Residue curve maps of reactive membrane separation

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Abstract

A batch reactive membrane separation process is analysed and compared with a batch reactive distillation process by means of residue curve maps. In both processes, the chemical reaction takes place (quasi-) homogeneously in the liquid bulk phase and vapour–liquid equilibrium is assumed to be established. Additionally, in the reactive membrane separation process, selective vapour phase permeation through a membrane is incorporated.

A model is formulated which describes the autonomous dynamic behaviour of reactive membrane separation at non-reactive and reactive conditions when vacuum is applied on the permeate side. The kinetic effect of the chemical reaction is characterized by the Damköhler number Da, while the kinetic effect of multicomponent mass transfer through the membrane is characterized by the matrix of effective mass transfer coefficients. The process model is used to elucidate the effect of selective mass transfer on the singular points of reactive membrane separation for non-reactive conditions (Da=0), for kinetically controlled reaction (0<Da<∞), and for equilibrium controlled reaction (Da→∞). Scalar, diagonal and non-diagonal mass transfer matrices are considered. As examples, the simple reaction AB+C in ideal liquid phase, and the cyclization of 1,4-butanediol to tetrahydrofurane in non-ideal liquid phase are investigated.

Introduction

During the last decade Reactive Distillation (RD) has emerged as one of the most important innovative separation technologies. As advantages of RD, chemical equilibrium limitations can be overcome, higher selectivities can be achieved, the heat of reaction can be recovered in situ for distillation, auxiliary solvents can be avoided, and azeotropic or closely boiling mixtures can be more easily separated than in non-reactive distillation. Increased process efficiency and reduction of investment and operational costs are the direct results of the integration of chemical reaction and distillation. Some of these advantages are realized by using reactions to improve separation, others are realized by using separation steps to improve the chemical reaction (Taylor and Krishna, 2000; Sundmacher and Kienle, 2003).

For the conceptual design of RD processes, Residue Curve Maps (RCM) were introduced as a very important and powerful tool and were used by many researchers (e.g. Venimadhavan et al., 1994; Ung and Doherty, 1995a; Thiel et al., 1997; Qi et al., 2002). RCMs represent the dynamic behaviour of the liquid phase composition in a simple batch reactive distillation process, as depicted in Fig. 1a. The analysis of the location and stability of the singular points in RCMs, i.e. the steady states of this simple process, yields valuable information on the attainable products of a RD process. The existence of these stationary points was also proven experimentally (Song 1997, Song 1998).

For the stationary points in a distillation system undergoing equilibrium-controlled chemical reactions the term reactive azeotrope was introduced by Doherty and coworkers (Barbosa and Doherty 1988a, Barbosa and Doherty 1988b; Ung and Doherty, 1995b). In RD systems with kinetically controlled chemical reactions, the singular points are called kinetic azeotropes according to Rev (1994) who investigated the general situation of the simultaneous occurrence of a chemical reaction and a separation process. Several groups studied the bifurcations of kinetic azeotropes in homogeneous systems (Venimadhavan et al., 1994; Thiel et al., 1997) and also in mixtures undergoing liquid phase splitting (Qi and Sundmacher, 2002). Most of these singularity analyses were carried out using the Damköhler number of first kind, Da, as most important bifurcation parameter. As important limiting cases, at Da=0 the classical azeotropes of non-reactive distillation are recovered, and at Da=∞ the (chemical equilibrium controlled) reactive azeotropes are found.

As has been shown in the cited works, new types of azeotropes will be formed by combining distillation and chemical reactions, even in ideal reaction mixtures without any non-reactive azeotrope. Due to this, despite the convincing success of RD in many applications, such as esterifications and etherifications, RD is not always advantageous. In some cases RD does not yield the desired products (Sundmacher and Kienle, 2003).

In non-reactive azeotropic distillation processes, Castillo and Towler (1998) and Springer et al. (2002) investigated the importance of vapour–liquid interface mass transfer with respect to the feasible products. The latter authors found that it is possible to cross distillation boundaries by mass transfer effects. Schlünder 1977, Schlünder 1979 and Fullarton and Schlünder (1986) demonstrated that separational limitations imposed by azeotropes can be overcome by application of an entraining medium. Due to different diffusion rates of the components in the entrainer, the azeotropic points are shifted. Since these points are formed under mass transfer control, the term pseudo-azeotrope was proposed. Analogously, Nguyen and Clement (1991) observed and analysed pseudo-azeotropic points which appear in the separation of water–ethanol mixtures–water at pervaporation membranes.

From the analysis of non-reactive systems one can expect that selective vapour–liquid mass transfer will also have a significant effect on the attainable products of reactive separation processes. In particular, the stationary points of reactive distillation processes might be influenced in a desired manner by selective membranes, as has been shown recently by Aiouache and Goto (2003) who integrated a pervaporation membrane into a reactive distillation process.

In the present work, in order to get a deeper understanding of the role of membranes on the feasible products of RD processes, the batch reactive membrane separation process in Fig. 1b is considered. The considered batch process is the equivalent of a continuous membrane process, as depicted in Fig. 1c. There, the time coordinate is replaced by the axial special coordinate. Therefore, the RCM acquired from the batch process can be directly used for continuous process design. The main objective of this work is to analyse the RCM and the stationary operating points of the proposed reactive membrane separation process and to elucidate the role of the membrane mass transport properties for the feasible products. For this purpose, a process model is formulated which is applied to an ideal reaction system with constant relative volatilities and to a strongly non-ideal reaction system, namely the cyclization of 1,4-butanediol.

Section snippets

Model of reactive membrane separation

The process model is based on the following assumptions (see also Fig. 1b):

  • The liquid phase and the retentate vapour bulk phase are assumed to be in phase equilibrium based on the fact that the membrane holds major mass transfer resistance.

  • Vacuum is applied on the permeate side of the membrane (pp→0).

  • The chemical reaction takes place at boiling temperature in the reactive holdup Hr of the liquid phase, i.e. either as a homogeneous reaction in the liquid bulk (Hr=H), or at a heterogeneous

Example I: Ideal reaction system

As first example, the effect of a selective membrane on the ternary mixture A/B/C undergoing a single reversible chemical reaction in ideal liquid phase is considered:A⇔B+CB:mainproduct,C:byproduct.The dimensionless rate of the chemical reaction obeys the kinetic lawR=xAxBxCKwith K as chemical equilibrium constant.

For the sake of a simplified analysis, the following assumptions are made:

  • The chemical equilibrium constant is independent of temperature: K=0.2.

  • The rate constant kf is independent

Conclusions

As demonstrated by means of residue curve analysis, selective mass transfer through a membrane has a significant effect on the location of the singular points of the considered batch reactive separation process. The analysis was carried out for a vapour permeation process, i.e. the membrane is considered to be placed in the vapour phase above the reactive liquid phase. However, the proposed methodology can be also applied to a reactive liquid permeation process (pervaporation).

The integration

Notation

ailiquid phase activity of component i
a1a6coefficients in the quadratic equation, Eq. (27a–f)
A, B, Cchemical species
DaDamköhler number, Eq. (6)
Hmolar liquid holdup, mol
H0initial molar liquid holdup, mol
Hrholdup in which the reaction proceeds, mol
kfforward reaction rate constant, 1/s
kf,refforward reaction rate constant at reference temperature, 1/s
[k]matrix of binary effective mass transfer coefficients, Eq. (11)
kijeffective binary mass transfer coefficients of pair ij, m/s
Kchemical

Acknowledgements

The authors like to thank Dr.-Ing. Michael Mangold from the Max Planck Institute in Magdeburg for his linguistic advice when creating the word “arheotrope”.

References (27)

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