Make distillation boundaries work for you!

Make distillation boundaries work for you! Michaela Tapp*, Simon T. Holland, Diane Hildebrandt and David Glasser Centre for Optimization, Modeling and Process Synthesis School of Process and Materials Engineering University of the Witwatersrand Private Bag 3, WITS 2050, Johannesburg, South Africa Abstract There has been much discussion in the literature regarding whether column profiles can cross distillation boundaries and by how much. The traditional crossing of boundaries demonstrated by Wahnschafft et al. (1993) represents a very constraint case and was of academic interest only as the operating region for columns was small. The goal of this paper is to show how the design by using column sections and the difference point equation can extend the operating region for columns crossing distillation boundaries and therefore allow for more feasible separations. Keywords: Distillation boundaries, column section, difference point equation, column profile maps, short-cut technique 1. Introduction Residue curve maps for azeotropic three component mixtures can consist of different regions. These regions are divided by distillation boundaries. These boundaries make certain splits extremely difficult if not impossible. Wahnschafft et al. (1993) demonstrated that the crossing of boundaries at infinite reflux requires a sequence of columns as well as a curved distillation boundary. Although running a column at total reflux is not practical as no product can be drawn off. However separations that are infeasible at total reflux might be possible with finite reflux ratios. It has been found, that certain reflux ratios lead to better separation (e.g. Petlyuk 1978). Crossing boundaries at finite reflux can be done in a single column, but by using the traditional set of differential equations describing the path of the column profile in a rectifying or stripping section, it is only possible if certain criteria are met. These criteria are explained in detail by Tapp et al. (2004) and include a sufficiently curved boundary, a distillate or bottoms composition that lies close and on the concave side of the boundary and the distillation column needs to operate at a certain range of reflux ratios. If these conditions are met profiles can be generated that flip over the distillation boundary, see figure 1. This phenomenon has been observed for decades but was more of

academic interest, as the operating region for columns where this flipping over occurs is small. Benzene X D B A R = 6 R = 3 R = 4 R = 5 R Chloroform Acetone Figure 1: Flipping over of profiles for certain reflux ratios which cross a distillation boundary from region A to region B for the Acetone/Benzene/Chloroform system. The goal of this paper is to apply a new approach introduced by Tapp et al. (2003) and Holland et al. (2003). This approach makes use of column sections, the difference point with its parameters R and X and the resulting transformed space. It enables us to cross distillation boundaries with finite reflux ratios for compositions that lie far from the boundary leading to a much wider region where columns can operate at. We will demonstrate this powerful technique by looking at two topologically very different nonideal systems: the chloroform / acetone / benzene system and the methanol / ethanol / acetone system. The intermediate boiler in ideal systems behaves as a saddle node, thus it cannot be directly approached by a rectifying or stripping profile and therefore requires an infinite number of stages. We will also show how distillation boundaries can be used to generate profiles that run into the intermediate boiler, and therefore can result in an enormous cost saving. In other words how to make distillation boundaries work for you. 2. Crossing Distillation Boundaries 2.1 The difference point equation and column profile maps Column sections are defined as sections with no feed addition or side stream withdrawal. Analogous to the derivation of the differential equations by Doherty and Perkins (1978), a

mass/mole balance over a column section leads to the difference point equation, see equation 1. dx dn with X R + 1 1 ( x y ) + ( X x) 1 * = R V Y L X T T = L ; R = and = ( V L) 0 (1) represents the net molar flow in a column section, whereas X represents the net flux of components in a column section. They can be changed from one section to another by i.e. feed addition, sidestream withdrawal, column section coupling or side condensers and reboilers. For R the difference point equation collapses to the residue curve equation. Integration with different initial conditions results in a residue curve map (RCM). Specifying the design parameters X and R and integrating the difference point equation with different initial conditions results in a column profile map (CPM). It has been shown (Holland et al. 2003) that CPM s are transformed RCM s. 2.2 The acetone/chloroform/methanol system The acetone/chloroform/methanol system consists of four distillation boundaries inside the mass balance triangle (MBT) due to three binary and one ternary azeotrope occurring in the system. A separation from region 1 to region 4 crossing the distillation boundary is an extremely difficult if not impossible separation considering rectifying and stripping only see figure 2. Due to the fact that X represents a difference point and not an actual composition hence it does not need to lie inside the MBT, (this has been discussed in detail by Tapp et al. 2003) there exist a wide range of values for X and R to achieve the desired shifting of the topology. An example of single profiles with the respective values of X, R and X T running from region 1 to region 4 and from region 2 to region 4 are shown in figure 2 as the dotted and the dashed line respectively. It is interesting to note, that distillation boundaries are residue curves. It is therefore not surprising, that the shifting of the entire CPM (the entire CPM consist of profiles inside and outside the MBT, see Tapp et al. 2003) depending on the values of X and R shifts the distillation boundaries as well and allows profiles cross the distillation boundaries for infinite reflux.

Acetone Column section profile: X T = [0.05; 0.9] X = [0.05; -0.9] (L/V) = 0.95 1 Column section profile: X T = [0.42; 0.54] X = [0.05; -0.9] (L/V) = 0.95 2 4 3 Chloroform Methanol Figure 2: Column Section Profiles Crossing Distillation Boundaries for the acetonechloroform-methanol system. 2.3 The Methanol/Ethanol/Acetone system The distillation boundary in the methanol/ethanol/acetone system divides the space inside the MBT into two distillation regions. A difficult separation would be to achieve pure methanol, as the methanol node behaves as a saddle node. Figure 3 shows a possible profile as a result Ethanol Column section profile: X T =[0.16 0.75] X =[1.2 0.5] R = 5 Methanol Acetone Figure 3: Column Section Profiles Crossing Distillation Boundaries for the ethanol/methanol/acetone system.

2.4 Ideal system How can the flipping over of profiles benefit the designer for systems that have no azeotrope? Sampling a pure component that behaves as a saddle point requires infinite number of stages. The intermediate boiler in ideal systems would be an example for this case. Figure 4 shows a CPM determined by R = 8 and X = [-0.3-0.3]. CPM MBT The topology of this CPM shows two regions of similar behaviour, these are regions where profiles begin and terminate at the same node, with the dashed line being the flipping over boundary between the regions. This choice of parameters shifted the topology in such a way, that profiles can be achieved that run directly into the corner. In other words it is possible to sample the intermediate component with a finite number of stages and 100% purity. 3. Conclusions X Profiles running towards the intermediate boiler Figure 4: CPM for the parameters R = 8 and X = [-0.3-0.3]. The design of distillation systems can be based on differential equations and column profiles in other words it can be based on the topology of the system. Hence the feasibility of separation processes depends on the occurrence of distillation boundaries. The more distillation boundaries occur the more difficult the separation? In this paper we have shown, that distillation boundaries in non ideal systems can be crossed from far off the boundary by using the difference point approach and by choosing the appropriate X and R. This creates a much wider region in which columns can operate at and allows for more feasible separations. We also showed, that the occurrence of distillation boundaries can be an advantage. By shifting a distillation boundary inside the MBT, see figure 4, pure components that are initially of the saddle point type can be

approached by profiles that run straight into the intermediate boiler. This requires a finite number of stages and therefore results in a great cost saving. In conclusion this technique allows us to make use of the diversity of systems (occurrence of distillation boundaries) to achieve and better desired separations. Nomenclature [kmol] Net molar flow inside the column section (V-L) L [kmol] Liquid flowrate n [-] Stages V [kmol] Vapour flowrate x, y [-] Liquid, Vapour composition R [-] Reflux ratio(l/) X [-] Difference Point X T,Y T [-] Liquid, Vapour composition on top of the column section y * [-] Vapour composition vector in equi librium with the residue composition x References Doherty, M.F., Perkins, J.D., 1978, Chem. Eng. Sci., Vol. 33: On the dynamics of distillation processes 1-3. Holland, S.T., Tapp, M., Hildebrandt, D., Glasser, D., Hausberger, B., 2003, accepted for publication in Computers & Chemical Engineering PSE proceedings: Novel Separation System Design Using Moving Triangles. Petlyuk, F.B., 1978, Theor. Found. Chem. Eng. Vol 12: Rectification of Zeotropic, Azeotropic and Continuous Mixtures in Simple and Complex Infinite Columns with Finite Reflux. Tapp, M., Holland, S.T., Hildebrandt, D., Glasser, D., 2003, accepted for publication in Ind. & Eng.Chem. Res: Column Profile Maps. 1. Derivation and Interpretation. Tapp, M., Holland, S.T., Hildebrandt, D., Glasser, D., 2004, submitted for publication in Ind. & Eng.Chem. Res: Column Profile Maps. 2. Singular Points and Phase Diagram Behaviour for Ideal and Non-ideal Systems. Wahnschafft, O.M., Koehler, J.W., Blass, E., Westerberg, A.W., 1993, Ind. Eng. Chem. Res., Vol. 31: The Product Composition Regions of Single-Feed Azeotropic Distillation Columns.