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Synthesis of heat-integrated distillation sequence systems
Journal of the Taiwan Institute of Chemical Engineers 43 (2012) 525–534
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Journal of the Taiwan Institute of Chemical Engineers journal homepage: www.elsevier.com/locate/jtice
Synthesis of heat-integrated distillation sequence systems Santosh Jain a, Robin Smith a, Jin-Kuk Kim b,* a b
Centre for Process Integration, School of Chemical Engineering and Analytical Science, The University of Manchester, Sackville Street, Manchester M13 9PL, United Kingdom Department of Chemical Engineering, Hanyang University, 17, Haengdang-dong, Seongdong-gu, Seoul 133-791, Republic of Korea
A R T I C L E I N F O
A B S T R A C T
Article history: Received 26 July 2011 Received in revised form 16 January 2012 Accepted 25 January 2012 Available online 7 March 2012
Energy-efficient distillation systems can be achieved through the mathematical optimisation of distillation sequencing in which heat integration is simultaneously considered. Genetic algorithms have been employed to optimise the most appropriate sequences based on both simple and complex columns for a given separation requirement, with rigorous economic trade-offs between energy and capital costs used in the determination of distillation sequence. Thermodynamic and economic performance of distillation columns has been simulated and measured with short-cut models, while a conceptual decomposition method has been applied for evaluating complex columns. An incidence matrix has been proposed to identify the optimal heat recovery between available heat sources and sinks existing in the distillation sequence. Two case studies have been presented to demonstrate the importance of considering heat integration simultaneously in the optimisation of distillation sequencing, and 8–17% of overall cost savings have been achieved, compared to the conventional synthesis method. ß 2012 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Keywords: Energy minimisation Heat integration Distillation sequencing Optimisation Distillation columns
1. Introduction Distillation is a mature separation technology. However, it is an energy-intensive operation which consumes considerable energy. In a typical distillation operation, hot utility (steam, flue gas exhaust, hot oil, etc.) is required to provide a driving force for distilling lighter components from heavier ones. Condensing vapour streams to enable reflux in the column is facilitated by rejecting heat to cold utility (e.g. cooling water, refrigeration, etc.). Decreased use of external heating and cooling sources in distillation is essential for achieving cost-effective separation. Furthermore, energy-efficient distillation systems contribute to reduce carbon emissions discharged to the atmosphere, which is a further incentive to reduce energy consumption. The economic and environmental benefits, which can be potentially gained from the successful implementation of energy-efficient distillation systems, will be significant, as huge energy is currently consumed in distillation-based processing. For example, the US petroleum refining industries account for about 7% of total U.S. energy consumption (based on year of 1994) [1] and distillation contributes about up to 40% of energy used in refining processes [2]. One of the reasons for thermodynamic inefficiency in distillation is irreversible mixing effects inside columns, and the energy efficiency of distillation operation can be improved with various measures, including:
* Corresponding author. Tel.: +82 02 2220 2331. E-mail address: [email protected] (J.-K. Kim).
internal column modifications (e.g. efficient tray or column internals, etc.) integrated (or complex) column configurations (e.g. sidestripper, side-rectifier, prefractionator, etc.) changing operating conditions (e.g. changing operating pressure, changing feed conditions, etc.), or enhanced or intensified heat transfer in heat exchangers. Although these structural and operational options can be effective for reducing energy demand in distillation columns, it should be noted that large energy consumption often results from inefficient heat recovery between hot and cold process streams, or inappropriate selection of utilities (e.g. steam, cooling water, refrigeration) for process streams. When distillation is employed to separate a multi-component mixture in which several distillation columns are interconnected in a sequence, combinatorial decision-making is necessary in order to determine the most appropriate stream matching and utility selections. Poor energy management is likely to occur if heat recovery is not fully considered. The design complexity increases exponentially when the degrees of freedom in the distillation sequence synthesis are simultaneously considered in the energy management [3], such as: choice of sequence (e.g. direct or indirect or combined sequence) choice of simple column1 or integrated columns choice of thermal coupling2 1 Simple column refers a distillation column which separates two products from single feed, and has a reboiler and condenser. 2 The heat is transferred through using materials flows i.e. direct contact.
1876-1070/$ – see front matter ß 2012 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jtice.2012.01.012
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S. Jain et al. / Journal of the Taiwan Institute of Chemical Engineers 43 (2012) 525–534
Nomenclature MGBP a
million pounds annum
choice of utilities choice of heat recovery mechanisms and design of heat exchanger networks. However, this complex sequencing of distillation systems also provides considerable opportunities for engineers to achieve energy-efficient and cost-effective design of distillation systems. Overall energy requirements can be reduced by introducing integrated heat recovery matching to the distillation sequence. Many successful applications using heat integration have been observed in various industrial sectors [4,5]. This allows achievable targets (or optimal conditions) in energy minimisation projects through the design of heat exchanger networks. It also gives fundamental understanding, design guidelines and conceptual insights for the problem to be dealt with, rather than simply presenting solutions or targets. The current article will highlight how distillation system design can benefit from a systematic approach to heat integration and why this integrated methodology is effective to improve energy efficiency in the synthesis of distillation sequences. Note that it is not intended to cover the basics of heat integration in this article, for which details can be found elsewhere [3,5–7]. Various attempts had been made to improve the thermodynamic efficiency of distillation sequence and its heat integration. One of the early efforts in the context of process systems engineering was to apply design methods based on pinch technology, including energy composite curves and grand composite curves, which allows finding the most appropriate heat recovery arrangement of a distillation column within the process [8]. Another possibility of improving energy efficiency of distillation column is to reduce inherent thermodynamic inefficiency of the column itself, for example, identifying minimum exergy loss for the column through exergy analysis [9] or distillation targeting method with the aid of light key and heavy key method [10]. These graphical design methods support users to obtain valuable conceptual understanding in energy recovery for distillation columns, and hence had been proved to be very effective in improving energy efficiency, however, simultaneous consideration between heat integration and design of distillation columns had not been fully addressed. In order to design the sequence of simple distillation columns and heat recovery systems together, a superstructure-based automated design method with an MINLP formulation was proposed by using a deterministic optimisation technique [11]. Shah and Kokossis [12] introduced an MILP optimisation framework for solving distillation sequencing problems which includes both simple columns and complex columns, although the full potential of heat recovery was not materialised during the design of distillation sequences. Later, Caballero and Grossmann [13] proposed an MINLP optimization model for considering all the possible complex and simple columns in the design, together with heat integration, by applying a disjunctive programming technique. Considerable computational efforts are required for an automated design using the MINLP formulation, as there are highly non-linear elements and complex combinatorial nature of structural options existed in the model. In order to overcome computational difficulties within deterministic optimization methods, stochastic methods have been recently applied to the
design of distillation sequencing, which includes An and Yuan’s works [14] using simulated annealing, and Wang and Li’s works [15] based on the application of stochastic genetic programming. These studies had addressed the application of different optimization techniques, but both methodologies are limited in the application as only simple columns are employed in the sequences. Also, most of available design methods do not fully facilitate all the possible heat recovery options existing in the design of distillation sequencing, for example, one heat recovery matching from a particular reboiler or condenser to multiple exchangers is allowed in the optimization study of An and Yuan [14], and heat recovery is allowed between condensers and reboilers, only, not feed preheating or pre-cooling [15]. With the synthesis framework for distillation sequencing proposed by Shah and Kokossis [12], complex columns considered were constructed by merging simple separation tasks, but their design method did not consider a large number of complex alternative arrangements which can be generated by combining non-sharp separation with simple and complex columns, such that at least one component or mixture is recovered in at least two different locations, and these sections cannot be grouped to make conventional Petlyuk or prefractionator columns [16,17]. The key contribution made in this work is, therefore, to simultaneously consider distillation sequencing and energy integration in a holistic manner, as the systematic incorporation of energy recovery in the context of distillation sequencing has not been fully appreciated before. Also, there has been limited attempt to use a GA (genetic algorithm) for the optimisation of the synthesis of distillation columns, and the current study also aims to demonstrate how GA can be successfully applied to the complex optimisation problem. In the next section, there will be an explanation for heat recovery options available in the context of distillation sequencing, which is then followed by optimisation model for heat-integrated distillation sequencing. Finally, the case study will be presented to demonstrate the design method proposed in this paper.
2. Energy minimisation in distillation sequencing In the synthesis of distillation systems which separate a multicomponent mixture, a large number of sequences can be generated. For example, for a 5-component mixture, 14 sequences are possible when simple columns are used. Each sequence presents a different heat integration problem, because operating conditions are uniquely chosen at the given sequence and consequently, heating and/or cooling requirements for the distillation columns becomes specific to the sequence chosen. Therefore, a large number of heat integration options are possible in the synthesis of distillation sequence. Fig. 1 illustrates available heat integration options for indirect distillation sequence which separates 3 components A, B and C. Inter-column heat recovery: Heat can be exchanged between a reboiler of one column and a condenser of the other one. Fig. 1 illustrates the possibility of heat transfer from the condenser in Column I to the reboiler of Column II. Column operating pressures can be adjusted to enable such an inter-column heat recovery without violating minimum temperature approach, DTmin. Heat exchange with other process streams: When heat sources and sinks exist beyond the distillation section, heat recovery with background processes (e.g. reactor, other separation, utility generation, etc.) can be considered. Heat exchange with utility: If efficient, practical or economic stream matching for heat recovery between process streams is
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Inter-column heat recovery Feed preheating/ cooling
A B C
A
A B
A B
Column II
A B Column I C B C
Heat exchange with other process stream
Heat exchange with utility
Fig. 1. Heat integration options.
limited within/beyond distillation systems, the required heat is provided from hot utility streams (e.g. steam, hot oil, etc.). Alternatively, the surplus heat is discharged to cold utility (e.g. cooling water) or utilised in heat recovery systems (e.g. boiler feed water heating). Selection of utilities and corresponding matching-decisions should consider quality, cost and availability of utilities. Feed pre-heating or pre-cooling: Feed can be preheated or precooled by exchanging heat with condenser(s) or reboiler(s) or other process streams or utility streams. There are some difficulties that arise in the analysis of these heat integration options for distillation systems. First, all heat
integration opportunities are to be screened and optimised simultaneously. Second, structural or configurational decisions in distillation sequencing are not straightforward. For example, a three component mixture can be separated with the direct sequence shown in Fig. 2(a), which can be evolved to a sequence with thermal coupling. Such thermally-coupled sequences (Fig. 2(b)) can consume less energy than the conventional ones. However, overall heat is provided at a higher temperature for the thermally-coupled sequence, which leads to different heat recovery in the separation systems. Finally, the choice of operating conditions for the columns (pressure, feed conditions and reflux ratio), affects not only the design of a column (e.g. size, number of stages, etc.) but also its thermodynamic
Fig. 2. Design complexity in the design of heat-integrated distillation sequencing.
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characteristics (i.e. operating temperature and heat flow rates). As illustrated in Fig. 2(c), system-wide heat recovery is heavily influenced by the operating conditions of columns. Consequently, heat integration opportunities should be considered simultaneously with the determination of operating conditions for the columns. There can be operational constraints or practical limitations to be imposed on the design, for example, forbidden matches, maximum number of heat exchangers allowed for the condensation of reflux, etc. Heat recovery opportunities are significantly affected by these constraints, especially for retrofit cases. Therefore, all the relevant decisions on structure and operating conditions of the distillation sequence should be investigated, together with heat integration analysis, as a single synthesis problem. Conventional engineering practice for the design of distillation sequence performs the synthesis of distillation systems first without considering heat integration. Once the sequence is chosen, the design of heat recovery systems or heat exchanger network is carried out to satisfy energy demands for a given sequence. Such a non-integrated approach is not able to reflect design interactions systematically between distillation sequencing and heat integration, and consequently, often fails to capture optimal or near-optimal designs.
3. Optimisation of heat-integrated distillation sequencing A systematic methodology is required in the design of distillation sequences in which all the available opportunities for heat integration are fully considered. The method needs to screen and evaluate a large number of different flowsheets, as well as their energy recovery (i.e. heat integration together with decision for structural and operating conditions of the flowsheet). Therefore, the development of an automated design using optimisation techniques is appropriate, rather than relying on conventional design tools including graphical techniques, heuristics or engineering judgement. Using an optimisation method also facilitates easy implementation of practical or operational constraints (e.g. forbidden matches, quality of available utility, etc.), and allows rigorous trade-off between capital and operating costs to be considered. In order to build an optimisation framework for heat-integrated distillation sequencing, the following three sections are the main elements considered in mathematical modelling:
3.1. Generation of distillation sequences The superstructure approach can be used to generate potential candidates of flowsheets for distillation sequencing and identify the optimal flowsheet, subject to the objective function and constraints. The sequence can be simply generated based on combinatorial formulation or combination of distillation tasks [12], as shown in Fig. 3. For example, for four-component feed (A, B, C and D), a distillation task can be applied to separate A from BCD, or to separate B from CD or separate B from AD, etc. This can be more effective in the optimisation, as far fewer calculations are required for column sizing and costing. Complex columns, as well as simple columns, are considered in the superstructure approach in which complex columns or hybrid tasks are considered by merging simple tasks. An example is illustrated in Fig. 3 where a side-stripper arrangement for the separation of A/B/C combines two simple separation tasks between AB/C and A/B [3]. Complex columns considered in this study include side rectifier, side stripper, vapour side-draw column, liquid side-draw column, prefractionator and Petlyuk column, which are yielded from the aggregation of simple tasks. 3.2. Simulation of distillation sequence A quantitative modelling framework is required to evaluate the distillation sequence by performing economic costing or measuring another performance index, for example vapour flow rate, during the optimisation. Short-cut models for simulating simple or complex columns will be preferred at the conceptual design stage, because computational difficulties occurred during the optimisation when rigorous models are used. Short-cut models employed for estimating key design information for simple columns are the Underwood equations for estimating minimum reflux ratio, the Fenske equation for determining minimum number of equilibrium stages, the Gilliland correlations for calculating actual number of stages, and the Kirkbride equations for identifying feed tray location. These shortcut methods [3,18] are presented in below: Fenske equation for determining the minimum number of equilibrium stages (Nmin): N min ¼
log½ðF L;D =F H;D ÞðF H;B =F L;B Þ log½am
(1)
where,
am, mean relative volatility of top and bottom stage of a column Sequences
Distillation tasks
1
A/BCD
B/CD
C/D
2
A/BCD
BC/D
B/C
3
AB/CD
A/B
C/D
4
ABC/D
A/BC
B/C
5
ABC/D
AB/C
A/B
A/BCD
A/BC
A/B
AB/CD
AB/C
B/C
B/CD
C/D
ABC/D
BC/D
FL,D, light key component flow in the distillate product FH,D, heavy key component flow in the distillate product FL,B, light key component flow in the bottom product FH,B, heavy key component flow in the bottom product. Underwood equations for estimating minimum reflux ratio (Rmin): n X ai xi;F ¼1q a u i¼1 i
Rmin þ 1 ¼
A
n X ai xi;D a u i¼1 i
Side-stripper
A B C
B C
Fig. 3. Representation of separation sequence for four-product separation.
where, n, number of components q, liquid fraction of feed xi,F, mole amount fraction of i in feed xi,D, mole amount fraction of i in distillate
(2)
(3)
S. Jain et al. / Journal of the Taiwan Institute of Chemical Engineers 43 (2012) 525–534
ai, relative volatility of component i to the heaviest component u, root of Eq. (A2). Gilliland correlations for calculating actual number of stages (N): 1 þ 54:4X X 1 0:5 Y ¼ 1 exp (4) 11 þ 117:2X X
N N min R Rmin ;X ¼ Y¼ Nþ1 Rþ1
FVSuppl ¼ FVmain þ FVside
(6)
FLSuppl ¼ FLmain
(7)
where, FVSuppl ; vapour flowrate in the supplementary section FVmain ; vapour flowrate in the main column FVside ; flowrate of vapour side-draw FLSuppl ; liquid flowrate in the supplementary section FLmain ; liquid flowrate in the main column RBU, boilup amount ratio.
(10)
(11)
(5)
For the modelling of complex columns generated in the superstructure, a complex column is conceptually decomposed into a thermodynamically equivalent arrangement with simple columns, and overall performance of the complex column is then obtained by combining individual design information of simple columns estimated through short-cut models. For example, the side-stripper shown in Fig. 3 can be modelled such that a feed to and a side-stream from the side column are approximated by the feed to and liquid returned from the hypothetical condenser of the first main column. Short-cut models for simple columns are then extended or modified to determine reflux ratio and number of stages required in each column. Decomposition techniques and the corresponding application of short-cut models for complex columns can be found in details from Refs. [3,18,19], which are described as below. Side-draw columns: An available shortcut model for simulating side-draw columns is as given in Triantafyllou and Smith [19]. For the case of vapour side-draw, the model estimates the minimum faction of heavy components in the side stream with the fixed reflux ratio, while the minimum faction of light components in the side stream is predicted at the fixed boilup ratio. For a vapour sidedraw column, the boliup ratio is given by Eqs. (6)–(8), and the Underwood equations are used for calculating the composition of the vapour side-draw.
FVSuppl FB
F L Suppl FD
(9)
where, FLside ; flowrate of liquid side-draw R, reflux ratio.
where, Nr, number of stages above feed stage Ns, number of stages below feed stage zH, mole amount fraction of heavy key component in feed zL, mole amount fraction of light key component in feed FB, molar flowrate of bottom product FD, molar flowrate of distillate product xB,L, mole fraction of light key component in bottom product xD,H, mole fraction of heavy key component in distillate product.
RBU ¼
FVSuppl ¼ FVmain
R¼
R, actual reflux ratio. Kirkbride equations for identifying feed tray location: " # Nr zH F B xB;L 2 ¼ 0:206log log Ns zL F D xD;H
For a liquid side-draw column, the reflux ratio is calculated by Eqs. (9)–(11) with which Underwood equations are applied to estimate the composition of the liquid side-draw.
FLSuppl ¼ FLmain þ FLside
where,
529
(8)
Side-rectifier and side-stripper: The side-rectifier is decomposed into a conventional main column and a vapour side-draw column. The main column has a partial reboiler, which facilitates a partial vapourisation of liquid from the main column and creates a mixture of liquid and vapour in equilibrium. The second column is then modelled as a vapour side-draw column, such that the vapour sidestream is extracted from one stage below the feed stage in the main column [3,20,21]. For a side-stripper, a similar decomposition strategy is used in the simulation by taking liquid side-draw at one stage above the feed stage and by calculating the partial condensation in the main column. Calculations of mass balances and VLE (vapour–liquid equilibrium) are performed around the connecting streams between side column and main column. Prefractionator: The prefractionator is decomposed into three simple columns: the first column represents a prefactionating section with a partial reboiler and condenser, while the second and third columns represent rectifying and stripping section of main column. The first column has a partial reboiler and a condenser, which is integrated with the second and third columns. The vapour and liquid stream traffic exchanged between second and third columns should be equalised in the modelling [19]. For the prefractionator, Petlyuk column and diving wall columns, the first column is thermally coupled with the main column. For the simulation, it is required to simulate simultaneously one simple column with a partial reboiler and a condenser, one vapour side-draw column, and one liquid sidedraw column. Again, equating vapour and liquid flow rates between top of liquid side-draw column and bottom of vapour side-draw column is necessary [19]. Cost models for operating and capital costs are then applied to evaluate the full economic impact of sequences being considered during the optimisation. 3.3. Design of heat recovery systems Both graphical and mathematical methods are available for the design of heat exchanger networks for the distillation sequence. A wide range of models are available and should be selected based on the objectives of the energy minimisation project. In this study, an incidence matrix is introduced to effectively deal with heat integration in the distillation sequencing problems, as illustrated in Fig. 4. This contains all the possible matches for heat recovery existing in the distillation sequence and their feasibility information. The incidence matrix shown in Fig. 4 represents the potential heat recovery existing in a sequence of three simple distillation columns, of which hot and cold energy is provided by two types of hot utilities and one type of cold utility. The numbers indicated between rows and columns of the matrix can be either
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Row: available heat sinks C2
R1
R2
R3
CU1
C1
0
1
1
1
Feasible match
C2
0
0
1
1
Infeasible or forbidden match
C3
0
0
0
1
HU1 0
1
1
0
HU2 1
1
1
0
C1
R2 R1
C3
R3
Hot utility: HU1, HU2 Cold utility: CU1
No match between utilities
Incidence matrix Fig. 4. Incidence matrix.
1 (active) or 0 (inactive), of which optimal values are determined according to the objective function. Also, infeasible matches, for example heat transfer between utilities, and forbidden matches resulting from engineering difficulty implementing the heat transfer, due to plant layout and so on, can be added. The heat recovered for each match is systematically determined through mathematical optimisation, subject to the objective function and model constraints. The heat integration model developed in this study is given below. The objective function given here is provided when overall utility cost is minimised, which is represented as: Minimise
N X M X C i j Qi j i
(12)
j
It should be noted that the objective function in Eq. (1) can be extended to consider the cost of heat exchangers with an annualisation factor. Model constraints:
QHF j ¼
N X
Qi j
(13)
i
QHF ¼ i
M X
Qi j
(14)
j
Tiin T out DT min j
when Qi j > 0
(15)
Tiout T in j DT min
when Qi j > 0
(16)
LBi j Qi j UBi j
when Qi j > 0
(17)
where, I, {i j i is a hot stream}, i = 1,2, . . ., N J, {j j j is a cold stream}, j = 1,2, . . ., M Cij, utility cost parameters (Cij = 0 when i and j are process streams) Qij, heat flow rate of heat recovery between hot stream i and cold stream j QHF i ; overall heat flow rate of a hot stream i QHF j ; overall heat flow rate of a cold stream j Tiin ; starting temperature of a hot stream i Tiout ; target temperature of a hot stream i T in j ; starting temperature of a cold stream j T out j ; target temperature of a cold stream j DTmin, minimum approach temperature LB, lower bound for heat flow rate UB, upper bound for heat flow rate.
3.4. Optimisation framework The overall optimisation model includes the superstructure of distillation sequences, short-cut modelling equations for simple and complex columns and the heat recovery model, while design variables to be optimised are the sequence of separation tasks, column types, feed flowrate for columns, column operating conditions and heat recovery matches. The model may include constraints for complexities or designer preference, for example, maximum number of complex columns allowed in the sequence. The objective function in the optimisation is to minimise the overall annualised cost, which is the summation of column capital costs, heat exchanger costs and utility costs. Information for capital costs is provided in Appendix A. The optimisation has been carried out to determine the most appropriate operating conditions of the columns, such as the column pressure, within operating ranges limited by physical properties and the quality of utilities available. Once the mathematical model is formulated, robust and reliable optimisation-solving strategy should be implemented to obtain high quality optimal solutions. The optimisation of heat-integrated distillation sequencing is often formulated as an MINLP (mixed integer non-linear programming) problem. The optimisation can be carried out with deterministic or stochastic methods. If nonlinearity can be avoided or linearised without loosing too much accuracy, deterministic methods can be an attractive approach to solve the problem. Otherwise, stochastic methods (e.g. simulated annealing or genetic algorithms) can be applied for dealing with highly non-linear problems, which is often the case for the synthesis of heat-integrated distillation sequences. In the current study, genetic algorithms have been used to identify optimal distillation sequences, together with column design, operating conditions and optimal heat recovery networks. Fig. 5 shows schematically the flow of information within the optimization framework applied in this study. A series of candidates are generated by the GA optimization engine, the initialised population is evaluated through simulation, and its fitness is assessed with objective function and penalty functions. Genetic operators employed in the algorithm create a new population. Those two steps are repeated until termination criteria are met. The simulation and optimisation model were programmed with FORTRAN, and has been implemented in the COLOM1, which is an in-house software of Centre for Process Integration, The University of Manchester. 4. Case study The case study illustrates the importance of considering heatintegration in the design of distillation sequences and the cost benefits from using a simultaneous approach.
S. Jain et al. / Journal of the Taiwan Institute of Chemical Engineers 43 (2012) 525–534
531
CW
Genetic algorithm Simulation
Benzene
Superstructure approach
Construction of distillation sequences
Short-cut column models
Simulation of distillation sequences
Heat integration model
Design of heat recovery systems
Cost models
Economic costing
1.0bar CW Parameter boundaries New set of solutions
Feed
1.0 bar
User constraints
CW HP
Termination criteria met?
Optimal solution
Toluene
p-Xylene
HP
No
Yes
2.3 bar
o-Xylene
Fig. 5. Optimisation frameworks.
Total cost = 1.6 MGBP/a (11 % improvement)
Table 1 Data for utilities.
Cooling water LP steam MP steam HP steam
Temperature [8C]
Cost [£/(kW a)]
25 150 190 250
33.3 27.8 55.6 83.3
Fig. 7. Optimal heat-integrated sequence using simple columns (Case A).
integration is applied to the distillation sequence obtained, which is a base case for comparison (Fig. 6). The energy recovery is identified such that the feed of column 1 is preheated by available heat from the condenser of column 3, and inter-column heat recovery is made between the reboiler of column 2 and the condenser of column 3. The simultaneous synthesis for distillation sequence and heat integration is then applied for the case study. Two different cases are considered: (i) distillation sequence using simple columns, and (ii) distillation sequence using complex columns. The optimal solutions for both cases are shown in Figs. 7 and 8, where significant savings are obtained. It should be noted that inclusion of the background processes will provide more promising solutions as they are likely to give more opportunities for heat recovery.
4.1. Case A The distillation sequence is designed for four-component mixture (benzene, toluene, p-xylene and o-xylene). Feed flowrate is 0.1 kmol/s with equal distribution of amount mole fractions. The desired recovery is 99% for benzene and toluene, and 90% for pxylene and o-xylene. Data for available utilities and operating costs are given in Table 1. A minimum approach temperature of 10 8C is taken for the HEN design. First, the sequence is optimised without consideration of heat integration during synthesis of distillation systems. Then heat
CW
Benzene CW
2 CW LP
1
Toluene
Optimal sequence without heat integration
3 HP
LP
o-Xylene
p-Xylene
Heat integration
CW
CW
Benzene
2 1.04 bar HP
1 1.0 bar HP HP
3 2.3 bar
Toluene
Total cost = 1.8 MGBP/a (Base case)
HP
o-Xylene
p-Xylene
Fig. 6. Conventional design approach for distillation sequencing (Case A).
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CW Benzene CW A B C 1.1bar D
Feed Toluene 1.4 bar
CW HP
CW
B 2.5bar C D
p-Xylene
2.3 bar
LP C D 4.4bar
MP o-Xylene
HP
Total cost = 1.5 MGBP/a
Total cost = 1.39 MGBP/a (7.9 % improvement)
(17 % improvement) Fig. 8. Optimal heat-integrated sequence using complex columns (Case A).
Fig. 10. Optimal heat-integrated sequence using simple columns (Case B).
CW
CW
A 1.3bar B CW A B C D
A 2.96 bar B C D
LP
3.3bar CW
HP
HP
C D 4.5bar
C 4.37 bar D HP
HP
Total cost = 1.27 MGBP/a (15.8 % improvement) Fig. 11. Optimal heat-integrated sequence using complex columns (Case B).
Total cost = 1.50 MGBP/a Fig. 9. Conventional design approach for distillation sequencing (Case B).
Table 2 Optimisation results for column design (Case B). Cases
Column
Type
Separation task
Feed preheating heat flow rate [kW]
Feed precooling heat flow rate [kW]
Pressure [bar]
Condenser heat flow rate [kW]
Reboiler heat flow rate [kW]
Condenser temp. [8C]
Reboiler temp. [8C]
Conventional design approach
1 2 3
Simple Simple Simple
AB/CD A/B C/D
2148.9 – 106.5
– 340.14 –
3.286 1.317 4.492
2101.9 4259.7 6862.9
4672.5 2214.8 7006.7
143.8 89.0 204.1
189.6 120.0 210.1
Optimal sequence using simple columns
1 2 3
Simple Simple Simple
A/BCD B/CD C/D
1296.8 420.2 184.8
– – –
1.127 2.460 4.365
3173.0 3163.8 6860.1
3626.5 3411.9 7002.9
83.8 145.0 202.6
123.7 176.0 209.0
Optimal sequence using complex columns
1 2
Prefractionator Simple
A/B/CD C/D
2053.9 128.3
– –
2.968 4.365
4184.3 6860.1
4899.9 7002.9
119.7 202.6
184.8 209.0
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Table 3 Optimisation results for heat integration (Case B). Cases
Source
Sink
Heat transferred [kW]
Conventional design approach
Column 3 Column 3 Column 3
Condenser Condenser Condenser
Column 1 Column 1 Column 2
Reboiler Feed preheating Reboiler
4672.5 2148.9 41.5247
Optimal sequence using simple columns
Column Column Column Column
3 3 2 2
Condenser Condenser Condenser Condenser
Column Column Column Column
2 1 1 1
Reboiler Reboiler Reboiler Feed preheating
3411.9 3448.2 178.3 1296.8
Optimal sequence using complex columns
Column 2 Column 2
Condenser Condenser
Column 1 Column 1
Reboiler Feed preheating
4899.9 1960.2
Table 4 Optimisation results for product compositions (Case B). Column 1
Cases
Conventional design approach
Flowrate [kmol/s] Molar composition
Optimal sequence using simple columns
Flowrate [kmol/s] Molar composition
Column 3
Top Product
Bottom Product
Feed
Top Product
Bottom Product
Feed
Top Product
Bottom Product
Benzene Toluene p-Xylene o-Xylene
0.10 0.40 0.35 0.20 0.05
0.0753 0.531 0.462 0.007 0.000
0.0247 0.000 0.007 0.790 0.203
0.0753 0.531 0.462 0.007 0.000
0.0398 0.996 0.004 0.000 0.000
0.0356 0.0113 0.975 0.014 0.000
0.0247 0.000 0.007 0.790 0.203
0.0193 0.000 0.009 0.986 0.005
0.0054 0.000 0.000 0.090 0.910
Benzene Toluene p-Xylene o-Xylene
0.1 0.40 0.35 0.20 0.05
0.0398 0.996 0.004 0.0 0.0
0.0602 0.007 0.578 0.332 0.083
0.0602 0.007 0.578 0.332 0.083
0.0356 0.011 0.975 0.014 0.0
0.0247 0.0 0.007 0.790 0.203
0.0247 0.0 0.007 0.790 0.203
0.0193 0.0 0.010 0.986 0.005
0.0054 0.0 0.0 0.090 0.910
Column 1
Cases
Optimal sequence using complex columns
Column 2
Feed
Flowrate [kmol/s] Molar composition
Benzene Toluene p-Xylene o-Xylene
Column 2
Feed
Top product
Middle product
Bottom product
Feed
Top product
Bottom product
0.1 0.40 0.35 0.20 0.05
0.0397 0.999 0.001 0.0 0.0
0.0357 0.011 0.975 0.014 0.0
0.0246 0.0 0.005 0.792 0.203
0.0246 0.0 0.005 0.792 0.203
0.0193 0.0 0.009 0.986 0.005
0.0054 0.0 0.0 0.090 0.910
4.2. Case B Different feed compositions (40% benzene; 35% toluene; 20% pxylene; 5% o-xylene) and recoveries (99% for benzene and toluene, 95% for p-xylene and 98% for o-xylene) are applied, while other design and costing parameters are the same with Case A. Figs. 9–11 demonstrate the applicability and effectiveness of the optimisation method proposed in this paper, such that the simultaneous optimisation of heat integration and distillation sequencing has significant benefits for saving costs for multi-component separation. Care must be taken to select operating conditions in the selection of distillation sequences. Table 2 shows temperatures of condensers and reboilers, as well as heat exchanged in the feed preheaters and/or coolers. Table 3 explains the heat integration matches between sources and sinks. Table 4 shows flowrate and amount of substance composition for feed and product streams of the columns. 5. Conclusions When distillation is applied for multiple-component feeds, the selection of the most appropriate sequence is not a straightforward task, due to combinatorial characteristics in design. Although heat integration is an important degree of freedom in the design of distillation systems, simultaneous consideration of energy recovery and distillation sequencing has not been highlighted in the past. A new approach has been developed for the synthesis of heatintegrated distillation sequencing, which fully accommodates heat
recovery options in the distillation sequencing and design of columns. The heat-integrated distillation sequencing can be carried out using stochastic optimisation of a superstructure, and the case study demonstrated benefits from integrated modelling and design philosophy. Acknowledgements This research was supported by a grant from the GAS Plant R&D Center funded by the Ministry of Land, Transportation and Maritime Affairs (MLTM) of the Korean government, and also supported by Process Integration Research Consortium (PIRC) at the University of Manchester.
Appendix A. Capital cost data Capital cost estimation for distillation columns shown in the below are from Refs. [22–24]: Column height (h): h ¼ d Nt þ V s where, Nt, the number of trays d, spacing between plates Vs, vapour disengaging space at the top of the column.
(A1)
S. Jain et al. / Journal of the Taiwan Institute of Chemical Engineers 43 (2012) 525–534
534 Table A1 Indices for Eq. (A4). W
x1
x2
y1
y2
W < 3.12 3.12 W < 4 4W<5 5W<6 6W<7 7W<8 8W<9 9 W < 10 10 W < 20 20 W < 30 30 W < 40 40 W < 50 50 W < 60 60 W < 70 70 W < 80 80 W < 90 90 W < 100 W > 100
W 3.12 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100
3.12 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100 W
5 5 4.33 3.79 3.36 3.12 2.9 2.7 2.54 1.9 1.66 1.51 1.44 1.39 1.35 1.33 1.32 1.3
5 4.33 3.79 3.36 3.12 2.9 2.7 2.54 1.9 1.66 1.51 1.44 1.39 1.35 1.33 1.32 1.3 1.3
C HE ¼ 5391 þ 113:4A 0:32A2 þ 9:013 104 A3 1:027 106 A4 þ 4:095 1010 A5
(A6)
where, A, heat exchanger area [m2].
References
Table A2 Indices for Eq. (A5). D (m)
x1
x2
y1
y2
Ctray
D<1 1D<2 2D<3 3D<4 4D<5 5D<6 D>6
– 1 2 3 4 5 –
– 2 3 4 5 6 –
– 569 1085 1990 3116 4391 –
– 1085 1990 3116 4391 5791 –
569 Eq. (A4)
Shell diameter of a distillation column (D): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi FV D¼ flood ð1 ’Þ p Vmax flood ¼ CSsb Vmax
It is assumed that the capital cost of dividing wall columns is equivalent to that of the thermally-coupled prefractionator arrangement. The design model of dividing wall column used in this paper is to design with the same number of trays for both sections of the divided column [19]. Assumption is made that there is no difference for the cost between dividing wall and conventional columns, although in reality there will be some small extra cost for the dividing wall. This allows the costing of dividing wall column with information given in this appendix. Capital cost estimation for shell and tube heat exchangers (CHE):
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rliq rvap
rvap
5791
(A2)
(A3)
where, FV, vapour flowrate flood Vmax ; vapour speed at flooding point w, downcomer and cross-sectional area ratio CSsb, empirical parameter for flooding velocity calculation rliq, liquid density rvap, vapour density. The cost of column shell (Cshell): m x1 C shell ¼ m ðy2 y1 Þ þ y1 x2 x1
(A4)
where, m, weight of column shell x1, x2, y1, y2, indices given in Table A1. Cost of a tray (Ctray): d x1 C tray ¼ Nt ðy2 y1 Þ þ y1 x2 x1 where, x1, x2, y1, y2 are indices given in Table A2.
(A5)
[1] DOE. Monthly energy review: April 1998. U.S. Department of Energy; 1998. [2] DOE. Technology roadmap for the petroleum industry. U.S. Department of Energy; 2000. [3] Smith R. Chemical process design and integration. West Sussex: John Wiley & Sons; 2005. [4] Smith R. State of art in process integration. Appl Therm Eng 2002;20(15– 16):1337–45. [5] Klemes J, Friedler F, Bulatov I, Varbanov P. Sustainability in the process industry: integration and optimization. New York: McGraw-Hill; 2010. [6] Linnhoff B, Townsend D, Boland D, Hewitt G, Thomas B, Guy A, Marsland R. User guide on process integration for the efficient use of energy. Rugby: IChemE; 1982. [7] Kim J, Robin S. Pinch design and analysis: a chapter in encyclopedia of chemical processing. Marcel Dekker; 2005. p. 2165–80. [8] Linnhoff B, Dunford H, Smith R. Heat integration of distillation columns into overall processes. Chem Eng Sci 1983;38:1175–88. [9] Zemp R. Thermodynamic analysis of separation systems. PhD Thesis, UMIST, UK; 1991. [10] Dhole VR, Linnhoff B. Distillation column targets. Comput Chem Eng 1983;17:549–60. [11] Floudas CA, Paules GE. A mixed-integer nonlinear programming formulation for the synthesis of heat-integrated distillation sequences. Comput Chem Eng 1988;12:531–46. [12] Shah P, Kokossis A. New synthesis framework for the optimisation of complex distillation systems. AIChE J 2002;48:527–50. [13] Caballero JA, Grossmann IE. Structural considerations and modeling in the synthesis of heat-integrated-thermally coupled distillation sequences. Ind Eng Chem Res 2006;45(25):8454–74. [14] An WZ, Yuan XG. A simulated annealing-based approach to the optimal synthesis of heat-integrated distillation sequences. Comput Chem Eng 2009;33:199–212. [15] Wang XH, Li YG. Stochastic GP synthesis of heat integrated nonsharp distillation sequences. Chem Eng Res Des 2010;88:45–54. [16] Giridhar A, Agrawal R. Synthesis of distillation configurations: I. Characteristics of a good search space. Comput Chem Eng 2010;34(1):73–83. [17] Giridhar A, Agrawal R. Synthesis of distillation configurations: II: A search formulation for basic configurations. Comput Chem Eng 2010;34(1):74–95. [18] King J. Separation processes. New York: McGraw-Hill; 1980. [19] Triantafyllou C, Smith R. Design and optimisation of fully thermally coupled distillation columns. Chem Eng Res Des 1992;70(A2):118–32. [20] Carlberg NA, Westerberg AW. Temperature heat diagrams for complex columns – 2: Underwood’s method for side strippers and enrichers. Ind Eng Chem Res 1989;28:1379–86. [21] Carlberg NA, Westerberg AW. Temperature heat diagrams for complex columns – 3: Underwood’s method for the Petlyuk configurations. Ind Eng Chem Res 1989;28:1386–97. [22] Triantafyllou C. The design, optimization and integration of dividing wall columns. PhD Thesis, UMIST, UK; 1991. [23] Shah P. Conceptual programming: a new approach for the optimisation, analysis and novel development of simple and complex separation systems. PhD Thesis, UMIST, UK; 1999. [24] Wang J. Synthesis and optimisation of low temperature gas separation processes. PhD Thesis, UMIST, UK; 2004.
Contents lists available at SciVerse ScienceDirect
Journal of the Taiwan Institute of Chemical Engineers journal homepage: www.elsevier.com/locate/jtice
Synthesis of heat-integrated distillation sequence systems Santosh Jain a, Robin Smith a, Jin-Kuk Kim b,* a b
Centre for Process Integration, School of Chemical Engineering and Analytical Science, The University of Manchester, Sackville Street, Manchester M13 9PL, United Kingdom Department of Chemical Engineering, Hanyang University, 17, Haengdang-dong, Seongdong-gu, Seoul 133-791, Republic of Korea
A R T I C L E I N F O
A B S T R A C T
Article history: Received 26 July 2011 Received in revised form 16 January 2012 Accepted 25 January 2012 Available online 7 March 2012
Energy-efficient distillation systems can be achieved through the mathematical optimisation of distillation sequencing in which heat integration is simultaneously considered. Genetic algorithms have been employed to optimise the most appropriate sequences based on both simple and complex columns for a given separation requirement, with rigorous economic trade-offs between energy and capital costs used in the determination of distillation sequence. Thermodynamic and economic performance of distillation columns has been simulated and measured with short-cut models, while a conceptual decomposition method has been applied for evaluating complex columns. An incidence matrix has been proposed to identify the optimal heat recovery between available heat sources and sinks existing in the distillation sequence. Two case studies have been presented to demonstrate the importance of considering heat integration simultaneously in the optimisation of distillation sequencing, and 8–17% of overall cost savings have been achieved, compared to the conventional synthesis method. ß 2012 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Keywords: Energy minimisation Heat integration Distillation sequencing Optimisation Distillation columns
1. Introduction Distillation is a mature separation technology. However, it is an energy-intensive operation which consumes considerable energy. In a typical distillation operation, hot utility (steam, flue gas exhaust, hot oil, etc.) is required to provide a driving force for distilling lighter components from heavier ones. Condensing vapour streams to enable reflux in the column is facilitated by rejecting heat to cold utility (e.g. cooling water, refrigeration, etc.). Decreased use of external heating and cooling sources in distillation is essential for achieving cost-effective separation. Furthermore, energy-efficient distillation systems contribute to reduce carbon emissions discharged to the atmosphere, which is a further incentive to reduce energy consumption. The economic and environmental benefits, which can be potentially gained from the successful implementation of energy-efficient distillation systems, will be significant, as huge energy is currently consumed in distillation-based processing. For example, the US petroleum refining industries account for about 7% of total U.S. energy consumption (based on year of 1994) [1] and distillation contributes about up to 40% of energy used in refining processes [2]. One of the reasons for thermodynamic inefficiency in distillation is irreversible mixing effects inside columns, and the energy efficiency of distillation operation can be improved with various measures, including:
* Corresponding author. Tel.: +82 02 2220 2331. E-mail address: [email protected] (J.-K. Kim).
internal column modifications (e.g. efficient tray or column internals, etc.) integrated (or complex) column configurations (e.g. sidestripper, side-rectifier, prefractionator, etc.) changing operating conditions (e.g. changing operating pressure, changing feed conditions, etc.), or enhanced or intensified heat transfer in heat exchangers. Although these structural and operational options can be effective for reducing energy demand in distillation columns, it should be noted that large energy consumption often results from inefficient heat recovery between hot and cold process streams, or inappropriate selection of utilities (e.g. steam, cooling water, refrigeration) for process streams. When distillation is employed to separate a multi-component mixture in which several distillation columns are interconnected in a sequence, combinatorial decision-making is necessary in order to determine the most appropriate stream matching and utility selections. Poor energy management is likely to occur if heat recovery is not fully considered. The design complexity increases exponentially when the degrees of freedom in the distillation sequence synthesis are simultaneously considered in the energy management [3], such as: choice of sequence (e.g. direct or indirect or combined sequence) choice of simple column1 or integrated columns choice of thermal coupling2 1 Simple column refers a distillation column which separates two products from single feed, and has a reboiler and condenser. 2 The heat is transferred through using materials flows i.e. direct contact.
1876-1070/$ – see front matter ß 2012 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jtice.2012.01.012
526
S. Jain et al. / Journal of the Taiwan Institute of Chemical Engineers 43 (2012) 525–534
Nomenclature MGBP a
million pounds annum
choice of utilities choice of heat recovery mechanisms and design of heat exchanger networks. However, this complex sequencing of distillation systems also provides considerable opportunities for engineers to achieve energy-efficient and cost-effective design of distillation systems. Overall energy requirements can be reduced by introducing integrated heat recovery matching to the distillation sequence. Many successful applications using heat integration have been observed in various industrial sectors [4,5]. This allows achievable targets (or optimal conditions) in energy minimisation projects through the design of heat exchanger networks. It also gives fundamental understanding, design guidelines and conceptual insights for the problem to be dealt with, rather than simply presenting solutions or targets. The current article will highlight how distillation system design can benefit from a systematic approach to heat integration and why this integrated methodology is effective to improve energy efficiency in the synthesis of distillation sequences. Note that it is not intended to cover the basics of heat integration in this article, for which details can be found elsewhere [3,5–7]. Various attempts had been made to improve the thermodynamic efficiency of distillation sequence and its heat integration. One of the early efforts in the context of process systems engineering was to apply design methods based on pinch technology, including energy composite curves and grand composite curves, which allows finding the most appropriate heat recovery arrangement of a distillation column within the process [8]. Another possibility of improving energy efficiency of distillation column is to reduce inherent thermodynamic inefficiency of the column itself, for example, identifying minimum exergy loss for the column through exergy analysis [9] or distillation targeting method with the aid of light key and heavy key method [10]. These graphical design methods support users to obtain valuable conceptual understanding in energy recovery for distillation columns, and hence had been proved to be very effective in improving energy efficiency, however, simultaneous consideration between heat integration and design of distillation columns had not been fully addressed. In order to design the sequence of simple distillation columns and heat recovery systems together, a superstructure-based automated design method with an MINLP formulation was proposed by using a deterministic optimisation technique [11]. Shah and Kokossis [12] introduced an MILP optimisation framework for solving distillation sequencing problems which includes both simple columns and complex columns, although the full potential of heat recovery was not materialised during the design of distillation sequences. Later, Caballero and Grossmann [13] proposed an MINLP optimization model for considering all the possible complex and simple columns in the design, together with heat integration, by applying a disjunctive programming technique. Considerable computational efforts are required for an automated design using the MINLP formulation, as there are highly non-linear elements and complex combinatorial nature of structural options existed in the model. In order to overcome computational difficulties within deterministic optimization methods, stochastic methods have been recently applied to the
design of distillation sequencing, which includes An and Yuan’s works [14] using simulated annealing, and Wang and Li’s works [15] based on the application of stochastic genetic programming. These studies had addressed the application of different optimization techniques, but both methodologies are limited in the application as only simple columns are employed in the sequences. Also, most of available design methods do not fully facilitate all the possible heat recovery options existing in the design of distillation sequencing, for example, one heat recovery matching from a particular reboiler or condenser to multiple exchangers is allowed in the optimization study of An and Yuan [14], and heat recovery is allowed between condensers and reboilers, only, not feed preheating or pre-cooling [15]. With the synthesis framework for distillation sequencing proposed by Shah and Kokossis [12], complex columns considered were constructed by merging simple separation tasks, but their design method did not consider a large number of complex alternative arrangements which can be generated by combining non-sharp separation with simple and complex columns, such that at least one component or mixture is recovered in at least two different locations, and these sections cannot be grouped to make conventional Petlyuk or prefractionator columns [16,17]. The key contribution made in this work is, therefore, to simultaneously consider distillation sequencing and energy integration in a holistic manner, as the systematic incorporation of energy recovery in the context of distillation sequencing has not been fully appreciated before. Also, there has been limited attempt to use a GA (genetic algorithm) for the optimisation of the synthesis of distillation columns, and the current study also aims to demonstrate how GA can be successfully applied to the complex optimisation problem. In the next section, there will be an explanation for heat recovery options available in the context of distillation sequencing, which is then followed by optimisation model for heat-integrated distillation sequencing. Finally, the case study will be presented to demonstrate the design method proposed in this paper.
2. Energy minimisation in distillation sequencing In the synthesis of distillation systems which separate a multicomponent mixture, a large number of sequences can be generated. For example, for a 5-component mixture, 14 sequences are possible when simple columns are used. Each sequence presents a different heat integration problem, because operating conditions are uniquely chosen at the given sequence and consequently, heating and/or cooling requirements for the distillation columns becomes specific to the sequence chosen. Therefore, a large number of heat integration options are possible in the synthesis of distillation sequence. Fig. 1 illustrates available heat integration options for indirect distillation sequence which separates 3 components A, B and C. Inter-column heat recovery: Heat can be exchanged between a reboiler of one column and a condenser of the other one. Fig. 1 illustrates the possibility of heat transfer from the condenser in Column I to the reboiler of Column II. Column operating pressures can be adjusted to enable such an inter-column heat recovery without violating minimum temperature approach, DTmin. Heat exchange with other process streams: When heat sources and sinks exist beyond the distillation section, heat recovery with background processes (e.g. reactor, other separation, utility generation, etc.) can be considered. Heat exchange with utility: If efficient, practical or economic stream matching for heat recovery between process streams is
S. Jain et al. / Journal of the Taiwan Institute of Chemical Engineers 43 (2012) 525–534
527
Inter-column heat recovery Feed preheating/ cooling
A B C
A
A B
A B
Column II
A B Column I C B C
Heat exchange with other process stream
Heat exchange with utility
Fig. 1. Heat integration options.
limited within/beyond distillation systems, the required heat is provided from hot utility streams (e.g. steam, hot oil, etc.). Alternatively, the surplus heat is discharged to cold utility (e.g. cooling water) or utilised in heat recovery systems (e.g. boiler feed water heating). Selection of utilities and corresponding matching-decisions should consider quality, cost and availability of utilities. Feed pre-heating or pre-cooling: Feed can be preheated or precooled by exchanging heat with condenser(s) or reboiler(s) or other process streams or utility streams. There are some difficulties that arise in the analysis of these heat integration options for distillation systems. First, all heat
integration opportunities are to be screened and optimised simultaneously. Second, structural or configurational decisions in distillation sequencing are not straightforward. For example, a three component mixture can be separated with the direct sequence shown in Fig. 2(a), which can be evolved to a sequence with thermal coupling. Such thermally-coupled sequences (Fig. 2(b)) can consume less energy than the conventional ones. However, overall heat is provided at a higher temperature for the thermally-coupled sequence, which leads to different heat recovery in the separation systems. Finally, the choice of operating conditions for the columns (pressure, feed conditions and reflux ratio), affects not only the design of a column (e.g. size, number of stages, etc.) but also its thermodynamic
Fig. 2. Design complexity in the design of heat-integrated distillation sequencing.
S. Jain et al. / Journal of the Taiwan Institute of Chemical Engineers 43 (2012) 525–534
528
characteristics (i.e. operating temperature and heat flow rates). As illustrated in Fig. 2(c), system-wide heat recovery is heavily influenced by the operating conditions of columns. Consequently, heat integration opportunities should be considered simultaneously with the determination of operating conditions for the columns. There can be operational constraints or practical limitations to be imposed on the design, for example, forbidden matches, maximum number of heat exchangers allowed for the condensation of reflux, etc. Heat recovery opportunities are significantly affected by these constraints, especially for retrofit cases. Therefore, all the relevant decisions on structure and operating conditions of the distillation sequence should be investigated, together with heat integration analysis, as a single synthesis problem. Conventional engineering practice for the design of distillation sequence performs the synthesis of distillation systems first without considering heat integration. Once the sequence is chosen, the design of heat recovery systems or heat exchanger network is carried out to satisfy energy demands for a given sequence. Such a non-integrated approach is not able to reflect design interactions systematically between distillation sequencing and heat integration, and consequently, often fails to capture optimal or near-optimal designs.
3. Optimisation of heat-integrated distillation sequencing A systematic methodology is required in the design of distillation sequences in which all the available opportunities for heat integration are fully considered. The method needs to screen and evaluate a large number of different flowsheets, as well as their energy recovery (i.e. heat integration together with decision for structural and operating conditions of the flowsheet). Therefore, the development of an automated design using optimisation techniques is appropriate, rather than relying on conventional design tools including graphical techniques, heuristics or engineering judgement. Using an optimisation method also facilitates easy implementation of practical or operational constraints (e.g. forbidden matches, quality of available utility, etc.), and allows rigorous trade-off between capital and operating costs to be considered. In order to build an optimisation framework for heat-integrated distillation sequencing, the following three sections are the main elements considered in mathematical modelling:
3.1. Generation of distillation sequences The superstructure approach can be used to generate potential candidates of flowsheets for distillation sequencing and identify the optimal flowsheet, subject to the objective function and constraints. The sequence can be simply generated based on combinatorial formulation or combination of distillation tasks [12], as shown in Fig. 3. For example, for four-component feed (A, B, C and D), a distillation task can be applied to separate A from BCD, or to separate B from CD or separate B from AD, etc. This can be more effective in the optimisation, as far fewer calculations are required for column sizing and costing. Complex columns, as well as simple columns, are considered in the superstructure approach in which complex columns or hybrid tasks are considered by merging simple tasks. An example is illustrated in Fig. 3 where a side-stripper arrangement for the separation of A/B/C combines two simple separation tasks between AB/C and A/B [3]. Complex columns considered in this study include side rectifier, side stripper, vapour side-draw column, liquid side-draw column, prefractionator and Petlyuk column, which are yielded from the aggregation of simple tasks. 3.2. Simulation of distillation sequence A quantitative modelling framework is required to evaluate the distillation sequence by performing economic costing or measuring another performance index, for example vapour flow rate, during the optimisation. Short-cut models for simulating simple or complex columns will be preferred at the conceptual design stage, because computational difficulties occurred during the optimisation when rigorous models are used. Short-cut models employed for estimating key design information for simple columns are the Underwood equations for estimating minimum reflux ratio, the Fenske equation for determining minimum number of equilibrium stages, the Gilliland correlations for calculating actual number of stages, and the Kirkbride equations for identifying feed tray location. These shortcut methods [3,18] are presented in below: Fenske equation for determining the minimum number of equilibrium stages (Nmin): N min ¼
log½ðF L;D =F H;D ÞðF H;B =F L;B Þ log½am
(1)
where,
am, mean relative volatility of top and bottom stage of a column Sequences
Distillation tasks
1
A/BCD
B/CD
C/D
2
A/BCD
BC/D
B/C
3
AB/CD
A/B
C/D
4
ABC/D
A/BC
B/C
5
ABC/D
AB/C
A/B
A/BCD
A/BC
A/B
AB/CD
AB/C
B/C
B/CD
C/D
ABC/D
BC/D
FL,D, light key component flow in the distillate product FH,D, heavy key component flow in the distillate product FL,B, light key component flow in the bottom product FH,B, heavy key component flow in the bottom product. Underwood equations for estimating minimum reflux ratio (Rmin): n X ai xi;F ¼1q a u i¼1 i
Rmin þ 1 ¼
A
n X ai xi;D a u i¼1 i
Side-stripper
A B C
B C
Fig. 3. Representation of separation sequence for four-product separation.
where, n, number of components q, liquid fraction of feed xi,F, mole amount fraction of i in feed xi,D, mole amount fraction of i in distillate
(2)
(3)
S. Jain et al. / Journal of the Taiwan Institute of Chemical Engineers 43 (2012) 525–534
ai, relative volatility of component i to the heaviest component u, root of Eq. (A2). Gilliland correlations for calculating actual number of stages (N): 1 þ 54:4X X 1 0:5 Y ¼ 1 exp (4) 11 þ 117:2X X
N N min R Rmin ;X ¼ Y¼ Nþ1 Rþ1
FVSuppl ¼ FVmain þ FVside
(6)
FLSuppl ¼ FLmain
(7)
where, FVSuppl ; vapour flowrate in the supplementary section FVmain ; vapour flowrate in the main column FVside ; flowrate of vapour side-draw FLSuppl ; liquid flowrate in the supplementary section FLmain ; liquid flowrate in the main column RBU, boilup amount ratio.
(10)
(11)
(5)
For the modelling of complex columns generated in the superstructure, a complex column is conceptually decomposed into a thermodynamically equivalent arrangement with simple columns, and overall performance of the complex column is then obtained by combining individual design information of simple columns estimated through short-cut models. For example, the side-stripper shown in Fig. 3 can be modelled such that a feed to and a side-stream from the side column are approximated by the feed to and liquid returned from the hypothetical condenser of the first main column. Short-cut models for simple columns are then extended or modified to determine reflux ratio and number of stages required in each column. Decomposition techniques and the corresponding application of short-cut models for complex columns can be found in details from Refs. [3,18,19], which are described as below. Side-draw columns: An available shortcut model for simulating side-draw columns is as given in Triantafyllou and Smith [19]. For the case of vapour side-draw, the model estimates the minimum faction of heavy components in the side stream with the fixed reflux ratio, while the minimum faction of light components in the side stream is predicted at the fixed boilup ratio. For a vapour sidedraw column, the boliup ratio is given by Eqs. (6)–(8), and the Underwood equations are used for calculating the composition of the vapour side-draw.
FVSuppl FB
F L Suppl FD
(9)
where, FLside ; flowrate of liquid side-draw R, reflux ratio.
where, Nr, number of stages above feed stage Ns, number of stages below feed stage zH, mole amount fraction of heavy key component in feed zL, mole amount fraction of light key component in feed FB, molar flowrate of bottom product FD, molar flowrate of distillate product xB,L, mole fraction of light key component in bottom product xD,H, mole fraction of heavy key component in distillate product.
RBU ¼
FVSuppl ¼ FVmain
R¼
R, actual reflux ratio. Kirkbride equations for identifying feed tray location: " # Nr zH F B xB;L 2 ¼ 0:206log log Ns zL F D xD;H
For a liquid side-draw column, the reflux ratio is calculated by Eqs. (9)–(11) with which Underwood equations are applied to estimate the composition of the liquid side-draw.
FLSuppl ¼ FLmain þ FLside
where,
529
(8)
Side-rectifier and side-stripper: The side-rectifier is decomposed into a conventional main column and a vapour side-draw column. The main column has a partial reboiler, which facilitates a partial vapourisation of liquid from the main column and creates a mixture of liquid and vapour in equilibrium. The second column is then modelled as a vapour side-draw column, such that the vapour sidestream is extracted from one stage below the feed stage in the main column [3,20,21]. For a side-stripper, a similar decomposition strategy is used in the simulation by taking liquid side-draw at one stage above the feed stage and by calculating the partial condensation in the main column. Calculations of mass balances and VLE (vapour–liquid equilibrium) are performed around the connecting streams between side column and main column. Prefractionator: The prefractionator is decomposed into three simple columns: the first column represents a prefactionating section with a partial reboiler and condenser, while the second and third columns represent rectifying and stripping section of main column. The first column has a partial reboiler and a condenser, which is integrated with the second and third columns. The vapour and liquid stream traffic exchanged between second and third columns should be equalised in the modelling [19]. For the prefractionator, Petlyuk column and diving wall columns, the first column is thermally coupled with the main column. For the simulation, it is required to simulate simultaneously one simple column with a partial reboiler and a condenser, one vapour side-draw column, and one liquid sidedraw column. Again, equating vapour and liquid flow rates between top of liquid side-draw column and bottom of vapour side-draw column is necessary [19]. Cost models for operating and capital costs are then applied to evaluate the full economic impact of sequences being considered during the optimisation. 3.3. Design of heat recovery systems Both graphical and mathematical methods are available for the design of heat exchanger networks for the distillation sequence. A wide range of models are available and should be selected based on the objectives of the energy minimisation project. In this study, an incidence matrix is introduced to effectively deal with heat integration in the distillation sequencing problems, as illustrated in Fig. 4. This contains all the possible matches for heat recovery existing in the distillation sequence and their feasibility information. The incidence matrix shown in Fig. 4 represents the potential heat recovery existing in a sequence of three simple distillation columns, of which hot and cold energy is provided by two types of hot utilities and one type of cold utility. The numbers indicated between rows and columns of the matrix can be either
S. Jain et al. / Journal of the Taiwan Institute of Chemical Engineers 43 (2012) 525–534
530
Row: available heat sinks C2
R1
R2
R3
CU1
C1
0
1
1
1
Feasible match
C2
0
0
1
1
Infeasible or forbidden match
C3
0
0
0
1
HU1 0
1
1
0
HU2 1
1
1
0
C1
R2 R1
C3
R3
Hot utility: HU1, HU2 Cold utility: CU1
No match between utilities
Incidence matrix Fig. 4. Incidence matrix.
1 (active) or 0 (inactive), of which optimal values are determined according to the objective function. Also, infeasible matches, for example heat transfer between utilities, and forbidden matches resulting from engineering difficulty implementing the heat transfer, due to plant layout and so on, can be added. The heat recovered for each match is systematically determined through mathematical optimisation, subject to the objective function and model constraints. The heat integration model developed in this study is given below. The objective function given here is provided when overall utility cost is minimised, which is represented as: Minimise
N X M X C i j Qi j i
(12)
j
It should be noted that the objective function in Eq. (1) can be extended to consider the cost of heat exchangers with an annualisation factor. Model constraints:
QHF j ¼
N X
Qi j
(13)
i
QHF ¼ i
M X
Qi j
(14)
j
Tiin T out DT min j
when Qi j > 0
(15)
Tiout T in j DT min
when Qi j > 0
(16)
LBi j Qi j UBi j
when Qi j > 0
(17)
where, I, {i j i is a hot stream}, i = 1,2, . . ., N J, {j j j is a cold stream}, j = 1,2, . . ., M Cij, utility cost parameters (Cij = 0 when i and j are process streams) Qij, heat flow rate of heat recovery between hot stream i and cold stream j QHF i ; overall heat flow rate of a hot stream i QHF j ; overall heat flow rate of a cold stream j Tiin ; starting temperature of a hot stream i Tiout ; target temperature of a hot stream i T in j ; starting temperature of a cold stream j T out j ; target temperature of a cold stream j DTmin, minimum approach temperature LB, lower bound for heat flow rate UB, upper bound for heat flow rate.
3.4. Optimisation framework The overall optimisation model includes the superstructure of distillation sequences, short-cut modelling equations for simple and complex columns and the heat recovery model, while design variables to be optimised are the sequence of separation tasks, column types, feed flowrate for columns, column operating conditions and heat recovery matches. The model may include constraints for complexities or designer preference, for example, maximum number of complex columns allowed in the sequence. The objective function in the optimisation is to minimise the overall annualised cost, which is the summation of column capital costs, heat exchanger costs and utility costs. Information for capital costs is provided in Appendix A. The optimisation has been carried out to determine the most appropriate operating conditions of the columns, such as the column pressure, within operating ranges limited by physical properties and the quality of utilities available. Once the mathematical model is formulated, robust and reliable optimisation-solving strategy should be implemented to obtain high quality optimal solutions. The optimisation of heat-integrated distillation sequencing is often formulated as an MINLP (mixed integer non-linear programming) problem. The optimisation can be carried out with deterministic or stochastic methods. If nonlinearity can be avoided or linearised without loosing too much accuracy, deterministic methods can be an attractive approach to solve the problem. Otherwise, stochastic methods (e.g. simulated annealing or genetic algorithms) can be applied for dealing with highly non-linear problems, which is often the case for the synthesis of heat-integrated distillation sequences. In the current study, genetic algorithms have been used to identify optimal distillation sequences, together with column design, operating conditions and optimal heat recovery networks. Fig. 5 shows schematically the flow of information within the optimization framework applied in this study. A series of candidates are generated by the GA optimization engine, the initialised population is evaluated through simulation, and its fitness is assessed with objective function and penalty functions. Genetic operators employed in the algorithm create a new population. Those two steps are repeated until termination criteria are met. The simulation and optimisation model were programmed with FORTRAN, and has been implemented in the COLOM1, which is an in-house software of Centre for Process Integration, The University of Manchester. 4. Case study The case study illustrates the importance of considering heatintegration in the design of distillation sequences and the cost benefits from using a simultaneous approach.
S. Jain et al. / Journal of the Taiwan Institute of Chemical Engineers 43 (2012) 525–534
531
CW
Genetic algorithm Simulation
Benzene
Superstructure approach
Construction of distillation sequences
Short-cut column models
Simulation of distillation sequences
Heat integration model
Design of heat recovery systems
Cost models
Economic costing
1.0bar CW Parameter boundaries New set of solutions
Feed
1.0 bar
User constraints
CW HP
Termination criteria met?
Optimal solution
Toluene
p-Xylene
HP
No
Yes
2.3 bar
o-Xylene
Fig. 5. Optimisation frameworks.
Total cost = 1.6 MGBP/a (11 % improvement)
Table 1 Data for utilities.
Cooling water LP steam MP steam HP steam
Temperature [8C]
Cost [£/(kW a)]
25 150 190 250
33.3 27.8 55.6 83.3
Fig. 7. Optimal heat-integrated sequence using simple columns (Case A).
integration is applied to the distillation sequence obtained, which is a base case for comparison (Fig. 6). The energy recovery is identified such that the feed of column 1 is preheated by available heat from the condenser of column 3, and inter-column heat recovery is made between the reboiler of column 2 and the condenser of column 3. The simultaneous synthesis for distillation sequence and heat integration is then applied for the case study. Two different cases are considered: (i) distillation sequence using simple columns, and (ii) distillation sequence using complex columns. The optimal solutions for both cases are shown in Figs. 7 and 8, where significant savings are obtained. It should be noted that inclusion of the background processes will provide more promising solutions as they are likely to give more opportunities for heat recovery.
4.1. Case A The distillation sequence is designed for four-component mixture (benzene, toluene, p-xylene and o-xylene). Feed flowrate is 0.1 kmol/s with equal distribution of amount mole fractions. The desired recovery is 99% for benzene and toluene, and 90% for pxylene and o-xylene. Data for available utilities and operating costs are given in Table 1. A minimum approach temperature of 10 8C is taken for the HEN design. First, the sequence is optimised without consideration of heat integration during synthesis of distillation systems. Then heat
CW
Benzene CW
2 CW LP
1
Toluene
Optimal sequence without heat integration
3 HP
LP
o-Xylene
p-Xylene
Heat integration
CW
CW
Benzene
2 1.04 bar HP
1 1.0 bar HP HP
3 2.3 bar
Toluene
Total cost = 1.8 MGBP/a (Base case)
HP
o-Xylene
p-Xylene
Fig. 6. Conventional design approach for distillation sequencing (Case A).
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CW Benzene CW A B C 1.1bar D
Feed Toluene 1.4 bar
CW HP
CW
B 2.5bar C D
p-Xylene
2.3 bar
LP C D 4.4bar
MP o-Xylene
HP
Total cost = 1.5 MGBP/a
Total cost = 1.39 MGBP/a (7.9 % improvement)
(17 % improvement) Fig. 8. Optimal heat-integrated sequence using complex columns (Case A).
Fig. 10. Optimal heat-integrated sequence using simple columns (Case B).
CW
CW
A 1.3bar B CW A B C D
A 2.96 bar B C D
LP
3.3bar CW
HP
HP
C D 4.5bar
C 4.37 bar D HP
HP
Total cost = 1.27 MGBP/a (15.8 % improvement) Fig. 11. Optimal heat-integrated sequence using complex columns (Case B).
Total cost = 1.50 MGBP/a Fig. 9. Conventional design approach for distillation sequencing (Case B).
Table 2 Optimisation results for column design (Case B). Cases
Column
Type
Separation task
Feed preheating heat flow rate [kW]
Feed precooling heat flow rate [kW]
Pressure [bar]
Condenser heat flow rate [kW]
Reboiler heat flow rate [kW]
Condenser temp. [8C]
Reboiler temp. [8C]
Conventional design approach
1 2 3
Simple Simple Simple
AB/CD A/B C/D
2148.9 – 106.5
– 340.14 –
3.286 1.317 4.492
2101.9 4259.7 6862.9
4672.5 2214.8 7006.7
143.8 89.0 204.1
189.6 120.0 210.1
Optimal sequence using simple columns
1 2 3
Simple Simple Simple
A/BCD B/CD C/D
1296.8 420.2 184.8
– – –
1.127 2.460 4.365
3173.0 3163.8 6860.1
3626.5 3411.9 7002.9
83.8 145.0 202.6
123.7 176.0 209.0
Optimal sequence using complex columns
1 2
Prefractionator Simple
A/B/CD C/D
2053.9 128.3
– –
2.968 4.365
4184.3 6860.1
4899.9 7002.9
119.7 202.6
184.8 209.0
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Table 3 Optimisation results for heat integration (Case B). Cases
Source
Sink
Heat transferred [kW]
Conventional design approach
Column 3 Column 3 Column 3
Condenser Condenser Condenser
Column 1 Column 1 Column 2
Reboiler Feed preheating Reboiler
4672.5 2148.9 41.5247
Optimal sequence using simple columns
Column Column Column Column
3 3 2 2
Condenser Condenser Condenser Condenser
Column Column Column Column
2 1 1 1
Reboiler Reboiler Reboiler Feed preheating
3411.9 3448.2 178.3 1296.8
Optimal sequence using complex columns
Column 2 Column 2
Condenser Condenser
Column 1 Column 1
Reboiler Feed preheating
4899.9 1960.2
Table 4 Optimisation results for product compositions (Case B). Column 1
Cases
Conventional design approach
Flowrate [kmol/s] Molar composition
Optimal sequence using simple columns
Flowrate [kmol/s] Molar composition
Column 3
Top Product
Bottom Product
Feed
Top Product
Bottom Product
Feed
Top Product
Bottom Product
Benzene Toluene p-Xylene o-Xylene
0.10 0.40 0.35 0.20 0.05
0.0753 0.531 0.462 0.007 0.000
0.0247 0.000 0.007 0.790 0.203
0.0753 0.531 0.462 0.007 0.000
0.0398 0.996 0.004 0.000 0.000
0.0356 0.0113 0.975 0.014 0.000
0.0247 0.000 0.007 0.790 0.203
0.0193 0.000 0.009 0.986 0.005
0.0054 0.000 0.000 0.090 0.910
Benzene Toluene p-Xylene o-Xylene
0.1 0.40 0.35 0.20 0.05
0.0398 0.996 0.004 0.0 0.0
0.0602 0.007 0.578 0.332 0.083
0.0602 0.007 0.578 0.332 0.083
0.0356 0.011 0.975 0.014 0.0
0.0247 0.0 0.007 0.790 0.203
0.0247 0.0 0.007 0.790 0.203
0.0193 0.0 0.010 0.986 0.005
0.0054 0.0 0.0 0.090 0.910
Column 1
Cases
Optimal sequence using complex columns
Column 2
Feed
Flowrate [kmol/s] Molar composition
Benzene Toluene p-Xylene o-Xylene
Column 2
Feed
Top product
Middle product
Bottom product
Feed
Top product
Bottom product
0.1 0.40 0.35 0.20 0.05
0.0397 0.999 0.001 0.0 0.0
0.0357 0.011 0.975 0.014 0.0
0.0246 0.0 0.005 0.792 0.203
0.0246 0.0 0.005 0.792 0.203
0.0193 0.0 0.009 0.986 0.005
0.0054 0.0 0.0 0.090 0.910
4.2. Case B Different feed compositions (40% benzene; 35% toluene; 20% pxylene; 5% o-xylene) and recoveries (99% for benzene and toluene, 95% for p-xylene and 98% for o-xylene) are applied, while other design and costing parameters are the same with Case A. Figs. 9–11 demonstrate the applicability and effectiveness of the optimisation method proposed in this paper, such that the simultaneous optimisation of heat integration and distillation sequencing has significant benefits for saving costs for multi-component separation. Care must be taken to select operating conditions in the selection of distillation sequences. Table 2 shows temperatures of condensers and reboilers, as well as heat exchanged in the feed preheaters and/or coolers. Table 3 explains the heat integration matches between sources and sinks. Table 4 shows flowrate and amount of substance composition for feed and product streams of the columns. 5. Conclusions When distillation is applied for multiple-component feeds, the selection of the most appropriate sequence is not a straightforward task, due to combinatorial characteristics in design. Although heat integration is an important degree of freedom in the design of distillation systems, simultaneous consideration of energy recovery and distillation sequencing has not been highlighted in the past. A new approach has been developed for the synthesis of heatintegrated distillation sequencing, which fully accommodates heat
recovery options in the distillation sequencing and design of columns. The heat-integrated distillation sequencing can be carried out using stochastic optimisation of a superstructure, and the case study demonstrated benefits from integrated modelling and design philosophy. Acknowledgements This research was supported by a grant from the GAS Plant R&D Center funded by the Ministry of Land, Transportation and Maritime Affairs (MLTM) of the Korean government, and also supported by Process Integration Research Consortium (PIRC) at the University of Manchester.
Appendix A. Capital cost data Capital cost estimation for distillation columns shown in the below are from Refs. [22–24]: Column height (h): h ¼ d Nt þ V s where, Nt, the number of trays d, spacing between plates Vs, vapour disengaging space at the top of the column.
(A1)
S. Jain et al. / Journal of the Taiwan Institute of Chemical Engineers 43 (2012) 525–534
534 Table A1 Indices for Eq. (A4). W
x1
x2
y1
y2
W < 3.12 3.12 W < 4 4W<5 5W<6 6W<7 7W<8 8W<9 9 W < 10 10 W < 20 20 W < 30 30 W < 40 40 W < 50 50 W < 60 60 W < 70 70 W < 80 80 W < 90 90 W < 100 W > 100
W 3.12 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100
3.12 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100 W
5 5 4.33 3.79 3.36 3.12 2.9 2.7 2.54 1.9 1.66 1.51 1.44 1.39 1.35 1.33 1.32 1.3
5 4.33 3.79 3.36 3.12 2.9 2.7 2.54 1.9 1.66 1.51 1.44 1.39 1.35 1.33 1.32 1.3 1.3
C HE ¼ 5391 þ 113:4A 0:32A2 þ 9:013 104 A3 1:027 106 A4 þ 4:095 1010 A5
(A6)
where, A, heat exchanger area [m2].
References
Table A2 Indices for Eq. (A5). D (m)
x1
x2
y1
y2
Ctray
D<1 1D<2 2D<3 3D<4 4D<5 5D<6 D>6
– 1 2 3 4 5 –
– 2 3 4 5 6 –
– 569 1085 1990 3116 4391 –
– 1085 1990 3116 4391 5791 –
569 Eq. (A4)
Shell diameter of a distillation column (D): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi FV D¼ flood ð1 ’Þ p Vmax flood ¼ CSsb Vmax
It is assumed that the capital cost of dividing wall columns is equivalent to that of the thermally-coupled prefractionator arrangement. The design model of dividing wall column used in this paper is to design with the same number of trays for both sections of the divided column [19]. Assumption is made that there is no difference for the cost between dividing wall and conventional columns, although in reality there will be some small extra cost for the dividing wall. This allows the costing of dividing wall column with information given in this appendix. Capital cost estimation for shell and tube heat exchangers (CHE):
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rliq rvap
rvap
5791
(A2)
(A3)
where, FV, vapour flowrate flood Vmax ; vapour speed at flooding point w, downcomer and cross-sectional area ratio CSsb, empirical parameter for flooding velocity calculation rliq, liquid density rvap, vapour density. The cost of column shell (Cshell): m x1 C shell ¼ m ðy2 y1 Þ þ y1 x2 x1
(A4)
where, m, weight of column shell x1, x2, y1, y2, indices given in Table A1. Cost of a tray (Ctray): d x1 C tray ¼ Nt ðy2 y1 Þ þ y1 x2 x1 where, x1, x2, y1, y2 are indices given in Table A2.
(A5)
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