Michael F. Malone

Computing Azeotropes in Multicomponent Mixtures

Abstract The problem of computing the temperatures and compositions of all azeotropes predicted by thermodynamic models for nonideal, multicomponent mixtures can be formulated as a multi-dimensional root-finding problem. This problem is complicated by the presence of multiple solutions, constraints on the compositions and the complexity of realistic vapor—liquid equilibrium descriptions. We describe a homotopy method which, together with an arc length continuation, gives an efficient and robust scheme for finding solutions. The homotopy begins with a hypothetical ideal mixture described by Raoults Law for which all of the solutions to the problem are known trivially, since they are simply the pure components. There are as many solution branches for the homotopy as there are pure components, and one or more of the branches shows a bifurcation when azeotropes are present in the mixture. Solutions for the azeotropes are found from the limiting behavior of the homotopy and we show that azeotropes containing c components can be found from a series of c -1 bifurcations in the solution branches of lower dimensions. There is no restriction on the dimension of the problems other than the availability of an accurate thermodynamic model; examples containing up to five components are described.

Multiple steady states in reactive distillation: kinetic effects

Abstract A model is developed to describe kinetic effects in reactive distillation. A Damkohler number (Da), the ratio of a characteristic residence time to a characteristic reaction time, is the key parameter. A comprehensive picture of solutions is found with arc length continuation methods that trace solution branches as functions of Da, reboil ratio, or reflux ratio. For methyl tert-butyl ether (MTBE) synthesis in the Jacobs–Krishna column configuration, the model reproduces known solution multiplicities in the limit of reaction equilibrium. In addition to these previously known equilibrium solutions, we report new results concerning the effect of kinetics on solution multiplicity. In particular, isolated solutions branches are found at several values of Da; the isola shrinks and disappears below a critical value of Da. Results for tert-amyl methyl ether (TAME) synthesis in a model for the test column of Mohl et al. [Chem. Eng. Sci. 54 (1999) 1029] are in sharp contrast; multiplicities present in the kinetic regime disappear above a critical value of Da for all values of reflux ratio.

Feasibility and Separation Sequencing in Multicomponent Batch Distillation

Abstract Batch distillation of azeotropic mixtures usually produces azeotropes. Various techniques such as pressure swing or extractive distillation are currently available to break azeotropes in continuous columns. We describe methods to break azeotropes using a homogeneous entrainer in a conventional or inverted batch column. We show that the use of an inverted configuration is essential to break minimum boiling azeotropes. The entrainer selection is determined from an analysis of the batch distillation regions in the limit of a large number of stages and large reflux ratio or large reboil ratio. Several possible schemes for breaking binary azeotropes are described. We find that most ternary azeotropes can be broken into pure components and binary azeotropes using only an appropriate choice of the initial feed. We finally describe how to obtain a feasible sequence to separate an azeotropic mixture of methyl acetate, methanol, ethyl acetate and ethanol, and present some sequence alternatives.

Simulation of kinetic effects in reactive distillation

Abstract This paper describes a simulation and modeling methodology for kinetically controlled, stage-wise reactive distillation columns, taking into account equimolar or non-equimolar reactions, side-reactions, effects of heat of reaction, non-constant latent heat effects, a distribution of liquid holdups on the reactive stages and hybrid sections in a column. A Damkohler number, which is the ratio of a characteristic liquid residence time to a characteristic reaction time, is introduced into the mathematical model. By changing the Damkohler number, the transition behavior from the nonreactive to the equilibrium reactive limits can be described. Combining the model type and the holdup distribution type on the reactive stages, four simulation strategies are studied: (1) non-heat effects model and constant molar holdup; (2) non-heat effects model and non-constant molar holdup; (3) heat effects model and constant molar holdup; (4) heat effects model and non-constant molar holdup. These strategies can be used to handle very diverse reactive distillation systems. The modeling tool capabilities are demonstrated with case studies for the metathesis of 2-pentene, MTBE synthesis and the hydration of ethylene oxide to ethylene glycol. For MTBE synthesis, the output multiplicities present at chemical reaction equilibrium disappear at lower extents of reaction (i.e. at lower residence times or Damkohler numbers).

Reactive Distillation for Methyl Acetate Production

We describe a hierarchy of methods, models, and calculation techniques that support the design of reactive distillation columns. The models require increasingly sophisticated data needs as the hierarchy is implemented. The approach is illustrated for the production of methyl acetate because of its commercial importance, and because of the availability of adequate published data for comparison. In the limit of reaction and phase equilibrium, we show (1) the existence of both a minimum and a maximum reflux, (2) there is a narrow range of reflux ratios that will produce high conversions and high purity methyl acetate, and (3) the existence of multiple steady states throughout the entire range of feasible reflux ratios. For finite rates of reaction, we find (4) that the desired product compositions are feasible over a wide range of reaction rates, up to and including reaction equilibrium, and (5) that multiple steady states do not occur over the range of realistic reflux ratios, but they are found at high reflux ratios outside the range of normal operation. Our calculations are in good agreement with experimental results reported by Bessling et al., [Chemical Engineering Technology 21 (1998) 393].

Patterns of composition change in multicomponent batch distillation

Abstract A simple dynamic model has been developed to study the behavior of multicomponent batch distillation. The distillate compositions obtained for ideal mixtures behave in accord with intuition since the fractions contain the individual pure components in order of increasing boiling point. Azeotropic mixtures are more complex and counter-intuitive, in some cases displaying non-adjacent distillate fractions which have the same composition. The general behavior of ternary azeotropic batch distillation is described in simple terms based on the nature of the distillate and still composition changes in the phase plane. At large reflux ratio and number of stages, the sequence of distillate fractions generated from any initial composition in the still can be found with little or no computational effort.

Influence of phase separation on the linear viscoelastic behavior of a miscible polymer blend

The influence of phase separation on the linear viscoelastic response has been studied in miscible blends of polystyrene and poly(vinyl methyl ether) with a lower critical solution temperature near 110 °C. At temperatures between 25 and 155 °C, and for compositions in the range 20% to 60% polystyrene, the complex moduli G’ and G‘ were measured at frequencies in the range of 0.01 to 100 rad/s. Time–temperature superposition was applied in the single phase region to obtain the complex modulus over eight decades of frequency. Increasing the polystyrene content resulted in an increase in the zero‐shear viscosity and a shift of the terminal behavior to lower frequencies or longer times. The phase separation above the lower critical solution temperature was measured as a sudden increase in the fluorescence intensity of an anthracene‐labeled polystyrene (approximately 1 wt % in the blend), using an optical probe in the rheometer fixture. For the 20/80 and 40/60 PS/PVME samples, the terminal zone was in the acces...

Extensional Flow Induced Miscibility in a Polymer Blend

SummaryExtensional flows can induce miscibility in a polymer blend of polystyrene with poly(vinyl methyl ether). Miscibility is observed as a change from turbidity to optical clarity when a phase separated blend flows isothermally in planar extension. In a start-up experiment at temperatures above the LCST, optical clarity does not appear instantaneously but after a time which depends on the rate of extension and the temperature, and it appears first near the region of highest extension. This effect is opposite to the observation for polymer solutions which exhibit shear-induced demixing. We attribute this to the fact that enthalpic effects largely determine blend miscibility, while the phase behavior of solutions is essentially controlled by entropic contributions. Since a deformation field decreases the configurational degrees of freedom of a polymer molecule, demixing is favored in solutions. However, the alteration of specific interactions rather than this entropic effect appears to be much more important in blends.

Discovery of a reactive azeotrope

Mixtures are azeotropic if they can be distilled (or condensed) without a change of composition. The existence of azeotropes in multicomponent mixtures in the absence of chemical reactions is well understood phenomenologically, and theoretically,. Azeotropes place a fundamental limit on the compositions attainable in mixtures by fractional distillation, but they can in some cases be ‘broken’ by carrying out chemical reaction and separation simultaneously rather than sequentially. Here we report the discovery of a boiling state of constant composition and temperature in a mixture of acetic acid, isopropanol, isopropyl acetate and water that is simultaneously in both reaction and phase equilibrium. These states, which we call reactive azeotropes, were predicted recently,. Without reaction, the mixture exhibits three two-component azeotropes, one three-component azeotrope but no four-component azeotrope; the last appears only under equilibrium reaction conditions. These findings may constrain technologies in which reaction and separation are conducted simultaneously, for example by limiting the conditions under which an azeotrope can be broken by chemical reactions to yield a high-purity product. Inother cases the presence of a reactive azeotrope may be advantageous.

A purely hyperbolic model for unsteady viscoelastic flow

Abstract A purely hyperbolic model for unsteady, two-dimensional viscoelastic flow is developed. The model uses a pressure-density relationship in the continuity equation to obtain a dynamic equation for the pressure, and the Giesekus constitutive equation with zero retardation time to describe the extra stress. The small degree of compressibility allowed by the model is negligible for practical purposes but important mathematically because it changes the unsteady governing equations from parabolic-hyperbolic to a purely hyperbolic system. This allows the application of a numerical method designed specifically for solving hyperbolic problems, and thus, to better treat the hyperbolic nature of the flow which is dominant at high Deborah numbers. The method is used to predict the velocity and stress fields in a square cavity. The results for the creeping, Newtonian limit compare well with previously published calculations. Viscoelastic flow computations are presented for Deborah numbers up to 4. Comparison of the results obtained on several grids show that the calculations increase in smoothness with mesh refinement, and that the scheme is numerically stable. The calculations predict flows exhibiting significant elastic effects. A transition from single vortex flow to flow containing multiple vortices, occurs under creeping flow conditions for Deborah numbers greater than 1.