Design And Synthesis Of Distillation Systems Using

Chemical Engineering and Processing 43 (2004) 251–262

Design and synthesis of distillation systems using a driving-force-based approach Erik Bek-Pedersen, Rafiqul Gani∗ CAPEC, Department of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark Received 8 November 2002; received in revised form 7 April 2003; accepted 7 April 2003

Abstract A new integrated framework for synthesis, design and operation of distillation-based separation schemes is presented here. This framework is based on the driving force approach, which provides a measure of the differences in chemical/physical properties between two co-existing phases in a separation unit. A set of algorithms has been developed within this framework for design of simple as well as complex distillation columns, for the sequencing of distillation trains, for the determination of appropriate conditions of operation and for retrofit of distillation columns. The main feature of all these algorithms is that they provide a simple “visual” method to obtain near-optimal solutions in terms of energy consumption without rigorous simulation and/or optimisation. Several illustrative examples highlighting the application of the integrated approach are also presented. © 2003 Published by Elsevier B.V. Keywords: Driving force; Distillation; Integrated system; Synthesis; Design; Optimal solution

1. Introduction Most separation processes in the chemical industry make use of some kind of driving force to achieve the desired separation. It is therefore advantageous to perform a driving force analysis at the earliest possible stage of the design of a process. By definition, driving forces exploit differences in chemical/physical properties between two co-existing phases in a separation unit. So, if the feed mixture to be separated is a homogeneous single-phase solution, the generation or addition of a second phase is a necessary condition for the separation to take place. Driving forces can be generated or caused by various techniques related to different chemical/physical properties such as addition of heat or a force field. For distillation, the driving force defined in this work as the difference in composition of a component i between the vapor phase and the liquid phase is caused by a difference in the volatilities of component i and all other components in the system. This driving force is calculated for a binary mixture or a binary pair of key components of a multi-component mixture. Therefore, the driving force is always calculated

∗

Corresponding author. E-mail address: [email protected] (R. Gani).

0255-2701/$ – see front matter © 2003 Published by Elsevier B.V. doi:10.1016/S0255-2701(03)00120-X

with reference to the second component forming the binary pair. As the driving force approaches zero, separation of the corresponding key component i from the mixture becomes difficult, while as the driving force approaches a maximum, the energy necessary to maintain the two-phase system is a minimum. This is because the driving force is inversely proportional to the energy added to the system to create and maintain the two-phase (vapour–liquid) system. Therefore, if the distillation design is based on maximizing the driving force, it should lead to a highly energy efficient design. Note that this definition of the driving force does not require the two co-existing phases to be in equilibrium. The methodology presented here consists of calculation of the driving force for the pair of key (binary pair) components of a binary or multi-component mixture, based on phase composition data (which may be experimentally measured or generated through a model). By plotting the driving force as a function of composition, the location where the maximum driving force exists can be identified, and based on this knowledge, design variables such as feed stage location, reflux ratio, reboil ratio and number of stages can be determined, together with estimates of the column composition and temperature profiles. Adding the bubble point pressure curve to the driving force diagram gives the column pressure [2].

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The objective of this paper is to introduce a framework of driving-force-based algorithms for the synthesis and design of separation schemes. This framework comprises algorithms for the design of simple distillation columns (one feed with two products), complex columns (one or more feed and/or side products), separation of binary as well as ternary and/or multi-component mixtures and distillation column sequencing (multi-component separations). These algorithms can be visualized in two dimensions and therefore, they also provide a useful visualization of the problem solution and are valid for equilibrium as well as non-equilibrium systems, and ideal as well as non-ideal and/or reactive systems. The validation of these visual synthesis and design algorithms is illustrated through comparison of the results obtained through the use of rigorous models. It is shown that the optimal solutions obtained through the rigorous models not only lie close to the solution obtained with the driving-force-based algorithms but also may be used as very good initial estimates for the rigorous-model-based simulations. In this way, the efficiency and robustness of the rigorous-model-based solution methods is improved. This paper presents the application of some of the new algorithms belonging to the framework for synthesis and design of distillation columns. The examples highlight the simplicity, the visual effect as well as the accuracy of the algorithms.

2. Methodology The driving force has been defined by Gani and Bek-Pedersen [3], and is given by Fij = yi − xi =

xi βij − xi 1 + xi (βij − 1)

(1)

As seen in the model equation above, the driving force is defined as the difference in composition. The terms xi and yi denote liquid and vapour phase compositions of i, and Fij is the driving force for component i for property j. The relative separability βij is a parameter for component i with respect to property (or separation technique) j, which may or may not be composition-dependent and provides a measure of the driving force. Note that in Eq. (1), all the component indices are in principle with respect to the second component k (in the binary pair). However, since the composition of the second component k can always be estimated from that of component i, this index is not used in the Eq. (1) and the following equations in this paper. The parameter βij is obtained from a model describing the differences in composition between two co-existing phases, or measured composition data. Note in this context that βij = f (T, P, composition, θ), where θ indicates external factors such as resistance to mass and heat transfer. From the driving force model equation (Eq. (1)), it can also be noted that at fixed P (or T), two-dimensional plots of |Fij | versus xi (or yi ) can be made where each data point may also indicate a different T (or P). Therefore, these diagrams can be used to design

and configure separation schemes, including conditions of operation. It has already been shown by Gani and Bek-Pedersen [3] how the driving force diagrams with respect to relative volatility can be used for near-optimal (with respect to energy consumption) single distillation column design. Bek-Pedersen et al. [1] have shown how the driving force diagrams can be used to obtain near-optimal (with respect to energy consumption) sequence of distillation trains. Bek-Pedersen et al. [2] extended and modified these algorithms to allow for the presence of azeotropes in the multi-component mixtures, to generate hybrid separation schemes and to allow for scaling in the distillation column design when “extreme” conditions for the feed mixture exist, or non-sharp product compositions are desired. Note that as the location of the feed point on the Dx –Dy line is determined (see Fig. 1), the corresponding reflux and reboil ratios are also determined, based upon knowledge of the products (denoted by A and B). For only one high purity product, it is necessary to relocate the feed point in order to achieve the optimal combination of reboil and reflux ratios. Effects of non-key components are taken into account through mixture analysis related to mutual solubility, azeotropic data and the desired separation. In the proposed framework, six algorithms related to separation synthesis and retrofit design have been developed. The first algorithm deals with single-column distillation and serves as the basis for the development of the driving force concept, and therefore also the other algorithms. The second algorithm is for the design of complex distillation columns. The third algorithm deals with pressure allocation in a sequence of distillation columns. The fourth algorithm deals with the sequencing of simple distillation columns for multi-component separations and the corresponding conditions of operation. The fifth algorithm is for generation of hybrid separation schemes. The last algorithm deals with retrofit design of distillation columns. The application of these algorithms is dependent on the condition that two product specifications of the column lie on either sides of the maximum driving force. Otherwise, no appreciable difference can be noted when compared with other methods, as the driving force would not be maximized. In this paper all design algorithms (algorithms developed previously and new ones) have been integrated in an integrated framework for synthesis and design of distillation-based separation systems. First each of the algorithms are presented in terms of a step-by-step algorithm. Algorithm D1 (Single-distillation column design). Algorithm D1 is a base-case design (single distillation column), which is illustrated through Fig. 1. It is shown here how the driving force method is applied to obtain the easiest separation in a simple visual way, by the determination of driving force (its size and location) as the design parameter.

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253

0.3

D

FDi

Dy

Driving force, FDi

D' Dx B

A 0 0

1

xi Fig. 1. Driving force diagram for constant βij = 3.

This algorithm solves the following problem: given a mixture to be separated into two products in a distillation column with N stages, what is the optimal (with respect to cost of operation) feed plate location and the corresponding reflux ratio for different product purity specifications? 1. Generate or retrieve from a database the vapor–liquid data for the binary system in the column. For a multi-component system, select the two key components to define the “split” (separation task) and use them as the binary (key) mixture. 2. Calculate the driving force between the two (key) components at the actual operating pressure. Plot the calculated driving force as a function of the light key component composition. 3. Locate the point Dx as the point on the x-axis that corresponds to the largest driving force. 3.1. In case of an azeotrope, rescale the x-axis and locate the point Dx as the relative distance between the two points, one on each side of D, where the driving force is zero on the x-axis. (The two points are the azeotropic point and the bottom/top product.) 4. Specify the desired product specifications. 5. Calculate the minimum reflux ratio (from the slope of the line BD). 6. Determine whether rescaling needs to be applied. If condition 1 or 2 is satisfied, scaling is needed and go to 7. Otherwise, go to 8. 7. If condition 1 (see Table 1) is satisfied, go to 7.1. Else condition 2 (see Table 1) is satisfied and go to 7.2. 7.1. If condition 1a is satisfied, then relocate NF between 5 and 10% up in the column. Else condition 1b is satisfied, then relocate NF between 5 and 10% down in the column. 7.2. If condition 2a is satisfied, then relocate NF 10% down. Else, if condition 2b is satisfied, then relocate NF 5% down.

Else, if condition 2c is satisfied, then relocate NF 5% up. Else, if condition 2d is satisfied, then relocate NF 10% up. 8. Apply Eq. (1) (taking the scaling factors determined in step 4 into consideration) to compute NF for a given value of N. NF = N(1 − Dx )

(2)

Algorithm D2 (Design of complex distillation columns (one feed and three products)). To solve the design problem for one distillation column with three products (side-draw column), the following algorithm is proposed. The algorithm requires the two driving force diagrams between the two sets of binary key compounds. The algorithm then determines the location of the feed stage, as well as the side-draw stage and the minimum reflux ratio.

1. List the three key compounds according to their boiling points. C1 is the lightest boiling, C2 is the intermediate boiling, and C3 is the heaviest boiling. Table 1 Conditions of distillation column feed and products that require a scaling factor to be included in the design procedure Condition 1

Condition 2

(a) xHK,Z > 0.8 and Dx < 0.7

(a) [(1 − xLK,D )/(1 − xHK,B )] < 0.01 and Dx < 0.7 (b) [(1 − xLK,D )/(1 − xHK,B )] < 0.1 and Dx < 0.7 (c) [(1 − xHK,B )/(1 − xLK,D )] < 0.1 and Dx > 0.3 (d) [(1 − xHK,B )/(1 − xLK,D )] < 0.01 and Dx > 0.3

(b) xLK,Z > 0.8 and Dx > 0.3

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2. Generate or retrieve VLE data for components C1 and C2 , and for components C2 and C3 . 3. Check if C1 and C2 , or C2 and C3 , form an azeotrope. If yes: stop. 4. Calculate and plot the two driving force diagrams corresponding to the two sets of VLE data. 5. Determine which of the two plots exhibits the larger driving force. 6. Configure the column accordingly. 6.1. If the largest driving force occurs between C1 and C2 , then the feed should be between the top and the side draw in the column. 6.2. Else, if the largest driving force occurs between C2 and C3 , then the feed should be between the bottom and the side draw in the column. 7. Generate the joint driving force curve such that the largest total driving force is achieved. 7.1. If the feed is introduced between the top and the side draw, then the driving force curves should be joined such that the largest driving force is in the top of the column. 7.2. Else, if the feed is introduced between the bottom and the side draw, then the driving force curves should be joined such that the largest driving force is in the bottom of the column. 8. Give the number of plates, N, in the column. 9. Calculate the minimum reflux required in the column. 10. Give specifications on the products. Note that the size of the side draw must be consistent with the overall mass balance of the column. 11. From the joint driving force curve, determine the near-optimum position of the side-draw stage. 11.1. Locate the point DS where the two driving force curves intersect. 11.2. Calculate the near-optimum position of the side-draw stage from NS = N(1 − DS ), where N is counted from the top. 12. From the binary driving force plot that exhibits the largest driving force, locate the near-optimum feed stage location. 12.1. Locate the point Dx , the position on the composition axis corresponding to the largest driving force. 12.2. If the feed is introduced above the side draw, then calculate the near-optimum feed stage from NF = NS (1 − Dx ), where NS is counted from the top. (Note: NS is used instead of N because there are only NS stages in the sections represented by the driving force plot.) 12.3. Else, if the feed is introduced below the side draw, then calculate the near-optimum feed stage from NF = NS + (N − NS )(1 − Dx ). Algorithm D3 (Operating conditions). For the determination of operating pressures in the columns in a distillation

train, the following algorithm has been developed. For application of this driving-force-based method for determination of distillation column pressures, it is necessary that the distillation column sequence has already been determined. This could for example have been done by Algorithm S1 in this paper. Besides, an appropriate thermodynamic model for the prediction of mixture bubble points must be available. 1. Calculate data for the P–x–y diagram for the two key components in the first distillation column at the bubble point temperature of the feed. Set k = 1. 2. Draw the driving force curve from the data calculated in step 1 together with the bubble point curve. 2.1. Identify the point Dx as the composition xi , where the driving force reaches its maximum value (Dy ). 2.2. Identify the bubble point pressure at the point Dx . Allocate this pressure as the operating pressure for the condenser in distillation column k. 2.3. Based on a specified pressure drop per plate, determine the reboiler pressure for column k. 3. Calculate data for the P–x–y diagrams for the two key components in the next distillation column (k + 1) as a function of the temperature. Identify the temperature at which the P–x–y diagram gives the maximum bubble point pressure to within 5% of the reboiler pressure of column k. Select this temperature as the feed temperature. 4. Repeat step 3 until all the condenser and reboiler pressures have been allocated in the distillation column sequence. Note. If the pressure in one or more of the columns in the distillation train is found to be lower than atmospheric, a higher pressure in the first column should be considered as an alternative. Algorithm S1 (Sequencing of distillation columns). This algorithm provides a driving-force-based solution to the problem of synthesizing a distillation train. Input data to this algorithm is the identity of the compounds in the feed mixture and vapour–liquid phase compositions. The algorithm determines the NC-1 separation tasks (that is adjacent pairs to be separated) and the sequence in which they should occur. 1. List all the compounds in the mixture, NC, according to their relative separability, βij (or relative volatility). 2. Rank the compounds by normal boiling points. Retrieve the vapour–liquid data available for each binary pair of adjacent key compounds in the NC-1 splits. 3. Calculate the driving force diagrams for the binary pairs of key compounds, all at the same pressure (usually atmospheric pressure). 4. In total, NC-1 driving force curves are calculated. Set k = 1. If a binary pair forms an azeotrope, multiply the maximum driving force for this pair by a penalty factor

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6. 7.

8.

2. Calculate and plot the corresponding driving force diagrams for all separation techniques (each corresponding to a property j). 3. For the specified product purities, identify all feasible paths, allowing a switch from one separation technique to another if necessary, by moving along the driving force curves (see Fig. 2). Note: if one separation technique is unable to achieve the desired separation, switch to another that is feasible. 4. For each feasible path, identify the corresponding separation techniques and operating conditions from the driving force diagram (using Algorithm S1). 5. Select as the initial flowsheet one with the largest total driving force. 6. Use the information from steps 4 and 5 to formulate and solve a structural optimisation problem to determine the optimal flowsheet (not covered in this paper).

Note that this sequencing algorithm provides the largest total driving force for the generated flowsheet. In this way the overall separation becomes the easiest possible, and will thus require the least amount of energy input.

This algorithm formulates an optimisation problem in the last step and only the solution of the last step may provide the optimal solution. However, if the theory of driving force being inversely proportional to energy consumption and separability is correct, the result from step 5 should provide a very good estimate to the optimal solution (from step 6). In step 6, a rigorous model may be used. This algorithm therefore serves as a tool for formulation of the synthesis/design problem as an optimisation problem and for providing good initial estimates to the solution.

Algorithm S2 (Generation of hybrid separation sequence). This driving-force-based algorithm solves problems related to the identification of the optimal separation sequence(s) for a given separation task. The phase composition data for the compounds to be separated, for all the separation methods to be considered, are used as input data (available knowledge). Based on this data, the algorithm determines the set of feasible solutions and identifies the solution with the largest driving force. 1. For any binary pair of components that forms an azeotrope (or eutectic points or exhibits mutual solubility), retrieve the sets of composition data corresponding to two co-existing phases. Note that each set of data corresponds to a different separation technique. Also, two sets of data at different operating conditions for the same separation technique are considered here as two different separation techniques.

Algorithm R1 (Retrofit design of distillation columns). This algorithm solves retrofit problems where the design of any existing distillation column is known and it is necessary to determine if it can be used to separate a specific mixture (and the corresponding condition of operation) and/or the set of mixtures together with the conditions of operation where the use of the distillation column would be feasible.

0.6

0.6 Xi Max Max FDi

Xi Max

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0.0

Max FDi

5.

((Dy,min /Dy,max )Dy,azeotrope ) in order to make the value the smallest among all the binary pairs. For the split k, select the adjacent pair having the largest driving force. Add a distillation column for the separation task k. Remove the split between the selected adjacent pair from the list. Set k = k + 1, and repeat the algorithm from step 4 until only one split remains to be allocated. Otherwise, go to step 7. For each column of the distillation flowsheet, the feed stage location may now be determined, if desired, through Algorithm 1.

255

0.0 0

2

4

6

8

10

12

Constant Alfa Fig. 2. Plot of largest driving force, and the corresponding location of it as function of alfa.

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The starting point for this algorithm is the design of an existing column in terms of number of stages and a range of locations for the feed. Now, given the desired product specifications, the objective is to determine which mixtures can be separated into desired products and the corresponding conditions of operation. On the other hand, if the mixture identity is also known, then the algorithm simply checks if the desired separation is feasible. In this way, the retrofit design of distillation columns is the “reverse” of a distillation column design problem where given the mixture to be separated, the design of the column and the condition of operation is determined.

Table 2 Corresponding values of reflux ratio, minimum reflux ratio, number of stages, product purities and driving force FDimax

XLK,Dist

XLK,Bot

RRmin

RRmin × C

Nideal

0.045

0.995 0.98 0.95 0.90

0.005 0.02 0.05 0.10

9.89 9.56 8.9 8.22

14.83 14.36 13.35 12.33

96 71 54 41

0.065

0.995 0.98 0.95 0.90

0.005 0.02 0.05 0.10

7.33 7.10 6.64 5.72

11.0 10.65 9.96 8.58

67 50 38 29

0.101

0.995 0.98 0.95 0.90

0.005 0.02 0.05 0.10

4.50 4.35 4.05 3.56

6.74 6.52 6.08 5.33

44 33 25 19

0.146

0.995 0.98 0.95 0.90

0.005 0.02 0.05 0.10

2.94 2.84 2.63 2.29

4.41 4.26 3.95 3.44

31 23 18 14

0.172

0.995 0.98 0.95 0.90

0.005 0.02 0.05 0.10

2.35 2.26 2.09 1.80

3.53 3.40 3.13 2.70

27 20 15 12

0.195

0.995 0.98 0.95 0.90

0.005 0.02 0.05 0.10

2.06 1.98 1.82 1.57

3.09 2.97 2.74 2.35

24 18 14 11

0.225

0.995 0.98 0.95 0.90

0.005 0.02 0.05 0.10

1.73 1.67 1.53 1.37

2.60 2.50 2.30 1.97

21 16 12 9

0.268

0.995 0.98 0.95 0.90

0.005 0.02 0.05 0.10

1.37 1.31 1.20 1.02

2.06 1.97 1.80 1.52

18 13 10 8

0.382

0.995 0.98 0.95 0.90

0.005 0.02 0.05 0.10

0.82 0.78 0.70 0.57

1.23 1.17 1.05 0.86

13 10 8 6

0.478

0.995 0.98 0.95 0.90

0.005 0.02 0.05 0.10

0.54 0.51 0.44 0.34

0.81 0.76 0.67 0.51

10 8 6 5

1. Specify the desired product specifications (purities). 2. Determine the minimum reflux ratio RRmin (using Table 2) and actual reflux ratio RR (from Table 2 by selecting a value of C for the known Nideal . 3. Use Table 2 to check if for the calculated values of RRmin , the specified product purities can be matched. If this is not matched, return to step 2 with another product specification. 4. Determine the corresponding values of FDimax of the column from Table 2 using the known values of number of stages (last column). Use linear interpolation, if necessary. This may give more than one value of FDimax since a single value of Nideal in Table 2 corresponds to multiple values of FDimax . This gives an upper and lower bound of FDimax . 5. Determine the range of relative volatilities, a, (from Fig. 2) that corresponds to the calculated values of FDimax . This also produces an upper and lower bound for a. 6. For a known mixture to be separated, check if the mixture exhibits this range of a. If no: stop, as the use of the given distillation column is infeasible for the desired separation. If yes, go to step 8. If the mixture to be separated is not known, go to step 7. 7. Search a database or other knowledge bases in order to identify a binary pair or a ternary mixture (where the third component is a solvent, and calculating the a on a solvent-free basis) that matches the calculated a from step 4. Note that in this step, binary mixtures that match the calculated a and/or solvents that, when added to a binary mixture, match the calculated a can be determined. 8. Apply Algorithm D1 to verify the feed location. Note that Fig. 2 may be used together with Table 2 for retrofit design, when the number of stages and desired product purities are known and/or for simulation purposes. For example, given the mixture to be separated and the number of stages, determine the product compositions and the corresponding composition profiles. By following Algorithm R1, one in principle moves from the right side of Table 1 towards the left side. One knows the number of stages and the desired product purities, this then gives the minimum reflux ratio, which then again gives the driving force available. Once the driving force is known, the range of relative volatility, α, can be found from Fig. 2. In Table 1, a value for C = 1.5 has been applied, where C is the multiplication factor of RR to RRmin . The algorithms presented above have been integrated into a systematic framework for synthesis, design and retrofit. This framework is illustrated in Fig. 3. Here the algorithms are classified in terms of classes and, within each categories (level 1), calculations (level 2). The categories of level 1 define the problem type in terms of synthesis, design and retrofit. The calculation or level 2 defines the detailed calculations and sub-problems under any category.

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Level 2

Level 1

Synthesis of Distillation Based Separation Schemes

Design of Distillation Columns

257

Retrofit of Distillation Columns

Sequencing of Distillation Columns

Hybrid Separation Schemes

Simple Distillation Column Design

Complex Distillation Column Design

Operating Conditions

Retrofit Design of Distillation Columns

algorithm S1

algorithm S2

algorithm D1

algorithm D2

algorithm D4

algorithm R1

Given: Composition and Key Compounds

Given: xDist, xBot, Experimental Phase Eq. Data

Given:

Given:

P, NP, xDist, xBot

P, NP, x Dist, xBot

Find: Order of splits in the distillation scheme

Find: Combination of Units to achieve separation

Find:

Find:

RRmin, NF

RRmin, NF, NS

Given: Compounds in splits, Inlet Pressure

Given:

Find: Operating Pressure in Distillation Seq.

Find:

NP, RR min

NF, xDist, xBot

Fig. 3. Framework for synthesis, design and retrofit, connecting the algorithms presented.

Level 1: In the first level the character of the problem is determined, and it is assigned to one of the three categories: (1) synthesis, (2) design and (3) retrofit. While the retrofit category only has one sub-problem associated to it, the synthesis and design categories have more sub-problems associated.

Level 2: In the second level, the solution paths for individual synthesis, design and retrofit problems are outlined. Each problem has a driving-force-based algorithm associated to it. For the individual algorithm, it is then given what is required as input to the algorithm, and what is the

Table 3 Data sheet for Example 1 Action Algorithm S2

Steps 1 and 2

Identify azeotrope and retrieve data for different separation techniques

Step 3

Step 4

Each component must be near unity in composition (thus the azeotrope must be broken). Identify feasible paths Identify separation techniques for each feasible path

Step 5

Choose combination with largest driving force

Validation Step 1 Step 2

Identification of alternatives Rigorous calculation of energy duties

Alternatives: (1) Distillation and pervaporation; or (2) distillation with solvent; or (3) distillation with solvent and pervaporation A hybrid flowsheet of distillation combined with pervaporation is chosen as initial flowsheet Distillation + pervaporation. Add solvent to distillation Distillation and pervaporation consumes a maximum of 73% of the energy for a distillation column and a solvent recovery column

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Table 4 Data sheet for example 2a Action

Problem 1 feed (0.05, 0.90, 0.05)

Algorithm 2 0.20

PentaneHexane

0.16

Calculate 2 FD curves; Dx = 0.45; Pentane–hexane exhibits the larger driving force

0.12

FDi

Steps 1–5

HexaneHeptane

0.08 0.04 0.00 0.0

0.2

0.4

0.6

0.8

1.0

Composition (x light key) 0.20

D

III

Steps 6, 7

II

Generate joint curve. Ds = 0.32

FDi

F

0.16

HexaneHeptane

0.12

PentaneHexane

0.08

S

0.04

I

0.00 0.0

B Step Step Step Step Step Step Step

8 9 10a 10b 10c 11 12

0.2

0.4

0.6

0.8

1.0

Relative composition Give number of stages Determine RRmin Give Spec 1 Give Spec 2 Determine side draw Determine NS Determine NF

N = 36 (given already) 2.02 XD (pentane) = 0.998 XB (heptane) = 0.85 Side draw = feed × 0.90 NS = 36(1–0.32) = 24.48 ∼ 24 NF = 24(1–0.45) = 13.2 ∼ 13

Validation

Step 1

Simulation for various NS . NSopt = 23

Reboiler Duty (GJ/h)

23 21 19 17 15 17

19

21

23

25

27

Side Draw Stage, NS

Step 2

Simulation for various NF . NFopt = 14

Reboiler Duty (GJ/h)

17.0 16.5 16.0 15.5 15.0 10

12

14

16

Feed Stage Location, NF

Step 3

Actual RR/V/F

116.7/5.78

18

20

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259

Table 5 Data sheet for example 2b Action

Problem 1 feed (0.34, 0.33, 0.33)

Algorithm 2 0.20

PentaneHexane

0.16

Hexane Heptane

FDi

0.12

Calculate 2 FD curves; Dx = 0.45

Steps 1–5

0.08 0.04 0.00 0.0

0.2

0.4

0.6

0.8

1.0

Composition (x light key) 0.20

D

III II

Generate joint curve; Ds = 0.32

Steps 6, 7

FDi

F

0.16

HexaneHeptane

0.12

PentaneHexane

0.08

S 0.04

I

0.00 0.0

B Step Step Step Step Step Step Step

8 9 10a 10b 10c 11 12

0.2

0.4

0.6

0.8

1.0

Relative composition Give number of stages Determine Rrmin Give Spec 1 Give Spec 2 Determine side draw Determine NS Determine NF

N = 36 (given already) 2.02 XD (pentane) = 0.998 XB (heptane) = 0.85 Side draw = feed × 0.33 NS = 36(1–0.32) = 24.48 ∼ 24 NF = 24(1–0.45) = 13.2 ∼ 13

Validation

Step 1

Simulation for various NS ; NSopt = 24

Reboiler Duty (GJ/h)

8

7

6

5 19

21

23

25

27

29

Side Draw Stage, NS

Step 2

Simulation for various NF ; NFopt = 12

Reboiler Duty (GJ/h)

6.5

6.0

5.5

5.0 8

10

12

14

16

Feed Stage Location, NF

Step 3

Actual RR/V/F

4.91/1.67

18

20

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Table 6 Data sheet for Example 3 Action

Problem 1 feed (0.33, 0.33, 0.34)

FDi

Algorithm 2 0.16

Benzene Toluene

0.12

Toluene - Xylene

0.08

Calculate 2 FD curves; Dx = 0.46

Steps 1–5

0.04

0.00 0.0

0.2

0.4

0.6

0.8

1.0

Composition, Light Key Compound 0.16

0.12

D

FDi

III F

Steps 6, 7

0.08

Generate joint curve; DS = 0.38

II

Benzene Toluene

0.04

S

Toluene - Xylene

I 0.00 0.0

0.2

0.4

B

Step Step Step Step Step Step Step

8 9 10a 10b 10c 11 12

0.6

0.8

1.0

Relative composition

Give number of stages Determine RRmin Give Spec 1 Give Spec 2 Determine side draw Determine NS Determine NF

N = 40 (given already) 3.28 XD (benzene) = 0.995 XB (xylene) = 0.92 Side draw = feed × 0.33 NS = 40(1–0.38) = 24 NF = 24(1–0.46) = 12.96 = 12/13

Validation

Step 1

Simulation for various NS ; NSopt = 23

Reboiler Duty (GJ/h)

28 26 24 22 20 18 18

20

22

24

26

28

Side Draw Stage, NS

Step 2

Simulation for various NF ; NFopt = 12

Reboiler Duty (GJ/h)

22.0 21.5 21.0 20.5 20.0 8

10

12

Feed Plate Location, NF

Step 3

Actual RR/V/F

21.7/7.13

14

16

E. Bek-Pedersen, R. Gani / Chemical Engineering and Processing 43 (2004) 251–262

output from the algorithm. In this way it is easy to get a clear overview of what is needed for applying the algorithms in a systematic way. 3. Applications The applicability and scope of the driving-force-based algorithms are illustrated by a number of application examples. Algorithm D1 has been verified for a great number of binary and multi-component mixtures, some of which have been highlighted in [3]. These examples show clearly that the minimum energy consumption corresponds to the feed stage located on the relative position of the largest driving force, as predicted according to Algorithm D1. In all these examples the energy consumption has been calculated for the following specified variables, NP , NF , product specifications (points A, B in Fig. 1) and feed mixture details. Applications of Algorithms S1, S2 and D3 have been reported elsewhere (see, e.g. [1] for S1 application examples, and [2] for S2 and D3 application examples). In this paper, therefore, examples highlighting the applications of the most recent developments in the framework for synthesis and design are presented. One example of Algorithm S2 is also given; otherwise, the focus is on the algorithms of complex distillation design (Algorithm D2) and retrofit design (Algorithm R1). In each example an appropriate property model has been used to determine the driving force as a function of composition, and the algorithms have been followed according to the steps outlined above. For Algorithm D2, a large number of examples have been worked out. This is partly due to the fact that the same systems have been applied for various feed compositions (see also Example 2). The results obtained from the Algorithms D2, S2 and R1 have been verified through rigorous-model-based simulations (using the steady state

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distillation model in PRO/II [4]). The results from the examples are given in the form of individual data sheets, where the individual steps of each algorithm can be followed easily. Example 1 (Separation of ethanol and water). This is a well-known example of separation of ethanol and water, which forms a binary azeotrope. This example serves to illustrate Algorithm S2. In the figure given in Table 3, the driving force curves for three different two-phase separation techniques are given. These are then compared throughout the range of composition for the desired separation, and the combination of separation techniques exhibiting the largest total driving force is identified. As illustrated in Table 3, the combination of distillation with a membrane unit for pervaporation clearly is more efficient considering only energy consumption during operation. Example 2 (Separation of three hydrocarbons). In this example, the separation of pentane, hexane and heptane in one column is considered. Tedder and Rudd [5] studied this system in the context of the design of complex distillation columns. Two scenarios are treated in this example: one where the feed mixture contains hexane (90%) and 5% of each of the two other compounds, and one where the feed mixture is nearly equimolar. In both cases it is given that the columns operate at 5 atm pressure and have 36 stages. The two driving force diagrams for this system are given as figures in Tables 4 and 5. It is clearly seen that the pentane–hexane split is the easier split (in terms of size of driving force). Therefore this split is the primary split, which is then followed by a stripping section in the column to perform the split between hexane and heptane, as shown in the sketch of the column under steps 6 and 7 in Tables 4 and 5.

Table 7 Data sheet for Example 4 Action Algorithm R1 Step 1

Determine desired products

XB,HK = 0.995, XD,LK = 0.995

Steps 2, 3 Step 4 Step 5

Find RRmin Find FDimax Find range of α

Rrmin ∼ 6.4 ∼0.07 α ∼ 0.33–0.34

Step 7

Check for mixtures with these properties

(1) (2) (3) (4) (5)

Step 8

Check for feed location

For all the above binary mixtures, the feed location is matched.

Butane–i-butane, 5 atm Cycloheptanol–cyclooctanol, 5 atm 1,4-Butanediol–1,3-butanediol, 15 atm Hexanol–hexanal, 12 atm Diethylene glycol–1,6-hexanediol, 3 atm

α ∼ 1.33–1.34, FDi ∼ 0.074 α ∼ 1.34–1.38, FDi ∼ 0.080 α ∼ 1.3–1.85, FDi ∼ 0.065−−1.45 α ∼ 1.24–1.57, FDi ∼ 0.05−−1.0 α ∼ 1.22–1.34, FDi ∼ 0.05−−0.07

Verification Mixture 1 Mixture 2 Mixture 3 Mixture 4 Mixture 5

Butane–i-butane, 5 atm Cycloheptanol–cycleoctanol, 5 atm 1,4-Butanediol–1,3-butanediol, 15 atm Hexanol–hexanal, 12 atm Diethylene glycol–1,6-hexanediol, 3 atm

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When the order of the splits has been determined, the actual positions of the feed and the side draw are determined accordingly. The results of the predictions have been verified with rigorous simulation, as is indicated in Tables 4 and 5. Example 3 (Separation of BTX mixture). Another example is a classical separation problem, where the mixture of benzene, toluene and xylene is to be separated. This mixture is also to be separated in a column with three product streams, and Algorithm D2 has been applied to solve this problem. The column is specified to operate at 10 atm pressure and has 40 stages. Just as in Example 2, the steps of the algorithm are presented in a schematic form in Table 6. Example 4 (Retrofit design). This is an example of the retrofit Algorithm R1. Here we are dealing with a column of 60 stages, and we have options to feed on stages 33 and 38. The steps outlined above for Algorithm R1 has been followed, making use of Table 2, and Fig. 2. The results of the example are listed in Table 7. With the given product specifications, and the corresponding driving force, the corresponding range of relative volatility was easily identified, and three mixtures suitable for separation in this column were immediately found on this basis. Note that in step 6, different mixtures match the calculated relative volatilities at different operating pressures.

4. Conclusions An integrated framework for synthesis and design of distillation-based separation systems has been developed and validated. The framework is based on the driving force approach [3] and further extends it, enabling thereby the solution of a wide range of problems related to distillation columns. The framework consists of six algorithms that in an integrated manner interactively enable the visual determination of the near-optimal (if not optimal) design, as well as separation sequences together with the corresponding condition of operation for both conventional and complex distillation columns. The integrated approach also allows the generation of hybrid separation schemes where different separation techniques are allowed. With this approach, the only requirements for application of the integrated framework are the co-existing phase composition data. The approach requires no rigorous simulation or optimisation. The methodology not only identifies the feasibility of different separation techniques for a given separation task, but also indicates the optimum methods of separation. Consequently, it is possible to make early decisions on separation sequences and distillation configurations that are near-optimum solutions. It is evident that this extended methodology is able to generate near-optimum designs of even very complicated

distillation columns, based on the simple and visual driving force techniques. Finally, the results appear to confirm the theory that separation at the highest driving force is the easiest separation and, therefore, should require a near minimum of energy since energy is needed to create the driving force. One limitation of the method is that the two adjacent products from the distillation column must lie on either side of the maximum driving force.

Appendix A. Nomenclature A B C D Ds Dx Dy F Fij , FDi HK LK RR RRmin N NF NP NS P T xi yi

product composition specification (see Fig. 1) product composition specification (see Fig. 1) multiplication factor for RRmin to RR largest driving force relative position of side-draw driving force relative position of largest driving force size of largest driving force feed (kmol/h) driving force heavy key compound light key compound reflux ratio minimum reflux ratio number of stages feed stage number of stages side draw stage pressure (atm) temperature (K) liquid composition of compound i vapour composition of compound i

Greek letters α relative volatility β relative separability θ resistance factor Subscripts B, Bot bottom composition D, Dist distillate composition Z feed composition

References [1] E. Bek-Pedersen, M. Hostrup, R. Gani, Eur. Symp. Comput. Aid. Process Eng. 10 (2000) 955–960. [2] E. Bek-Pedersen, R. Gani, O. Levaux, Comput. Chem. Eng. 24 (2000) 253–259. [3] R. Gani, E. Bek-Pedersen, AIChE J. 46 (6) (2000) 1271–1274. [4] PRO-II Users Guide, Simulation Sciences—An Invensys Company, Brea, CA, 2001. [5] D.W. Tedder, D.F. Rudd, AIChE J. 24 (2) (1978) 303–315.