, DMOEA-DD.34 It was found that IMODE performs better than DMOEA-DD, giving smaller inverse generational distance and using fewer function evaluations, for the MOO problems tested. A detailed description of the IMODE algorithm is given in Sharma et al.31 IMODE has been implemented in MS Excel using worksheets as user interface and VBA for coding the optimization algorithm. In this work, IMODE program was integrated with the Aspen Plus simulation of the FA process via Happ library, included in Aspen software package. Initial values of crossover and mutation probabilities in IMODE algorithm were chosen as 0.5, and the population size was set to 40. Two optimization runs were made: the first using MNG = 90 and the second using MNG = 100. The non-dominated solutions from both runs were combined and then sorted for non-dominance within MS Excel, in order to find the Pareto-optimal front for the FA process design.

4. Base case results and discussion 4.1 The Pareto-optimal front The Pareto-optimal front obtained for the base case process for FA production is shown together with some intermediate results in Figure 3. As depicted in this figure, there are no significant improvements in the objective functions after 60 generations, suggesting that the solutions have converged to an optimal front. This front has many optimal solutions showing trade-off between utility cost and (grassroots) capital cost. Quantitatively, utility cost decreases from 0.223 USD/kg to 0.218 USD/kg for an increase of $0.34 million in capital cost, and then it decreases to 0.211 USD/kg whereas capital cost increases by $1.3 million from $16.4 million to $17.7 million. Further decrease in utility cost is marginal as the capital cost increases by ~14% to $20.1 million. Note that the utility cost in Figures 3 and 4 is for one kg of FA produced.


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Figure 3 – Pareto-optimal front and intermediate results for the base case FA process It is interesting to study variation of objective functions with DVs corresponding to the Pareto-optimal front. The following variables are scattered in the range given in brackets without any clear trend: DC2 pressure (3.820 to 4.130 bar), DC3 no. of stages (34 to 42), DC3 vapor distillate fraction (1.01×10-3 to 1.05×10-3), CSTR1 residence time (0.53 to 0.73 h), CSTR1 temperature (60 to 110oC), CSTR1 pressure (20 to 35 bar) and CSTR2 residence time (0.19 to 0.21 h). This indicates that these variables, within the range studied, do not have much effect on objectives. The following variables were found to be nearly constant at the optimal solutions: DC1 no. of stages (at 15 or 16), DC1 feed stage (at 0.35 to 0.38), DC3 feed stage (at 0.75 to 0.85) and DC4 feed stage (at 0.49 to 0.52). This indicates that these DVs are not responsible for the conflict between the objective functions. For example, DC1 feed stage giving reduction in DC1 steam consumption may also lower the capital cost, as the column diameter decreases with smaller reboiler duties. Finally, the remaining variables (DC2 no. of stages, DC2 feed stage, DC4 no. of stages and DC5 no. of stages) present a clear trend when plotted against the objective functions, as shown in Figure 4. The conflicting trend of objective functions with respect to no. of stages shown in Figure 4 can be easily understood. More stages will directly increase the capital cost since no. of trays and consequently column height increase. However, more stages will make the separation easier, and thus reboiler duty (and hence cost of steam) is expected to decrease. The trend for DC2 feed stage is not as intuitive as the previous one. Results show that no. of stages in the stripping section dictates the feed stage of DC2 column. The optimal no. of 15 ACS Paragon Plus Environment


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stages in DC2 stripping section is 9 or 10. Indeed, 38 of 41 solutions forming the Paretooptimal front have DC2 stripping section within this range. Therefore, the trend observed in Figures 4c and 4d is in order to keep the no. of stages in DC2 stripping section constant. For the sake of clarity, the domains of the plots in Figure 4 have been limited to optimal DV values present in the Pareto-optimal front. For some DVs (e.g. DC2 feed stage and DC5 no. of stages), this range is considerably smaller than the range from lower to upper bounds considered for optimization (see Table 2). This means the conflicting trend is only observed in a subinterval of the bounds presented in Table 2.

(a)

(b)

(c)

(d)

(e)

(f)


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(g)

(h)

Figure 4 – Variation of capital cost (left-side plots) and utility cost (right-side plots) with DV values corresponding to the Pareto-optimal solutions in Figure 3 4.2 Selected optimal solution and its economics After performing MOO, it is necessary to select one solution from the Pareto-optimal front. In this work, one of the optimal solutions has been chosen in order to minimize the total annual cost (TAC) defined as:35

!" "#

+ ACCR FCI/PR

(4)

Here, COM (USD/kg of FA) is the cost of manufacture without depreciation, which includes all costs for plant operation, ACCR is the annual capital charge ratio, FCI is the fixed capital investment (here taken to be Grassroots Cost) and PR is the annual production rate (=27,100,000 kg/y). The value for ACCR is calculated based on plant lifetime and the annual interest rate. Plant lifetime is assumed as 15 years, using the upper bound of the range 10-15 years given in Brennan36 for project evaluation. Annual interest rate is taken as 0.15, similar to the one used in Niu and Rangaiah.19 These values give ACCR of 0.171. COM accounts for all costs of plant operation, such as Direct Costs (e.g. raw material, utilities and operating labor), Fixed Costs (e.g. plant overheads and insurance) and General Expenses (e.g. marketing and R&D). It can be estimated using the following formula:27

"#

0.18)"S/T + 2.73"UV + 1.23+"WX + "YX + "Z= 0

(5)

Here, COL stands for the Cost of Operating Labor, and CUT, CWT and CRM stand for Cost of Utility, Cost of Waste Treatment and Cost of Raw Material, respectively. All these are in USD/kg of FA. From eq. (5) and ACCR = 0.171, eq. (4) can be rewritten as: ab>-;c;d-;d:

efdg:9d:

+0.18 + 0.1710)"S/T + 1.23C[\ + ]^^^^^^^^_^^^^^^^^` !" ]^^^^^^^^^^_^^^^^^^^^^` 2.73"UV + 1.23+"YX + "Z= 0

(6)

In eq. (6), the term labeled ‘constant’ does not depend on DVs, and thus the data shown in Figure 3 is sufficient to choose the solution to minimize DV-dependent term. The 17 ACS Paragon Plus Environment


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chosen solution is that in the Pareto-optimal front, which minimizes TAC. This solution, hereafter referred simply as the optimal solution, has CUT = 0.218 USD/kg and FCI = $16,280,000. This is marked in Figure 3 as a black-filled bullet (•), and the corresponding DV values are presented in the last column of Table 2. Data for key process streams corresponding to the selected/optimal solution are tabulated in the supporting information. To proceed with the economic evaluation of the process, it is necessary to estimate the remaining terms in eq. (6). Annual COL is estimated according to the following equation:27

"UV

:f:9i df. fj fc;

Design, Optimization, and Retrofit of the Formic Acid Process I: Base

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