Membrane Residue Curve Map

Equation 9.14 is the membrane residue curve equation as identified by Peters et al. [14]. It is mathematically analogous to the residue curve equation derived in Chapter 2 for distillation processes. While the residue curve equation was derived 

Traditionally, it was believed that RCMs were only suitable for equilibrium-based separations and could not be used for the representation of kinetically based processes [15]. However, the differential equations which describe a residue curve are simply a combination of mass balance equations. Because of this, the inherent nature of RCMs is such that they can be used for equilibrium- as well as non-equilibrium-based processes. This now allows one to consider kinetically based processes, such as reactive distillation (see Chapter 8) as well as membrane separation processes. 

From any given initial condition (x ), integration of Equation 9.14 can occur in two directions. 

As with the distillation ROMs, the profiles lying outside the MET may not be physically achievable, but the relevance of this global map is veiy important, and will be highlighted in subsequent sections. Note that it is also possible to identify stable, unstable, and saddle nodes, and each of these stationary points nature and location provide insight into the behavior of the curves (refer to Section 2.5.2). 

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Peters, M., et al.. Derivation and properties of membrane residue curve maps. Industrial Engineering Chemistry Research, 2006, 45(26) 9080 9087. 

Solving this set of equations in Equation 9.14, in conjunction with the flux model (Equation 9.6), for a range of initial conditions (x") allows one to produce a membrane residue curve map (M-RCM) as shown in Figure 9.3. 

In analogous manner, residue curve maps of the reactive membrane separation process can be predicted. First, a diagonal [/e]-matrix is considered with xcc = 5 and xbb = 1 - that is, the undesired byproduct C permeates preferentially through the membrane, while A and B are assumed to have the same mass transfer coefficients. Figure 4.28(a) illustrates the effect of the membrane at nonreactive conditions. The trajectories move from pure C to pure A, while in nonreactive distillation (Fig. 4.27(a)) they move from pure B to pure A. Thus, by application of a C-selective membrane, the C vertex becomes an unstable node, while the B vertex becomes a saddle point This is due to the fact that the membrane changes the effective volatilities (i.e., the products xn a/a) of the reaction system such that xcc a. ca > xbbO-ba-... 

Fig. 4.28. Residue curve maps for reactive membrane separation ...

Fig. 4.30. Residue curve maps for reactive membrane separation 1,4-BD — THF + Water p= 5 atm Knudsen-membrane. (a) Da = 0 (b)...

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 a batch reactive separation process. The singular points are shifted, and thereby the topology of the residue curve maps can change dramatically. Depending on the structure of the matrix of effective membrane mass transfer coefficients, the attainable product compositions are shifted to a desired or to an undesired direction. 

The determination of feasible products is very important for conceptual process design and for the evaluation of competing process variants. In this chapter, methods have been discussed to identify feasible products as singular points of residue curve maps (RCM). RCM-analysis is a tool which is well established for nonreactive and reactive distillation processes. Here, it is shown how RCM can also be used for reactive membrane separation processes. 

We start the chapter by explaining the graphical thermodynamic representations for ternary mixtures known as Residue Curve Maps. The next section deals with the separation of homogeneous azeotropes, where the existence of a distillation boundary is a serious obstacle to separation. Therefore, the choice of the entrainer is essential. We discuss some design issues, as entrainer ratio, optimum energy requirements and finite reflux effects. The following subchapter treats the heterogeneous azeotropic distillation, where liquid-liquid split is a powerful method to overcome the constraint of a distillation boundary. Finally, we will present the combination of distillation with other separation techniques, as extraction or membranes. 

The work presented in this chapter is an abridged version of some of the material in the book Membrane Process Design Using Residue Curve Maps and has been reproduced with permission from John Wiley Sons, Inc. [1]. The reader is referred to that book for a more detailed appraisal of membrane design. 

In seeking the most efficient process possible, a designer will wish to explore a wide range of feasible designs. To make this possible, an efficient method for the synthesis and assessment of any hybrid separation process has been developed. Since both processes have been analyzed using similar mathematical backgrounds, it is possible to use residue curve maps and column profile maps for both distillation and membranes to design hybrid systems of the two. 

Huang, Y. S., et al.. Residue curve maps of reactive membrane separation. Chemical Engineering Science, 2004, 59(14) 2863 2879. 

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