Distillation Residue Curves
5.1.1.1 Governing Equations
Residue curves descnbe the composition profiles that result when a mixture is subject to simple batch distillation as shown in Figure 5.1. The liquid composition changes as the more volatile components of the mixture are removed preferentially. Eventually, the composition of the residue approaches a stable node that is either a nonvolatile pure component or a highboiling azeotrope.
The equations governing this process are the material balances (equations 5.1 and 5.2), the energy balance (equation 5.3) which can be simplified at bubble point by assuming that the temperature is a function of the composition only (effectively equation 5.4) and phase equilibrium (equations 5.5 and 5.6):
dt d(MxJ dt
Figure 5.1  Simple Distillation Process d(MH) „ T,TrV
dt dt
Figure 5.1  Simple Distillation Process
The physical properties (activities, enthalpies and vapour pressures) can be calculated by any appropriate method. The UNIFAC model, SoaveRedlichKwong equations and published Antoine coefficients are recommended for the ETBE system (and the MTBE system). The steady state solution of these equations is of no significance but the transient solutions form residue curves. The required boundary conditions are pressure (P), initial volume (M0), initial composition (fy), and the heating rate (Q) but only the pressure and initial composition affect the residue curve trajectory. The ratio of Q to M determines the boiling rate and, therefore, the sampling time required to obtain a curve with good resolution.
The residue curves are not unique for a given combination of pressure and composition as any point on the residue trajectory can be used as the initial point for that curve. Reversing the sign of equations (5.1)(5.3) allows residue curves to be constructed towards an unstable node (volatile pure component or lowboiling azeotrope).
5.1.1.2 ETBE System
Figures 5.25.4 show families of residue curves for the quaternary system of ethanolisobuteneETBE(nbutene). Isobutene and nbutene have been lumped together for clearer visualisation. Three different operating pressures were considered: atmospheric pressure (Figure 5.2), 950 kPag (Figure 5.3) and 1500 kPag (Figure 5.4). The three diagrams only differ with respect to the location of the ethanolETBE azeotrope although the curvature of the residue trajectories near the ETBEC« border also varies somewhat.
5.1.1.3 MTBESystem
Residue trajectories for the MTBE system are shown in Figure 5.5 for comparison with the ETBE system. A ternary system consisting only of methanol, MTBE and nbutene was used to construct the diagram to highlight the azeotrope between methanol and nbutene. In practice, this azeotrope only acts as a pinch point as there is no azeotrope between methanol and isobutene. Pure C4 is a feasible distillate composition, but only in a column which approaches perfect fractionation (infinite stages and infinite reflux ratio, or the oo/oo case).
5.1. J. 4 Significance for Reactive Distillation Column Design
Although residue curves are based on a batch distillation process, the trajectory of each curve corresponds closely to the composition profile which is seen in a column with perfect fractionation (i.e. the oo/oo case). Residue curve diagrams also define distillation regions and boundaries that cannot be crossed by simple distillation. These boundaries extend from the ethanolETBE azeotrope to the C4 node in the ETBE system (Figures 5.25.4) and from the methanolMTBE azeotrope to the methanol(nbutene) azeotrope in the MTBE system (Figure 5.5).
The practical significance of distillation boundaries pertains to the directional effect that fractionation has on the residue composition. For example, a mixture whose composition lies in the upper distillation region of the ETBE residue curve diagram (e.g. 10% ETBE, 60% ethanol and 30% C4) can only be distilled to increase the ethanol purity while a mixture whose composition lies in the region below the boundary (e.g. 60% ETBE, 5% ethanol and 35% C4) can only be distilled towards the ETBE node. Clearly, an ETBE column should be designed to produce a high purity ETBE product so that (at least) the stripping section of the column must be enclosed within the lower distillation region.
Figure 5.5  Residue Curve Dunram for the MTBE System at 950 kPag
Figure 5.5  Residue Curve Dunram for the MTBE System at 950 kPag
Residue curve diagrams are also useful for identifying potential distillation pinch points. Azeotropes in a system introduce curvature in the residue curves. Excessive curvature can indicate a pinch that increases the fractionation requirement. For example, it is easier to increase ETBE purity in a mixture with little ethanol as the residue curves run more smoothly towards the ETBE vertex. In such a separation, the ethanol concentration will initially increase (since the residue trajectories curve towards the ETBEethanoI azeotrope).
Similar conclusions can be made about the rectifying section of an ETBE column. Clearly, there is an incentive to minimise ETBE (and ethanol) in the distillate product. This can be achieved more readily if there is little ETBE in the rectifying section as the residue trajectories are curved towards the ETBEethanol azeotrope. It is theoretically possible to completely eliminate both ETBE and ethanol from the distillate product since there exists a node that corresponds to pure C4. However, distillation towards this node places restrictions on the composition of the bottoms product since ethanol must leave the system in at least one product. It is also clear from the ETBE residue curve diagram that it is not possible to produce a distillate product with ethanol but without ETBE. This is different to the MTBE system, where there exists a node that contains only methanol and C4.
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