Chemical Engineering Science 55 (2000) 2089}2097
Optimisation of the conceptual design of reactive distillation columns Sanne Melles!, Johan Grievink!,*, Stany M. Schrans",1 !Department of Chemical Process Technology, Delft University of Technology, Delft, Netherlands "Shell Research & Technology Centre, Amsterdam, Shell International Oil Products B.V., Netherlands Received 3 December 1998; accepted 9 September 1999
Abstract It is shown that the introduction of a di!erent tray holdup in the stripper and rectifyer section of a continuous kinetically controlled reactive distillation column facilitates the design procedure. It also creates a range of design alternatives, generating the possibility to optimise for both the total number of trays and the total liquid holdup in the column. This allows for minimising investment related costs such as the column height and the amount of catalyst. When investigating the in#uence of product speci"cations and process parameters such as the heat of reaction and the stoichiometric sum on column design, the introduced range of design alternatives should be compared rather than single designs. ( 2000 Elsevier Science Ltd. All rights reserved. Keywords: Reactive distillation; Design method; Sensitivity curves; Optimisation
1. Introduction Reactive distillation is a commercially proven alternative for carrying out liquid-phase chemical reactions (Agreda, Partin & Heise, 1990; Smith & Huddleston, 1982). Compared to conventional technology, reactive distillation is attractive because it results in lower capital and operating costs, energy is integrated directly and higher product purities can be achieved. For the analysis of behaviour of such a reactive distillation process, relevant static and dynamic simulations have been performed (Jacobs & Krishna, 1993; Abufares & Douglas, 1995). Reactive distillation column design which is essentially di!erent from a simulation, is in a state of development because existing conceptual design methods are still quite restrictive and relatively di$cult to use. It is the objective of this paper to facilitate reactive distillation column design. A continuous reactive distillation column design method developed by Doherty and his co-workers (Barbosa & Doherty, 1988; Buzad & Doherty, 1994; 1995) is the &Boundary Value Design Method'. This
* Corresponding author. 1 Current address: Shell International Trading and Shipping Co Ltd, Shell-Mex House, London WC2R 0ZA, UK.
method essentially consists of "rst specifying the bottom and top product compositions and choosing a value for the re#ux ratio. Then the goal is to "nd a value for the holdup, i.e. the volume on the trays in which the kinetically controlled reaction actually proceeds, such that when calculating the composition on each tray, the composition pro"les of the stripper and rectifyer intersect. Furthermore, the holdup has to be manipulated such that when an intersection of the composition pro"les occurs, the component material balances over the column are virtually satis"ed and the right amount of reaction has taken place. Finally, the number of trays in each section is counted up to the intersection which results in the total number of trays. A common assumption of the &Boundary Value Design Method' is a uniform tray holdup in the column. This assumption is made in order to make the design procedure more manageable since a non-uniform tray holdup increases the complexity of the problem considerably (Pekkanen, 1995). However using this uniform tray holdup assumption, it appears that few speci"ed bottom and top compositions lead to a feasible column design. Furthermore, one is tempted to search for a feasible combination of the re#ux ratio and the holdup which might actually not exist. In this paper the uniform holdup assumption is relaxed and the use of diwerent tray holdups per section of the column is investigated. The advantages of using a
0009-2509/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 4 9 7 - 2
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Nomenclature
N S
C i B D Da b
N T N c R r rd S t < < o < R < S x j,i x i
Da t Eo T F H H j H o H R H S H T *H r *H v K %2 K i k f m n N R
generic name for a component i dimensionless bottom #ow rate, mol/s distillate #ow rate, mol/s DamkoK hler number in batch experiment, dimensionless DamkoK hler number of a tray in a continuous column, dimensionless total extent of reaction, mol/s feed #ow rate, mol/s molar liquid tray holdup, mol molar liquid holdup on tray j of a continuous column, mol initial molar liquid holdup in batch reactive distillation, mol molar liquid holdup of a tray in the rectifyer section of a continuous column, mol molar liquid holdup of a tray in the stripper section of a continuous column, mol total molar liquid holdup of a continuous column, mol reaction enthalpy, J/mol enthalpy of evaporation, J/mol reaction equilibrium constant, dimensionless vapour}liquid equilibrium constant, dimensionless forward reaction rate constant, 1/s generic tray number in rectifyer section, dimensionless generic tray number in stripper section, dimensionless number of trays in rectifyer section, dimensionless
di!erent holdup per section are illustrated in a discussion of the in#uence of several process parameters on column design. Furthermore, the &Boundary Value Design Method' is extended to a more general case, taking heat e!ects and a non-zero stoichiometric sum into account. The e!ects of purity of the bottom product, the reaction enthalpy and the stoichiometric sum of the reaction on column design using a di!erent holdup per section are investigated. The premises of a three component mixture, single feed, ideal vapour}liquid equilibrium and constant volatilities are maintained.
2. Conceptual design of continuous reactive distillation columns In this section the necessary equations for the design of a continuous reactive distillation tray column are given
x y i
number of trays in stripper section, dimensionless total number of trays in column, dimensionless number of components, dimensionless re#ux ratio, dimensionless reaction rate, mol/s driving force of reaction, dimensionless reboiler ratio, dimensionless time, s vapour #ow rate, mol/s initial vapour #ow rate, mol/s vapour #ow rate to condensor, mol/s vapour #ow rate from reboiler, mol/s molar fraction of component i on tray j, mol/mol mole fraction of component i in the liquid phase, mol/mol composition vector of the liquid phase, mol/mol mole fraction of component i in the vapour phase, mol/mol
Greek letters a i m
volatility of component i relative to a reference component, dimensionless warped time in batch reactive distillation experiment, dimensionless
Subscripts F D B
feed, dimensionless distillate product, dimensionless bottom product, dimensionless
and brie#y discussed. In conceptual reactive distillation column design the values of parameters which directly in#uence the size of the column such as the re#ux ratio, the number of trays and the holdup on a tray have to be determined. To achieve this the material and enthalpy balances over the column are solved to calculate the top and bottom product #ow and the amount of reaction which has to take place. Then the stage-to-stage balances are solved to determine the liquid and vapour #ow, the composition and the amount of reaction on each tray. As seen from Fig. 1 the column consists of two sections which meet at the feed tray. In both sections the stage-to-stage balances are elaborated starting at the top and bottom, respectively, and calculating towards the feed tray. First, the assumptions and system boundaries which hold in this paper are given. The equations are derived for a general single reaction in the liquid phase on each
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following holds: Nc + x "1. (6) i i/1 The described reaction kinetics are strongly idealised and temperature independent. This gross simpli"cation is motivated by the fact that the elementary material and enthalpy balances for conceptual column design do not allow a temperature calculation on a tray. A more general reaction scheme can be introduced easily. 2.1. External balances Fig. 1. Schematic representation of a reactive distillation column and its rectifyer section.
tray of the column. Furthermore, the design method accounts for heat e!ects and a non-zero stoichiometric sum. Finally an ideal mixture, vapour}liquid equilibrium, constant relative volatilities and a column with a non-reactive total condensor and a non-reactive partial reboiler are assumed. All assumptions can be relaxed easily. Now all equations are given which are necessary for reactive distillation column design. Since a reaction term occurs in the material balances, the used reaction kinetics are shown "rst. The reaction is written as Nc + l C "0, (1) i i i/1 with N is the total number of present components, C is c i a generic component name and l is the stoichiometric i coe$cient which is positive for products and negative for reactants. For a ternary system with reactant C and products A and B, Eq. (1) is reduced to Dl DC H l A#l B. 3 1 2 The stoichiometric sum l
(2) T
N l "+ l (3) T i i/1 indicates whether the reaction generates (l '0) or conT sumes (l (0) moles. T For the reaction rate the following expression is assumed: c
r"k rd, (4) f where k is the forward reaction rate constant and rd is f the composition dependent driving force of the reaction. 1 Nc Nc (5) rd" < x(1@2)(@li @~li )! < x(1@2)(@li @`li ). i i K %2 i/1 i/1 In Eq. (5), K is the reaction equilibrium constant and %2 x is the liquid mole fraction of component i for which the i
If the feed, the distillate and the bottom #ow are represented by F, D and B, respectively (see Fig. 1), then the overall and the component molar balances over the column are written as F"B#D!l Eo , (7) T T Fx "Bx #Dx !l Eo , i"1, 2,2, N !1, (8) F,i B,i D,i i T c where H is the liquid molar holdup on tray j. Eo is the j T total extent of reaction, NT Eo "k + H rd (9) T f j j j/1 with N "N #N #1 is the total number of trays. T R S The total number of trays does not include the condensor and the reboiler. The overall material and the component balances are combined in a &transformed component balance' by eliminating the reaction term from Eqs. (7) and (8),
A
B A A B
B
l l F 1! T x "B 1! T x l F,i l B,i i i l #D 1! T x , i"1, 2,2, N !1. (10) c l D,i i For a ternary system one can eliminate F resulting in an expression for D/B, D/B"[(1/l )(x !x )!(1/l )(x !x ) 1 B,1 F,1 2 B,2 F,2 !(l /l l )(x x !x x )]/ T 1 2 B,1 F,2 F,1 B,2 [(1/l )(x !x )!(1/l )(x !x ) 1 F,1 D,1 2 F,2 D,2 !(l /l l )(x x !x x )]. (11) T 1 2 D,2 F,1 F,2 D,1 Using Eqs. (10) and (11), values for D and B can be calculated in case of a ternary system when the top and bottom product compositions and the feed #ow and composition are speci"ed. In a system with more than three components and a "xed feed #ow and composition, it is not allowed to completely specify the compositions of the top and bottom products in order to avoid overspeci"cation of the degrees of freedom.
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Finally the overall enthalpy balance is given. This balance is used to relate the condensor and reboiler duties. Assuming that heat losses and dissipation are equal to zero and that changes in the liquid enthalpy are negligible compared to the enthalpies of evaporation and reaction then the enthalpy balance over the column is (12) *H < !*H < !*H Eo "0. v R v S r T Here *H < is the condensor duty, *H < is the reboiler v R v S duty and *H is the reaction enthalpy.2 Furthermore it is r assumed that the feed consists of saturated liquid. 2.2. Internal balances Now the stage to stage material and enthalpy balances are solved to determine the liquid and vapour #ow and the liquid composition on each tray in both sections. The rectifyer section (see Fig. 1) Stream balance: < #¸ !¸ !< #l H k rd "0, m`1 m~1 m m T m f m Enthalpy balance:
(13)
(14) *H (< !< )#*H H k rd "0, v m m`1 r m f m where m"1,2, N with N is the number of stages in R R the rectifyer section. The vapour #ow through the rectifyer is written as *H m < "< # r k + H rd, with < "D#¸ "< m`1 1 *H f 1 o R j j v j/1 and ¸ "RD. (15) o Here, *H is the heat of evaporation which has a positive v value. It is seen from Eq. (15) that for an exothermic reaction (*H (0) and a positive reaction rate the var pour #ow decreases as the stage number increases (top down). The stoichiometric sum of the reaction does not in#uence the rectifyer vapour #ow, which is explained by the fact that the reaction only takes place in the liquid phase. The liquid #ow on a tray in the rectifyer is described as follows:
A
B
*H m r #l k + H rd. ¸ "¸ # (16) m o T f j j *H v j/1 It is seen from Eq. (16) that for an exothermic, equimolar reaction and a positive reaction rate the liquid #ow decreases as the stage number increases (top down). Apart from the in#uence of the reaction enthalpy, the stoichiometric sum in#uences the liquid #ow. A positive stoichiometric sum contributes to an increasing liquid #ow as the stage number increases. 2 *H is negative for exothermic reactions and positive for endotherr mic reactions.
Solving the component balance over a tray the following general recursive equation is found: y #¸ x !< y m`1 m`1,i m~1 m~1,i m m,i (17) !¸ x #l k H rd m m,i i f m m with y "x "x . Substitution of the component 1,i 0,i D,i balance over the condensor,
0"<
< y !¸ x "Dx , (18) 1 1,i o D,i D,i in Eq. (17) gives the possibility to derive the recursive composition equation for the rectifyer section of a reactive distillation column:
A
B
m Dx #¸ x !l k + H rd . (19) j j D,i m m,i i f m`1 j/1 This equation describes the vapour composition on a tray of the rectifyer section as a function of the liquid composition on the tray above, the distillate composition and the sum of the reaction rates in the trays above. Since vapour}liquid equilibrium is assumed, the liquid composition can be calculated if the vapour composition is known and vice versa using the following equation: y " m`1,i <
1
y "K x . (20) m,i m,i m,i The parameter K is a function of the relative volalities of i the components and the composition of the liquid phase, a i K" . (21) i +Nc x a j/1 j j Note that Eqs. (15), (16), (19) and (20) are su$cient to generate #ow and composition pro"les in the recti"er section top down. For the stripper section the equations are derived similarly. Notice that in this section the numbering of the trays is bottom up. *H n < "< ! r k + H rd with < "SB, (22) n o *H f o j j v j/1 n *H r #l k + H rd with ¸ "¸ ! j j n`1 1 T f *H v j/1 ¸ "B#< , (23) 1 o 1 n x " Bx #< y !l k + H rd n`1,i ¸ B,i n n,i i f j j n`1 j/1 0)n)N (24) S with x "x , y "K x and n"1,2, N with 0,i B,i 0,i 0,i 0,i S N is the number of stages in the stripper section. S Finally, the enthalpy balance Equation (12) is used to connect both sections. This results in the following relation:
A
B
A
A
B
B
1 *H r Eo . S" D(1#R)# B *H T v
(25)
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In Eq. (25) the reboil ratio is determined as a function of the re#ux ratio, the top and bottom product #ows, the ratio of the reaction and evaporation enthalpies as well as the total extent of reaction. 2.3. Design procedure Using the given equations a reactive distillation column can be designed following a procedure which is brie#y described. The design procedure consists of "rst specifying the feed composition, the bottom and top product compositions and choosing product #ows consistent with Eq. (10) (or Eq. (11) for a ternary system). The feed #ow can than be calculated. Eq. (7) yields the total extent of reaction which has to take place. Choosing a value for R, the reboil ratio can be calculated using Eq. (25). The goal now is to "nd values for the liquid holdup, H , such that when one recursively calculates the n composition on each tray, the composition pro"les of the stripper and rectifyer intersect. At the intersection continuity is e!ected, i.e., Dx R !x S D(e , i"1, 22, N !1, (26) N `1,i N `1,i 1 c where the pro"les intersect, the material balance over the column has to be checked to ensure that the right amount of reaction has taken place, i.e.,
K
K
NR NS k + H rd#k + H rd#k H rd !Eo (e . (27) f j j f j j f F F T 2 j/1 j/1 When both conditions (26) and (27) are met then the number of trays in both sections is consolidated and the total number of trays is thus determined as the sum of the number of trays in both sections and the feed tray. It is up to the judgement of the designer to decide for which values of e and e continuity and the overall material 1 2 balance is satis"ed. An overview of the model parameters in the design procedure is given in Fig. 2. In the remainder of this section of the paper the liquid holdup is assumed equal on all trays: (H "H ). This j j`1 leads to a simpli"cation of all equations in which the holdup term appears. In these equations the parameter H behind the summation sign is replaced by the paraj meter H in front of the summation sign. It is convenient to introduce the tray DamkoK hler number, which is a dimensionless ratio of a characteristic liquid residence time of a tray (H/F) to a characteristic reaction time (1/k ), f H Da " k . (28) 5 F f
A large value of the tray DamkoK hler number (Da <1) 5 indicates that the reaction has the largest contribution to the change in composition on a tray. If Da ;1 then the 5 reaction is relative slow and distillation will dominate. Using the "xed point design method (Buzad & Doherty,
Fig. 2. Information #ow in the design procedure.
1994) an initial guess for the tray DamkoK hler number can be made by calculating the so-called critical DamkoK hler numbers of the stripper and rectifyer sections. A critical DamkoK hler number of a section is determined by "nding a value for the liquid holdup such that the compositions on succeeding trays of a section approach a "xed point within the composition space: lim x "xH. (29) n n?= Our practical experience supports the observation by Buzad that the critical DamkoK hler numbers of both sections should be approximately equal in order to "nd a solution for the design problem (Buzad, 1994). Calculating the critical DamkoK hler numbers thus indicates at an early stage of the design procedure whether the design will be feasible. It is our experience that when using a uniform holdup throughout the column only few combinations of top and bottom product composition appear to lead to a feasible design. This is a disadvantage since a designer should be able to design a reactive distillation column for many combinations of top and bottom product compositions. In the next section the uniform holdup assumption is thus relaxed.
3. Di4erent holdups in stripper & rectifyer: optimisation of a column design For both the stripper and the rectifyer section a di!erent value for the molar liquid holdup and thus a di!erent design value of the tray DamkoK hler number can be chosen. It is no longer necessary for the critical DamkoK hler numbers to be approximately equal, which
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considerably increases the possibility to "nd a column design matching a speci"ed bottom and top product. Using di!erent tray holdups in the stripper and the rectifyer introduces an additional degree of freedom, which results in a range of designs belonging to one set of product speci"cations. This is illustrated with an example which was used before in the doctoral dissertation of Buzad (1994). Assume a ternary system with speci"cations as given in Table 1, which is called the basecase. In accordance with the speci"cations of the basecase several reactive distillation column designs have been made. In each design a di!erent number of trays for the rectifyer is chosen after which matching values for the liquid holdups and the number of trays in the stripper are determined. These values are given in Table 2. In the last row of the same table a design is included if a constant holdup in the column were assumed. In this table and the rest of the document the feed tray is included in the rectifyer section. As is seen in Table 2 the value for the liquid holdup in each section has to be speci"ed more accurately as the number of trays in the section increases. This is explained by the fact that the DamkoK hler number approaches its critical value, around which the composition pro"les show extreme sensitivity towards the DamkoK hler number (Buzad & Doherty, 1994) (Fig. 2). For a value of the holdup corresponding with the critical DamkoK hler number, the number of trays goes to in"nity as de"ned in Eq. (29). The data in Table 2 and the Figs. 3 and 4 clearly show that a minimum occurs for both the total number of trays in the column, N and the total liquid holdup, H . T T The minimum indicates a design alternative preferable compared to the design with the constant holdup in the column. The total liquid holdup is the sum of the holdup over all trays. An optimisation possibility is thus intro-
Table 1 Reactive distillation example; basecase
duced for investment cost related parameters such as column height and total amount of catalyst. The curves show the design possibilities belonging to a speci"c set of product speci"cations. We will call these curves the &Design Sensitivity Curves'.
4. Comparison of design sensitivity curves: reactive distillation mechanism It will be demonstrated that design sensitivity curves should be compared rather than single designs when the Table 2 Design alternatives for the basecase and the basecase with a constant holdup in the column H (mol/tray) R
N (!) H (mol/tray) R S
N (!) H (mol) N (!) S T T
11.48753 11.48705 11.486785 11.486625 11.486470 11.48639825
14 15 16 17 19 22
10.702 11.32 12.30 13.15 14.44 16.5
13 10 8 7 6 5
299.95 285.51 282.19 287.32 304.88 335.20
27 25 24 24 25 27
11.48705
15
11.48705
10
287.18
25
Fig. 3. &Design Sensitivity Curve': total number of trays as a function of the number of trays in the rectifyer for the basecase.
Component molefraction
A x 1
B x 2
C x 3
The feed composition Speci"cation of the bottom composition Speci"cation of the distillate composition The volatilities relative to component B, a i The reaction is reversible The equilibrium constant, K %2 The forward reaction rate constant, k f The re#ux ratio, R The top product #ow, D Resulting bottom product #ow, B Resulting feed #ow, F
0 0.01
0 0.81
1 0.18
0.803
0.003
0.194
5
1
3
2C H A#B 0.25 1 2.1 50 50 100
Fig. 4. &Design Sensitivity Curve': total number of trays in relation to the total liquid holdup in the column for the basecase.
S. Melles et al. / Chemical Engineering Science 55 (2000) 2089}2097
in#uence of process parameters on reactive distillation column design is investigated. In Fig. 5 the design sensitivity curves are given for both the basecase and a case with the same product speci"cations but with a reaction with a positive stoichiometric sum: 1.5 C H A#B. It should be noted that the product #ows B and D are kept constant, which results in a smaller required value of the feed #ow, F compared to the basecase. It is seen that in this example the positive stoichiometric sum results in a column with a larger number of trays. The increase in total number of trays is not equally distributed over the two sections. The relative position of the two curves indicates that the number of trays in the rectifyer has increased more than the number of trays in the stripper. Such an increase would be rather di$cult to observe when comparing individual designs only. To show the use of the &Design Sensitivity Curves' an analysis has been made of the e!ects of product speci"cations, heat e!ects and the stoichiometric sum of reaction on reactive distillation column design. In Table 3 the di!erences in speci"cations relative to the base case are shown. The observed changes in design are discussed and explained relative to the speci"c example of Table 1. To enhance physical chemical understanding of the reactive distillation mechanism the column is conceptually split into two functional tasks: a reaction function and a distillation function. Figs. 6 and 7 are used to illustrate the changes in design. In Fig. 6 &Design Sensitivity Curves' are used to show the changes in number of trays and the distribution of the trays over the two sections. The dashed line in this "gure represents situations where relative to the base case the absolute increases of the number of trays in the stripper and rectifyer are equal, *N "*N . In Fig. 7 &Design R S Sensitivity Curves' visualise the changes in total holdup. In these "gures a minimum for both the total number of trays and the total holdup of the column can be seen. 4.1. Ewects of the stoichiometric sum of the reaction When a reaction with a positive stoichiometric sum occurs, the critical DamkoK hler numbers in both sections have smaller values compared to the base case.3,4 This indicates that the reaction function of the column becomes less important. From the overall mole balance is seen that less feed is needed to produce the same amount of product compared to the base case. Less reaction has to take place to meet the design speci"cations, which explains the decrease in total holdup as is seen in Fig. 7 (curve 2). With a smaller value of Da and a smaller feed#ow, F, the design holdups in both the rectifyer and the stripper have decreased considerably. The residence time on a tray of the rectifyer and the stripper has therefore 3 basecase: Dac "0.1148637, Dac "0.10348. r s 4 non-equimolar case: Dac "0.0604486, Dac "0.069658. r s
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Fig. 5. &Design Sensitivity Curves': total number of trays plotted against the number of trays in the rectifyer. The non equimolar reaction is 1.5 CHA#B.
decreased compared to the base case. This results in less production per tray, which is compensated with additional trays. From Eqs. (15), (16), (22), (23) and (25) it is derived that the average liquid and vapour #ows in a column with reaction with positive stoichiometric sum and a "xed re#ux ratio are larger in the rectifyer and smaller in the stripper compared to the #ows in the base case. The residence time in the rectifyer has thus decreased more compared to the stripper. To meet the design speci"cations, the rectifyer must therefore increase compared to the stripper, which can be seen in Fig. 6. The curve has moved to the right of the dashed line. 4.2. Ewects of a change in the purity of the bottom product The column as speci"ed by Table 1 is also designed with a tighter bottom product speci"cation in which less of component A is allowed. From a distillation point of view the number of trays in the stripper section has to increase to maintain the speci"ed bottom product. This can be seen from the fact that pro"le 3 in Fig. 6 has moved to the left of the dashed line. The stripper critical DamkoK hler number has a smaller value5 compared to the base case, which results in a smaller holdup per tray in the stripper section. This obviously follows the expected functional shift towards distillation in this section. Fig. 7 shows that the total holdup requirement near the minimum number of trays is a little smaller, which is explained by the fact that required extent of reaction is slightly smaller compared to the base case. Less component C has to be converted. 4.3. Heat ewects As can be derived from Eq. (25) the reboil ratio in the column with the exothermic reaction, *H /*H "!0.2, r v 5 Pure case: Dac "0.1148679, Dac "0.035446. r s
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Table 3 Speci"cation alternatives for the basecase Stoichiometry
Base case
2 C H A#B
Non-equimolar case
1.5C H A#B
Pure case
2 C H A#B
Pure non-equimolar case
1.5C H A#B
Exothermic case
2 C H A#B
reaction enthalpy enthalpy of evaporation *H r "0 *H v *H r "0 *H v *H r "0 *H v *H r "0 *H v DHr 5!0.2 DH*
x B,1
x B,2
0.010
0.810
0.010
0.810
0.005
0.805
0.005
0.805
0.010
0.810
the stripper. From a distillation point of view the number of trays, especially in the stripper section has to increase somewhat to maintain the required product speci"cations. This is consistent with the observations of Okasinski (Okasinski & Doherty, 1998). Furthermore, it can be seen that the critical DamkoK hler numbers have virtually remained constant compared to the base case.6
5. Conclusions and recommendations
Fig. 6. &Design Sensitivity Curves': total number of trays plotted against the number of trays in the rectifyer. All columns are designed according to the speci"cations given in Tables 1 and 3: (1) base case, (2) non-equimolar case, (3) pure case, (4) pure non-equimolar case, (5) exothermic case.
Fig. 7. &Design Sensitivity Curves': total number of trays plotted against the total liquid holdup in the column. All columns are designed according to the speci"cations given in Tables 1 and 3: (1) base case, (2) non-equimolar case, (3) pure case, (4) pure non-equimolar case, (5) exothermic case.
and a "xed re#ux ratio is smaller compared to the reboil ratio in the column of the base case. In the whole column the mole #ows have decreased compared to the basecase, which counts especially for the vapour #ow in
In this paper the possibility of designing a reactive distillation column with a di!erent tray holdup in both the rectifyer and the stripper section of the column is introduced. Physically this implies a di!erent e!ective reaction volume per tray (amount of catalyst) in each section. It increases the possibility to design a column for any speci"ed top and bottom product and introduces an additional degree of freedom which results in a range of feasible designs. In this paper it is demonstrated that within this range of designs a minimum occurs for the total number of trays and the total column holdup. A possibility for optimisation is thus introduced. A next logic step would be an investigation into the use of a di!erent holdup on every tray of the column. Since this increases the number of design decision variables considerably, it will be di$cult to manage the design problem with the boundary value design method described in this paper. Varying the holdups on the trays can possibly in#uence the composition pro"le of a continuous reactive distillation column in a similar way as the heating policy does in a batch reactive distillation still (Re`v, 1994) (Venimadhavan, Buzad, Doherty & Malone, 1994).
6 Exothermic case: Dac "0.1145477, Dac "0.1032804. r s
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It has been shown that the introduced &Design Sensitivity Curves', which represent the design alternatives belonging to one set of design speci"cations, are very usefull to study the in#uence of process parameters on continuous reactive distillation column design. The roles of the heat of reaction, the stoichiometric sum of reaction and the product speci"cations have been investigated. As a result the discussed example improves insight and physical chemical understanding in reactive distillation column design. Demanding a more pure bottom product results in an increase in the total number of trays, especially in the stripper section. However the total e!ective reaction volume hardly changes. Exothermicity of a reaction and a "xed re#ux ratio result in an increase in total number of trays compared to the example with negligible heat e!ects. The absolute increase in number of trays of the stripper section is larger compared to the increase of the rectifyer section. Additionally more e!ective reaction volume or catalyst is needed. Furthermore, the reboil ratio has decreased compared to the base case. A column with a reaction with a positive stoichiometric sum and a "xed re#ux ratio leads to a larger number of trays compared to the case with an equimolar reaction. The increase in number of trays of the rectifyer section is larger than the increase in the stripper section. Less e!ective reaction volume is needed. Furthermore, the reboil ratio has decreased compared to the base case Finally, the authors recommend to use an other di!erent holdup on the feed tray to quicken the design procedure. The holdups of the stripper and rectifyer can be used to almost satisfy the design conditions (Eqs. (26) and (27)) after which the feed tray holdup is used to completely satisfy these conditions. Acknowledgements This paper is an extension of the MSc thesis of the "rst author, &The Conceptual Design of Reactive Distillation
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Columns' at the faculties of Mechanical Engineering and Chemical Technology of the Delft University of Technology. We would like to thank Prof. J. de Graauw and Ir. C. Luteijn for their advice and support. Furthermore we gratefully acknowledge a grant from Shell Research, Amsterdam.
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