Minimum Energy emand and Split easibility for a Class of Reactive istillation Columns Rosa Y. Urdaneta, Jürgen ausa + and olfgang Marquardt * Lehrstuhl für Prozesstechnik RTH Aachen University, Templergraben 55, 52056 Aachen, Germany Abstract A new approach for the calculation of the minimum energy demand (ME) of reactive distillation columns is presented here. Continuous distillation boundaries in the limit of chemical reaction equilibrium are used to determine minimum energy demand of the process. At the same time, split feasibility can be confirmed. The method is applicable to mixtures without or with phase split if the number of independent components equals two. A similar concept has been applied to conceptual design of heteroazeotropic distillation columns. It carries over to reactive distillation because both processes are characterized by strongly curved composition profiles in composition space. The method is illustrated by two esterification examples, one of them showing liquid phase split in the rectifying section. Keywords: reactive distillation, conceptual design, shortcut methods, continuous distillation boundaries, minimum energy demand, split feasibility.. Introduction The integration of reaction and separation in a single vessel is known as reactive distillation (R). The use of R processes in the chemical and petrochemical industries has successfully reduced process costs and environmental emissions. However, the complex behavior of R processes demands simple calculation tools to be applied for conceptual design in order to allow a quick evaluation of the feasibility of the separation, to assess the effort required to reach the desired products, to gain insight in the process, and to provide reliable initial values for rigorous procedures to be applied subsequently (Sundmacher and Kienle, 2002). In recent years, special attention has been paid to processes in the kinetically controlled reaction regime. However, chemical reaction equilibrium (CRE) often provides first approximate results of sufficient quality for many reactive systems. or the limit of reaction equilibrium, this work shows how continuous distillation boundaries (C) can be employed to predict split feasibility for a certain class of R processes and to determine the ME. hen liquid phase split occurs in the column, the procedure is able to calculate multiple heterogeneous stages if required to reach a feasible separation under minimum reflux conditions. + Present address: ayer Technology Services, Leverkusen, Germany * Author to whom correspondence should be adressed : marquardt@lpt.rwth-aachen.de
2. Chemical Equilibrium versus Reaction Kinetic Regime Under the assumption of CRE, the number of degrees of freedom of a chemical system is reduced by the number of independent chemical equilibrium reactions. This can simplify the representation of a chemical system with multiple components and reactions. Often, a simple two-dimensional reaction space of transformed compositions can be employed. Using this coordinate transformation, residue curve maps (RCM) for reactive columns can be obtained. The well-known conceptual design methods based on RCM for nonreactive columns can be readily extended to reactive columns (e.g. Ung and oherty, 995, Espinosa et al., 995, essling et al., 997). So far, the use of such design methods has been considered satisfactory in such cases. However, it has been observed just recently, that RCM based design methods are of limited applicability even in the case of nonreactive distillation processes (Urdaneta et al., 2002). or ternary heteroazeotropic distillation processes the use of RCM and the corresponding simple distillation boundaries (S) for studies of split feasibility and minimum energy demand can lead to misleading results because of large differences between S and the real distillation boundaries of the system (continuous distillation boundaries, C), which depend on product composition and energy duty. The highly nonlinear behavior responsible for these deviations is also observed for R processes in both chemical equilibrium and kinetically controlled regimes. Hence, it is very likely that RCM is not appropriate for the study of feasibility in R. It has been also observed that the trajectory of R column profiles is influenced by the fixed points of the system, i.e. the pinch points, in both cases. These pinch points of a column section are always located on the CRE manifold (Chadda et al., 2000). This result justifies studies of reactive distillation under CRE limit at least for a first approximation. The analysis in the kinetic regime normally requires a multiparametric study (Lee et al., 2003). Hence, a reliable previous analysis of the system under CRE allows for a better understanding of the reactive system since only one operational parameter, i.e. the energy duty has to be considered in the analysis. 3. Estimation of Minimum Energy emand The boundary value method (VM) is a well-known shortcut method for the determination of minimum energy demand (ME) in nonreactive distillation which has been extended by arbosa and oherty (988) to R columns under the assumption of CRE. Given the desired product compositions and streams, the material and energy balances of every column section are recursively solved for different reflux ratios until a feasible column design is obtained, i.e. until the calculated tray-by-tray profiles of the stripping and the rectifying sections intersect each other. Two important disadvantages of this method have been observed in nonreactive distillations: the high sensitivity of the column profile to traces in product compositions, and the requirement of a complex three-parametric analysis in heteroazeotropic distillation (i.e. energy duty, number of heterogeneous trays in the rectifying section and phase ratio on the last heterogeneous tray of this section) to calculate the profiles. The use of pinch based shortcut methods avoids both of these problems. An efficient procedure for the determination of ME in multicomponent nonreactive and nonideal systems is the rectification body method (RM) by ausa et al. (988). This is a pinch tracking method where linear rectification
bodies are constructed between product composition and pinch points in every column section as an approximate envelope for all possible tray-by-tray profiles. The general rule for the construction of the bodies is that the number of stable eigenvectors in the pinch point visited by a tray-by-tray profile must increase monotonously. This criterion can easily be extended to R under the assumption of CRE as shown by ausa (200). However, the quality of approximation by polyhedrons deteriorates significantly in cases where the concentration profiles show strong curvature as observed in heteroazeotropic distillation. Urdaneta et al. (2002) combine pinch tracking and tray-bytray calculation to determine the C of every column section. This approach allows to overcome the limitations of the VM and RM as discussed above. Hence, a higher reliability of the results can be reached. The use of C to bound the highly curved distillation regions can be considered as a generalization of the polyhedral R. 3. Calculation of continuous distillation boundaries The C in every column section can be determined from tray-by-tray calculations started at pinch points after some small perturbations into the direction of all eigenvectors of the pinch points. This approach is based on the fact that pinch points and product concentrations are connected by a concentration profile in a column section with an arbitrary high number of stages at finite reflux. Transformed coordinates (arbosa and oherty, 988) are not use here for calculations but only for the representation of the results. Rather, the equations are formulated in physical coordinates similar to the equations shown by Urdaneta et al. (2002) for nonreactive systems extended by a reaction term (conversion of every reaction) and by an additional equation (condition of equilibrium in every reaction). This equation is given by C C 0 = K reac ν j (x,t, p) x i,j ν i - x i, j i, () i= i= ν i,j <0 ν i,j >0 where K j reac is the equilibrium constant for reaction j on depending liquid composition x, temperature T and pressure p. C is the number of components, and ν i,j is the stoichiometric coefficient of component i in reaction j (positive for products and negative for reactants). After solving the corresponding set of equations, the stability of the liquid phase is checked by means of the phase stability test of ausa and Marquardt (2000). ifferent sets of equations for tray-by-tray calculation are used according to the results of the stability test to account for reactive homogeneous or reactive heterogeneous trays in the downward and upwards calculations. This procedure allows the determination of multiple heterogeneous stages within the R column in case of phase splitting. The system of equations which determines the pinch points, requires physical equilibrium (like shown in Section 3.3 of Urdaneta et al., 2002) and also chemical equilibrium. Using a homotopy continuation method, all pinch solutions can be detected reliably (see ausa, 200, for more details). The calculation of the pinch points requires the energy duty as parameter. Therefore, once a value for the reboiler duty is given, the pinch solutions and subsequently the C can be calculated.
Table. Specifications and results of R and CR methods for reactive systems in transformed coordinates (pressure=.03 bar, GE-Model: UNIQUAC, ideal vapor phase). Q min / [MJ/kmol] reactive mixture / R CR formic acid / methanol / methyl acetate / water reference component: water water / n-butyl acetate / n-butanol / acetic acid reference component: n-butyl acetate X orac X MeOH X Meor X X uoh X AA 0.5 0.5 0-0.0208 0.508 0.53 - - 0 0 0.9475 0.04 0.0384 0.5 79.76 79.76 0.527 40.4 36.3 3.2 Use of C The determination of ME and the assessment of split feasibility is an extension of the procedure proposed by Urdaneta et al. (2002) in Section 6 for nonreactive heteroazeotropic distillation columns. Only small differences have to be considered: (i) All specification products have to lie on the CRE manifold. Therefore, the application of this method is limited to those cases where the desired products belong to this manifold. (ii) The possible existence of reactive heteroazeotropes should be considered in step of the procedure named above. (iii) The continuous distillation regions (CR) are formed from the C using the rules from Urdaneta et al. (2002). They will lie on the CRE manifold because of the chemical equilibrium assumption. 4. Illustrative Examples The suggested criterion will be illustrated by two highly nonideal systems. oth are esterification processes, one of them showing liquid phase split at the top of the column. The specifications and minimum energy results are shown in Table. 4. Esterification of ormic Acid with Methanol The equilibrium reaction of the esterification of formic acid (orac) with methanol (MeOH) to methyl formate (Meor) and water () follows: orac + MeOH Meor +. A single-feed column with a stoichiometric feed of orac and MeOH should produce Meor as distillate and as bottoms product. igure shows the C and corresponding CR for two different reboiler duties Q. ig.a shows a minimum energy situation (Q = Q min ). At lower energy duty (Q < Q min ) two additional pinch solutions exist in the rectifying section causing the existence of two additional CR (see igure.b). Step 5 of the design procedure of Urdaneta et al. (2002) allows to identify that the distillate composition x does not belong to that CR of the rectifying section (CR,I ) that intersect the CR of stripping section (CR ) for Q < Q min (ig..b). Therefore the energy duty has to be increased causing the pinch points close to the product x to vanish and the existence of only one CR (CR in ig.a). oth CR and CR do not just intersect but overlap significantly due to the ocurring tangent pinch. The results of the calculation are shown in Table. It can be seen that the same value for Q min is obtained by the linear R and by its extension to CR, because the ME is determined by the existence of the tangent pinch despite the significant differences between the CR and the R as shown in ig.c. These deviations often
orac 00.76 o C Meor 3.78 o C CR VLE azeotrope: 08.70 o C (a) CR 00. o C MeOH 64.47 o C azeotropes feed and product compositions saddle stable node unstable node C CR,III orac (/0/0) Meor (0/0/) R,II orac Meor CR,II CR (b) (c) CR,I R R,I (//-) MeOH (0//0) MeOH igure. CR and R of rectifying and stripping sections for the esterification of formic acid with methanol. (a): CR at minimum energy (Q,min /=79.76 MJ/kmol), (b): CR at lower energy (Q / = 60 MJ/kmol), (c): R at minimum energy (Q,min /=79.76 MJ/kmol). result in larger values for ME estimation, in particular if a tangent pinch does not exist. 4.2 Esterification of Acetic Acid with n-utanol In this case a reactive column showing liquid phase split at the top is presented. Acetic acid (AA) and n-butanol (uoh) react to n-butylacetate (uac) and water (): AA + uoh uac +. uac is obtained as bottoms product. At the top the separation is limited by the presence of a reactive heteroazeotrope. Using a decanter at the top of the column allows to obtain a distillate product of almost pure water from the aqueous rich phase of the decanter. The specifications of the column are given in Table. igure 2 shows the C and CR obtained when ME is reached. It can be observed that in rectifying section only one stable node solution exists and therefore only one C can be obtained in this section. If x were homogeneous such C must run through x and intersect the CR to guarantee feasibility, but as x is one of the phases of a heterogeneous liquid it is only necessary that the C intersects the corresponding decanter tie line as well as the CR. Such conditions are reached for an energy duty of Q min / = 36.3 MJ/kmol. At lower energy duty the C and CR intersect each other but the C does not intersect the decanter tie line. Hence, a non feasible column profile is obtained in the rectifying section. Table shows that RM overestimate the ME in 9.54%. To reach intersection between linear rectification bodies the energy duty must be increased until new pinch solutions are found in rectifying section.
uoh 7.92 o C 9.32 o C 92.65 o C 00.0 o C decanter tie line 7.2 o C C miscibility gap uac 26 o C AA 8 o C CR 6.03 o C azeotropes reactive azeotrope feed and product compositions saddle stable node unstable node C igure 2. CR and C of rectifying and stripping section for the esterification of acetic acid with butanol at ME (Q,min / = 36.3 MJ/kmol) 5. Conclusions A design method for the determination of ME and for the assessment of split feasibility has been presented for reactive distillation columns operating in the reaction equilibrium regime. The method is based on continuous distillation boundaries determined by means of tray-by-tray calculations from pinch points. It represents an improvement on previous techniques and allows a better understanding of the process under the chemical equilibrium assumption. The application of continuous distillation boundaries could be extended to columns operating in a kinetic regime. However, such a method would be limited to three component systems because the computational effort to calculate the boundaries is prohibitive for more complex distillation systems. References arbosa,. and M.. oherty, 988, Chem. Eng. Sci., 523, 43. ausa, J., 200, Näherungsverfahren für den konzeptionellen Entwurf und die thermodynamische Analyse von destillativen Trennprozessen, VI Verlag, Aachen (in German). ausa, J., R.v. atzdorf and. Marquardt, 988, AIChE J., 28, 44. ausa, J. and. Marquardt, 2000, Comput. Chem. Eng., 2447, 24. essling,., G. Schembecker and K.H. Simmrock, 997, Ind. Eng. Chem. Res, 3032, 36. Chadda, N., M.. Malone and M.. oherty, 2000, AIChE J., 923, 46. Espinosa, J., P.A. Aguirre and G.A. Pérez, 995, Ind. Eng. Chem. Res., 853, 34. Lee, J.., S. rüggemann and. Marquardt, 2003, AIChE J., 47, 49. Sundmacher, K. and A. Kienle, 2002, Reactive istillation Status and uture irections, iley-vhc. Ung, S. and M.. oherty, 995, Ind. Eng. Chem. Res., 2555, 34. Urdaneta, R.Y., J. ausa, S. rüggemann and. Marquardt, 200, Ind. Eng. Chem. Res. 3849, 4.