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Chemical Engineering Science, Vol. 53, No. 5, pp. 963—976, 1998 ( 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0009–2509(97)00418–1 0009—2509/98 $19.00#0.00

Influence of multicomponent mass transfer on homogeneous azeotropic distillation F. J. L. Castillo and G. P. Towler* Department of Process Integration, UMIST, PO Box 88, Manchester M60 1QD, U.K. (Received 10 May 1997; accepted 16 November 1997) Abstract—Residue-curve and distillation-line maps are useful tools for the design of azeotropic distillation sequences. The calculation of residue curves uses the assumption that the vapour and liquid are always in equilibrium. The computation of distillation lines assumes that the vapour and liquid leaving a tray are in equilibrium. In this work, the equations defining residue curves and distillation lines are extended to take into account mass transfer effects that occur in real distillation columns. A general relationship between the composition of the vapour and liquid leaving a tray at total reflux is developed and used to calculate the maps. The curvature of the residue curves and distillation lines changes, significantly affecting the shape of the maps. The consideration of mass transfer in azeotropic distillation columns produces quantitative changes in the behaviour of the liquid composition path for distillation columns at total reflux, and in some cases, a qualitative change in the products formed can also be observed. No change has been found in the bounds on the product composition at minimum reflux when mass transfer effects are taken into account. The pinch-point curves or distillation limits remain the same. Entrainers should be selected considering not only how much they modify the vapour—liquid equilibrium, but also how much they affect the multicomponent mass transfer that takes place in real distillation columns. ( 1998 Elsevier Science Ltd. All rights reserved. Keywords: Azeotropic distillation; residue curve maps; mass transfer; distillation line maps.

this work has recently been published by Widagdo and Seider (1996).

1. INTRODUCTION

1.1. Azeotropic distillation design The separation of azeotropic mixtures into pure products is a common task in the chemical and speciality chemical industries. By definition, a binary mixture that forms an azeotrope can not be distilled into pure components. If pressure-swing distillation is not economical or practical, a third component, the entrainer, must be added to the azeotropic mixture to allow separation. Entrainer selection introduces an extra degree of freedom not present in zeotropic separation problems. In principle, any substance can be an entrainer but not every substance can ‘break’ the azeotrope: separation feasibility is an important issue in azeotropic distillation. To help in the screening of entrainers, it is desirable to assess the influence that the entrainer will have on the vapour—liquid equilibrium before any column is designed and simulated. Once the entrainer is selected, the synthesis of distillation sequences requires that the limits for every proposed split should be clearly identified. Residue-curve and distillation-line maps have emerged as useful tools to tackle these problems. An excellent review of

* Corresponding author. Tel.: 0161 200 4386; 0161 236 7439; e-mail: [email protected].

fax:

1.2. Residue-curve maps In recent years, much attention has been paid to the separation of azeotropic mixtures due to the pioneering work of Doherty and co-workers on residue-curve maps. Residue-curve maps have been widely used to characterise azeotropic mixtures, establish feasible splits by distillation at total reflux and for the synthesis and design of column sequences that separate azeotropic mixtures. Schreinemakers (1901) defined a residue curve as the locus of the liquid composition during a simple distillation process. Residue curves are conceived for n-component systems, but can be plotted only for ternary or, with more powerful graphical tools and some imagination, quaternary systems. They help to understand the limits imposed on the separation by the non-ideal vapour—liquid equilibrium when distillation columns are operated at total reflux. Residue-curve maps have been divided into regions where the residue curves have the same pair of initial and final points (Doherty and Perkins, 1979). The residue curves that act as separatrices between regions are called simple-distillation boundaries. Doherty and Perkins (1979) showed that in the separation of

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a homogeneous mixture by simple distillation, the composition profile cannot cross a simple-distillation boundary. Residue-curve maps have proven particularly useful in the synthesis and design of columns and column sequences. It has been demonstrated that residue curves represent operating lines (or liquid composition profiles) of continuous packed columns operating at total reflux (Van Dongen and Doherty, 1985). Assuming that the behaviour of staged columns can be approximated by the behaviour of packed columns, the constraints on simple-distillation separations identified using residue-curve maps also limit continuous distillation at total reflux. A proposed column is feasible if: (a) the top and bottom products belong to the same residue curve and (b) the feed and products satisfy a material balance, i.e. they are on a straight line in the composition diagram (Van Dongen and Doherty, 1985; Laroche et al., 1992). Simple-distillation boundaries play an important role in the synthesis of distillation sequences (Doherty and Caldarola, 1985). Laroche et al. (1992) show that only straight simple-distillation boundaries are strict boundaries for continuous columns at total reflux. It is possible to design a distillation column that crosses a simple-distillation boundary at total reflux if the boundary has sufficient curvature, i.e. it is possible for the column feed and products to be located in different simple-distillation regions. Because of this, the

existence, location and curvature of simple-distillation boundaries are all important in azeotropic distillation design. Figure 1 shows the residue-curve map for methanol, ethanol and water at 101.3 kPa. This system presents a simple-distillation boundary between pure methanol and the ethanol—water binary azeotrope. 1.3. Distillation line maps Although considerably less popular than residue curves, distillation-line maps are equally useful for the synthesis and design of distillation columns and sequences. By definition, distillation lines are not smooth curves but a discrete series of points that represent the composition of the vapour and liquid phase at each stage for a column operating at total reflux (Stichlmair, 1987). Normally, the composition points that belong to the same column are joined together with tie lines that assist in graphical interpretation but have no physical meaning. Distillation lines have the same graphical limitation of residue curves; i.e. they are defined for n-component systems but can be plotted only for ternary or quaternary systems. Although distillation lines and residue curves are clearly different, representing staged and packed columns respectively, they have identical properties near singular points. Furthermore, systems that present simple-distillation boundaries will have an equivalent

Fig. 1. Residue-curve map for methanol, ethanol and water at 101.3 kPa.

Homogeneous azeotropic distillation

distillation-line boundary (Widagdo and Seider, 1996). Distillation-line maps are therefore used for the synthesis of distillation sequences in the same manner as residue-curve maps. Figure 2 shows the distillation-line map for methanol, ethanol and water at 101.3 kPa. This system presents a distillation-line boundary between pure methanol and the ethanol— water binary azeotrope. 1.4. Finite reflux: pinch-point curves and distillation limits Wahnschafft et al. (1992) extended the above methodologies to account for separation at finite reflux. They proved that at the pinched tray of a column, the tangent to the residue curve must pass through the product composition. The locus of points on residue curves at which the tangent passes through a product composition is the product pinch-point curve. In a similar manner, the feed pinch-point curve can be calculated. Together with the mass balance and the total reflux operation, the feed pinch-point curve limits all the feasible products for a given feed. A similar approach has been proposed by Fidkowski et al. (1993). They refer to the feed pinch-point curve as the distillation limit. Their procedure has the advantage that it takes into account the thermodynamic condition of the feed (or feed quality), providing the proper bounds for the feasible products at finite reflux.

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2. DEFINING EQUATIONS

2.1. Residue curve maps Doherty and Perkins (1978) showed that the simple distillation process is modelled by dx i"x !y . i i dh

(1)

If the vapour leaving the still is considered to be in equilibrium with the liquid residue, then: y "y%2"K x i i i i

(2)

dx%2 i "x (1!K ) i i dh

(3)

therefore,

A residue-curve map can be obtained by solving eq. (3) for different initial compositions. There is only one residue-curve map for any given system and pressure. The equilibrium constant is calculated at the pressure, bubble point and composition of the liquid residue. Every azeotrope and pure component in the system will be a singular point of eq. (3). 2.2. Distillation line maps Various alternative sets of equations have been used for the calculation of distillation lines (Hoffman,

Fig. 2. Distillation-line map for methanol, ethanol and water at 101.3 kPa.

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1964; Stichlmair, 1987). In this work, we propose a formulation that facilitates the comparison with residue curves. The change in the operating line at any stage of a staged column (Fig. 3) can be represented by

mixture (Stichlmair et al., 1989). The computational effort involved in plotting distillation lines is considerably less than that required to plot residue curves.

*x "x !x . (4) i,n i,n~1 i,n If a column operated at total reflux is considered (Fig. 3), no product is withdrawn from the column; therefore, the mass balance on any component performed around any tray is

3. THEORY

» y "¸ x n i,n n~1 i,n~1 and the overall mass balance is » "¸ . n n~1

(5)

3.1. Non-equilibrium stages at total reflux Figure 4 illustrates an actual tray, where the vapour and the liquid streams leaving the tray are not in equilibrium. For each tray (or each theoretical stage of packing), the departure from equilibrium can be represented by the Murphree vapour tray efficiency for each species: y !y i,n`1 EMV, i,n i,n y%2 !y i,n i,n`1

(6)

Hence,

(11)

where

y "x . (7) i,n i,n~1 Equation (7) holds regardless of whether or not equilibrium is achieved on the trays. Since no feed enters a column at total reflux, the stripping section and the rectifying section merge into one single section and eq. (7) is therefore valid for every stage in the column. Combining eqs (4) and (7)

y%2 "K x . i,n i,n i,n Combining eqs (7), (11) and (12)

*x "y !x . (8) i,n i,n i,n If the vapour and the liquid leaving the stage are in equilibrium, then

y "(1#EMVK !EMV )x . (14) i,n i,n i,n i,n i,n Equation (14) provides a general expression that relates the compositions of the vapour and liquid streams leaving a real stage operating at total reflux. It modifies the relationship between the vapour and liquid compositions to account for the mass transfer that occurs on a real column tray. Although eq. (14) is only valid at total reflux, this assumption is already implicit in both residue-curve and distillation-line maps. If the stage efficiency of a component is one, i.e. the component reaches equilibrium, then eq. (14) simplifies to the equilibrium relationship (9) regardless of the value of the equilibrium constant. On the other

y "y%2 "K x i,n i,n i,n i,n

(9)

hence, *x%2 "x (K !1). (10) i,n i,n i,n A set of solutions of eq. (10) for different initial bottom compositions is a distillation-line map. There is only one distillation-line map for any given system and pressure, although the apparent shape seems to depend on the choice of initial points when tie lines are drawn. The equilibrium constant is calculated at the pressure, bubble point and composition of the liquid

Fig. 3. Column operating at total reflux, rectifying section.

y /x !1 y !x i,n " i,n i,n . EMV" i,n i,n K x !x K !1 i,n i,n i,n i,n Rearranging eq. (13)

Fig. 4. Real tray.

(12)

(13)

Homogeneous azeotropic distillation

hand, if the equilibrium constant is equal to one, then eq. (14) simplifies to y "x (15) i i which is the condition of an azeotrope or a pure component, regardless of the value of the component efficiency. Therefore, as expected, the composition of an azeotrope is not affected by mass transfer effects. Similar expressions can be derived using alternative definitions for the component stage efficiencies, e.g. the matrix formulation suggested by Taylor and Krishna (1993). 3.2. Non-equilibrium residue curves Equation (14) can be used instead of the equilibrium relationship (2) for the calculation of residue curves. Substituting eq. (14) in eq. (1) will give dx i"x !x (1#EMV K !EMV ) i i i i i dh

(16)

dx i"EMV x (1!K ). i i i dh

(17)

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and vapour—liquid equilibrium on the liquid composition profile during distillation at total reflux. The non-equilibrium and equilibrium residue-curve maps [solutions to eqs (17) and (3), respectively] can only be identical if the stage efficiencies of all the components are equal. Since this is a very unlikely situation in multicomponent systems, we expect that the non-equilibrium and equilibrium residue-curve maps will always be different, with the degree of difference depending upon the difference between the component stage efficiencies. Figure 5 shows the equilibrium and non-equilibrium residue-curve maps for the system formed by n-pentane, n-hexane and nheptane at 101.3 kPa. Even for an ideal system with no azeotropes, the maps are not the same. The characteristics of the pure components and azeotropes in the residue-curve map are not affected when mass transfer is incorporated, therefore, the nature and location of the singular points will not change and, consequently, no new simple-distillation boundaries are introduced in the system.

hence,

The non-equilibrium residue curve map can be obtained by solving eq. (17) for different initial points. This map shows the combined effects of mass transfer

3.3. Non-equilibrium distillation lines In a similar manner, eq. (14) can be combined with eq. (8) to calculate distillation lines: *x "(1#EMVK !EMV )x !x i,n i,n i,n i,n i,n i,n *x "EMVx (K !1). i,n i,n i,n i,n

Fig. 5. Equilibrium and non-equilibrium residue-curve map for n-pentane, n-hexane and n-heptane at 101.3 kPa. Tray dimensions: h : 0.100 m; D: 2 m. Liquid phase in plug flow. w

(18) (19)

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Equation (19) provides the means for calculating the effect of mass transfer on distillation lines. Because distillation lines are a discrete series of points, the non-equilibrium and equilibrium distillation-line maps [solutions to eqs (10) and (19), respectively] will be the same only if all the component stage efficiencies are equal to one. Even if all the species transfer with the same rate, i.e., they have the same efficiency, the liquid composition path will be different, especially if the equilibrium constants have high values. Figure 6 illustrates the equilibrium and non-equilibrium distillation-line maps for n-pentane, n-hexane and nheptane at 101.3 kPa. The difference between the maps is greater than in the case of residue curves. 3.4. Physical interpretation An equilibrium separation vector can be defined as the tie-line in a composition diagram between the composition of the liquid and vapour leaving an equilibrium stage [Fig. 7(a)]. This vector points in the direction of composition change during distillation. Consider a real stage, where the streams leaving the stage are not in equilibrium. The separation vector will be different from the equilibrium separation vector. If all the components have the same stage efficiency [Fig 7(b)], it can be shown from eq. (11) that the separation vector will be co-linear with the equilibrium separation vector. We expect that more stages

will be required, but the composition profile will lead towards the same node of the diagram. In this case, considering mass transfer introduces quantitative but not qualitative changes in the composition path plots. If the stage efficiencies of all the components are not equal [Fig. 7(c)], then from eq. (14) the separation vector must form an angle to the equilibrium separation vector. This will cause a more significant change in the path followed by the composition profile and, therefore, in addition to the quantitative change in the number of stages, we may also observe qualitative changes in the map of composition paths when mass transfer is considered, possibly even to the extent of the residue curve or distillation line from a given point leading to a different node than is found in the equilibrium-stage case (e.g. if the boundary moves). 4. RESULTS

In general, the consideration of mass transfer effects in the plotting of distillation lines and residue curves increases their curvature. The boundaries are also affected by the higher curvature, facilitating the design of columns placed across them (Laroche et al., 1992). Figure 8 shows the equilibrium and non-equilibrium residue-curve maps for the system methanol, ethanol and water at 101.3 kPa. This system has one low-boiling binary azeotrope between ethanol and water. A simple-distillation boundary exists between

Fig. 6. Equilibrium and non-equilibrium distillation-line map for n-pentane, n-hexane and n-heptane at 101.3 kPa. Tray dimensions: h : 0.025 m; D: 1.5 m. Liquid-phase well-mixed. w

Homogeneous azeotropic distillation

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Fig. 7. Composition vectors for different stage models: (a) equilibrium stage; (b) non-equilibrium stage (binary systems) and (c) non-equilibrium stage (multicomponent system).

Fig. 8. Equilibrium and non-equilibrium residue-curve maps for methanol, ethanol and water at 101.3 kPa. Tray dimensions: h : 0.100 m; D: 2 m. Liquid-phase in plug flow. w

the binary azeotrope and pure methanol. The boundary is almost straight, with a slight bend towards the methanol—ethanol edge, when calculated assuming equilibrium stages. The curvature of this boundary increases when mass transfer effects are taken into account for the typical tray dimensions shown in Fig. 8. The distillation-line map for this system, shown in Fig. 9, exhibits similar behaviour. The discrete nature of staged columns makes the difference between equilibrium and non-equilibrium distillation lines even greater when compared to residue curves.

Consider now the system acetone, ethanol and water at 101.3 kPa. This system is very similar to the previous example (one azeotrope, the ethanol-water low-boiling binary azeotrope, and one simple-distillation boundary). The simple-distillation boundary calculated using the equilibrium-stage model presents a slight bend towards the water product (Fig. 10). Based on the equilibrium boundary, we are led to believe that acetone is even less attractive than methanol as an entrainer for ethanol—water mixtures. Nevertheless, when the calculation is based on the

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Fig. 9. Equilibrium and non-equilibrium distillation-line maps for methanol, ethanol and water at 101.3 kPa. Tray dimensions: h : 0.100 m; D: 2 m. Liquid phase in plug flow. w

Fig. 10. Equilibrium and non-equilibrium residue-curve maps for acetone, ethanol and water at 101.3 kPa. Tray dimensions: h : 0.100 m; D: 2 m. Liquid phase in plug flow. w

Homogeneous azeotropic distillation

non-equilibrium stage model for the typical tray dimensions shown in Fig. 10, the simple-distillation boundary shows a marked curvature towards the acetone—ethanol edge. The change in the curvature shows that acetone is a good candidate entrainer and crossing its boundary does not present major difficulties. Designs using acetone as entrainer could be economically attractive. The potential of acetone as an entrainer for ethanol—water mixtures is missed completely using equilibrium stage models. Figure 11 illustrates the equilibrium and non-equilibrium distillation-line maps for a system with two azeotropes. The system formed by ethanol, methyl acetate and water at 101.3 kPa has two binary minimum-boiling azeotropes, one between ethanol and water and the other between methyl acetate and water. A distillation-line boundary can be found between the two binary azeotropes. When calculated based on the equilibrium-stage model, the distillation line boundary presents considerable curvature, which facilitates the design of columns across it. Although it is still curved, the non-equilibrium distillation-line boundary calculated for the typical tray size shown in Fig. 11 bends towards the water product, reducing its curvature. The non-equilibrium boundary is hence harder to cross than is suggested by the equilibrium boundary. Separation sequences designed for this ternary system using equilibrium maps might underperform (or indeed not function) once they are built.

971

The system chloroform, acetone and methanol at 101.3 kPa has three binary azeotropes (one in each binary pair) and one ternary azeotrope (Fig. 12). Although the curvature of the lines of the map changes when the effect of mass transfer is considered, three of the four boundaries remain at the same location. Only the simple-distillation boundary between the chloroform-acetone binary azeotrope and the ternary azeotrope shows a significantly higher curvature. The authors have studied several cases and, in general, the mass transfer effects do not produce considerable changes in systems with many azeotropes, since they have shorter distances between nodes. In addition, the equilibrium constants tend to have values close to one, which reduces the effect that different component stage efficiencies will have on the diagrams. In contrast with the equilibrium case, there is no unique map for non-equilibrium residue curves and distillation lines, because different design parameters, such as the column diameter, weir height, etc. have different effects on the relative magnitude of the component stage efficiencies. Figure 13 shows the equilibrium and non-equilibrium residue-curve maps for diethyl ether, ethanol and water at 101.3 kPa. In the calculation of the non-equilibrium maps, two different stage designs have been used. Tray dimensions 1 refer to a small column, while tray dimensions 2 refer to a larger column. The difference in the maps and, more importantly, in the simple-distillation boundaries, is

Fig. 11. Equilibrium and non-equilibrium distillation-line maps for methylacetate, ethanol and water at 101.3 kPa. Tray dimensions: h : 0.05 m; D: 2 m. Liquid phase well-mixed. w

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Fig. 12. Equilibrium and non-equilibrium residue-curve maps for acetone, chloroform and methanol at 101.3 kPa. Tray dimensions: h : 0.100 m; D: 2 m. Liquid-phase plug flow. w

significant. As we see in the next section, this provides scope for the synthesis of novel flowsheets. The limits that vapour—liquid equilibrium nonidealities impose on separation, i.e. the total reflux boundary, might be at a different location than where the equilibrium stage model predicts. The inclusion of mass transfer effects is essential in determining these limits. If mass transfer is neglected, either the performance of the distillation column might be jeopardized once the tower is built, or else potential advantages presented by the entrainer might be overlooked. Either way, the design is more expensive. The diagrams shown in this work have been calculated using standard tray designs, whose objective is to maximize the mass transfer, and hence the efficiency. As the diagrams have shown, inefficient stages can be advantageous and the overall flowsheet might benefit if they are used properly. Stage designs that maximise the difference between the component stage efficiencies are of particular interest in this context. In general, inefficient trays are easier to build than highly efficient ones. 5. IMPLICATIONS FOR DISTILLATION COLUMN DESIGN

The existence, location and curvature of simpledistillation boundaries or distillation-line boundaries are very important in the synthesis of azeotropic dis-

tillation sequences (Van Dongen and Doherty, 1985). Incorporating mass transfer in the residue-curve maps does not affect the existence and location of boundaries, but it does modify the curvature of the boundaries. Diagrams based on equilibrium stage models might allow the design of sequences that are found to be unfeasible once mass transfer is taken into account. No amount of overdesign (e.g. by addition of extra trays or additional reflux) can overcome simple-distillation boundaries or distillation-line boundaries that curve unfavourably. Figure 14 shows a flowsheet that separates a mixture of ethanol and water into pure components using acetone as the entrainer. The equilibrium residuecurve map shows no scope for the use of acetone as an entrainer. Nevertheless, the non-equilibrium map for the tray dimensions shown in Fig. 14 indicates that acetone is a good candidate entrainer for the separation. As illustrated in Fig. 13, the boundary is modified to different extents by different stage designs. A given feed composition might be on one side of the boundary for columns built with one type of tray, but on the other side of the boundary for a different type of tray. This can create opportunities for distillation sequence synthesis by using distillation columns with less efficient stages to facilitate the crossing of

Homogeneous azeotropic distillation

Fig. 13. Equilibrium and non-equilibrium residue-curve maps for diethylether, ethanol and water at 101.3 kPa. Tray dimensions: (1) h : 0.025 m; D: 1 m. Liquid-phase well-mixed. (2) h : 0.150 m; D: 6 m; w w Liquid-phase well-mixed.

Fig. 14. Flowsheet that uses acetone as the entrainer to separate ethanol from water at 101.3 kPa. Tray dimensions: (1) h : 0.100 m; D: 2 m. Liquid phase in plug flow. w

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simple-distillation boundaries or distillation-line boundaries. Depending on how effectively stage efficiencies can be predicted for different tray dimensions, the designer is provided with a limited degree of control over the residue curves and simple-distillation boundaries or distillation lines and distillation-line boundaries. Figure 15 shows a flowsheet which uses two columns with different stage designs to obtain pure ethanol and water. Columns 1 and 2 have different tray dimensions, therefore, they experience different limits. The gap between the two limits is sufficient to allow the sequence to perform the separation. This opportunity would have been overlooked if only equilibrium trays had been considered. Mass transfer introduces quantitative and qualitative changes in the residue-curve and distillation-line maps of azeotropic systems. Hence, mass transfer should not be neglected even at the early stages of distillation sequence synthesis. 5.1. Minimum reflux The minimum reflux condition, i.e. the pinch-point curves or distillation limits, is not affected by mass transfer effects, since both of these assume an infinite number of stages. Agarwal and Taylor (1994) found that the minimum reflux ratio is the same regardless

of whether it is determined by an equilibrium stage model or by a non-equilibrium stage model. Hence, the composition on the pinched trays of the column does not change when the column is modelled using equilibrium or non-equilibrium stages. This means that the locus of pinch points will remain the same and the minimum reflux bound for a given feed or product remains unchanged. 6. NON-EQUILIBRIUM COMPUTATION

Computation of the non-equilibrium residue-curve or distillation-line maps requires estimation of the Murphree vapour stage efficiency (or whichever definition of efficiency has been used to derive the equations). Different approaches can be used for this calculation. If mass-transfer models (also known as rate-based models) are used, e.g. Krishnamurthy and Taylor (1985), then the efficiencies can be back-calculated once the performance of the stage is known. Alternatively, stage efficiency correlations (AIChE, 1958; Zuiderweg, 1982; Chan and Fair, 1984) or available experimental data can be used. Two important factors simplify the computation of stage efficiency. First, the efficiency is needed for stages operating at total reflux; hence, (7) is applicable. Second, the liquid composition leaving the tray is known, so it is only necessary to calculate the

Fig. 15. A mixture of ethanol and water is separated at 101.3 kPa using diethyl ether as entrainer. A double column arrangement is used to cross the simple-distillation boundary. Tray dimensions: (1) h : 0.025 m; D: w 1 m. Liquid-phase well-mixed. (2) h : 0.150 m; D: 6 m; Liquid-phase well-mixed. w

Homogeneous azeotropic distillation

composition of the vapour leaving the tray, reducing the number of iterations required. For the examples in this paper, the AIChE correlation was used to calculate the number of transfer units for the vapour and liquid phases for every binary pair in the ternary system. A modified version of the procedure described by Taylor and Krishna (1993) was used to calculate the overall number of transfer units, the point efficiency and the stage efficiency for each component on each tray, as described by Castillo (1997) and Castillo and Towler (1997). Although errors can be expected in the predicted values of the component efficiencies, we are less concerned with the absolute values of the component efficiencies than with their relative values, since it is the relative magnitude that determines the deviation of the separation vector from the equilibrium separation vector. The errors introduced by correlation tend to affect all components equally; therefore, the relative magnitudes of the component efficiencies are not strongly sensitive to the error in their absolute values. Although the difference between the stage efficiencies of the components may be small, the cumulative effect over many stages increases its impact. A difference of as little as 10% between the stage efficiencies of two of the species has been shown to be enough to produce a significant change in the curvature of residue curves and distillation lines.

7. CONCLUSIONS

The equations that define residue curves and distillation lines have been extended to include the effect of mass transfer on the composition of the streams leaving a stage. If all components are transferred at the same rate (i.e. all the component stage efficiencies are equal), then mass transfer has no effect on the residue-curve map. In general, however, a change in the appearance of the residue curve map is expected, and our results indicate that this change can often be considerable. The distillation-line map is even more strongly affected, since the non-equilibrium stage model almost never predicts all of the component stage efficiencies to be equal to one. It has been found that mass transfer effects tend to increase the curvature of simple-distillation/distillation-line boundaries, making them easier to cross. Sequences of distillation columns synthesised and simulated using tools based solely on equilibrium models can become unfeasible when mass transfer is considered and would not achieve the design separation if constructed. Although mass transfer effects do not lead to new simple-distillation/distillation-line boundaries or produce changes in the nature of the singular points of the residue-curve or distillation-line map, they must be included in the entrainer selection procedure, since diagrams based on equilibrium models can be substantially altered. The mass transfer effect does not change the bounds proposed for the minimum reflux condition.

975 Acknowledgements

The authors would like to acknowledge the support of the UMIST Process Integration Research Consortium. Special thanks to Dennis Y.-C. Thong for the preparation of the diagrams.

NOTATION

D EMV h h w K ¸ » x y

column diameter, m Murphree vapour stage efficiency, defined by eq. (4) dimensionless time or packing height exit weir height, m equilibrium constant liquid molar flowrate, mol/s vapour molar flowrate, mol/s liquid-phase mole fraction vapour-phase mole fraction

Superscript eq at equilibrium Subscripts i index for component i in a multicomponent mixture n index for stage number. Stage number 1 is at the top of the column REFERENCES

Agarwal, S. and Taylor, R. (1994) Distillation column design calculations using a non-equilibrium model. Ind. Engng Chem. Res. 33, 2631—2636. AIChE (1958) Bubble ¹ray Design Manual: Prediction of Fractionation Efficiency. AIChE, New York. Castillo, F. J. L. (1997) Synthesis of Homogenous Azeotropic Distillation Sequences. Ph.D. dissertation, UMIST. Castillo, F. J. L. and Towler, G. P. (1997) Application of linearised vapour—liquid equilibrium equations. Chem. Engng Sci. (accepted for publication). Chan, H. and Fair, J. R. (1984) Prediction of point efficiencies on sieve trays. 2. Multicomponent systems. Ind. Engng Chem. Proc. Des. Dev. 23, 820—827. Doherty, M. F. and Caldarola, G. A. (1985), Design and synthesis of homogeneous azeotropic distillations. 3. The sequencing of columns for azeotropic and extractive distillation. Ind. Engng Chem. Fundam. 24, 474—485. Doherty, M. F. and Perkins, J. D. (1979) On the dynamics of distillation processes—III: The topological structure of ternary residue curve maps. Chem. Engng Sci. 34, 1401—1414. Fidkowski, Z. T., Doherty, M. F. and Malone, M. F. (1993) Feasibility of separation for distillation of non-ideal ternary mixtures. A.I.Ch.E. J. 39, 1303— 1321. Hoffman, E. J. (1964) Azeotropic and Extractive Distillation. Interscience Publishers, Wiley, New York. Krishnamurthy, R. and Taylor, R. (1985) A non-equilibrium stage model of multicomponent separation processes. Part I. Model description and method of solution. A.I.Ch.E. J. 31, 449—456. Laroche, L., Bekiaris, N., Andersen, H. W. and Morari, M. (1992) Homogeneous azeotropic distil-

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