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DESIGN AND OPTIMIZATION OF FULLY THERMALLY COUPLED DISTILLATION COLUMNS Part 1: Preliminary Design and Optimization Methodology K. A. AMMINUDIN 1 , R. SMITH, D. Y.-C. THONG2 , and G. P. TOWLER3 Department of Process Integration; UMIST; Manchester; UK.

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he design of a fully thermally coupled distillation column, or its thermodynamically equivalent arrangement, the dividing wall distillation column, is more complex than conventional arrangements because of the greater number of degrees of freedom. All of these degrees of freedom must be initialized before rigorous simulation can be performed. The distribution of stages in the various sections of the column, the re ux ratio, vapour and liquid splits on either side of the fully thermally coupled columns and feed condition must all be initialized. Yet these are important degrees of freedom that all interact with each other in the design. A new approach to the design of fully thermally coupled columns is proposed in this paper. The procedure uses the equilibrium stage composition concept developed for the design of azeotropic distillation systems1. The method is semi-rigorous in nature, providing an initial design that is very close to the results of rigorous simulation. The approach then allows the degrees of freedom to be optimized simultaneously and an optimized initial design established for rigorous simulation. A case study has been used to demonstrate the application of the new method. Keywords: dividing wall distillation; Petyluk column; thermal coupling; short cut design; stage composition lines; optimization.

INTRODUCTION

and reboiler on the pre-fractionator) and the Petyluk arrangement. Figure 1a shows a Petyluk column. Its salient feature lies in the use of the pre-fractionator column from which a non-sharp split of light (A), medium (B) and heavy (C) components into two mixtures occurs. The top product of the pre-fractionator contains A and B and the bottom product contains B and C. These mixtures are introduced into the main column by the thermal coupling arrangement of the top and the bottom of the pre-fractionator. In the main column, these components are separated into three distinct products. Most of the energy savings in the Petyluk column arrangement are attributed to the pre-fractionator. A major source of separation inef ciency in conventional multicomponent distillation is the re-mixing effects that occur. A signi cant reduction in the re-mixing inef ciency is provided by a non-sharp split in the pre-fractionator10. In addition, the pre-fractionator minimizes the mixing losses at the feed tray. The distribution of the middle key component, B, between the top and the bottom of the pre-fractionator, allows greater freedom to match the column feed composition with the composition on one of the trays in the prefractionator11. These two major improvements can lead to typical energy savings of about 30% compared to the performance of a conventional distillation arrangement.

The energy consumption of distillation can have a signi cant in uence on overall plant pro tability. As a result, various strategies have been adopted to improve the energy performance of distillation systems. One non-conventional distillation system is the use of thermal coupling in which the transfer of heat is accomplished by a direct contact of material ow between the column. These thermal coupling arrangements are the side stripper, the side recti er and the fully thermally coupled column. Of the possible thermal coupling arrangements, the side stripper, has been widely used in re nery distillation2 and the side recti er has been used in cryogenic air separation3. Recently, the least industrially applied arrangement, the fully thermally coupled column, commonly known as the Petyluk column4, has gained acceptance in the process industries5 even though its concept was established some 50 years ago6–8. Alternative thermally coupled arrangements to that of Petyluk4 have been suggested by Agrawal and Fidkowski9. These alternative arrangements are a combination of the classical pre-fractionator arrangement (with partial condenser

Present address: 1Universiti Teknologi Petronas; Perak; Malaysia. 2 Degussa-Huls; Hanau; Germany. 3UOP; Des Plaines; Illinois; USA.

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AMMINUDIN et al. distribution and number of plates in each of the column sections, re ux ratio, liquid and vapour splits each side of the dividing wall, the feed stage locations and side-draw locations, must be established before simulation can be performed. These degrees of freedom all interact with each other and need to be optimized simultaneously to obtain the best design. This paper will develop a new method for the design and optimization of dividing wall columns, which follows a similar design concept to the design of the fully thermally coupled columns. PREVIOUS DESIGN PROCEDURES

Figure 1. The fully thermally coupled column (a) and the dividing wall column (b) are thermodynamically equivalent for no heat transfer across the dividing wall.

Instead of having an external pre-fractionator, the prefractionator can be incorporated into a single shell arrangement by installing an internal wall. This vertical wall divides the column into the pre-fractionator and the main column. This arrangement is called the dividing wall column or partition column as illustrated in Figure 1b. The energy savings of the Petyluk and dividing wall column arrangements are expected to be similar due to the fact that they are thermodynamically equivalent arrangements, providing there is no heat transfer across the dividing wall. However, the dividing wall column offers further bene ts in terms of reducing capital cost. Its single shell feature, single reboiler and condenser can save capital expenditure of typically 30% compared to the capital cost of the conventional two-column sequence on a stand-alone basis10. Lestak et al.12, examined the effect of heat transfer across the dividing wall and concluded that the dividing wall should be insulated for best performance. Although the two arrangements in Figure 1 are thermodynamically equivalent, the dividing wall column is preferred in practice, both for the capital cost incentives described above and to avoid the practical dif culties of taking a vapour side-draw from the main column as required by the Petyluk arrangement. Control studies have been carried out both theoretically and experimentally to demonstrate that the dividing wall column can be operated and controlled successfully in the same manner as conventional side-draw columns13. Despite the advantages of the dividing wall column, the process industries have been reluctant to apply them commercially. BASF AG has been the rst company to apply the dividing wall column commercially and have successfully commissioned and operated more than 12 such columns14,15. MW Kellogg Limited, together with BP (now BP Amoco), successfully commissioned a dividing wall column at BP’s Coryton re nery, UK16. Applied in a retro t situation, this application of the dividing wall column managed not only to double the throughput of the column, but also to improve the middle product yield by more than 50% compared with the previous simple side draw column. Sumitomo Heavy Industries Co., together with Kyowa Yuka, have also developed a dividing wall column17. Design of the dividing wall column is more complex than a simple column because there are more degrees of freedom that need to be speci ed. Key variables and parameters such as the

Most researchers18–23 concentrated their effort on developing short cut design procedures that allowed process screening and initialization for rigorous simulation. The methods were restricted in their application by simplifying assumptions such as ternary mixtures, sharp separations, saturated liquid feeds, constant molal over ow and constant relative volatility. Triantafyllou and Smith10 proposed a short cut design method for design and optimization of the fully thermally coupled column. Using a three-column model, they applied the conventional Fenske-Underwood-Gilliland short cut design technique in each column, not only for process screening, but also to provide a reliable initialization for rigorous simulation. They developed a simple optimization approach by considering both energy (minimizing the reboiler duty) and capital costs (minimizing the number of trays), instead of using the minimum vapour ow criteria24. Triantafyllou and Smith10 identi ed several design variables that need to be optimized, such as the re ux ratios and the recoveries of the key components in the pre-fractionator. They refuted the claim that was made by earlier authors25,26 that the vapour and liquid splits to the pre-fractionator are independent of the reboiler duty. In addition, further improvements to the earlier method of Triantafyllou and Smith10 were made to cater for wider applications, especially in petrochemical and oil re ning applications27. Despite the fact that the method of Triantafyllou and Smith10 allowed the trade-off between the energy and capital costs to be examined, it has a number of signi cant drawbacks. In particular the use of the Gilliland correlation to determine the number of trays can lead to signi cant errors due to its inherent limitations. Also, the use of the Kirkbride Equation to determine the location of the feed stage and the location of the stage numbers for the thermal coupling links to the main column leads to errors when the initial design is transferred to rigorous simulation. More recently Dunnebier and Pentelides28 used rigorous models in conjunction with the mathematical programming. However, this is achieved at the expense of the signi cant computing times required and is computationally more demanding relative to short cut design procedures. Also, the discrete (distribution of the trays) and continuous aspects of the problem are not handled adequately by this approach. A new short cut design procedure will now be developed based on a semi-rigorous model from the equilibrium stage composition concept, which has been applied previously to azeotropic separation problems29. In contrast with conventional short cut design procedures, such as the FenskeUnderwood-Gilliland technique, the method employing the equilibrium stage composition concept starts from the given Trans IChemE, Vol 79, Part A, October 2001

DESIGN AND OPTIMIZATION OF DISTILLATION COLUMNS: PART 1

products and works backwards to establish the design parameters. Therefore, the procedure needs to rst estimate feasible products from basic design information, such as feed condition and the product speci cations. Only after the feasible products are estimated can we proceed to design and optimize the fully thermally coupled column.

PRODUCT FEASIBILITY ESTIMATES The Need For Feasible Product Estimates In a typical separation problem two basic pieces of design information will usually be speci ed. Firstly, the feed compositions and its condition are given, and secondly the separation objective is given in terms of the product recovery and=or purity requirements of certain products. There is rarely any information on the product distributions at the initial stages of a design because at the conceptual design stage, the product distribution is typically not available until a rigorous simulation has been carried out. Another issue regarding the product distribution is feasibility. If a feasible product is established, it means that it is always possible to achieve such a product distribution from a distillation column with the appropriate number of trays and re ux. Thus a feasible product always implies a feasible distillation column. For this reason, the authors cannot simply specify arbitrarily the product distribution because it is not possible to guarantee such product compositions will be feasible. This is particularly true in multi-component separations involving more than three components, where there is considerable uncertainty in product distribution. This issue justi es a systematic approach to account for a feasible product distribution.

Introduction to the Product Feasibility Concept Most of the techniques developed to address product feasibility originate from work on the separation of azeotropic mixtures. Van Dongen and Doherty30 proposed an approximate technique to calculate composition pro les based on nite difference material balance equations. Starting from the product compositions, the liquid composition pro les were generated from different values of boil-ups and re ux ratios. If the pro les intersected then the proposed product was achievable in a distillation column. If the pro les did not intersect, then the proposed product and parameters corresponded to an infeasible design. Their method allowed the residue curve to be used for synthesis of continuous columns at total re ux. Similarly, distillation line maps31, which represent liquid composition pro le of stage columns at total re ux, can be used to establish continuous column feasibility. In addition, Van Dongen and Doherty30 determined all feasible products for a given feed at total re ux. At arbitrary re ux, Wahnschafft et al.32 and Fidkowski et al.33 proposed a procedure to determine product feasibility from feed composition, feed quality and column pressure to generate the feasible product regions or ‘bow-tie’ regions. Castillo et al.1 proposed the operation leaf for a ternary mixture separation as a visualization tool to determine whether product distribution was feasible. Each operation leaf represents a column section, corresponding to either rectifying or stripping section. Figure 2 illustrates an operation leaf for a stripping section. The leaf represents the composition pro les for different boil-up ratios at a speci ed bottom product, bi. The composition pro les can be calculated independently using the mass balance and an appropriate vapour-liquid-equilibrium (VLE) model29. Each point on the composition pro le represents the liquid composition on a certain equilibrium stage. Similarly, the operation leaf for the rectifying section can be generated

Figure 2. Operation leaf for stripping section generated by the composition pro les at different boil-up ratios for a given bottom product bi.

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Chloroform, 61.2°C

from the composition pro les for different re ux ratios for a speci ed distillate product. The operation leaf can be interpreted as a region of possible loci that the composition pro le can follow to meet the given product. Its unique feature lies in the leaf boundary, which corresponds to the two-operation limits of both total re ux and minimum re ux. Hence, any composition in the operation leaf can be achieved in a column section to achieve the desired product under appropriate re ux=boil-up ratios. On the other hand, any separation involving compositions outside the leaf will not achieve the desired product. Having brie y discussed the basic feature of the operation leaf, let us consider using the operation leaf concept to establish product feasibility for two potential products from a distillation column. As the operation leaves de ne the overall bounds for operation, the values of the re ux and boil-up ratios do not need to be repeatedly found to produce a point of intersection. The product feasibility must be established to ensure whether there is overlap between the operation leaves32. It follows that composition pro les intersect in the overlap region. Figure 3 demonstrates the feasibility of the proposed products using operation leaves29. In this illustration, three operation leaves corresponding to the distillate product D and two proposed bottom products, B1 and B2 are constructed. The leaves for products B1 and D overlap, indicating the feasibility of the proposed products, but the leaves for products D and B2 do not overlap, implying unfeasible separation to produce D and B2. Castillo29 also claimed that the constant molal over ow assumption does not contribute to a major source of error in generating composition pro les. He observed that the operation leaf is changed only slightly when this assumption is relaxed.

In summary, the use of the operation leaf allows a process designer to establish the feasibility of proposed products at a nite re ux. Its visualization capability apparently limits its application to ternary mixture systems. Even though the procedure to generate the composition pro les is general and can be extended easily for more than three components, the graphical visualization of composition space to establish product feasibility for such systems becomes extremely dif cult in multi-dimensional space. This substantially reduces the chances of using graphical tools to analyse such systems.

Comments on the Previous Work on Product Feasibility In the previous section, one feature common to all the procedures is that the procedures only apply to systems of ternary mixtures and use ternary diagrams extensively. To establish the product feasibility, two methods were normally taken, either starting from the proposed products29,30, or starting from a given feed32,33. If the proposed products are unfeasible, other products may be suggested. This iterative approach in searching for the feasible products is not systematic, especially when more than three components are involved. Since these procedures were mainly developed for azeotropic mixtures, extending the procedure to establish the product feasibility for multicomponent azeotropic mixtures would be extremely dif cult because the volatility order changes with compositions in azeotropic mixtures. Fortunately, for ideal mixtures, it is relatively easy to estimate a feasible product distribution from a given feed, as the volatility order of the components does not change with composition. Thus, the product distribution estimate is readily predictable for non-azeotropic mixtures.

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0.8 Azeotrope 64.5°C

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B1

D

0 0

Benzene, 80.2°C

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1

Acetone, 56.1°C

Figure 3. Operation leaves for the proposed products—D and B1 are feasible, D and B2 are unfeasible29.

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DESIGN AND OPTIMIZATION OF DISTILLATION COLUMNS: PART 1 Procedure to Estimate Product Feasibility Assumptions Certain assumptions must be made in order to establish a procedure for estimating product distribution from basic design information. These assumptions are as follows: a) Simplify to Constant Molal Over ow and Constant Relative Volatility In the absence of any other design information, and the fact that this work is focussed on mixtures not involving highly non-ideal behaviour, it is justi able to assume constant molal over ow and constant relative volatility at this stage. Such simplifying assumptions allow us to adopt a conventional short cut design technique for the purpose of nding feasible products. Despite the inherent limitations of the short cut design techniques for determining the number of theoretical stages and feed and side-draw stages, short cut techniques are good enough to provide a reliable estimate of product composition at this stage. The short cut design technique is not used here to establish any design parameters. b) Estimate Product Distribution at Minimum Re ux Any distillation operation lies between the two limits of total re ux and minimum re ux. At total re ux, the number of stages is minimized with maximum energy requirement. On the other hand, at minimum re ux, separation requires minimum energy, but the number of stages becomes in nite. Both conditions can be used to estimate a feasible product distribution. In the case of total re ux, the Fenske Equation can be applied to estimate the distribution of nonkey components. Similarly, at minimum re ux, the Underwood Equations can be used. The component distributions from both conditions are not expected to be the same, particularly for more than three components34. As a result, an appropriate choice between the two conditions must be made. Typically, during the conceptual design stage, a minimum energy consumption criterion is selected for a rapid assessment of distillation con gurations in the process screening stage35. The minimum energy consumption provides useful information, not only about energy savings, but also on capital cost, as column dimensions such as diameter and heat transfer areas depend on energy consumption. For this reason, use of the minimum re ux condition is justi ed to estimate a feasible product distribution.

Design Model Figure 4 illustrates a Petyluk column model and a simple three-column model for use in estimating the feasible products at minimum re ux. The detailed formulation of the model involved can be obtained from Amminudin27.

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D2 PS2 PF2

F1

B2 + D3

COL1

D2

D1MIN

M2

=

COL2

PF2 F1

PS2 B2

COL1

D3

PS3 PF3

PF3

COL3 B1MIN

PS3 B3

B3

Figure 4. Feasible product distribution in each of the product streams (D2, B2, D3 and B3) is estimated at minimum re ux.

arrangement (this can be accomplished by manipulating the design variables (degrees of freedom) corresponding to the recoveries from Columns 1, 2 and 3 using any non-linear equation solver, such as GAMS36):

· Compositions from Streams B2 and D3, in terms of mole fraction, should be equal to re ect middle product stream, especially for the middle key components. It is important to note that the equalization of vapour between the bottom of Column 2 and the top of Column 3 is not met for the purpose of estimating feasible products, because the authors have utilized all the degrees of freedom in satisfying the condition of the middle product composition. In addition, the feasible products and the minimum vapour ows are determined at minimum re ux, which corresponds with an in nite number of stages. Hence, it is not necessary to meet the equalization vapour ow condition at this stage11. The authors shall incorporate the equalization of vapour ow condition later when they consider designing the Petyluk column or dividing wall column in greater detail. In contrast with the proposed method here, Carlberg and Westerberg37 used the equalization vapour ow condition to nd the minimum re ux region in the Petyluk column. However, it has been observed that the bottom product from Column 2 and the top product of Column 3, which represents the middle product, are not equal in terms of composition; · overall mass balance satis ed; · product speci cations in terms of product recovery and=or purity. Output · compositions of top product (D2), middle product (B2 + D3), and bottom product (B3) in terms of mole fraction; · minimum re ux ratios; · minimum boil-up ratios. DESIGN AND OPTIMIZATION

Conditions to be met The following conditions must be satis ed to ensure the products, overall mass balance and product speci cations re ect the Petyluk column and the dividing wall column Trans IChemE, Vol 79, Part A, October 2001

Following estimation of a feasible product distribution, the second stage of the procedure involves the use of the equilibrium stage composition concept to estimate the number of stages, ow rates, feed stage and side draw locations for the fully thermally coupled column.

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A Review on the Equilibrium Stage Composition Concept Earlier, the need for an overlap of the operation leaves for column feasibility has been reviewed. However, for a staged column, an overlap of operation leaves is not a suf cient condition for establishing column feasibility. This is because the changes in the liquid composition pro les from a staged column are discrete as illustrated in Figure 5. The column is, thus, feasible when there is an exact overlap of liquid composition points from both the rectifying and stripping section leaves. A graphical representation has been proposed that is useful for stage-column design purposes that is based on a rearrangement of information from the operation leaves1. This representation, de ned as a staged composition line, is a locus of liquid compositions on a given stage at any re ux or boil-up ratio1. The line radiates across the operation leaf by connecting the liquid composition points from the same stage at different re ux or boil-up, as illustrated in Figure 6 for a stripping section. The line offers signi cant advantages compared with operating pro les, as every point on the stage composition line is achievable at some re ux or boil-up ratio. Similarly, a staged-composition line for a rectifying section can be made. While an overlap of rectifying and stripping section leaves is still required to ensure column feasibility, an intersection of a pair of staged composition lines corresponding to the rectifying and stripping sections is suf cient for staged column feasibility. At any given re ux and boil-up ratio, the intersection point re ects the feed tray composition and the feed tray can be determined by counting the lines up to the intersection point. Figure 7 demonstrates the column feasibility using the stagedcomposition lines. At re ux ratio of 4.4 and a boil-up ratio of 2.9, a feed stage occurs at stage 35 for the rectifying section and stage 10 for the stripping section. A corresponding column shows the transformation from the ternary diagram. A column design based on the stage-composition line procedure agrees well with the results generated from rigorous simulation, providing the same VLE model is used. This follows from the fact that the intersection of

0. 5

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s=5.0 0. 3

bi

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Figure 5. For staged columns, gaps between liquid composition points are meaningless.

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s=6 s=10 0

0

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0.8

s=20 1

Figure 6. All points on a stage-composition line are achievable at any boil-up ratios.

Figure 7. The intersection of a pair of stage composition lines is suf cient for a staged-column feasibility.

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DESIGN AND OPTIMIZATION OF DISTILLATION COLUMNS: PART 1 the staged composition lines is an exact converged solution, subject to errors in VLE or enthalpy models38. The procedure, which only maintains the constant molal over ow assumption, is more rigorous than traditional short-cut methods as the mass balance is solved rigorously at each stage using a VLE model, and thus removes the constant relative volatility assumption. The procedure is in fact not restricted to the constant molal over ow assumption and even this feature can be removed if desired. Multi-Component Mixtures The intersection of the staged composition lines and the composition pro les can be easily visualized for ternary systems. For more than three components (even though the procedure is general to more than three components), the visualization of the intersection of the lines is not possible because the lines intersect in hyper-space. If a feasible product distribution is used, there are not enough degrees of freedom to ensure an exact intersection will occur. As a result, the parameters associated with the stage composition lines and the composition pro les are no longer exact and this could in uence the overall accuracy of the procedure. Instead of lines intersecting, an approximation of intersection can be de ned as a minimum distance between a pair of lines. If any two points on a pair of lines are within this speci ed minimum distance, the lines are considered to ‘intersect’. This shall be exploited when determining the number of stages for the column. Applying the Concept to the Fully Thermally Coupled Column Design The procedure begins from xed feasible product distribution and works backwards to the feed. Figure 8 presents an overall design framework of the fully thermally coupled column using the equilibrium stage composition concept. At this stage, the conditions of equal vapour ows from the bottom of Column 2 and the top of Column 3, and equal compositions of the middle products must be met. Note that the side-draw compositions (PS2i and PS3i) are necessary

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for the method to work and later it will be shown how these compositions can be determined. The known or input parameters are the feed and product compositions, while the ow rates of the products and the thermal coupling links are the unknown parameters to be determined through solving the mass balance models. Input Parameters The following input parameters are required for the procedure:

· · · ·

total molar owrate of feed, F1; mole fraction of feed component, f 1i ; thermal feed quality, q; mole fractions of components in product stream as determined earlier: d2i—mole fraction of component i in Column 2 distillates; b2i —mole fraction of component i in Column 2 bottoms; d3i—mole fraction of component i in Column 3 distillates; b3i —mole fraction of component i in Column 3 bottoms. Note that: b2i = d3i (middle product composition) Initialization of Design Variables

Six design variables are identi ed for the fully thermally coupled column and their values must be assumed for initialization purposes: r1—re ux ratio for Column 1 (pre-fractionator); s1—boil-up ratio for Column 1 (pre-fractionator); r2—re ux ratio for Column 2; s2—boil-up ratio for Column 2; r3—re ux ratio for Column 3; s3—boil-up ratio for Column 3. The initial values must be speci ed between the lower and upper bounds of the respective design variables. In the case of the lower bound, the minimum re ux ratios as determined from the Underwood Equations, can be used for this purpose. Similarly, the lower bound for the boil-up ratio can be estimated in a similar way. For the upper bounds, any realistic upper limit for both re ux and boil-up ratios can be incorporated into the procedure. Solution of the Pre-Fractionator Arrangement Model By exploiting the similarity between the thermally coupled column and pre-fractionator arrangements (with partial condenser and reboiler on the pre-fractionator), the design can be simpli ed further and initialized by transforming the thermally coupled column into a three-simple column or the pre-fractionator arrangement. This model, shown in Figure 9, details the design parameters and variables to be determined by solving the mass balance equations as listed below:

Figure 8. Overall picture of the dividing wall column design shows the approach begins from the xed feasible products and feed.

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a) Solve for r1; s1; r2; s2; r3; s3; D2; B2; D3 and B3 by satisfying the following mass balance equations:

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i) overall mass balance: F1 = D2 + B2 + D3 + B3

(1) L1

ii) Column 2: (B2)(s2 + 1) = (r2)(D2)

(2)

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V1

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B2 D3

b) Component mass balance relationship Overall column: F1 . f 1i = D2 . d2i + B2 . b2i + D3 . d3i + B3 . b3i (5) Column 2:

A

3 V3 B3

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iv) equalization of vapour ow between columns 2 and 3 (B2)(s2) = (D3)(r3 + 1) (4)

L1

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1

iii) Column 3:

f 2i =

D2 L1+L2

D2

L2

2

L2 B2 D3

1 3 V1

V3 V1+V3 B3

Figure 10. Transformation from pre-fractionator arrangement (left) to Petyluk column arrangement (right) emphasizes a need to change both re ux and ratio (L1 + L2) of Column 2 and boil-up ratio (V1 + V 2) of column 3 in the Petyluk Column.

made by the ows in the main column to both side-draw liquid (L1 + L2) and vapour (V 1 + V 3) ow rates. Column 2 (re ux ratio):

s2 + 1 . d2i + s2 + 1 + r2

r2 . b2i s2 + 1 + r2

(6)

r3 + 1 . b3i s3 + 1 + r3

(7)

r20 =

L1 + L2 D2

(9)

Column 3: f 3i =

s3 . d3i + s3 + 1 + r3

Mass balance around Column 1 to relate q: F3(s1 + 1 - q) = (r1 + q)F2

(8)

As noted in Figure 9, the intermediate feeds, F2 and F3, represent the vapour and liquid feeds respectively. Rearrangement of the Thermally Coupled Column for Initialization Following the pre-fractionator arrangement, a rearrangement of the thermally coupled column is made for initialization purposes for the fully thermally coupled column design. Figure 10 illustrates the required transformation from the pre-fractionator arrangement to the Petyluk column arrangement, by revising the pre-fractionator arrangement re ux and boil-up ratios to those shown in equations (9) and (10) to re ect the Petyluk column. Both the re ux and the boilup ratios must be adjusted to account for the contribution

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s1

s30 =

V1 + V3 B3

(10)

Estimate Number of Stages for the Main Column (Columns 2 and 3) The values from r20 ; s2; r3 and s30 are then used in calculating the number of stages from a pair of composition pro les for each column based on constant molal over ow. As described earlier in this paper, each liquid composition data point in the pro les represents a particular stage. These pro les are generated from dew point and bubble point calculations, as described by Castillo29, for the rectifying and stripping sections respectively. In the case of Column 2, the models for the pro les are as follows: Column 2: Dew point (Rectifying section of the column): xi;n+ 1rec =

r20 . xi;nrec + d2i Ki;n+ 1rec . (r20 + 1)

(11)

Bubble point (Stripping section of the column):

r2 r1

Column 3 (boil-up ratio):

D2 d2i

L2 F2 2 f2i s2 L1 (V) B2 b2i D3 d3i V1 F3 r3 f3i 3 (L) V3 B3 s3 b3i

xi;n+ 1strip = b2i = d3i

Figure 9. Procedure begins by solving the mass balance for the three simple-column pre-fractionator arrangement model.

s2 . Ki;nstrip . xi;nstrip + b2i (s2 + 1)

(12)

Condition for Feed Stage Location The intersection or overlap point between rectifying and stripping section pro les indicates a feed stage location. This point, de ned as minimum composition difference, is determined from the minimum distance between the rectifying and the stripping composition data points. For each stage in a stripping section, the composition difference can be calculated, as de ned in equation (13) below, between this stage and every rectifying stage. Trans IChemE, Vol 79, Part A, October 2001

DESIGN AND OPTIMIZATION OF DISTILLATION COLUMNS: PART 1 j i= 1

(xi;nrec - xi;nstrip )2

A

(13)

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Feed

PS3 i = y n

The solution to the feed stage location will be the stage on the stripping section and the stage on the rectifying section that gives the minimum composition difference.

n+1

n xn

yn y n-1

n-1

Feed stage: Xn+1 Xn

Number of Stages

x n+1

b3 i

s3’

B

Once the feed stage is established, the number of stages can be counted from the data points (stages) in each pro le with one data point (stage) to be removed to account for the overlap point (feed stage). Both rectifying and stripping sections begin the stage numbering from the top product and the bottom product respectively.

C

Figure 12. Vapour side-draw composition takes the vapour composition from Stage n in the stripping section.

side-draw composition from Column 3. By de nition, the vapour side-draw for the fully thermally coupled column takes place from one stage below the feed stage. Since the composition pro les represent the liquid composition, a vapour side-draw composition, PS3i or yn, must be determined from the mass balance that relates the feed stage composition, xn+ 1 , bottom product composition, b3i, and the boil-up ratio, s30 , as shown in equation (14).

Example: The results from the minimum composition difference indicate ve stages for the rectifying and six stages for the stripping sections. This gives ten stages for the column with a feed stage occurs on Stage 5. Column 3: Repeat a similar procedure as above to estimate the number of stages for Column 3 using its relevant parameters; r3; s30 ; d3i and b3i; and the relevant composition pro le models.

yi;n =

(s30 + 1)xi;n+ 1 - b3i s30

(14)

Solution of the Thermally Coupled Column Model The values obtained for both side-draw compositions, the re ux and boil-up ratios allow us to solve the mass balance model for the thermally coupled column in Figure 13.

Estimate Both Liquid and Vapour Side Draw Composition Column 2—Liquid side draw composition, PS2i , in mole fraction Once the feed stage location is established, as shown in the ternary diagram in Figure 11, the liquid side-draw composition for the thermally coupled column section of Column 2 can be found. Based on the de nition of the sidedraw location for the fully thermally coupled column, this location is taken from one stage above the feed stage (see the corresponding stage diagram in Figure 11). The liquid side-draw composition, PS2i , is withdrawn from a liquid composition on Stage n, xn , in the rectifying section.

r2’ PS2

D2 d2i

PS2i PF2 PF2i

2

s2 B2 b2i D3 d3i r3

1 F1 f1i q PS3 PF3 PF3i 3 PS3i

Column 3—Vapour side draw composition, PS3i , in mole fraction Similarly, a thermally coupled column section for Column 3 can be established from the feasible column. Figure 12 illustrates the procedure to estimate the vapour

s3’

Figure 13. The thermally coupled column model indicates all the variables and parameters to be used for dividing wall column design.

r2’ d2i

d2i

Û

n-1

PS2 i = xn Feed

b2i

B

C

Figure 11. Following a feasible column design, a liquid side-draw composition can be established.

Trans IChemE, Vol 79, Part A, October 2001

b2i = d3i

B3 b3i

A X n-1 Xn PS2 i Feed stage

b3i

n

xn-1 xn

AMMINUDIN et al.

710

The complete mass balance model of the thermally coupled column is given below, based on the constant molal over ow assumption. Note that some of the mass balance equations may be complementary to one another.

F1 . F1i = D2 . d2i + B2 . b2i + D3 . d3i + B3 . b3i (29)

· equalization of vapour ow between Columns 2 and 3:

Estimate Number of Stages for Pre-Fractionator (Column 1)

(D3)(r3 + 1) = (s2)(B2)

(15)

· overall mass balance around Columns 1, 2 and 3: F1 = D2 + B2 + D3 + B3

(16)

· mass balance around Columns 2 and 3: PF2 = PS2 + D2 + B2

(17)

PF3 = PS3 + D3 + B3

(18)

· mass balance around Column 1 to relate q: Liquid: F1 . q + PS2 = PF3 Vapour: F1 . (1 - q) + PS3 = PF2

(19) (20)

· mass balance around Columns 2 and 3 in terms of r20 ; s2; r22; r3; s30 and r33. Thong39 derived the following relationships from equations (21) to (28) to account for the presence of the sidedraw columns using the stage composition lines: D2 s2 + 1 = 0 B2 r2 - r22 where:

(21)

- r33 r3 + 1

s30

(23)

PS3 r33 = (24) B3 and PS3 = V 1 (from the pre-fractionator arrangement). A component mass balance around Column 2 in terms of r20 ; s2 and r22 gives: s2 + r20 + 1 + r22 . s2 b2 = (25) s2 + 1 r20 - r22 . b2i s2+ 1

(26)

A component mass balance around Column 3 in terms of r3; s30 and r33 gives: b3 =

xi;n+ 1rec =

A: xi;nrec - PS2i + PF2i Ki;n+ 1rec

(30)

where: PS2 PF2

(31)

Bubble Point (Stripping Section of the Column) xi;n+ 1strip = PF3i +

Ki;nstrip . xnstrip - PS3i B

(32)

where:

where:

b2 . PF2i = d2i + r22 . PS2i +

Dew Point (Rectifying Section of the Column)

A=

PS2 r22 = (22) D2 and PS2 = L1 (from the pre-fractionator arrangement). An additional mass balance around Column 3 relates r3; s30 and r33: D3 = B3

Similarly, the composition pro le approach is used to estimate the number of stages for the pre-fractionator connected by thermally coupled streams to the main column (Columns 2 and 3). Thus, a new pair of composition pro les to account for this thermal coupling link must be developed and, thus, these new pro les are shown below from equations (30) to (33). Based on the values obtained for PF2; PF2i; PS2; PS2i; PF3; PS3; PS3i and PF3i, the number of stages can be determined from dew point and bubble point calculations to generate a pair of composition pro les for the prefractionator (Column 1).

r3 + 1 + r33 . r3 + s30 r3 + 1

b3 . PF3i = b3i + r33 . PS3i +

(27) s30 - r33 . d3i r3 + 1 (28)

· overall component mass balance check around Columns 1, 2 and 3:

B=

PF3 PS3

(33)

Similar procedures and criteria will be used to nd the feed stage and the number of stages. (See equation (13).) Design Optimization The sequential nature of the procedure nally produces an initial design for the fully thermally coupled column. As a nal step, a design optimization for the fully thermally coupled column can be carried out based on this initial design. The design variables, the re ux and boil-up ratios introduced earlier are the degrees of freedom for optimization. However, the recoveries in the pre-fractionator are no longer the optimization variables at this stage because they have been used, and hence lost as degrees of freedom, in determining the feasible products as described in the early part of the paper. The objective function for optimization is to minimize the total cost as shown in equation (34). In addition, the detailed sizing and costing of distillation columns and heat exchangers to generate a comprehensive capital cost estimate can be incorporated into the objective function10. Trans IChemE, Vol 79, Part A, October 2001

DESIGN AND OPTIMIZATION OF DISTILLATION COLUMNS: PART 1

minimum total cost = energy cost + capital cost

711

Summary of the Procedure (34)

where: energy cost = f (reboiler duty and=or condenser duty) capital cost = f (number of stages from Columns 1; 2 and 3; column diameter; vapour flow; heat exchangers) The constraints for the objective function have been implicitly de ned in earlier steps while solving the mass balance models for each con guration. These constraints include among others the equalization of vapour ow between Columns 2 and 3, the column feed and product speci cations. The step-by-step procedure proposed in this paper allows us to employ any established non-linear optimization solver40. To facilitate optimization convergence for nonlinear optimization, appropriate initial values should be selected.

As a summary, the block diagram of Figure 14 presents the overall design procedure and optimization of the fully thermally coupled column design. Start with feasible products and assume initial values for the following: r1—re ux ratio for Column 1 (pre-fractionator); s1—boil-up ratio for Column 1 (pre-fractionator); r2—re ux ratio for Column 2; s2—boil-up ratio for Column 2; r3—re ux ratio for Column 3; s3—boil-up ratio for Column 3.

Case Study—Replacement of Depropanizer and Debutanizer Columns with a Dividing Wall Column The new design procedure will now be demonstrated in a case study to show its strength and to reveal any limitations in the design of a dividing wall column. The case study involves a new design of a dividing wall column to replace conventional debutanizer and depropanizer columns in a separation train of a re nery complex.

Feed Information The feed is predominantly a light hydrocarbon mixture, which consists of nine components as given in Table 1. The components are:

· · · · ·

feed ow rate: 1600 kmol h- 1 (90% liquid); pressure: 14.9 bar; temperature: 79° C; use MP steam for the reboiler @ 5 bar; use cooling water at 25° C for the condenser.

Separation Objective It is intended to achieve the following product speci cations:

· top product: 94% recovery of n-propane (nC3); · middle product: 95% mole purity of middle products (i-butane, 1-butene and n-butane); · bottom product: 97% recovery of iC5. Table 1. Feed composition.

Figure 14. A complete procedure for dividing wall column design.

Trans IChemE, Vol 79, Part A, October 2001

Feed components

Mole fraction

Ethylene (Et) Propylene (C3) n-propane (nC3) i-butane (iC4) 1-butene (1but) n-butane (nC4) i-pentane (iC5) n-pentane (nC5) n-hexane (nC6)

0.0128 0.0760 0.2312 0.1443 0.2683 0.0409 0.0940 0.1008 0.0317

AMMINUDIN et al.

712 Assumptions

Reflux ratio : 4.8 503 kmol/h

Based on the separation objective, the key and non-key components are:

· light key (LK): n-propane (nC3); · middle keys (MK): i-butane (iC4), 1-butene (1butene), n-butane (nC4); · heavy key (HK): i-pentane (iC5); · lighter than LK: Ethylene (Et) and Propylene (C3); · heavier than HK: n-pentane (nC5) and n-hexane (nC6). Vapour liquid equilibrium will be assumed ideal. This is not a limitation of the procedure as any other thermodynamic model can be used for generating the relative volatilities for the short cut design procedure. The overall procedure is in two parts. The rst part of the procedure is to estimate a feasible product distribution at minimum re ux. In the second part of the procedure design and optimization are carried out.

Feasible Product Estimate The feasible product distribution according to the product speci cations will be determined from the Underwood Equations. The results from this estimate based on a procedure in the early part of this paper are given in Table 2 in terms of mole fraction.

1

779 kmol/h

1600 kmol/h q = 90% liquid

3 4

1 9 3

651 kmol/h

Feed (mole frac.) Et : 0.0128 C3: 0.0760 NC3: 0.2312 IC4: 0.1443 1but: 0.2683 NC4: 0.0409 IC5: 0.0940 NC5: 0.1008 NC6: 0.0317

6

1273 kmol/h

13 14 23 445 kmol/h

Reboiler Duty : 13140 kW Figure 15. Final short cut design of the dividing wall column based on the

Comparison with Rigorous Simulation Final Design of the Dividing Wall Column Using the feasible products, as input parameters to the procedure, the design and optimization procedure can be carried out. For illustration purposes in the case study, the composition pro le is generated using ideal VLE. Any VLE model could have been used in principle. For optimization purposes, it has been assumed that the capital cost is three times the energy cost41. Figure 15 shows the nal design, giving the optimized number of stages, side-draw ow rates and the re ux ratio. These results de ne the overall design parameters that are necessary for carrying out the subsequent rigorous simulation. Whilst the design shown in Figure 15 is shown as a Petyluk arrangement it could be constructed as either a Petyluk column or a dividing wall column, but most likely be constructed as a dividing wall column. Table 2. Feasible product distribution estimated from the Underwood equations. Comp. Ethylene Propylene n-propane i-butane 1-butene n-butane i-pentane n-pentane n-hexane

Top product estimate

Middle product estimate

Bottom product estimate

0.040 0.239 0.689 0.013 0.019 1.9E-4 1E-5 1E-5 1E-6

1E-5 0.001 0.034 0.344 0.543 0.069 0.007 0.002 3.9E-4

0. 0 1.E-6 1.E-4 0.146 0.046 0.331 0.362 0.115

The same thermodynamic basis will be maintained for the rigorous simulation. The results from the new short cut approach will be used to initialize the rigorous simulation. The new short cut design provides an initialization for the simulation to converge successfully. Table 3 presents the results from the simulation run and comparison with the feasible product estimates. It demonstrates not only that the fully thermally coupled column design or dividing wall column design from the new procedure allows convergence to be achieved easily, but also the product distribution from the simulation compares well with the feasible product estimates determined earlier. It might be expected that there would be greater differences between the results because the rigorous simulation employs mass and energy balance models at each tray, while the new short cut design does not account for the energy balance in the procedure. However, this is not the case and the results are much improved when compared with the previous approaches10. As a result, no signi cant ne-tuning is necessary, leading to less danger of over design from the ne-tuning.

Comparison with Other Ternary Distillation Systems To complete the analysis of the case study, a comparison has been carried out to investigate the energy performance of other ternary distillation arrangements apart from the Petyluk column or the dividing wall column. In making the comparison, the number of stages, product purities and the ow rates for all designs have been maintained as in the Petyluk column design in Figure 15. To be conservative, the stages in the preTrans IChemE, Vol 79, Part A, October 2001

DESIGN AND OPTIMIZATION OF DISTILLATION COLUMNS: PART 1

713

Table 3. Results from the rigorous simulation show a strong agreement with the estimated feasible products especially for the key components.

Comp. Ethylene Propylene n-propane i-butane 1-butene n-butane i-pentane n-pentane n-hexane

Feasible product estimate (Top)

Rigorous simulation (Top)

Feasible product estimate (Middle)

Rigorous simulation (Middle)

Feasible product estimate (Bottom)

Rigorous simulation (Bottom)

0.040 0.239 0.689 0.013 0.019 1.9E-4 1.E-5 1.E-5 1.E-6

0.041 0.235 0.682 0.022 0.019 0.001 0 0 0

1E-5 0.001 0.034 0.344 0.543 0.069 0.007 0.002 3.9E-4

0 0.006 0.042 0.318 0.554 0.069 0.006 0.005 0

0. 0. 1.E-6 1.E-4 0.146 0.046 0.331 0.362 0.115

0 0 0 0.030 0.132 0.044 0.326 0.355 0.114

fractionator of the Petyluk column are counted into the total number of stages. Table 4 summarizes the results obtained from these distillation arrangements, indicating the energy performance in each design. A direct sequence of simple columns has been chosen as a basis for comparison. The results show that energy savings of about 20% can be obtained from the dividing wall column when compared with the direct sequence. However, if only the trays in the main column section of the Petyluk column are counted, which assumes a pre-fractionator to be an integral part as in the dividing wall column, the energy savings are 26%. In addition, further savings from the capital cost can be generated as the dividing wall column can be constructed in a single shell. Table 4 also indicates that the performance of the other thermally coupled columns, such as the side stripper and side recti er, and the pre-fractionator arrangement are comparable with each other but the side recti er consumes more energy relative to other thermally coupled column arrangements. From Table 4, the simple side draw requires the highest energy consumption to achieve the product speci cations. This observation demonstrates that the dividing wall column can be applied to boost the product quality of the middle products in an ef cient way. CONCLUSIONS Improvements to the earlier design procedure of Triantafyllou and Smith10 have been made to cater for wider applications27. However, the previous short cut design method for the fully thermally coupled column, which

Table 4. Relative performance of the dividing wall column with other ternary distillation systems. Total reboiler duty kW

employed the Fenske-Underwood-Gilliland short cut technique, is unreliable for initialization of rigorous simulation. Fine-tuning using trial-and-error to make the rigorous simulation meet the design speci cation is not systematic, timeconsuming and can lead to non-optimal designs. The reasons for the inconsistency are attributed primarily to the use of the empirical correlations in determining both the number of stages and the feed stage location, and the assumption of constant relative volatility. In this paper, a new design procedure for the fully thermally coupled column has been proposed to overcome these limitations. The new procedure adopts the equilibrium stage composition concept to de ne a liquid composition pro le by solving the mass balance rigorously on each equilibrium stage, while restricting the procedure to the assumption of constant molal over ow. Due to its semirigorous nature, there is no need to assume constant relative volatility. The procedure follows from the feasible product distribution, which must be estimated at minimum re ux conditions prior to the use of the concept for designing the fully thermally coupled column. While maintaining the use of a model based on three simple columns, as in previous approaches, the procedure begins with the use of a pre-fractionator arrangement to initialize and simplify the design of the dividing wall column. By transforming the design from the pre-fractionator to the fully thermally coupled column arrangement, the design can proceed to estimate the side-draw locations, composition, ow rates and the number of stages. Based on this framework, optimization to exploit the degrees of freedom can be carried out. The new method has been found to improve the initialization considerably. A case study has demonstrated that the resulting nal design agrees well with rigorous simulation without the need for ne-tuning.

% of energy usage

Simple column arrangements 1. Direct sequence (Base case) 2. Indirect sequence

16389 17060

100 104

Complex column arrangements 1. DWC and Petyluk column 2. Pre-fractionator arrangement 3. Side stripper 4. Side recti er 5. Simple side draw

13140 13285 13281 13761 29600

80 81 81 84 180

Trans IChemE, Vol 79, Part A, October 2001

NOMENCLATURE HK LK MK

heavy key light key middle key

Variables and Parameters A ratio of side-draw liquid owrate, PS2, to feed owrate of column 2 in Petyluk column, PF2, as de ned in equation (31) B ratio of feed owrate of column 3 in Petyluk column, PF3, to side-draw vapour owrate, PS3, as de ned in equation (33) B2 bottom ow rate from Column 2 B3 bottom ow rate from Column 3

AMMINUDIN et al.

714 D2 D3 F1 F2 F3 L1 L2 M2 PF2 PF3 PS2 PS3 q r1 r2 r3 r22 r33 r20 s1 s2 s3 s30 V1 V3

top distillate ow rate from Column 2 top distillate ow rate from Column 3 fresh feed ow rate to the fully thermally coupled column, dividing wall column or the pre-fractionator column vapour feed ow rate from the pre-fractionator to the main column in the pre-fractionator arrangement liquid feed ow rate from the pre-fractionator to the main column in the pre-fractionator arrangement liquid re ux ow rate from Column 1 liquid re ux ow rate from Column 2 total middle product from B2 and D3 (B2 + D3) vapour feed ow rate from the pre-fractionator to the main column in the Petyluk column liquid feed ow rate from the pre-fractionator to the main column in the Petyluk column liquid side draw ow rate from the main column to prefractionator vapour side draw ow rate from the main column to prefractionator thermal feed quality re ux ratio for Column 1 in pre-fractionator arrangement (new procedure) re ux ratio for Column 2 in pre-fractionator arrangement (new procedure) re ux ratio for Column 3 in pre-fractionator arrangement (new procedure) ratio of the side-draw liquid owrate, PS2, to top distillate owrate of Column 2, D2, as de ned in equation (22) ratio of the side-draw vapour owrate, PS3, to bottom owrate of column 3, B3, as de ned in equation (24) re ux ratio for Column 2 in Petyluk column (new procedure) boil-up ratio for Column 1 boil-up ratio for Column 2 boil-up ratio for Column 3 boil-up ratio for Column 3 in Petyluk column (new procedure) vapour boil-up ow rate from Column 1 vapour boil-up ow rate from Column 3

Greek symbols b2 mass balance factor as de ned in equation (25) b3 mass balance factor as de ned in equation (27) Composition d2i mole fraction of component i in Column 2 distillates d3i mole fraction of component i in Column 3 distillates b2i mole fraction of component i in Column 2 bottoms b3i mole fraction of component i in Column 3 bottoms f 1i mole fraction of feed component i in the fresh feed to the fully thermally coupled column, dividing wall column or prefractionator arrangement F 2i mole fraction of component i in the vapour feed to the main column in the pre-fractionator arrangement F 3i mole fraction of component i in the liquid feed to the main column in the pre-fractionator arrangement Ki equilibrium constant for component i PF 2i mole fraction of component i in stream PF2 PF 3i mole fraction of component i in stream PF3 PS 2i mole fraction of component i in stream PS2 PS 3i mole fraction of component i in stream PS3 xi;n+ 1 mole fraction of liquid component i in stage (n + 1) yi;n mole fraction of vapour component i in stage (n)

REFERENCES 1. Castillo, F. J. L., Thong, D. Y.-C. and Towler, G. P., 1998, Homogeneous azeotropic distillation: 1. Design procedure for single-feed columns at non-total re ux, Ind Eng Chem Res, 37(3): 987. 2. Watkins, R. N., 1979, Petroleum Re nery Distillation, 2nd Ed. (Gulf Publishing, Houston, Texas, USA). 3. Seidel, M., 1935, German Patent 610503. 4. Petyluk, F. B., Platonov, V. M. and Slavinskii, D. M., 1965, Thermodynamically optimal method for separating multicomponent mixtures, Int Chem Eng, 5(3): 555. 5. Hairston, D., 1999, The divide in distillation, Chem Eng, April: 32. 6. Brugma, A. J., 1937, Dutch Patent No 41;850, October 15. 7. Brugma, A. J., 1942, U. S. Patent No 2;295;256, September 8. 8. Wright, R. O., 1949, U. S. Patent 2;471;134; May 24.

9. Agrawal, R. and Fidkowski, Z. T., 1999, New thermally coupled schemes for ternary distillation, AIChEJ, 45: 485. 10. Triantafyllou, C. and Smith, R., 1992, The design and optimization of fully thermally coupled distillation columns, Trans IChemE; Part A; Chem Eng Res Des, 70(A2): 118. 11. Triantafyllou, C., 1991, The Design Optimization and Integration of Dividing Wall Distillation Columns, Ph.D. Thesis (UMIST, UK). 12. Lestak, F., Smith, R. and Dhole, V. R., 1994, Heat transfer across the wall of dividing wall columns, Trans IChemE; Part A; Chem Eng Res Des, 72(A5): 639. 13. Abdul Mutalib, M. I. and Smith, R., 1998, Operation and control of the dividing wall distillation columns. Part 1: Degrees of freedom and dynamic simulation, Trans Inst Chem Eng; Part A; Chem Eng Res Des, 76(A3): 308. 14. Kaibel, G., 1988, Distillation column arrangement with low energy consumption, IChemE Symposium Series no 109, p 43–59. 15. European Chemical News (ECN), 1995, 2–8 October, p 26. 16. M. W. Kellogg Limited press release, 11 September, 1998. 17. Parkinson, G. (ed), 1998, Chementator, Chem Eng, July: 21. 18. Stupin, W. J. and Lockhart, F. J., 1968, The distribution of non-key components in multicomponent distillation, 61st Annual Meeting of AIChE, (Los Angeles, December 1–5). 19. Fonyo, Z., Szabo, J. and Foldes, P., 1974, Study of thermally coupled distillation columns, Acta Chim, 82: 235. 20. Tedder, D. W. and Rudd, D. F., 1978, Parametric studies in industrial distillation: Part 1, 2 and 3, AIChE J, 24(2): 303. 21. Cerda, J. and Westerberg, A. W., 1981, Shortcut methods for complex distillation column 1. Minimum re ux, Ind Eng Chem Process Des Dev, 20: 546. 22. Spadoni, G. and Stramigioli, C., 1983, Optimum design of a thermally coupled distillation system, 3rd Int Cong Comp and Chem Eng, Paris, no 27: 44. 23. Nikolaidas, I. P. and Malone, M. F., 1987, Approximate design of multiple feed=side stream distillation systems, Ind Eng Chem Res, 26(9): 1839–1845. 24. Fidkowski, Z. T. and Krolikowski, L., 1987, Minimum energy requirement of thermally coupled distillation systems, AIChE J, 33(4): 643. 25. Stupin, W. J., 1970, The Separation of Multicomponent Mixtures in Thermally Coupled Distillation Systems, Ph.D. Thesis (University of Southern California, USA). 26. Glinos, K. and Malone, M. F., 1988, Optimality regions for complex column alternatives in distillation systems, Trans IChemE; Part A; Chem Eng Res Des, 66(A3): 229. 27. Amminudin, K. A., 1999, Design and Optimization of the Dividing Wall Distillation Column, Ph.D. Thesis (UMIST, UK). 28. Dunnebier, G. and Pentelides, C. C., 1999, Optimal design of thermally coupled distillation columns, Ind Eng Chem Res, 38: 162. 29. Castillo, F. J. L., 1997, Synthesis of Homogeneous Azeotropic Distillation Sequences, Ph.D. Thesis (UMIST, UK). 30. Van Dongen, D. B. and Doherty, M. F., 1985, Design and synthesis of homogeneous azeotropic distillations. 1. Problem formulation for a single column, Ind Eng Chem Fundam, 24: 454. 31. Hoffman, E. J., 1964, Azeotropic and Extractive Distillation (Interscience Publishers, John Wiley and Sons., New York). 32. Wahnschafft, O. M., Kohler, J., Blass, J. W. and Westerberg, A. W., 1992, The product composition regions of single-feed azeotropic distillation columns, Ind Eng Chem Res, 31: 2345. 33. Fidkowski, Z. T., Doherty, M. F. and Malone, M. F., 1993, Feasibility of separation for distillation of non-ideal ternary mixtures, AIChE J, 39: 1303–1321. 34. Walas, S. M., 1988, Chemical Process Equipment (Butterworth Publishers, Boston, USA). 35. Koehler, J., Poellmann, P. and Blass, E., 1995, A review on minimum energy calculations for ideal and non-ideal distillation, Ind Eng Chem Res, 34: 1003. 36. Brooke, A., Kendrick, D. and Meeraus, A., 1992, GAMS- A User Guide (Redwood City, Scienti c Press). 37. Carlberg, N. A. and Westerberg, A. W., 1989, Temperature-heat diagrams for complex columns. 3. Underwood’s method for the Petyluk con guration, Ind Eng Chem Res, 28: 1386. 38. Thong, D. Y.-C., Castillo, F. J. L. and Towler, G. P., 2000, Distillation design and retro t using stage-composition lines, Chem Eng Sci, 55: 625. 39. Thong, D. Y.-C., 1998, personal communication. 40. Edgar, T. F. and Himmelblau, D. M., 1988, Optimization of Chemical Processes (McGraw-Hill, New York). 41. Humphrey, J. L. and Keller II, G. E., 1997, Separation Process Technology (McGraw-Hill, New York).

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715

ACKNOWLEDGEMENTS

ADDRESS

The authors would like to thank the European Union under Joule Project (JOU3-CT 95-0035) and the member companies of the UMIST Process Integration Research Consortium for their nancial support of the work described in this paper.

Correspondence concerning this paper should be addressed to Professor R. Smith, Department of Process Integration, UMIST, P. O. Box 88, Manchester M60 1QD, UK. E-mail: [email protected] The manuscript was received 21 July 2000 and accepted for publication after revision 23 January 2001.

Trans IChemE, Vol 79, Part A, October 2001

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