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Conceptual Design of Equilibrium Reactor-Reactive Distillation Flowsheets Guido Daniel* and Megan Jobson Centre for Process Integration, School of Chemical Engineering and Analytical Science, The UniVersity of Manchester, P.O. Box 88, Manchester, M60 1QD, United Kingdom
Economic and environmental reasons have led to process intensifications in the process industries. Reactive distillation is the most prominent example. However, often it is a challenge to satisfy the requirement for sufficient catalyst volume for the reaction while providing the interfacial area needed for mass transfer. The combination of a reactive distillation column with a pre-reactor is a valuable alternative. This paper presents an approach to identify promising designs for such flowsheets and the optimum distribution of the reaction extent between the pre-reactor and the reactive distillation column. The methodology uses a boundary value method for the design of the column; chemical equilibrium is assumed. The column usually consists of a reactive “core”, two rectifying sections, and one stripping section. The methodology will be demonstrated for the production of ethyl-tert-butyl-ether (ETBE). 1. Introduction To exploit the potential of reactive distillation, various methods have been developed for preliminary process design. Two major approaches exist for the generation of alternatives for a given reaction-separation problem. Mathematical optimization methods have been developed.1-6 These methods are generally very powerful for searching different alternatives, including even multicomponent systems. However, they do not provide valuable and necessary insights into the process and are generally computationally intensive. Graphically based methods overcome this problem.7-13 Hauan et al. used the difference point method to identify feasible column designs. They also considered the alternative of a reactor and reactive distillation column.14 However, these methods are often highly iterative, especially when searching for different design alternatives. The boundary value method has often been used to identify only one specific design for the reactive distillation column for the minimum reflux ratio.7,12,15-17 Recently, Dragomir and Jobson presented a methodology for reactive distillation columns based on a boundary value method (BVM) which generates multiple designs without highly iterative procedures.18 As powerful as the design methods presented are, they often fail to address the practical problems of the proposed columns. For example, in heterogeneously catalyzed reactive distillation columns, the catalyst volume inside the column often has to be maximized,19 especially in slow reaction systems. This requirement might lead to situations where the interfacial area needed for mass transfer is difficult to realize. Another drawback of reactive distillation is the controllability of the process.20 These practical issues, together with process economics, might lead to only partially integrated flowsheets. A flowsheet configuration to overcome the mentioned practical problems for reactive distillation columns is the combination of reactive distillation with a pre-reactor. In industry, often, a substantial part of the conversion is carried out in reactors upstream of the reactive distillation column21-25 thus reducing the amount of catalyst volume in the column. Furthermore, the reactor acts as a guard bed against catalyst poisoning for the following reactive distillation column and thus increases the * To whom all correspondence should be addressed. Phone: 0044 (0) 161 306 4390. Fax: 0044 (0) 161 236 7439. E-mail: G.Daniel@ postgrad.manchester.ac.uk.
operating time of the process. Figure 1 shows the flowsheet for the ETHERMAX process24 for the production of methyl-tertbutyl-ether (MTBE). In this process, the major part of the reaction is carried out in an isothermal tubular reactor and the remaining part in the following “finishing” reactive distillation column. The excess methanol provided is recovered in a separation section, normally consisting of a methanol extraction with water and a methanol distillation column in order to recycle unused methanol. This paper presents a methodology to identify near-optimal flowsheets as presented in Figure 1. The aim is to identify the optimal distribution of the reaction extent between the reactor and the finishing reactive distillation column. The methodology uses a graphically based boundary value method for identifying the promising column designs for a chosen pre-reactor configuration. Column details, including the number of nonreactive and reactive stages, as well as operating parameters, such as reflux and reboil ratios, are calculated. A cost function will be used to rank the feasible designs. The analysis includes the heat exchangers up- and downstream of the pre-reactor, the reactor, and the column with its reboiler and condenser. The feed pretreatment and subsequent separation steps are not considered. Chemical equilibrium is assumed on every reactive stage of the column and for the pre-reactor. For the proposed design procedure, there is no restriction on the number of reactions involved. However, since the probability of identifying designs decreases significantly as the number of reactions increases and as the assumption of multiple reactions being simultaneously in chemical equilibrium is not realistic, only the main reaction is considered in this paper. Especially if side reactions are important, a detailed simulation of the column designs obtained is necessary to test whether these side reactions would occur. The methodology is best suited to systems where the main reaction is dominant and side reactions are not of great concern. The methodology will be illustrated for the production of ethyltert-butyl-ether (ETBE). 2. Reactive Distillation Flowsheet Design 2.1. General Considerations. To analyze a flowsheet consisting of a pre-reactor and a reactive distillation column, promising configurations of both unit operations must be identified. A methodology building on the boundary value method (BVM) will be presented for the design of the reactive
10.1021/ie0604831 CCC: $37.00 © 2007 American Chemical Society Published on Web 12/08/2006
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Figure 1. Process flow diagram for the ETHERMAX process for MTBE production.
Figure 2. Process flowsheet for the pre-reactor and reactive distillation column.
distillation column. The methodology considers flowsheet configurations as shown in Figure 2. The feed stream, F, is heated in heat exchanger HXI from temperature T0 to the temperature of the plug-flow reactor, TR, which can be operated in adiabatic or isothermal mode. An expansion valve depressurizes the feed from the reactor pressure (chosen such that the reactor effluent is in the liquid phase) to the pressure of the reactive distillation column. In the following heat exchanger HXII, the pre-reacted feed, FPR, can be cooled or heated to the temperature TF prior to entering the column. It is assumed that, in the pre-reactor, as well as on every reactive stage of the column, chemical equilibrium (i.e., phase and reaction equilibrium) is reached. This approach is valuable when only information about equilibrium, but not for the kinetic behavior, of the reaction system is available. Since it is not possible to specify the catalyst volumes in the column or reactor without knowing the reaction kinetics, the designs generated using the proposed methodology are only indicative. An extension of the approach to account for reaction kinetics is currently under development. 2.2. Methodology. The following assumptions enable the use of the boundary value method for the design of the reactive distillation column: • The feed flow rate and composition to the pre-reactor are fixed and given. • The desired product purities are given. • A suitable range for the pre-reactor temperature is given (e.g., limited by the maximum operating temperature of the catalyst). • The pressure of the column and reactor are chosen. The design parameters of the flowsheet are the inlet temperature of the pre-reactor, TR, the inlet temperature of the column, TF, and the design details of the column itself, namely, the operating conditions reboil and reflux ratio, the number of nonreactive and reactive stages inside the column, and the feed stage location. The algorithm to solve this design problem is shown in Figure 3. For a set of operating conditions of the prereactor, the designs for the reactive distillation column are calculated based on boundary value methods.
Figure 3. Algorithm for the identification of near-optimal pre-reactorreactive distillation flowsheets.
The costs for the flowsheets (see the Appendix for details on the cost function) are calculated, and the flowsheets are ranked accordingly. For the design of the column itself, the product purities have to be specified beforehand and the remaining variables, such as the distillate and bottom flow rates, have to be calculated. Once the overall reaction extent, ξTot, is fixed via the chosen purities and feed composition, an overall mass balance around envelope I in Figure 2 will provide the complete compositions and flow rates for the design of the column:
F ) B + D - νTotξTot
(1)
FxF,i ) BxB,i + DxD,i - νiξTot i ) 1, ..., c - 1
(2)
The procedures for the design of the reactive distillation column start from the product compositions xD, xB and flow rates B and D. The approach will be explained in detail in the next sections. In the design procedure for reactive distillation columns, the feed temperature and condition are calculated via an overall energy balance for the identified design. For each selected prereactor temperature, the energy balance around envelope II in Figure 2 has to be calculated, since the composition of the prereacted feed leaving the reactor depends on the reactor inlet temperature:
FPRhF ) DhD + BhB + QC - QR hF ) f(xPR)
(3)
Note that if the enthalpies are calculated based on the elemental reference state, as in Aspen Plus, the heat of reaction is not explicitly incorporated. Once the inlet temperatures for the reactive distillation column, TF, have been calculated, all information needed for the evaluation of the flowsheets is available and the designs for different pre-reaction extents (each corresponding to a given pre-reactor inlet temperature) can be ranked according to an appropriate cost function, as discussed below. Overall, the methodology involves two blocks, which can be calculated independently. The first block is the pre-reaction step, including HXI, the pre-reactor, and the expansion valve. The second block is the conceptual design of the reactive distillation column. The two blocks are coupled via the energy balance around envelope II, which allows the calculations for HXII. The cost function for the flowsheets involves capital costs for the following: heat exchangers HXI, HXII, the pre-reactor, and the reactive distillation column (including reboiler and condenser). For the design of the heat exchangers, suitable utilities have to be chosen first. Furthermore, operating costs for the utility requirements are considered.
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The capital cost is multiplied by installation factors and is annualized. Approximate costs for the catalyst and the packing have been kindly supplied by SULZER.26 Nevertheless, to calculate the catalyst volume for the pre-reactor is not straightforward since it is assumed that chemical equilibrium is reached. To overcome this problem, kinetic data from a similar reaction can be chosen, if available, and the volume required to nearly reach equilibrium conversion can be calculated. In the same fashion, information about approximate residence times as functions of composition and temperature could be used. The design procedure can be summarized as follows (see also Figure 3): (1) For the given feed composition and flow rate and chosen product purities, calculate the mass balance around envelope I in Figure 2 to determine the unknowns (e.g., distillate flow rate) for the design problem. (2) Design HXI and the pre-reactor for a given range of prereactor temperatures, and calculate the condition of the column feed at the outlet of the expansion valve. (3) Generate the designs for the reactive distillation column based on the approach presented in the next section. (4) For each reactive distillation column design, calculate the feed temperature via an overall energy balance around envelope II in Figure 2 and design the heat exchanger HXII. (5) Rank the designs with respect to a cost function. The proposed methodology can be used to identify design alternatives for pre-reactor-reactive distillation flowsheets as illustrated by Figure 2. Although the designs assume chemical equilibrium, they can give an initial indication of promising flowsheet configurations. 3. Conceptual Design of Finishing Reactive Distillation Columns 3.1. Boundary Value Methods. The design methodologies using the boundary value method are based on the ideas first developed for reactive distillation columns by Barbosa and Doherty.7 For fully specified product compositions, a feasible design is characterized by a continuous composition profile throughout the column, starting from the products. The profiles are generally calculated via tray-by-tray calculations for a given reflux (or reboil) ratio and a fixed feed condition. Fixing the feed condition can, however, lead to a tedious search procedure, where only one of the two operating conditions reflux and reboil ratio can be chosen independently. Instead, Dragomir18 uses a range of reflux and reboil ratios to generate designs and calculates the feed condition from an overall energy balance for the designs generated. This approach allows rapid screening of different design alternatives for a given design problem. Most approaches using the BVM have in common that they assume that the feed is positioned within the reactive section. This assumption may lead to backward reaction inside the column depending on the operating conditions.16 In general, these methodologies lead to designs where the reaction extent is concentrated around the feed stage, and it may happen that on many reactive stages almost no reaction takes place. In order to identify feasible and economic designs for a given design problem, reactive stages should only be used when necessary, due to their high cost. Thus, a design methodology should incorporate information on the reaction extent during the calculation procedure. The only published approach that incorporates this information is that of Espinosa et al.,16 who developed an approach for identifying the feasibility and design for finishing reactive distillation columns. However, this approach aims to identify one design for the minimum reflux and
Figure 4. Structure and different zones for finishing reactive distillation columns.
concentrates on feasibility and no attempt is made to generate or evaluate design alternatives. In the proposed approach for the design of finishing reactive distillation columns, the reaction extent is used explicitly throughout the design procedure to guarantee that the minimum number of reactive stages needed is used. 3.2. Structure of the Finishing Reactive Distillation Column. This work presents a methodology to identify nearoptimal designs for finishing reactive distillation columns. It is assumed that the major part of the reaction takes place in a pre-reactor upstream of the column. Reactor-reactive distillation flowsheets are a typical implementation of reactive distillation in industry.23,24 The advantages of reactive distillation, e.g., increasing conversion, etc., are exploited while the difficulties mentioned earlier of providing the necessary amount of catalyst inside the column are avoided. The columns are normally structured as shown in Figure 4. The column consists of four different zones with different tasks. The structure shown is especially well suited to etherification reactions, such as the production of ETBE, MTBE or TAME, etc. In the nonreactive stripping section, the main product (e.g., ETBE) is purified from the reactants. In the nonreactive rectifying section II, the product, which has been brought into the column via the pre-reacted feed stream, is separated from the reactants of the reaction. This section allows the product concentration to be considerably reduced before the reactants enter the reactive zone. Thus, the opportunity for backward reactions to occur is greatly reduced. This zone is necessary to avoid backward reaction in the lower part of the reactive section. In the reactive section, the remaining part of the reaction takes place. In the nonreactive rectifying section I, the remaining product is separated from the inert and other reactants. Columns with the reactive core in the stripping section may be treated in an analogous way. 3.3. Design Procedure for Finishing Reactive Distillation Columns. The first step in the design procedure is to identify the product composition and the reaction extent needed in the column. The input for the methodology is the composition and flow rate at the outlet of the pre-reactor. The definition of product purities for the bottom and distillate product allows the calculation of the overall mass balance of the column. This leads to the reaction extent inside the column and the distillate and bottom product flow rates. Thus, the reaction extent inside the pre-reactor, ξPR, is coupled with the reaction extent inside the column, ξRD. Once the purities for the bottom product and distillate are given, the column profiles can be calculated starting from the
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Figure 5. Boundary condition and feasibility criterion (ξPR, ξRD, and ξTotal represent the reaction extent in the column, reactor and overall process, respectively).
products. In order to identify a range of feasible designs and to identify an economically near-optimal solution, the profiles are calculated for a range of different operating conditions. The composition profiles for the rectifying section I are calculated stage by stage for a range of reflux ratios. It is assumed that phase equilibrium is reached on every stage. In the next step, the starting point for the reactive core section has to be identified. Here, the distance of the nonreactive rectifying I profiles to the reactive equilibrium surface (the reactive surface represents all points in composition space where reactive equilibrium is reached) is taken as a measure. For the calculation of the reactive profiles, reactive and phase equilibrium is assumed. The calculation of the reactive core proceeds down the column until the required reaction extent in the column is attained (see Figure 5). At the stage where this boundary condition is satisfied, the calculation of the nonreactive rectifying section II can begin. The composition profiles can be calculated in the same manner as for the primary nonreactive rectifying section with the difference that the starting point is the last reactive stage and not the distillate. The nonreactive stripping profile will be calculated starting from the bottom product for a range of reboil ratios. The calculation of the profiles inside the column can incorporate energy balances if needed. Since at the boundaries of the sections the flows can vary considerably, energy balances are always used for these stages. The calculation of the profiles in the corresponding sections will be explained in more detail in the following sections. For a feasible column design, a continuous profile throughout the column has to exist. The feasibility criterion for a design is the intersection of the stripping section profile and the profile of the nonreactive rectifying section II (see also Figure 5). The search for the intersection of composition profiles can be rather tedious and the probability of profiles intersecting can be low in the case of systems with more than three components. In order to improve the procedure, a methodology similar to the one proposed by Thong27 is used. Instead of choosing the exact composition for the product, only the purities for the main product are specified, and thus, a limit is set for the impurities. On the basis of this information, composition manifolds can be generated, which cover a subspace of the n-dimensional composition space (for a four-component mixture, the manifolds cover a surface inside the composition space). Intersections between these manifolds and the rectifying II profiles are more probable and thus enhance the calculation procedure.
Figure 6. Composition profiles calculated from similar product compositions and the corresponding manifold for a specific stage number and reboil ratio.
Figure 7. Product region for a product 95% pure in component C and manifold construction starting from the specified product region.
Composition Manifolds. It is widely accepted that the composition profiles calculated with the boundary value method are highly sensitive to small changes in the product compositions.27,28 In Figure 6, several stripping profiles for a fixed reboil ratio starting from nearly the same bottom product are shown. A manifold can be constructed which for a given reboil ratio and stage number contains all possible compositions of profiles starting from nearly the same product (see the shaded area in Figure 6). The linear approximation of the manifold is the triangle between the three points on the binary edges of the composition space, xAC, xBC, and xDC. Normally, the purity requirement for a product stream will be between 90 and 99% of the dominating component. Once the minimum requirement for the desired component is specified, a product region can be defined. A product region is the set of all compositions that meet the specified purity requirements. Figure 7 shows such a product region for a purity of 95% for the desired component. Instead of a single composition profile, composition manifolds can be constructed. To do so, composition profiles are calculated starting from the representative points of the product region, lying on the binary edges of the composition space. For a fourcomponent mixture, as shown in Figure 7, the profiles are calculated starting from the points xB2-xB4. While a point on a composition profile represents the composition on a certain stage for a specific reboil ratio leading to a specified product composition, a composition manifold represents all the possible compositions on a certain stage for the specified reboil ratio leading to a product composition inside the product region. The linear approximations of the manifolds are in case of four-
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Figure 8. Nonreactive rectifying section I.
component mixture triangles constructed from the corresponding points on the binary edges for a specific stage number and reboil ratio. In the case of an n-component mixture, the calculation of the profiles is started from all representative compositions of the product region. For an n-component mixture, the calculation starts from n - 1 binary edges and the manifolds are approximated by linear hyperplanes in the (n - 1)-dimensional composition space.27 However, especially for mixtures with nonideal phase behavior, these manifolds are curved and bend toward or away from the product region. In the case of a four-component mixture, this effect is captured in this work. The manifolds are represented using a spherical approximation. As an additional starting point for the calculation of the composition profiles, the center point of the product region, xB1, is chosen (see Figure 7). The points from the corresponding composition profiles starting from the corners of the product region and the center point are used to calculate the radius and center point of a sphere containing all four points.29 The part of the sphere which is contained within the composition space is used as an approximation of the manifold. The manifolds are used for the intersection search with the rectifying section II profiles. As can be deduced from Figure 7, the use of manifolds rather than composition profiles increases significantly the probability to identify intersections. Thus, the robustness of the whole design procedure is greatly increased by the use of manifolds. 3.3.1. Calculation of Composition Profiles. (A) Nonreactive Rectifying Section I. The composition profiles for the nonreactive rectifying section I are calculated stage by stage starting from the given top product composition for a range of reflux ratios and a given number of stages. A mass balance around the top of the column (see Figure 8) is used to calculate the profiles together with dew point calculations for the assumption of constant molar overflow:
yr,n+1,i )
R 1 + ∀ i ) 1, ..., c - 1 x x R + 1 r,n-1,i R + 1 D,i (4)
In case energy balances are to be included, the mass and energy balance equations for each stage are solved simultaneously. (B) Determination of the Starting Point of the Reactive Section. After the nonreactive rectifying section I profiles are calculated, the starting points for the reactive section have to be identified. Every starting point of the reactive section has to be in reactive and phase equilibrium. Thus, the condition is tested where the composition profiles for the nonreactive rectifying section I lie exactly on or are close enough to the reactive surface. The reactive surface represents all points in reactive equilibrium. Figure 9 illustrates the reactive
Figure 9. Starting point of the reactive section calculation, nonreactive rectifying section I profile, and reactive surface for reaction A + B T C, inert D (shaded area).
surface for a reaction of A and B to component C in the presence of the inert D. To calculate the distance to the reactive surface, a reactive dew point calculation is carried out for every vapor composition of the nonreactive rectifying I profiles. The norm of the difference between the resulting liquid composition in chemical equilibrium, xeq, and the nonreactive composition x is taken as a measure to decide if a valid starting point is identified. The procedure is illustrated in Figure 9. If the distance is below a specified tolerance, the point is accepted to lie on the reactive surface: c
|xi.eq - xi| e ∑ i)1
(5)
To increase the accuracy of the approach, eq 5 is also used for the gas-phase concentrations. The norm of the liquid- and gas-phase composition difference has to be below the specified tolerance. (Through sensitivity studies, it was found that a tolerance of 0.001 or smaller was effective in identifying starting points. A value of the tolerance for the case studies considered in the range of 0.001 is sufficient to guarantee that no possible starting points are missed.) Once such potential starting points are identified, the corresponding stages are recalculated as reactive ones (phase equilibrium calculations are replaced by chemical equilibrium calculations). If the calculated reaction extent ξi is above a specified limit, the starting point is accepted:
ξ i g ξ
(6)
Using this calculation procedure, reactive stages with a very low reaction extent are avoided and thus an unnecessary number of reactive stages. (C) Reactive Section. The reactive core section is calculated from the starting points identified for the corresponding reflux ratios downwards. The composition profiles are calculated stage by stage. The calculation is done in the transformed space introduced by Doherty and co-workers.30 These transformed variables can be derived via elimination of the reaction extent from the mass balances. It is guaranteed that the profiles are in simultaneous phase and reaction equilibrium. The equations for the reactive composition profiles in transformed variables are similar to the equations used for nonreactive systems.18 The corresponding operating line can be calculated as follows (see also the top of Figure 10):
Yp+1,i )
A hp A h n-1 + 1 A h n-1 X + Y X A h p + 1 p,i A h p + 1 n,i A h n-1 + 1 n-1,i ∀ i ) 1, ..., c - nR - 1 (7)
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Figure 11. Reaction extent for different reflux ratios as a function of the stage number in the reactive section.
Figure 10. Reactive core section and nonreactive rectifying section II.
A hp )
L hp V hn - L h n-1
A h n-1 )
L h n-1 V hn - L h n-1
(8)
(9)
The equations are deduced under the assumption of constant molar overflow in transformed space. This assumption reflects the influence of the change in the number of moles due to reaction on the internal flow rates:18
L h n-1 ) Ln-1(1 - νTtotV-1 ref xn-1,ref) ) const
NRC
ξi ∑ i)1
|ξTot - ξRD - ξPR| e
operating line under the assumption of constant molar overflow can be deduced from Figure 10:
yq+1,i ) yp+1,i + (xq,i - xp,i)A ∀ i ) 1, ..., c - 1 (13)
(10)
The calculation of the profiles continues until the remaining reaction extent to be reached in the column is accomplished. The reaction extent is therefore summed over the reactive stages:
ξRD )
Figure 12. Stripping section.
(11) (12)
NRC is defined as the number of reactive stages. However, it is unlikely that the criterion for the end of the reactive section (see eq 11) is reached exactly on a stage for the specified reflux ratio. The situation is likely to be as illustrated in Figure 11. For one reflux ratio (R1), the reaction extent to be reached in the column is exceeded, and for the other one (R2), the reaction extent is not reached completely for the identified stage (N*). An interval search is used to identify the values for the reflux ratio (R*) where the needed reaction extent is reached for the identified stage number (N*). From all identified starting points for the reactive core section, the interval search leads to several reflux ratios satisfying the overall reaction extent constraint. Together with the reflux ratio, the numbers of reactive stages needed are identified. (D) Nonreactive Rectifying Section II. Starting from the last stages of the reactive core, the composition profiles of the nonreactive rectifying section II can be calculated. The profiles of this section are calculated from all reactive stages satisfying the boundary condition for the reaction extent. The profiles are calculated for a given number of stages, stage by stage. The
A)
Lp Vp+1
(14)
(E) Stripping Section Manifolds. For the stripping section, composition manifolds are calculated stage by stage. To generate the manifolds, stripping composition profiles are calculated for a given set of reboil ratios and number of stages starting from the points defining the product region. The operating line used can be deduced from Figure 12 under the assumption of constant molar overflow:
xs,m+1,i )
S 1 + ∀ i ) 1, ..., c - 1 y x S + 1 s,m,i S + 1 B,i (15)
The manifolds are then constructed from the composition profiles for a specific stage and reboil ratio. In Figure 13, several manifolds are shown originating from the product region. It can be seen that the manifolds span throughout a considerable area within the composition space. 3.3.2. Intersection between Manifolds and Composition Profiles. For the finishing reactive distillation column, the feed stage is taken to be the last stripping stage as illustrated in Figure 14. To obtain feasible designs for the finishing reactive distillation column, a continuous liquid and vapor profile throughout the column has to exist. The feasibility criterion is that the composition of the vapor leaving the feed stage, m, is the same as the vapor entering the first stage in the nonreactive rectifying section II, stage n. This criterion can be reformulated in terms of liquid compositions: if an intersection between the vapor profiles exists, indicating feasibility, then an intersection
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xintersect,i ) xrII,n,i + R(xrII,n+1,i - xrII,n,i)
(17)
The value of a scalar parameter R is determined via an intersection search between this line and all spheres.29 For a feasible design, the value of R has to be in the interval [0,1], meaning that the line and sphere intersect (see Figure 15). From the intersection, the number of stages in the nonreactive rectifying section II, NRIIapprox, will be a fractional stage number:
NRIIapprox ) NRII + R
Figure 13. Composition manifolds for the stripping section originating from the product region.
Figure 14. Feed stage location for finishing reactive distillation columns and the feasibility criterion.
Figure 15. Intersection between nonreactive rectifying section II profiles and stripping manifolds.
between the liquid profiles, in phase equilibrium with the vapor, will also exist. This leads to the following equation for the feasibility criterion:
xs,m,i ) xrII,n+1,i ) xintersect,i ∀ i ) 1, ..., c - 1
(16)
The liquid composition leaving the feed stage, xs,m, has to coincide with the composition at the intersection point between rectifying II and stripping profile, xintersect. To identify feasible designs, an intersection search has to be carried out between the rectifying section II profiles and the stripping manifolds. Figure 15 illustrates the approach. An intersection between the profiles and the manifolds will guarantee a continuous profile and thus a feasible design for the column. A line connecting the compositions of two consecutive stages of a rectifying section II profile can be described as follows:
(18)
However, for the initialization of a simulation, the neighboring number of stages can normally be used without loss of accuracy. This intersection search is carried out for all stages of the nonreactive rectifying section II profiles and all stripping manifolds. Usually, many different designs can be identified. The use of the manifolds instead of line-to-line intersection search in three-dimensional space highly increases the robustness of the approach. 3.3.3. Design Procedure Summary. The calculation of the profiles inside the column can incorporate energy balances, if needed. Since at the boundaries of the sections the flow rates can vary considerably, energy balances are used for these stages. For each feasible design found, the feed condition can be determined, condenser and reboiler duties, column diameter, and column capital and operating costs. The feed condition is calculated via an overall energy balance around the column (see eq 3). Depending on which utilities are available, not every feed condition can be realized with the feed preheater. Consequently, in the design procedure, only combinations of reflux and reboil ratios are accepted which lead to an achievable feed condition. The complete procedure can be summarized as follows: (1) Specify the feed composition and flow rate of the prereactor outlet stream. Specify the distillate purity as well as the main product purity for the bottom product. (2) Calculate the remaining variables (reaction extent for the column and distillate and bottom flow rates) from the overall mass balance. (3) Calculate the composition profile for the nonreactive rectifying section I for a range of reflux ratios. (4) Calculate the starting point for the reactive core. All starting stages identified have to be recalculated as reactive ones and to be tested if the reaction extent is positive and greater than a chosen threshold. (5) Calculate the composition profile in the reactive core, starting from the points identified in step 4. Calculate the profiles until the boundary condition (see eq 11) for the reaction extent is reached. (6) Calculate the nonreactive rectifying profiles for section II starting from the points identified in 5. (7) Calculate the stripping profiles and generate the corresponding manifolds for a range of reboil ratios. (8) Search for intersections between the stripping manifolds and the profiles of nonreactive rectifying section II. (9) Calculate the costs of the designs and rank them accordingly. The condenser and reboiler duties are directly related to the reflux and reboil ratios and can, therefore, be calculated via an energy balance around the condenser and reboiler, respectively. Utility costs can then be calculated, given the temperatures and unit costs of available utilities. The capital costs for the condenser and reboiler can be calculated as a function of the heat exchange area. The capital cost model for the column takes into account the cost for the column shell and those for reactive and nonreactive packing. Annualized costs are calculated and
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Ind. Eng. Chem. Res., Vol. 46, No. 2, 2007 Table 2. Product and Feed Compositions for the ETBE System components
stoich coeff (-)
distillate comp (mol fr)
bottom prod comp (mol fr)
feed comp (mol fr)
-1 0 -1 1
5.9 × 10-6 a 0.952a 0.048 4.1 × 10-8 a 98.68
2.2 × 10-4 a 0.002 0.007a 0.991a 62.53
0.278a 0.421a 0.301a 0.0a 223.2a
isobutene n-butane ethanol ETBE flow rate (kmol/h) a
Specified values.
Table 3. Design Variable Ranges Considered during the Design Procedurea TR (°C)
R (-)
S (-)
NRI (-)
NRC (-)
NRII (-)
NS (-)
50-80
1-12
1-12
1-7
1-20
1-10
1-10
a
Figure 16. Composition space, reactive surface, and distillation boundary for the ETBE system. Table 1. Stationary Points for the ETBE System composition (mol fr)
stationary points
TB at 8 bar (°C)
isobutene
n-butane
ethanol
ETBE
isobutene n-butane/ethanola n-butane ethanol/ETBEa ethanol ETBE
60.8 68.4 69.4 135.6 142.1 156.7
1 0 0 0 0 0
0 0.94 1 0 0 0
0 0.06 0 0.63 1 0
0 0 0 0.37 0 1
a
Azeotrope.
are used to rank the designs. The calculation procedure is automated and implemented in FORTRAN within the program package COLOM (developed at the Center for Process Integration at The University of Manchester). 4. Case StudysETBE Production The proposed methodology has been used for the design of a reactive distillation flowsheet for the production of ETBE. This system has been studied during the European Union project INSERT. The feed stream consists of a C4 stream containing the reactive component isobutene as well as ethanol. The inert components present in the C4 fraction are lumped and represented by n-butane. The following reaction takes place over an ion-exchange resin catalyst, e.g., Amberlyst 15, as:31 Cat
Isobutene + EtOH 798 ETBE
(19)
The reaction equilibrium, which is assumed for the reactor and on all reactive stages in the reactive distillation column, is described by an equation presented by Sundmacher et al.:31
14580 - 232.9 ln(T) + 1.087T T (1.114 × 10-3)T2 + (5.538 × 10-7)T3 (20)
ln(Keq) ) 1140.912 -
Figure 16 shows the existing azeotropes and boiling temperatures at 8 bar. The reactive equilibrium surface and the existing distillation boundary are also shown. The composition and boiling temperatures for all stationary points are shown in Table 1. Pure ETBE can only be produced from a conventional distillation column if the feed to the column does not contain too much ethanol and thus is lying in the distillation region where ETBE is the highest boiling component. As ETBE does not lie on the reactive equilibrium surface, it can be seen that
TR corresponds to the pre-reactor temperature, R, to the reflux ratio, and S, to the reboil ratio; NRI-NS correspond to the number of stages used for the profile calculations in the four sections of the column: rectifying I, reactive core, rectifying II, and stripping.
a nonreactive stripping section is needed to obtain nearly pure ETBE. A column structure as shown in Figure 4 is suited to produce high purity ETBE. The industrial flowsheets for ETBE and MTBE production are identical32 (see Figure 1). The reactants are fed to a prereactor (isothermal or adiabatic), where chemical equilibrium is nearly reached. In the finishing reactive distillation column, the remaining part of the reaction takes place and ETBE is produced at the desired purity. For the design procedure, several decisions have to be made. First, the compositions of the feed, distillate, and bottom product have to be defined. These values are shown in Table 2. The feed stream is chosen to produce approximately 50 000 t/y of ETBE product. The feed contains an excess of ethanol (approximately 8%), relative to isobutene, to suppress side reactions and enhance the isobutene conversion. As the top product, a near azeotropic mixture between n-butane and ethanol is chosen. A nearly pure ETBE stream is taken from the bottom of the column. The chosen specifications (see Table 2) lead to a conversion of 99.97% of isobutene. The reactor pressure is 15 bar to guarantee liquid-phase operation. The reactor is assumed to be operated in isothermal mode. The operating pressure for the column is 8 bar. This value has to be chosen to guarantee that the temperature inside the column is suitable for the catalyst and that cooling water can be used within the condenser. Furthermore, the ranges for the design variables have to be chosen. The chosen ranges for the design variables are shown in Table 3. The range of reactor temperatures considered is 5080 °C which corresponds to the industrially chosen range of reactor temperatures.32 The ranges for the reflux and reboil ratio cover a wide range of operating conditions for the column. The pre-reactor is simulated with Aspen Plus. For all physical property calculations, an interface to Aspen Plus is used. The gas phase is assumed to show ideal behavior. The liquid phase is modeled via UNIFAC-DMD. The vapor-liquid equilibrium (VLE) behavior showed good accordance with the available experimental data.33-40 Before the design procedure is carried out, it has to be decided if energy balances have to be included or if the assumption of constant molar overflow is sufficient. Figure 17 shows the influence on the composition profiles for a nonreactive and a reactive section. It can be seen that energy balances should be included for nonreactive sections. The assumption of constant molar overflow in transformed space is adequate for the reactive section.
Ind. Eng. Chem. Res., Vol. 46, No. 2, 2007 567
Figure 17. Influence of the energy balance on composition profile calculations in (a) the nonreactive stripping section and (b) the reactive core section. Table 4. Several Column Designs Ranked by Total Annualized Cost for a 70-°C Pre-reactor Temperature NRI (-)
NRC (-)
NRII (-)
NS (-)
NTOT (-)
R (-)
S (-)
TF (° C)
cond. duty (kW)
reb. duty (kW)
total cost ($/y)
5 4 4 4 2 4 5 4 5
5 7 7 7 7 6 4 6 5
5.5 6.7 2.1 2.7 1.0 1.6 1.2 2.5 0.6
6 9 6 5 7 5 6 4 6
21.5 26.7 19.1 18.7 17 16.6 16.2 16.5 16.6
2.39 1.99 1.99 1.99 2.86 3.52 4.09 3.52 2.39
1.00 1.00 2.84 3.30 2.85 2.85 2.85 3.31 4.60
153.9 125.3 95.3 89.9 109.7 125.4 165.4 114.1 82.0
1699 1498 1498 1498 1931 2264 2547 2264 1699
415 415 1180 1371 1180 1180 1180 1371 1910
254 000 260 000 331 000 352 000 366 000 383 000 387 000 405 000 422 000
A 5-°C interval is used for the pre-reactor temperatures. Multiple column designs are obtained for these specifications for each temperature of the reactor. Table 4 shows several column designs for a reactor temperature of 70 °C. In Table 4, NRI denotes the number of nonreactive stages in rectifying section I, NRC, the number of reactive stages in the reactive core, NRII, the number of nonreactive stages in rectifying section II, NS, the number of nonreactive stripping stages, TF, the column feed temperature, R, the reflux ratio, and S, the reboil ratio. In general, several hundreds of different designs are calculated for a given reactor temperature. The designs differ in numbers of stages in the sections and in the operating parameters. The cost function involves the cost for reactive and nonreactive stages (via the cost for packing, cost for the column shell, and condenser and reboiler capital cost as well as utility cost for steam and cooling water). To annualize costs, the operating time (8500 h/y), the interest rate (10%), and the loan repayment period (5 y) are assumed. Installation factors are used to consider the cost for construction and utility equipment. The costs of the column shown in Table 4 do not consider any upstream equipment. It can be seen that the cheapest designs in Table 4 are identified for low reboil and reflux ratios. The reason for this is the high influence of the utility costs for the condenser and reboiler on the overall costs of the columns. Additionally, the reflux and reboil ratios influence the vapor and liquid streams in the column and thus the diameter of the column. The diameter of the column, however, influences the capital cost of the column, e.g., by changing the packing volume on a stage. Thus, the number of stages in the column sections, on its own, plays a minor role. The number of stages has always to be analyzed with respect to the corresponding operating conditions since the capital cost of the stage is based on the packing volume (see the Appendix). To illustrate that the column designs can be validated, the first design is used to initialize simulations with Aspen Plus. The column consists of five stages in the nonreactive rectifying
Table 5. Product Compositions Obtained by Simulation with Aspen Plus Based on Results from the Conceptual Design Procedure (Design 1 in Table 4) design feed components (mol fr) isobutene n-butane ethanol ETBE flow rate (kmol/h) a
0.041 0.560 0.072 0.327 168.15
Aspen
distillate (mol fr)
bottom (mol fr)
distillate (mol fr)
bottom (mol fr)
5.9 × 10-6 a 0.952a 0.048 4.1 × 10-8 a 98.68
2.2 × 10-4 a 0.002 0.007a 0.991a 62.53
5.0 × 10-6 0.950 0.050 3.7 × 10-8 98.72
3.9 × 10-4 0.005 0.004 0.991 62.51
Specified values.
section I (including the condenser), five reactive stages in the reactive section, six stages in the nonreactive rectifying section II, and six stripping stages (including the reboiler). The reflux ratio is 2.39, and the reboil ratio, 1; the feed temperature is 153.9 °C (superheated feed). The results are shown in Table 5. There is excellent agreement between the design specifications for the calculation procedure and the simulation results. The overall flowsheet design procedure leads to the results shown in Table 6. The best design for every pre-reactor temperature is shown. Here, the cost function includes the cost for the reactor, the heat exchanger up- and downstream of the reactor, and the corresponding utility costs. For the flowsheet, the optimal reactor temperature of 60 °C can be identified (shown in bold in Table 6). Figure 18 illustrates the best flowsheet design from Table 6 together with all design parameters for the flowsheet. The single cost contributions for the cheapest flowsheet design for a reactor temperature of 70 °C are shown in Table 7. As can be seen, the cost for the column dominates but the costs for the feed preheater, HXII, and the reactor and the heat exchanger upstream of the reactor, HXI, are also considerable. For a specific reactor temperature, the costs for the pre-reactor and the heat exchanger upstream of the reactor remain constant for all column designs. However, the cost for the feed preheater downstream of the reactor changes for every column design
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Table 6. Best Flowsheet Designs Based on Total Annualized Cost TRa (°C)
NRI (-)
NRC (-)
NRII (-)
NS (-)
NTOT (-)
R (-)
S (-)
TF (° C)
cond. duty (kW)
reb. duty (kW)
total cost ($/y)
50 55 60 65 70 75 80
1 1 1 4 4 4 4
7 7 7 7 7 7 7
6.4 6.0 6.9 6.8 6.7 2.4 3.8
9 8 7 10 9 6 5
23.4 22.0 21.9 27.8 26.7 19.4 19.8
1.63 1.75 1.88 1.85 1.99 2.15 2.34
1.00 1.00 1.00 1.00 1.0 2.85 2.85
117.4 118.4 120.9 118.4 125.3 96.9 98.8
1317 1375 1440 1427 1498 1579 1670
415 415 415 415 415 1181 1180
428 000 415 000 414 000 419 000 424 000 465 000 477 000
a
Note that TR corresponds to the pre-reactor temperature. Table 7. Cost Contributions for the Best Flowsheet Design for a Reactor Temperature of 70 °C
Figure 18. Best flowsheet design from Table 6.
depending on the different column feed temperatures (see also Table 4) calculated by the column design procedure. For example, for the first design in Table 4, the pre-reacted feed has to be preheated to 153.9 °C whereas for the second design the feed has only to be heated to 125.3 °C. Consequently, the costs for the feed pre-heater HXII are considerably higher for the first design (HXII cost for design 1 in Table 4: 166 300 $/y) compared to the second one (HXII cost for design 2 in Table 4: 86 000 $/y). This leads to a shift in the order of the column designs when ranked with the overall flowsheet cost. For example, for the designs for a reactor temperature of 70 °C as presented in Table 4, the second cheapest column designs will lead to the optimal overall flowsheet design (see Tables 4 and 6) since the pre-reacted feed stream at the outlet of the prereactor has to be heated to a lower temperature than necessary for the first design in Table 5. The cheapest column design in Table 4 is only ranked at the 101st place based on overall flowsheet costs. For the identification of the optimum distribution of the reaction extent between the reactive distillation column and the pre-reactor, major trade-offs exist. For lower reactor temperatures, the costs for the reactor increase since a higher conversion has to be accomplished within the pre-reactor. The catalyst costs as well as the costs for heat exchange area and the cooling water, to maintain the reactor temperature, increase. However, for lower reactor temperatures, the costs for the reactive distillation column are reduced since the lower reaction extent in the column leads to lower reactive stages and lower needed operating parameters. The optimal distribution of the reaction and thus the optimal reactor temperature is identified, where these two opposite effects lead to the best compromise. This is reached in the case of ETBE production for a reactor temperature of 60 °C. 5. Conclusions This paper presents a methodology for the conceptual design of pre-reactor-reactive distillation flowsheets. These are advantageous in cases where practical issues favor the use of a pre-reactor. The flowsheet under consideration consists of heat exchangers up- and downstream of the pre-reactor, the prereactor, and the finishing reactive distillation column including a condenser and reboiler. For the column, a structure consisting of four different zones is proposed. The column consists of a
reactor and heat exch I cost ($/y)
heat exch II cost ($/y)
column cost ($/y)
flowsheet cost ($/y)
78 000
86 000
260 000
424 000
reactive core, two rectifying sections, and one stripping section. This setup is especially suited for etherification reactions such as ETBE or MTBE, etc. Since the pre-reacted feed stream is fed in the nonreactive part of the column, the reaction products can be separated from the reactants before the reactive section of the column is reached. Thus, backward reaction is avoided. Chemical equilibrium is assumed to be reached in the reactor and on all reactive stages of the reactive distillation column. The methodology identifies the optimal distribution of the reaction extent between the column and pre-reactor. For a range of pre-reactor temperatures, the cost for the reactor and the heat exchanger upstream of the reactor are calculated. A boundary value method is used to identify the designs of the finishing reactive distillation column for each pre-reactor temperature. Afterward, the duty and costs for the feed pre-heater, upstream of the reactive distillation column, are calculated and included. The overall cost of the flowsheet is used to rank the designs. To identify column designs, a continuous composition profile throughout the column has to be identified. Composition profiles in the column sections are calculated starting from the specified products for a range of operating conditions. The use of a product region and composition manifolds instead of exactly specified products and composition profiles highly increases the robustness of the design procedure. The methodology is easily automated and typically generates several hundreds of different column designs for a given reactor temperature. The approach gives necessary insights into the process, and instead of producing only one optimal design, several different flowsheet designs are provided. The approach has been illustrated for the production of ETBE. For the identification of the optimum distribution of the reaction extent between the reactive distillation column and pre-reactor, major trade-offs exist. For lower reactor temperatures, the cost for the reactor increases since a higher conversion has to be accomplished within the pre-reactor. However, for lower reactor temperatures, the costs for the reactive distillation column are reduced since the lower reaction extent in the column leads to lower reactive stages and lower needed operating parameters. The optimal distribution of the reaction extent and thus the optimal reactor temperature is identified, where these two opposite effects lead to the best compromise. However, the procedure assumes chemical equilibrium to be reached in the pre-reactor as well as on all reactive stages. Thus, the influence of the kinetics of the reaction system is not captured. The results can give a first indication of which configuration to choose. The methodology has been illustrated for a four-component mixture. However, the use of product regions and composition manifolds enables the use of the
Ind. Eng. Chem. Res., Vol. 46, No. 2, 2007 569
methodology for n-component systems. Future work will incorporate double-feed configurations and kinetically controlled reaction systems.
m for nonreactive packing have been chosen)26 are provided by SULZER.
Acknowledgment
Total Annualized Cost. The total cost for the flowsheet is calculated as the annualized cost. The corresponding factor aann is a function of the interest rate i and the number of years for the loan n:
We acknowledge the financial support provided by the European Commision within the 6th Framework Program, Project “INSERT-Integrating Separation and Reaction Technologies”, Contract No. NMP2-CT-2003-505862.
CColumn ) (CapShell + CapPacking)(1 + Finstall)
aann )
Appendix The cost function used for ranking the reactive distillation flowsheets consists of annualized capital and utility costs. Cost Estimation. The equipment and operating costs are partly based on data from former years. Costs for 2006 are estimated using the chemical engineering plant cost index.42 For cost data from 1990, that means, e.g., that the following is true:
Cost2006 )
Cost Index2006 Cost1990 Cost Index1990
(A.1)
The capital costs are calculated as installed cost C. Thus, the capital costs are multiplied by an installation factor, Finstall, representing costs for erection, piping, instrumentation, electrics, civil works, structures, and building and lagging:43
C ) Cap(1 + Finstall)
(A.2)
Steam and Cooling Water Cost. The costs for cooling water and steam are taken from Timmerhaus et al.41 The data are given for high pressure, medium pressure, and exhaust steam: 9.4, 7.5, and 3.5 $/1000 kg, respectively. The cost for cooling water is 0.06 $/m3. The utilities are chosen such that a minimum temperature difference of 10 °C is guaranteed for the condenser, and 20 °C, for the reboiler. Capital Cost. The total capital costs include the cost for the heat exchangers (up- and downstream of the pre-reactor and the reboiler and condenser), the pre-reactor, and the column itself. 1. Heat Exchanger. The heat exchanger capital costs are dependent on the heat exchange area. The equation is fitted to the data given in:43
CHX ) (5391 + 113.4A - 0.32A2 + (9 × 10-4)A3 (1 × 10-6)A4 + (4 × 10-10)A5)(1 + Finstall) (A.3) 2. Reactor. The cost of the reactor is based on the cost for an isothermal reactor. The cost is calculated as the sum of the heat exchange area needed to maintain the reactor temperature and the cost of the catalyst needed for the reaction. Whereas chemical equilibrium is assumed during the design procedure, for the calculation of the catalyst amount needed, kinetic data have to be used. If no information is available, the reaction data from a similar reaction might be taken. For the ETBE case study, the data is taken from Sundmacher et al.31 The cost data for the catalyst have been kindly supplied by SULZER26 during the European Union Project INSERT:
CReactor ) (CapHX + CapCatalyst)(1 + Finstall)
(A.4)
3. Column. The capital cost of the column itself is calculated from the cost for the column shell,43 and the costs for reactive and nonreactive packing (HETP of 0.5 m for reactive and 0.25
(1 + i)n (1 + i)n-1
(A.5)
(A.6)
The total flowsheet cost CTotal is thus the summation of the operating cost Cop and the annualized capital cost:
CTotal ) Cop + aann(CHX + CReactor + CColumn) (A.7) Nomenclature A ) heat exchange area, m3 B ) bottom product molar flow rate, kmol/h c ) number of components, dimensionless D ) distillate molar flow rate, kmol/h F ) feed molar flow rate, kmol/h h ) specific enthalpy, kJ/kmol L ) liquid molar flow rate, kmol/h L h ) transformed liquid molar flow rate, kmol/h q ) feed quality, dimensionless Q ) heat duty, kW R ) reflux ratio, dimensionless S ) reboil ratio, dimensionless T ) temperature, °C V ) vapor molar flow rate, kmol/h V h ) transformed vapor molar flow rate, kmol/h x ) liquid mole fraction, dimensionless x ) vector of liquid mole fractions, dimensionless X ) transformed liquid mole fraction, dimensionless y ) vapor mole fraction, dimensionless Y ) transformed vapor mole fraction, dimensionless Greek Symbols R ) scalar parameter for intersection search, dimensionless νref ) stoichiometric coefficient of reference component, dimensionless νi ) stoichiometric coefficient of component i, dimensionless νTot ) sum of stoichiometric coefficients, dimensionless ξ ) reaction extent, kmol/h Subscripts and Superscripts B ) bottom product D ) distillate F ) feed i ) counter for components m ) stage number m n ) stage number n PR ) pre-reactor RD ) reactive distillation column ref ) reference component r ) rectifying section s ) stripping section Tot ) total AbbreViations ETBE ) ethyl-tert-butyl-ether EtOH ) ethanol BVM ) boundary value method
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ReceiVed for reView April 19, 2006 ReVised manuscript receiVed October 12, 2006 Accepted October 17, 2006 IE0604831
