Chemical Engineering Science 60 (2005) 4377 – 4395 www.elsevier.com/locate/ces
Conceptual design of single-feed hybrid reactive distillation columns Ramona M. Dragomir1 , Megan Jobson∗ Centre for Process Integration, School of Chemical Engineering and Analytical Science, The University of Manchester, P.O. Box 88, M60 1QD, Manchester, UK Received 2 August 2004; received in revised form 1 March 2005; accepted 2 March 2005 Available online 6 May 2005
Abstract It is well known that reactive distillation offers benefits by integrating distillation and reaction within a single unit. While there are procedures available for the synthesis of non-reactive distillation processes and of reaction-separation systems, the design of reactive distillation columns is still a challenge. This work presents a new synthesis and design methodology for hybrid reactive distillation columns, featuring both reactive and non-reactive sections; reactive equilibrium is assumed. The approach is based on graphical techniques; therefore it is restricted to systems with two degrees of freedom according to Gibbs phase rule. The design method allows rapid and relatively simple screening of different reactive distillation column configurations. The results are useful for initialising more rigorous calculations. The methodology is illustrated for MTBE and ethyl formate production. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Chemical processes; Design; Reactive distillation; Hybrid column; Process synthesis; Stage composition lines
1. Introduction Reactive distillation is a promising alternative to conventional processes, due to its well-known advantages. To exploit this potential, tools for conceptual design are needed. Methods applying optimisation techniques for column design are available (e.g. Ciric and Gu, 1994; Jackson and Grossmann, 2001), but are generally computationally intensive and seldom allow the design engineer to interact with the design algorithm. Other methodologies for reactive distillation column design, based on graphical techniques (e.g. Barbosa and Doherty, 1988; Bessling et al., 1997; Espinosa, 1995a,b, 1996; Lee, 2000; Groemping et al., 2004), have been developed during the past decade. Nevertheless, there is still a lack of systematic conceptual design methods, especially for complex column configurations. Many of the design methods available currently consider only fully reactive columns (Barbosa and Doherty, 1988; Bessling et al., 1997; Groemping, 2002). However, in some ∗ Corresponding author. Tel.: +44 161 306 4381; fax: +44 161 236 7439.
E-mail address:
[email protected] (M. Jobson). 1 Present address: Praxair Inc., Tonawanda, NY, USA.
0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.03.009
cases, a fully reactive column cannot be used to obtain the desired product. If reaction equilibrium is assumed, as in this work, a pure component can be obtained from a reactive section only if it is located on the reactive surface (Espinosa et al., 1996; Hauan et al., 2000). The reactive surface (reaction space) defines the locus of reachable compositions for a system undergoing an equilibrium reaction (Bessling et al., 1997). Hybrid configurations (featuring both reactive and non-reactive sections), such as columns with either a rectifying or stripping section that is reactive or columns with a reactive core, will extend the applicability of reactive distillation to a larger range of systems (e.g. etherification reactions, systems containing inerts). Fig. 1 illustrates the range of hybrid configurations considered in this work. There are also economic benefits of using hybrid columns. Reactive internals (whether stages or packing) are much more expensive than non-reactive internals. Therefore, the number of reactive stages used in a hybrid column will have a significant impact on the capital cost. It may be observed by simulation that in single-feed columns, especially for fast reactions reaching equilibrium in the column, the reaction is actually concentrated around the feed stage, where the
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Ramona M. Dragomir, M. Jobson / Chemical Engineering Science 60 (2005) 4377 – 4395
D F
F
F
B Type I (T)
Type I (B)
B Type III (T)
F
Type II (T)
D
B Type III (B)
B Type II (B)
D
- reactive section
F
F
D
B
B
D
F
D
D
(heterogeneously catalysed)
B Type IV
Fig. 1. Alternative hybrid single-feed column configurations: T—top-section reactive; B—bottom-section reactive.
concentration of the reactants is the highest. Costs can be significantly reduced, without affecting the overall performance of the reactive column, by replacing the reactive internals with non-reactive internals in those sections where the reaction conversion is low. The hybrid reactive distillation columns shown in Fig. 1 can be classified into four types: • Type I—top- or bottom-section reactive with the feed at the interface between the reactive and non-reactive sections. • Type II—top- or bottom-section reactive with the feed within the reactive section. • Type III—reactive core configuration with the feed at a reactive/non-reactive interface. • Type IV—reactive core configuration with the feed within the reactive core. Hybrid configurations of Types I and III are observed to apply typically to systems where a non-reactive section is necessary to obtain a desired product that does not lie on the reactive surface (e.g. etherification reactions). Configurations of Types II and IV appear to apply to systems where the desired products can be obtained from a fully reactive column as well, but a non-reactive section might be more economical (e.g. esterification or decomposition reactions). Note that hybrid configurations are suitable only for heterogeneous catalytic reactions, when we can introduce catalyst in specific sections. For homogeneous and autocatalytic reactions, the reaction takes place everywhere in the column, so hybrid configurations are not suitable. An important part of reactive distillation column design is to evaluate alternative column configurations for a given task. Published methods (Espinosa et al., 1996; Groemping
et al., 2004; Lee, 2000) have considered hybrid configurations, but to date there is no method for rapid screening of alternative configurations for a reactive distillation column. In this paper, a design methodology, based on the boundary value method (BVM), will be presented for columns with a single feed and two products. The approach allows rapid screening for the best hybrid configuration, and the corresponding operating parameters, for a reactive distillation column with a specified performance (reaction conversion and product compositions). The approach is restricted to systems with two degrees of freedom (according to the Gibbs phase rule for isobaric systems) attaining reaction equilibrium on every stage. The method generates multiple designs; these can be ranked using appropriate cost models.
2. Design methodology for hybrid single-feed reactive distillation columns 2.1. General considerations Many available methods for the conceptual design of reactive distillation columns with equilibrium reactions are based on the generation of composition profiles in twodimensional transformed composition space (Barbosa and Doherty, 1988; Espinosa, 1995a,b; Espinosa et al., 1996). In these boundary value methods, composition profiles are calculated starting from fully specified top and bottom product compositions, for a specified reflux (or reboil) ratio and a fixed feed condition (i.e., feed quality, usually saturated liquid). If the two profiles (rectifying and stripping) intersect, then a feasible design exists, corresponding to the specified reflux (or reboil) ratio; the number of stages in each section is given by the intersection point.
Ramona M. Dragomir, M. Jobson / Chemical Engineering Science 60 (2005) 4377 – 4395
These BVMs proposed for the conceptual design of reactive and non-reactive systems are restricted by the use of a fixed feed condition and result in highly iterative procedures. The methods focus more on assessing the feasibility of the specified products and generating one design which satisfies the specifications. Further iterations can identify improved, or optimal, designs. From the synthesis point of view, it is valuable to determine and compare multiple feasible designs, and to identify the best design, based on total cost, or the best few designs satisfying specific constraints, such as a specified number of stages (the latter objective would be useful in retrofit studies). A simple way to achieve this is by relaxing the constraint of specified feed condition, which will allow the reflux and reboil ratios to be specified independently, thus increasing the likelihood of finding feasible designs. The number of feasible designs can be further increased by considering a range of reflux and reboil ratios for calculating the composition profiles. By rearranging the information contained in the composition profiles calculated for a range of reflux or reboil ratios, stage composition lines (SCLs) can be obtained (Thong et al., 2000). Stage composition lines contain the same information as composition profiles: while a composition profile represents a tray-by-tray profile in a column section at a specified reflux (or reboil) ratio, a SCL represents the locus of compositions of a specific tray for all reflux (or reboil) ratios. Castillo (1997) and Thong et al. (2000) developed a design method for non-reactive systems, based on intersection of SCLs. The method proved to be efficient in assessing feasibility and obtaining multiple designs for simple and complex distillation columns separating azeotropic mixtures. The methodology was successfully extended by Groemping et al. (2004) for equilibrium reactive systems with two degrees of freedom, considering first fully reactive columns, and then extending the methodology to hybrid configurations. Fully reactive column designs are obtained using intersections of reactive SCLs in transformed composition space. Multiple designs are usually obtained; they can be ranked using more or less sophisticated cost models to give the best design with respect to the number of stages, operating costs or total annualised cost. In the extension of the methodology of Groemping et al. (2004) to hybrid configurations, intersections of reactive and non-reactive SCLs in transformed composition space indicate potentially feasible designs. An additional feasibility test is needed to guarantee feasibility, namely the mass balance for the reference component at the interface. For a feasible hybrid configuration to exist, the reactive and nonreactive SCLs should intersect in transformed composition space, and also the mass balance for the reference component at the intersection point must be satisfied. Because it is difficult to satisfy the additional feasibility test at the interface, the approach sometimes generates only a small number of feasible designs. Also, the approach can accommodate
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only top- or bottom-section reactive configurations (Type I configurations in Fig. 1). However, the methodology presented in Groemping et al. (2004) offers a good basis to develop a more systematic methodology for conceptual design of hybrid reactive distillation columns, able to accommodate a wider range of hybrid configurations. These include columns with either the topor bottom-section reactive or with a reactive core and with the feed situated either at the interface between the reactive and non-reactive sections or within the reactive section. This work extends the methodology presented by Groemping et al. (2004), using the concept of SCLs in transformed composition space, combined with specific insights and particularities of hybrid reactive distillation columns. 2.2. Calculation of composition profiles and stage composition lines and internal reflux and reboil ratios The equations for calculating the reactive composition profiles (operating lines) in transformed variables (Fig. 2a,b; Eqs. (1) and (2)) are similar to the equations used for nonreactive systems (Barbosa and Doherty, 1988). Hybrid configurations usually feature more than two sections; therefore composition profiles for the middle sections (rectifying or stripping) (Fig. 2c,d; Eqs. (3) and (4)) also need to be calculated. The operating line for a reactive rectifying section is given by Rn
Yr,n+1,i =
Xr,n,i +
Rn + 1 i = 1, . . . , C − R − 1
1 Rn + 1
XD,i , (1)
and for a reactive stripping section it is Sm 1 Ys,m,i + XB,i , Sm + 1 Sm + 1 i = 1, . . . , C − R − 1.
Xs,m+1,i =
(2)
The operating line for a reactive rectifying middle section is given by Yp+1,j =
Ap Ap + 1
Xp,j +
A0
−
Ap + 1
X0,j
A0 + 1 Ap + 1
Y1,j
∀j = 1, . . . , C − R − 1
(3)
while for a reactive stripping middle section it is Xp+1,j =
Bp Bp + 1 −
Yp,j +
B0 Bp + 1
Y0,j
B0 + 1 Bp + 1
X1,j
∀j = 1, . . . , C − R − 1,
(4)
where X and Y denote the transformed liquid and vapour compositions, and R and S are the transformed reflux and
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Vr,1 yr,1,i D, xD,i
1 ξ r,n
Vs,m ys,m,i
Ls,m+1 xs,m+1,i m
Lr,0, xr,0,i Rext = Lr,0 / D
ξ s,m Vs,0, ys,0,i
n Lr,n xr,n,i
1
B, xB,j
(a)
(b)
L0, x0
V1, y1
Lm+1, xm+1
ξn
Ln, xn
Sext = Vs,0 / B
Vr,n+1 yr,n+1,i
Ln-1, xn-1 Vn, yn
Vm, ym
ξn
ξm
Vn+1, yn+1
(c)
L1, x1
Ln, xn
V0, y0
Vn+1, yn+1
(e)
(d)
Fig. 2. (a) Reactive rectifying section; (b) reactive stripping section; (c) middle rectifying reactive section; (d) middle stripping reactive section; (e) reactive stage n.
reboil ratios defined by Eqs. (5) and (6) (Barbosa and Doherty, 1988): Rn = Sm =
Ln D
,
Vm B
.
L0 (1 − tot −1 xref,0 ) D (1 − tot −1 xref,D ) D D (1 − tot −1 xref,0 ) = Rext , (1 − tot −1 xref,D ) Ln
=
L0
Vm
=
V0
(9)
(1 − tot −1 yref,0 ) . (1 − tot −1 yref,m )
(10)
Rn = Rext
(6)
Sn = Sext
=
V0 (1 − tot −1 yref,0 ) B (1 − tot −1 xref,D ) B B −1 (1 − tot yref,0 ) = Sext . (1 − tot −1 xref,D )
Sm =
(1 − tot −1 xref,0 ) , (1 − tot −1 xref,n )
(5)
Under the assumption of constant molar overflow in transformed variables, the local transformed reflux and reboil ratios are linked with the external reflux and reboil ratios through the composition of the reference component (Eqs. (7) and (8)): Rn =
reflect the change in the internal flows due to reaction (Eqs. (9) and (10)):
The transformed ratios A and B used in the calculation of middle composition profiles are defined by Eqs. (11) and (12): Ap = Bp =
(7)
=
(8)
For a total condenser, xref,0 = xref,D and the transformed reflux ratio R n is the same as the external reflux Rext , even for reactive systems with a change in the number of moles. However, the internal reflux ratio, Rn , and reboil ratio, Sn , depend on the overall reaction stoichiometry; their values
Lp V 1 − L0 Vp L1 − V 0
,
(11)
.
(12)
Middle section composition profiles are calculated starting from the interface between a reactive and a non-reactive section. Internal liquid and vapour flows at the interface stage are needed to calculate the ratios A and B. It is very hard to estimate these internal flows using reflux and reboil ratios only, especially when the interface stage is a feed stage. The assumption of constant molar overflow does not generally hold at the interface between a reactive and a non-reactive section, even if transformed variables are considered to account for the change in the number of moles due to reaction. Internal flows change sometimes dramatically when a transition between a non-reactive and a reactive section occurs,
Ramona M. Dragomir, M. Jobson / Chemical Engineering Science 60 (2005) 4377 – 4395
D Reactive surface
0.8
Non-reactive SCLs
A
5
6
B
1.0
4
3 xB
0.8
1.0
0.6
0.4
0.2
1.0
0.6
0.4
0.4
0.2
0.2
C 0.0
(a)
D Intersections of nonreactive SCLs with the reactive surface
XD
0.8
0.6
4381
s – reboil ratio m – number of stripping stages 1
2
m = 15 s = 3.2 m = 16 3 s = 2.21
4
5 6
0.0 0.0
B
0.2
0.4 XB 0.6
0.8
1.0
A
(b)
Fig. 3. Non-reactive SCLs and their intersection with the reactive surface for an ideal system A + B ↔ C (inert D): (a) real mole fraction space; (b) transformed mole fraction space.
mainly because of the sharp change in composition caused by reaction, which will affect through VLE the distribution of liquid and vapour flows. To account for these changes, mass and energy balances are always used around the reactive interface stage (Eqs. (13)–(16)). After the interface stage, constant molar overflow in transformed variables may be used if appropriate. Mass balances around the reactive interface stage n (Fig. 2e) give Vn+1 + Ln−1 = Ln + Vn −
R
tot,j n,j ,
(13)
j =1
Vn+1 yn+1,i + Ln−1 xn−1,i R i,j n,j , = Ln xn,i + Vn yn,i −
i = 1, . . . , C. (14)
j =1
The energy balance over the reactive stage n is Vn+1 hVn+1,i + Ln−1 hL n−1,i V = L n hL n,i + Vn hn,i −
R
n,j Hreact,j .
(15)
j =1
The reactive equilibrium relationship is Keq (xr,n ) = Keq (T ).
(16)
The system of Eqs. (13)–(16) are solved for yn+1,i (i = 1, . . . , C), Ln , Vn+1 and n for a rectifying stage and for xn−1,i (i = 1, . . . , C), Vn , Ln−1 and n for a stripping stage (e.g. using a modification of Powell’s dogleg method, as implemented in IMSL routine DNEQLU). If the constant molar overflow assumption holds for each section, an alternate application of the rectifying (or rectifying middle) operating line and a dew point calculation (or
reactive dew point if the rectifying section is a reactive section) will give the rectifying composition profile. Similarly, the stripping profile is obtained by alternate application of the stripping (or middle stripping) operating line and a bubble point calculation (reactive bubble point if the stripping section is a reactive section). If the constant molar overflow assumption does not hold, then the composition profiles are calculated solving stage-by-stage for the rectifying, stripping or middle section, the system of Eqs. (13)–(16). Calculating the composition profiles for a set of reflux and reboil ratios and rearranging the information obtained will provide the SCLs.
2.3. Intersection of non-reactive SCLs with the reactive surface The BVM is based on the premise that a continuous composition profile between the top and bottom product compositions must exist for a column to be feasible (Levy et al., 1985). The approach presented in this work exploits the fact that in a hybrid reactive distillation column the composition of the liquid leaving the stage at the interface between the reactive and non-reactive sections is on both a non-reactive SCL and a reactive SCL, and hence on the reactive surface. A necessary condition for a continuous profile to exist, for the specified product compositions, is that at least one nonreactive SCL intersects the reactive surface as illustrated in Fig. 3a. The point of intersection is associated with a specific reflux or reboil ratio, as shown in Fig. 3b. An intersection thus corresponds to design parameters: number of nonreactive stages and reflux or reboil ratio. Columns with a reactive core can be addressed by calculating the intersection with the reaction surface for both rectifying and stripping sections.
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D, xD,i
D, xD,i nonreactive
reactive n-1
Ln-1, xn-1,i F, xF,i
F, xF,i
n
Ln, xn,i Lm+1, xm+1,i xintersect
n
Ln, xn,i
Vn, yn,i Interface Vm, ym,i
m
m,i
m
Lm, xm,i xintersect
m
Vn+1, yn+1,i V , y Interface Vm-1, ym-1,i m-1 reactive
nonreactive
B, xB,i
B, xB i
(a)
(b)
Fig. 4. Composition relationships at the interface stage in hybrid reactive distillation columns. (a) top-section reactive; (b) bottom-section reactive.
The intersection point is calculated using a non-linear root search routine (Brent, 1971), looking for that value of the reflux or reboil ratio which will result in a stage composition satisfying the reactive equilibrium relation. Appendix A provides details on this calculation. One or several sets of intersection points will result, corresponding to a specific number of stages, NRintersect , and a reflux ratio, Rintersect , for a non-reactive rectifying section, or NSintersect and a reboil ratio Sintersect , for a non-reactive stripping section. For a non-reactive stripping section, the intersection of a non-reactive stripping SCL with the reactive surface represents the composition of the liquid leaving the last rectifying stage n as shown in Fig. 4a. Similarly, for a non-reactive rectifying section (Fig. 4b) the intersection of a non-reactive rectifying SCL with the reactive surface represents the composition of the liquid in reactive equilibrium with the vapour leaving the last stripping stage m, where stages are numbered from the column ends towards the feed stage. The actual number of non-reactive stages is equal to the number of stages at the intersection point less one, as the composition at the intersection point is that of the liquid leaving the reactive stage at the interface. The composition and the number of stages at the intersection of non-reactive SCLs with the reactive surface are given by Xintersect = Xm+1 ,
(17)
NS = NSintersect − 1
(18)
for the stripping non-reactive section, as shown in Fig. 4a, and Xintersect = Xn+1 ,
(19)
NR = NRintersect − 1
(20)
for the rectifying non-reactive section, illustrated in Fig. 4b. The reactive stage at the interface may or may not be a feed stage, and depending on where the feed stage is placed in
the column, various hybrid configurations can be obtained: top- or bottom-section reactive with the feed within the reactive section or with the feed at the interface between the reactive and the non-reactive sections. The feed stage is always taken to be a reactive stage, as the feed is usually a reactive mixture, so it is reasonable to introduce it on a reactive stage. If the feed is located at the interface, the feed stage will be the last reactive stage, i.e., the last rectifying stage for columns with a top-section reactive and the last stripping stage for a column with a bottom-section reactive; therefore the feasibility criterion will be different for different types of configurations. A discussion of the feasibility criteria for various column configurations follows. 2.4. Feasibility criteria for hybrid reactive distillation columns For the hybrid columns illustrated in Fig. 1, the feed stage is always located on a reactive stage, but may lie in either the rectifying or the stripping section. For a feasible design to be possible the rectifying (or middle rectifying) composition profile should intersect the stripping (or middle stripping) composition profile. The feasibility criteria are formulated to reflect the various column configurations: 2.4.1. Feasibility criterion A—feed at the bottom of the reactive section In this case the feed stage is treated as the last rectifying stage, as shown in Fig. 5a. This arrangement corresponds to Type I(T) and III(T) configurations. The feasibility criterion is that the composition of the liquid leaving the reactive feed stage n must be the same as the composition of the liquid entering the non-reactive stripping stage m, or, equivalently, the composition of the intersection point of non-reactive SCL m+1 with the reactive surface. In Fig. 5a this point, xintersect , is denoted by a star. Using the intersection of non-reactive SCLs with the reactive surface in the feasibility criterion formulation allows the use of transformed variables for visualisation and column design, as all liquid composition points of interest will be located on the reactive surface. In terms of transformed compositions, the feasibility criterion is Xn = Xintersect .
(21)
2.4.2. Feasibility criterion B—feed at the top of the reactive section In Type I(B) and III(B) columns, the feed stage is taken to be the last stripping stage, as shown in Fig. 5b. These arrangements are analogous to Type I(T) and III(T) arrangements corresponding to criterion A. For feasibility, continuous vapour and liquid profiles should exist in the column. By analogy with criterion A, the composition of the vapour leaving the reactive feed stage m should be the same as the composition of the vapour entering the non-reactive rectifying stage n. This criterion
Ramona M. Dragomir, M. Jobson / Chemical Engineering Science 60 (2005) 4377 – 4395
Ln-1, xn-1,i F, xF,i
xintersect (a)
Ln, xn,i
Vn, yn,i
Vm, ym,i m
Reactive
F, xF,i Reactive Non-reactive
Vn+1, yn+1,i
Vn+1, yn+1,i
Ln, xn,i
Non-reactive
n
Ln, xn,i
nn
n
n-1
4383
F, xF,i
m
m
Lm, xm,i xintersect
Lm, xm,i
Vm-1, ym-1 i
Vm-1, ym-1,i m-1
m-
(b)
(c)
Fig. 5. Feed stage arrangements for hybrid reactive distillation columns: (a) column types I(T) and III(T); (b) column types I(B) and III(B); (c) column types II and IV.
can be reformulated in terms of liquid compositions: if an intersection between the vapour profiles exist, then an intersection between the profiles of liquid compositions, in thermodynamic and chemical equilibrium with the vapour, will also exist. The feasibility criterion for this type of feed arrangement (Eq. (22)) is that the composition of the liquid leaving the feed stage, xintersect , should coincide with the composition of the liquid leaving the last stripping stage m. All compositions of interest are located on the reactive surface; therefore the feasibility criterion can be expressed in transformed variables:
Table 1 Feasibility criteria for the hybrid column configurations shown in Fig. 1
Xm = Xintersect .
(22)
2.4.3. Feasibility criterion C—feed stage within the reactive section This arrangement is characteristic of configurations of Type II and IV (in Fig. 5c). Both rectifying (or middle rectifying) and stripping (or middle stripping) sections are reactive sections, and, taking the feed stage to be the last stripping stage, the general feasibility criterion is similar to that for non-reactive sections: the liquid composition leaving feed stage m should coincide with the composition leaving stage n + 1. The feasibility criterion may be expressed using transformed variables, as all liquid compositions are located on the reactive surface: Xm = Xn+1 .
(23)
The feasibility criteria for the configurations shown in Fig. 1 are summarised in Table 1. 2.5. Design methodology The feasibility criteria described in Table 1 are based on liquid compositions represented in transformed variables. Depending on the type of column configuration, the liquid composition can be a point on a reactive SCL, an intersection point of a non-reactive SCL with the reactive surface or a point on a middle-section composition profile. Reactive
Hybrid configuration
Feasibility criterion
Type I
(T) (B)
Xn = Xintersect Xm = Xintersect
Type II
(T) (B)
Xm = Xn+1 Xm = Xn+1
Type III
(T) (B)
Xn = Xintersect Xm = Xintersect
Type IV
—
Xm = Xn+1
SCLs for the rectifying and stripping sections are calculated using Eqs. (1) and (2), for a range of reflux and reboil ratios. Middle-section profiles can be calculated starting from each intersection point using the associated reflux or reboil ratio (Eqs. (3) or (4)). Fig. 6 illustrates how middle-section composition profiles may be calculated from the intersection points for the system A + B ⇔ C (inert D). Each intersection of a non-reactive SCL with the reactive surface is characterised by a specific reflux or reboil ratio, e.g. for stripping stage 9, the corresponding reboil ratio is 16.4. The reflux or reboil ratio and the composition at the intersection with the reactive surface are used to initiate the calculation of middle-section composition profiles using Eqs. (3) and (4). At the interface between a non-reactive and a reactive section, internal vapour and liquid flows change significantly due to reaction; therefore a heat balance is used on the first reactive stage to obtain internal flows. After the first stage (the interface stage) constant molar overflow, in transformed variables, is often a reasonable assumption for the middle reactive section. To obtain feasible designs, a search for intersections between different combinations of segments on reactive SCLs, middle-section composition profiles, or segments between two adjacent points of intersection of non-reactive SCLs with the reactive surface is performed, depending on the hybrid
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Ramona M. Dragomir, M. Jobson / Chemical Engineering Science 60 (2005) 4377 – 4395
B 1
Intersections of stripping SCLs with the reactive surface
0.9
Middle rectifying composition profile
NS = 9 S = 16.4
0.8
NS = 10 S = 6.4 NS = 11 S = 3.1
0.7 0.6
Middle stripping composition profile
NS = 12 S = 1.7 NR = 6 R = 7.1
0.5
NR = 7 R = 0.82
0.4 0.3
Intersections of rectifying SCLs with the reactive surface
0.2 0.1
A
0
D
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fig. 6. Middle composition profiles starting from intersection points of non-reactive SCLs with the reactive surface. A + B ↔ C (with inert D); Keq = 50.
Table 2 Intersections checked in the search for feasible hybrid columns designs Points used for intersection
Type I (T)
Rectifying SCLs Stripping SCLs Points of intersection of non-reactive SCLs with the reactive surface—rectifying section Points of intersection of non-reactive SCLs with the reactive surface—stripping section Middle rectifying composition profiles Middle stripping composition profiles
D Xs,D, NSD, SD
Xr,A, NRA, RA
α
A Rectifying segment
β
C
I
Stripping segment
B Xr,B, NRB, RB Xint, NRint, NSint, Rint, Sint
Xs,C, NSC, SC
Fig. 7. Graphical visualisation of the feasibility test for single-feed hybrid reactive distillation columns.
configuration. Table 2 lists the types of intersections checked to obtain feasible designs for various hybrid configurations. A general representation of the feasibility criterion for a single-feed hybrid configuration is presented in Fig. 7. To obtain feasible designs, a 2-D line–line intersection is
Type II (B)
X
(T)
Type III (B)
(T)
Type IV (B)
X X X
X X
X X X
X X X
X X
performed between a rectifying segment [AB] and a stripping segment [CD]. The rectifying segment [AB] can be: • a segment of a rectifying SCL, connecting points corresponding to two discrete reflux ratios; • a segment of middle-section rectifying composition profile, between two consecutive stages; • a segment connecting two adjacent points of intersection of non-reactive rectifying SCLs with the reactive surface. Similarly, the stripping segment [CD] can be: • a segment of a stripping SCL, connecting points corresponding to two discrete reboil ratios; • a segment of a middle-section stripping composition profile, between two consecutive stages; • a segment connecting two adjacent points of intersection of non-reactive stripping SCLs with the reactive surface.
Ramona M. Dragomir, M. Jobson / Chemical Engineering Science 60 (2005) 4377 – 4395
Depending on the type of configuration, 2-D line–line intersections between segments on SCLs, middle-section CPs or between two adjacent non-reactive interface points are checked (as presented in Table 2). The design details at the intersection point are estimated by linear interpolation (Eqs. (24)–(31)). Two scalar parameters, and , are used to describe the line segments. For a feasible design, and should have values within the interval [0, 1], meaning that the two segments intersect. (1) Segments from SCLs Rint = RA + (RB − RA ),
(24)
Sint = SC + (SD − SC ).
(25)
(2) Segments from middle CPs NMRint = NMRA + (NMRB − NMRA ),
(26)
NMSint = NMSC + (NMSD − NMSC ).
(27)
(3) Segments between two adjacent points of intersection of non-reactive SCLs with the reactive surface Rint = RA + (RB − RA ),
(28)
NRint = NRA + (NRB − NRA ),
(29)
Sint = SC + (SD − SC ),
(30)
NSint = NSC + (NSD − NSC ).
(31)
The main drawback of this approach is that the intersection of non-reactive SCLs with the reactive surface, as well as the composition profiles for the middle sections, are sets of discrete points. That means that the segment between two adjacent points of intersection of non-reactive SCLs with the reactive surface, or between two stages on a composition profile, has no physical meaning, as fractional stages cannot exist. However, because reactive systems are usually highly constrained, an approximation given by the interpolation between the two points will still provide a good initialisation for simulation or detailed design, even if a fractional number of stages will result. The general procedure for design is as follows: 1. Fully specify compositions for the top and bottom products. Also, set reflux and reboil ratios ranges to calculate SCLs, feed flow rate and the mole fraction for the reference component in the feed, xi,ref . For the overall mass balance, in order to satisfy the number of degrees of freedom, only one more parameter needs to be specified, chosen from D/F , B/F and xf,i=ref . 2. Calculate the remaining variables (remaining feed mole fractions, product flow rates and the reaction extent in the column) from the overall mass balance.
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3. Calculate reactive and non-reactive SCLs for both rectifying and stripping sections using the specified ranges for the reflux and reboil ratios. 4. Calculate intersections of non-reactive SCLs with the reactive surface for the rectifying and stripping sections. 5. If any intersection points are found in step 4, calculate for each of them middle-section composition profiles, using a heat balance to determine internal liquid and vapour flow rates. 6. Search for feasible designs for all types of configurations: fully reactive columns (Groemping et al., 2004) and all types of hybrid configurations. 7. Rank the feasible designs obtained, based on total cost (or other relevant parameters, e.g. number of stages, energy requirement). 8. Narrow the results to meet the constraints if necessary, e.g. feed condition, maximum number of stages, maximum total cost. For each feasible design found, one can determine the feed condition, condenser and reboiler duties, column diameter, and column capital and operating costs. The feed condition is calculated using an overall energy balance (Appendix B). The condenser and reboiler duties are directly related to the reflux and reboil ratios, and they can be easily calculated from an energy balance around the condenser or reboiler. Utility costs can then be calculated, given temperatures and unit costs of utilities, as can the capital cost for the heat exchangers. The capital cost model for the column should take into account different costs of reactive and non-reactive stages. Thus, we can rank the feasible designs to obtain the best few designs with respect to number of stages, energy requirement, operating costs, or total annualised cost. The design procedure can be easily automated, providing a tool to rapidly generate various configurations (useful at the synthesis stage) and to obtain feasible designs for reactive distillation columns. To generate multiple feasible designs it will take less than 1 min for an ideal system and less than 5 min for a highly non-ideal system, using a PIII 1.5 GHz personal computer. All thermodynamic data for VLE and physical properties calculation were obtained from the HYSYS v2.4 database (1995–2001), using a customised software interface. The method searching for intersections of SCLs with the reactive surface offers certain advantages over the method using intersection of SCLs in transformed variables (Groemping et al., 2004). First, the method avoids unnecessary searches, by using insights about where intersections can take place, and eliminates the need to search for feasible designs where no such designs will exist, i.e., away from the reactive surface. Secondly, the method of Groemping et al. (2004) can consider only configurations of Type I. The method proposed in this paper allows more complex configurations, such as Types II, II and IV, to be addressed.
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1.0
Non-reactive distillation distillation boundary
4: n-Butane 69.4°C 3: nB/MeOH azeotrope 67.0°C
4: Butane 69.4 °C
3 2: Azeotrope 67.0 °C
Reactive equilibrium surface
XTnB
3: Azeotrope, 69.37 ˚C
0.99
XTnB
2: i-Butene 61.4°C
(a)
7: MTBE 136.2°C 1: iB/MeOH azeotrope 5: MTBE/MeOH 59.6°C azeotrope 6: MeOH 128.0°C 119.9 °C
5: MeOH 127.9 °C
XTiB
1: Isobutene 61.4 °C
(b)
Fig. 8. (a) Real composition space and reaction space for the MTBE system at 8 bar; (b) residue curve map for the reactive MTBE mixture in the transformed composition space at 8 bar (Groemping, 2002).
The extension of the methodology to include double-feed columns is presented in Dragomir and Jobson (2005b). 3. Case study 1: MTBE production The first example to illustrate the procedure for feasibility assessment and column design is methyl tertiary butyl ether (MTBE) production. The reaction between iso-butene (IB) and methanol (MeOH) (Eq. (32)) takes place in the rectifying section, and pure MTBE is obtained as a bottom product. The reactive mixture contains the inert component nbutane. The thermodynamic data for VLE calculations were obtained from HYSYS v2.4 database. The reaction data (reaction equilibrium constant) were taken from Chen et al. (2000): Cat
IB + MeOH ←→ MTBE.
(32)
Fig. 8a shows the non-reactive azeotropes and reaction equilibrium surface in mole fraction space at a pressure of 8 bar. A distillation boundary divides the composition space into two distillation regions. Pure MTBE can only be produced from a conventional distillation column if the methanol concentration in the feed is low. Fig. 8b shows the residue curve map of the MTBE system in transformed composition space. The reference component is MTBE. Two azeotropes exist: one non-reactive low-boiling azeotrope and one reactive azeotrope, a quaternary saddle located very close to the n-butane vertex. The residue curve map (Fig. 8b; see also Fig. 4 of Ung and Doherty, 1995) indicates that the methanol/n-butane azeotrope is a potential product of a reactive rectifying section. If this reactive section is combined with a non- reactive stripping section, pure MTBE can be withdrawn as the bottom product. A composition close to the quaternary reactive azeotrope is chosen as the top product, and almost pure MTBE for the bottom product. The methanol conversion for the specified
products is 99.8%. Product and feed specifications are given in Table 3. Table 4 presents the range of operating conditions used to generate reactive stage composition lines. To verify whether constant molar overflow is a valid assumption for this system, composition profiles were calculated with and without energy balances. The results are presented in Fig. 9. It can be seen in Fig. 9a that for this highly non-ideal system, constant molar overflow in transformed variables is not a valid assumption for the reactive section. Therefore energy balances were used in calculation of the rectifying reactive SCLs. Fig. 9b shows that, for the nonreactive section, there is little influence of heat balances on composition profiles; constant molar overflow may therefore be assumed, to speed up the calculations. Because the distillate composition is very close to the quaternary reactive azeotrope, feasible designs are grouped close to a distillation boundary, as can be seen in Fig. 10. For the feasibility study, small steps for reflux and reboil ratios are needed to generate accurately the stage composition lines near to the distillation boundary. The best 10 designs, with respect to the total annualised cost, resulting from the conceptual design methodology are presented in Table 5. The simple cost correlations used for process screening and evaluation are presented in Appendix C. The cost of reactive stages was taken to be 5 times the cost of non-reactive stages.2 The configurations obtained are based on the top-section reactive hybrid configuration, as MTBE is a heavy component and it will be a bottom product, and a non-reactive section is needed in the stripping section for pure MTBE to be obtained. Design 1 from Table 5 was used to initialise a rigorous simulation using HYSYS v2.4, using 9 stages in the rectifying section (including the condenser) and 6 stages in the stripping section (including the reboiler). The results of the conceptual design method were used as specifications for 2 Personal communication, M. Groemping, Degussa (2003).
Ramona M. Dragomir, M. Jobson / Chemical Engineering Science 60 (2005) 4377 – 4395
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Table 3 Products and feed compositions for MTBE example Comp.
i-Butene MeOH MTBE n-Butane
Stoichiometry,
Boiling temp. (8 bar)
Distillate
(dimensionless)
TB (◦ C)
XD (transf.)
xD (mole fr.)
0.0977 0.0099 — 0.8924
0.091
−1 −1 1 0
61.4 128.0 136.4 69.4
Bottom
0.00151 0.00851 0.91
Feed
XB (transf.)
xB (mole fr.)
XF (transf.)
xF (mole fr.)
0.4945 0.5043 — 0.0012
0.00021
0.317 0.283 — 0.4
0.317 0.283 0.01 0.41
0.01951 0.9781 0.00231
1 Specified values.
Table 4 Specifications for generating stage composition lines Distillate flow rate, D (kmol/h)
Bottoms flow rate, Feed flow rate, F Feed quality, q B (kmol/h) (kmol/h) (dimensionless)
Reflux ratio range, Reboil ratio range, Rectifying stages r (dimensionless) s (dimensionless) range, n (dimensionless)
Stripping stages range, m (dimensionless)
44.35
27.94
0.2–20
1–30
100
Eq. (B.23)
- i-Butene - Methanol
0.2–20
1–30
Constant molar overflow
- MTBE - n-Butane
Energy balances included
1.0 1.0
0.9
0.9
0.8 0.7
Mole Fraction
Mole Fraction
0.8 0.7 0.6 0.5 0.4
0.5 0.4 0.3
0.3 0.2
0.2
0.1
0.1 0.0
0.0 0
(a)
0.6
5
10
15
20
25
30
35
Stage No.
0
5
10
15
20
25
30
35
Stage No.
(b)
Fig. 9. Influence of energy balances on composition profiles: (a) rectifying reactive section; (b) stripping non-reactive section.
rigorous simulation: a reflux ratio of 1.3, a reboil ratio of 3.0 and a feed condition 0.17. The product compositions predicted by simulation are compared to those specified in the conceptual design method in Table 6. The simulation shows good agreement with the conceptual design method.
(Eqs. (33) and (34)) in a two-step reaction; an intermediate component (methyl ethyl carbonate, MEC) is formed in the first step. Keq1
DMC + EtOH ←→ MEC + MeOH, Keq2
MEC + EtOH ←→ DEC + MeOH.
(33) (34)
4. Case study 2: diethyl carbonate system Diethyl carbonate (DEC) is obtained from a transesterification reaction of dimethyl carbonate and ethanol
If it is assumed that both reactions are equilibrium reactions, that the equilibrium is reached on all reactive trays and that the intermediate component MEC does not
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For the global reaction, Keq is calculated from Keq1 and Keq2 :
n-Butane 1.0
XD
0.9
Keq = Keq1 Keq2 .
0.8
0.6 0.5
The reaction data for the DEC system are taken from Luo and Xiao (2001) and the thermodynamic data were obtained from HYSYS v2.4 using the default parameters for the NRTL property package. The residue curve map in transformed composition space is presented in Fig. 11. A maximum-boiling binary reactive azeotrope is formed, containing 8.5 mol% DMC and 91.5 mol% MeOH. Product compositions for the distillate, close to the reactive azeotrope, and for the bottom product, nearly pure DEC, were chosen corresponding to a reaction conversion of 99%. Table 7 reports these compositions; DEC is the reference component. Both products are located on the reactive surface, so, for this case, both fully reactive and hybrid configurations are possible. To generate stage composition lines, the same ranges as in the MTBE example were chosen for reflux and reboil ratios (Table 4). Fig. 12 presents composition profiles calculated with and without energy balances. In the rectifying section, the constant molar overflow assumption has no influence on composition profiles, but in the stripping section the assumption affects both reactive and non-reactive stripping composition profiles. Based on this observation, heat balances were used
Middle-section composition profiles
0.7
Region of feasible designs
Intersections of nonreactive SCLs with the reactive surface
0.4 0.3 0.2
Reactive rectifying SCLs
0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
i-Butene
MeOH
Fig. 10. Stage composition lines and middle-section composition profiles from intersection points of non-reactive SCLs with the reactive surface for MTBE synthesis.
accumulate in the column, the global reaction (Eq. (35)) can be used. Keq
DMC + 2EtOH ←→ DEC + 2MeOH.
(36)
(35)
Table 5 Feasible designs for MTBE production, ranked based on total annualised cost No.Type NR (dimensionless)
NMR (dimen- NMS (dimen- NS (dimensionless) sionless) sionless)
NTOT (dimensionless)
R (dimen- S (dimen- q (dimen- Cond. duty Reb. duty Total cost sionless) sionless) sionless) (kW) (kW) (106 $/yr)
1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0
14.87 14.1 14.07 12.97 14.75 13.73 12.54 12.2 12.15 15.69
1.31 1.36 1.39 1.85 0.67 0.79 1.28 2.52 2.69 1.27
I(T) II(T) I(T) I(T) II(T) II(T) II(T) II(T) I(T) I(T)
9 7 8 7 6 5 4 5 6 10
0 1.1 0 0 3.75 3.73 3.54 1.2 0 0
5.87 6 6.07 5.97 5 5 5 6 6.15 5.69
3.01 2.78 2.74 2.82 4.52 4.52 4.52 2.78 2.70 3.31
0.17 0.08 0.06 −0.07 0.81 0.77 0.60 −0.31 −0.39 0.26
511 523 529 630 369 397 505 778 817 502
562 518 511 527 842 842 842 518 504 617
0.265 0.285 0.286 0.293 0.333 0.333 0.334 0.359 0.370 0.433
Table 6 Product compositions obtained by simulation, based on the results from the conceptual design procedure (Design 1 in Table 5) Component name
i-Butene MeOH MTBE n-Butane 1 Specified values.
Simulation results
Conceptual design specifications
Feed (mole fr.)
Distillate (mole fr.)
Bottom (mole fr.)
Feed (mole fr.)
Distillate (mole fr.)
Bottom (mole fr.)
0.3171 0.2831 0.01 0.41
0.0789 0.0000 0.0001 0.9210
0.0005 0.0000 0.9781 0.0214
0.317 0.283 0.01 0.41
0.091 0.00151 0.00851 0.91
0.00021 0.01951 0.9781 0.00231
Ramona M. Dragomir, M. Jobson / Chemical Engineering Science 60 (2005) 4377 – 4395
2
DEC (136.4 °C)
EtOH (128 °C)
1.8
Infeasible transformed space
1.6 1.4 1.2 1 0.8
Maximum boiling azeotrope: T = 75.76 °C XDMC=0.085 XMeOH= 0.915
0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
MeOH (69.4 °C)
1
DMC (61.4 °C)
Fig. 11. Residue curve map in transformed composition space for DEC system at 1 bar (algorithm from Barbosa and Doherty, 1988).
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in the calculation of both reactive and non-reactive composition profiles. Many feasible designs are possible for this system, including fully reactive and hybrid configurations. Because the number of feasible designs in this case is high (more than 400), a constraint was applied to restrict the feed condition to be between 0 and 1.2. The best 10 designs with respect to the total annualised cost and satisfying this constraint are listed in Table 8. The same cost models were used as in the MTBE example. As expected, hybrid configurations are preferred to fully reactive columns, reflecting lower capital costs. Even though the total number of stages in the hybrid configurations is the same or even higher than in fully reactive columns, fewer reactive stages are needed, leading to lower capital costs, as reactive stages are much more expensive than non-reactive stages. For example, Design 1 in Table 5 is a hybrid column of Type II(T) which is similar, in terms of number of stages
Table 7 Products and feed compositions for DEC example Stoichiometry,
Comp.
DMC Ethanol DEC Methanol
Boiling temp. at 1 bar, (◦ C)
(dimensionless)
TB
−1 −2 1 2
61.4 128.0 136.4 69.4
Distillate
Bottoms
Feed
XD (transf.)
xD (mole fr.)
XB (transf.)
xB (mole fr.)
XF (transf.)
xF (mole fr.)
0.006 0.008 — 0.986
0.0041 0.0041 0.0021 0.9901
0.986 1.97 — −1.956
0.0061 0.0101 0.9801 0.0041
0.334 0.666 — 0.0
0.334 0.666 0.01 0.01
Flow rates (kmol/h)
64.872
1001
35.1
1 Specified values.
- DMC - Methanol
Constant molar overflow
- Ethanol - DEC
Energy balances included
1.0
0.9
0.9
0.8
0.8
0.7
0.7
Mole Fraction
Mole Fraction
1.0
0.6 0.5 0.4
0.5 0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0 0
(a)
0.6
5
10
15
Stage No.
20
25
30
0
(b)
5
10
15
20
25
30
Stage No.
Fig. 12. Influence of constant molar overflow assumption on composition profiles: (a) non-reactive stripping section; (b) reactive stripping section.
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Table 8 Best 10 designs ranked based on total annualised cost for DEC system, where 0 qF 1.2 No. Type
NR (dimensionless)
NMR (dimensionless)
NMS (dimensionless)
NS (dimensionless)
NTOT (dimensionless)
R (dimensionless)
S (dimensionless)
q (dimensionless)
Cond. duty (kW)
Reb. duty (kW)
Total cost (106 $/yr)
1 2 3 4 5 6 7 8 9 10
4 5 5 5 4 4 5 5 5 5
— — — — — — — — — —
1.9 — 5.9 2.3 — — — — — —
18 17.4 18 17 16 15 20 19 21 18
23.9 22.4 28.9 24.3 20 19 25 24 26 23
2.24 2.04 0.90 0.76 2.28 1.99 0.96 0.92 0.99 0.87
3.04 3.54 3.04 3.88 3.10 3.74 2.90 3.06 2.79 3.27
0.11 0.41 0.80 1.20 0.11 0.52 0.71 0.79 0.65 0.90
1591 1494 932 866 1612 1469 963 945 976 920
1235 1435 1235 1571 1257 1516 1179 1241 1135 1326
0.370 0.389 0.456 0.459 0.616 0.629 0.633 0.634 0.635 1.354
II(T) I(T) II(T) II(T) F F F F F F
F —fully reactive column.
Qcond
1
2 D F
5
19
1
Reaction extent [kmol/h] -
2
0.180
3
0.085
4
0.224
5
32.348
6
0.009
7
0.020
8
0.026
9
0.024
10
0.018
Stage
11
20
B
Qreb
R = 2.28 S = 3.10 qF = 0.11 TAC = 0.616·106 $/yr
2 D F
0.007
13
0.004
14
0.002
15
0.001
16
0.001
17
0.001
18
0.002
19
0.002
1
Reaction extent [kmol/h] -
2
0.177
3
0.087
Stage
5 6
4
0.226
5
32.316
6
0.075
7
-
….. 23
0.011
12
20
Qcond
1
24 Qreb
B
20
-
21
-
22
-
23
-
24
-
- non reactive R = 2.24 - reactive S = 3.04 qF = 0.11 TAC = 0.37·106 $/yr
-
(a)
(b)
Fig. 13. Reaction distribution in a single-feed reactive distillation column: (a) fully reactive column (Design 5 in Table 8); (b) hybrid column type II(T) (Design 1 in Table 8).
and operating parameters (reflux and reboil ratio and feed condition), to Design 5, a fully reactive column. Fig. 13 illustrates the two designs. The total annualised cost of Design 1 is around 60% that of Design 5. The performance of the two columns is similar. It can be seen in Fig. 13 that in both columns the reaction is concentrated around the feed stage, and that most of the reactive stages in the stripping section of the fully reactive column can be replaced with non-reactive stages, without affecting the overall performance.
Design 1 from Table 8 was used to initialise a rigorous simulation using HYSYS v2.4. A column with 5 reactive stages and 17 non-reactive stages (plus the non-reactive condenser and the reboiler) was used; the feed was placed on stage 5. A reflux ratio of 2.24 and a reboil ratio of 3.04 were specified. Feed specifications are presented in Table 9. The rigorous simulation results presented in Table 9 show very good agreement with the conceptual design method.
Ramona M. Dragomir, M. Jobson / Chemical Engineering Science 60 (2005) 4377 – 4395
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Table 9 Product compositions obtained by simulation, based on the results from the conceptual design procedure (Design 1 in Table 8) Component name
DMC Ethanol DEC Methanol
Simulation results
Conceptual design results
Feed (mole fr.)
Distillate (mole fr.)
Bottom (mole fr.)
Feed (mole fr.)
Distillate (mole fr.)
Bottom (mole fr.)
0.3341 0.6661 0.01 0.01
0.0072 0.0046 0.0023 0.9859
3.9E−06 0.0100 0.9767 0.0133
0.334 0.666 0.01 0.01
0.0041 0.0041 0.0021 0.9901
0.0061 0.0101 0.9801 0.0041
1 Specified values.
5. Conclusions In this paper, the graphical design methodology developed for non-hybrid columns of Groemping et al. (2004) has been extended to accommodate hybrid columns. The methodology developed can be applied to assess feasibility and design columns for reactive systems with two degrees of freedom according to the Gibbs phase rule. It is assumed that equilibrium reactions take place in the liquid phase only. Further assumptions of constant molar overflow in the vapour phase and no pressure drop in the column are not fundamental to the approach. A preliminary test for the influence of the constant molar overflow assumption was performed to determine whether heat balances should be included when calculating internal flow rates. Based on insights specific to hybrid reactive columns, a systematic design methodology that is able to generate and compare feasible designs efficiently was developed. For synthesis purposes, both fully reactive (Groemping et al., 2004) and hybrid configurations were introduced in the same framework. Intersections of non-reactive SCLs with the reactive surface were used in the search routine allowing a rapid screening for feasible designs. Using intersections of non-reactive SCLs with the reactive surface allows a wide range of hybrid configurations and feed arrangements to be analysed, including top- or bottom-section reactive columns and columns with a reactive core, with the feed at either the interface between the reactive and the non-reactive sections or within the reactive section. The methodology can be easily automated and typically generates multiple designs. The approach does not require iteration to obtain column profiles, and is efficient in the way the information obtained from composition profiles is used. Designs of various configurations can be obtained for a given system; these can be ranked using more or less sophisticated cost models. This allows a fast evaluation of which configurations are most appropriate for the specified reactive distillation task. The case studies showed successful application of the methodology to highly non-ideal systems. The benefit of including both fully reactive and hybrid columns in the same framework was shown in one case, highlighting that hybrid configurations can be significantly more economic than fully
reactive columns. In all cases, the results obtained from the design methodology provided excellent initialisation for rigorous simulation. The concepts developed in this work for the synthesis and design of single-feed reactive distillation columns can be used to analyse more complex configurations, such as double-feed fully reactive and hybrid reactive distillation columns (Dragomir, 2004; Dragomir and Jobson, 2005b), as well as columns with side-draws, and dividing wall reactive columns. The method has been extended to account for kinetically controlled reactions (Dragomir, 2004; Dragomir and Jobson, 2005a). Notation B C D F F h Keq L L NMR NMS NR
NS NTOT q Q R Rext
bottoms molar flow rate, kmol/h number of components, dimensionless distillate molar flow rate, kmol/h feed molar flow rate, kmol/h transformed feed flow rate, kmol/h specific enthalpy, kJ/kmol thermodynamic equilibrium constant, dimensionless liquid molar flow rate, kmol/h transformed liquid molar flow rate, kmol/h number of stages in the rectifying middle section, dimensionless number of stages in the stripping middle section, dimensionless number of stages above the feed (rectifying section) for a column design (including condenser), dimensionless number of stages below the feed (stripping section) for a column design (including reboiler), dimensionless total number of stages in the column (including condenser and reboiler), dimensionless feed quality (q = 0: saturated vapour; q = 1: saturated liquid), dimensionless heat duty, kW number of reactions, dimensionless external reflux ratio, dimensionless
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Rn Rn Sext Sm Sm V V x xn,ref X y yn,ref Y
Ramona M. Dragomir, M. Jobson / Chemical Engineering Science 60 (2005) 4377 – 4395
local reflux ratio on stage n, dimensionless local transformed reflux ratio on stage n, dimensionless external reboil ratio, dimensionless local reboil ratio on stage m, dimensionless local transformed reboil ratio on stage m, dimensionless vapour molar flow rate, kmol/h transformed vapour molar flow rate, kmol/h liquid mole fraction, dimensionless vector of R reference component liquid mole fractions leaving stage n, dimensionless transformed liquid mole fraction, dimensionless vapour mole fraction, dimensionless vector of R reference component vapour mole fractions leaving stage n, dimensionless transformed vapour mole fraction, dimensionless
Greek letters
ref i tot
square matrix of dimension (R, R) of stoichiometric coefficients for the R reference components in the R reactions, dimensionless vector of R stoichiometric coefficients of component i, dimensionless vector of R sums of stoichiometric coefficients, dimensionless vector of R molar extents of reaction, kmol/h
Subscripts and superscripts B D F j L m n r ref s V
bottoms distillate feed counter for components (j = 1, . . . , C) liquid counter for stages in stripping section (including reboiler) (m = 1, . . . , NS) counter for stages in rectifying section (including condenser) (n = 1, . . . , NR) rectifying section reference component stripping section vapour
nB SCL VLE W
n-butane stage composition line vapour–liquidequilibrium water
Acknowledgements We acknowledge the financial support provided by the European Commission within the 6th Framework Programme, Project “INSERT—Integrating Separation and Reaction Technologies”; Contract no. NMP2-CT-2003-505862.
Appendix A. Calculation of the intersection of nonreactive SCLs with the reactive surface The intersections of non-reactive SCLs with the reactive surface are calculated using a non-linear root search routine, which calculates the value of the reflux or reboil ratio, for which the liquid (or vapour) leaving a certain stage will be in reactive equilibrium. On a stripping non-reactive SCL, the routine takes two liquid compositions corresponding to reboil ratios SA and SB , xA (SA ) and xB (SB ) (Fig. 14), and compares the value of the reaction equilibrium constant at the stage temperature, Keq (T ), with the value of the reaction equilibrium constant calculated from activities, Keq (a). If the difference Keq (T )− Keq (a) changes its sign from point A to point B, then there will be a value Sintersect between SA and SB for which the equality condition Keq (T )=Keq (a) will be satisfied. A nonlinear root search routine (Brent, 1971) is used to calculate the reboil ratio value Sintersect at the intersection point, and the corresponding liquid composition, xintersect . For a non-reactive rectifying SCL, the routine takes two vapour composition points yA (RA ) and yB (RB ) on a stage composition line m and calculates the liquid compositions in thermodynamic equilibrium, xA and xB . If the difference Keq (T )−Keq (a) changes signs from point A to B, then there is a reflux ratio Rintersect for which the liquid composition leaving stage m is in reactive equilibrium, i.e., satisfies the condition Keq (T ) = Keq (a). A non-linear root search routine (Brent, 1971) is used to calculate the reflux ratio value
xB(SB)
Abbreviations Keq(T) = Keq(a)
BVM DEC DMC EtOH H2 O IB MeOH MTBE
boundary value method diethyl carbonate dimethyl carbonate ethanol water iso-butene methanol methyl tertiary butyl ether
Keq(T) > Keq(a) Reactive surface
xintersect (Sintersect) xA(SA) Segment on stripping SCL m
Keq(T) < Keq(a) Fig. 14. Intersection of a non-reactive stripping SCL with the reactive surface.
Ramona M. Dragomir, M. Jobson / Chemical Engineering Science 60 (2005) 4377 – 4395
The feed enthalpy (hF ) can then be used to calculate either feed temperature or feed condition:
Qcond D, hD
q=
F, hF
4393
HF − h F , F
(B.2)
where HF represents the specific enthalpy of the feed as saturated vapour and F is the latent heat of vaporisation of the feed.
ξTOT ∆Hreact
Appendix C. Column cost correlations Qreb B, hB
C.1. Column diameter
Fig. 15. Overall energy balance for a reactive column, used in calculation of the feed condition.
Rintersect at the intersection point, and its corresponding liquid composition, xintersect .
Calculation of the diameter of the column is based on the vapour velocity at the bottom of the column. The vapour velocity is for normal column operation between 70% and 90% of the flooding velocity (Sinnott, 1993). Volumetric flow rate: Q=
Appendix B. Calculation of the feed condition The feed condition for reactive systems is calculated from an overall energy balance around the column, which takes into account the effect of the heat of reaction. The total reaction extent for each reaction is calculated from an overall mass balance (Fig. 15) for each reference component. For single-feed columns, feed enthalpy is calculated using Eq. (B.1), which is valid regardless where reactive stages are placed in the column. The overall enthalpy balance can be used for top- or bottom-section reactive columns, columns with a reactive core or fully reactive columns, as well as for non-reactive columns, where the total reaction extent is zero. Generally, the condenser and the reboiler are non-reactive, especially for heterogeneously catalysed reactions; therefore their duties are directly related to external reflux and reboil ratios. Even for homogeneously catalysed or autocatalytic reactions, the condenser and reboiler duties can be considered non-reactive, as reaction extent is usually very small at the ends of the column. If this assumption is not valid then the heat of reaction should be considered during the calculation of condenser and reboiler duties. F hF = DhD + BhB + Qcond − Qreb − 1 hF = F −
R
tot,i Hreact,i ,
i=1
tot,i Hreact,i .
Maximum velocity (flooding) is calculated using (Sinnott, 1993) L − G v=K , (C.2) G where K =f
tray spacing,
L G
G . L
(C.3)
For 80% flooding, Q Ar = , 0.8v 4Ar = ,
(C.4)
where Ar is the active area, m2 ; L the mass flow rate of the liquid, kg/s; G the mass flow rate of the vapour, kg/s; Q the volumetric flow rate, m3 /s; MW the molecular weight, kg/kmol; v the linear velocity, m/s; G , L the vapour and liquid density, kg/m3 ; and the column diameter, m.
The equipment and operating costs are based on the costs in 1990 (Cost index in 1990 = 357.6). Costs for 2002 are estimated using relative cost index to the cost index in 1990 (Peters and Timmerhaus, 1991), where the cost index for 2002 is 402 (Chemical Engineering, 1999):
DhD + BhB + Qcond − Qreb R
(C.1)
C.2. Cost estimation
i=1
V MW . G
(B.1)
Cost2002 =
Cost Index2002 Cost1990 . Cost Index1990
(C.5)
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Ramona M. Dragomir, M. Jobson / Chemical Engineering Science 60 (2005) 4377 – 4395
C.2.1. Steam and cooling water costs Data for the 1990 cost of steam and cooling water were taken from Peters and Timmerhaus (1991) and Sinnott (1993): the cost of high pressure, medium pressure and exhaust steam, respectively, is 7.938, 5.292 and $2.425/1000 kg. The cost of cooling water is $0.066/m3 . C.2.2. Capital cost The equations to calculate the column cost, heat exchanger cost and reboiler cost are derived from graph and table (Peters and Timmerhaus, 1980; Sinnott, 1993). The costs of the equipment in the current year are obtained using Eq. (C.5): Column cost: Ccol = N exp(0.958 ln() + 4.44)Fc Ci .
(C.6)
The capital column cost takes into account reactive and non-reactive stages. Cost correlations were not found in the open literature for reactive stages. Costs were based on information provided by reactive packing manufacturers (e.g. Sulzer); reactive stages were considered to be 5 times as expensive as non-reactive stages. Reboiler cost: Cr = (18 982 + 176.05A)Ci .
(C.7)
Condenser cost: Cc = (9599 + 137.25A)Ci .
(C.8)
Area of heat exchanger: A=
Q , U TLM
(C.9)
where A is the heat transfer area, m2 ; Ci the Cost Index2002 / Cost Index1990 ; Fc the pressure factor; N the number of stages; Q the heat duty, J/s; Cc the cost of condenser or feed pre-heat exchanger, $; Cr the cost of reboiler, $; Ccol the cost of column, $; U the overall heat transfer coefficient, J/(m2 s K); TLM the mean logarithmic temperature difference for a heat exchanger, K; and the column diameter, m. Capital cost Capital cost includes all equipment costs for the column, the condenser and the reboiler. Total installed cost is calculated using factor Fcap: Cap = (Ccol + Cr + Cc ) Fcap.
(C.10)
Operating cost: Op = Csteam + CCW ,
(C.11)
where Fcap is the total installed cost factor, i.e., ratio of total installed cost to equipment cost, Csteam the cost of steam and CCW the cost of cooling water.
Total annualised cost The capital cost expressed on an annual basis is (Smith, 1995) AC = TAC =
Tcapi(1 + i)n (1 + i)n−1
,
Tcapi(1 + i)n (1 + i)n−1
(C.12) + Opr,
(C.13)
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