(99b) Simulation of Batch Distillation with a Varying Alpha: The Ethanol-Water and Methanol-Water Systems at 1 Atm

Simulation of Batch Distillation with a Varying Alpha:
The Ethanol-Water and Methanol-Water Systems at 1 Atm    

Robert G. Kunz

RGK Environmental Consulting, L.L.C.

Hillsborough, North Carolina

Paper Proposed for Presentation at

2015 AIChE Spring Meeting 

April, 2015

Austin, Texas

Abstract            In a previous presentation [1], a newly developed technique was described that enables analytical integration of the Rayleigh Equation for batch distillation with a varying relative volatility.  Heretofore, integration in closed analytical form has required that a be assumed constant. This new technique produces a continuous analytical function for the Rayleigh Equation integral for a varying a and reduces algebraically to the traditional function when a is constant.  Detailed derivations are contained in the cited presentation. 

Both the traditional expression at constant a and the new equation were evaluated against numerical integration via Simpson’s Rule for a range of typical values of constant a, for a number of ideal and non-ideal binary vapor-liquid equilibrium (VLE) systems with varying a, and for an illustrative example contained in a chemical engineering textbook.  The method was then utilized successfully in a computer-simulated batch distillation of an ethanol-water solution at 1 atm pressure.  Results compared favorably with expected values. 

          The present paper reviews the ethanol-water case and extends the simulation procedure to methanol-water.  Batch distillation of these systems at atmospheric pressure is a popular student laboratory exercise in colleges and universities throughout the world. 

          A summary of VLE relationships for ideal and non-ideal systems plus temperature-dependent methods for analysis of constituent composition specific to both the ethanol-water and methanol-water systems are discussed in separate appendices.  These latter include, among others, estimates of liquid density for alcohol-water mixtures extended beyond the range of published data and refractive index measurements assembled from various sources.                The paper consists of new material supported by background information tutorial in nature.    

Keywords.     Alcohol “Proof”; Boiling Point Curves; Computer Simulation, Density, Refractive Indices, Gas Chromatography, Flash Points, and Auto-ignition Temperatures for Ethanol-Water and Methanol-Water Solutions; Numerical Integration; Rayleigh Equation; Simpson’s Rule; Systems: Ethanol-Water, Methanol-Water, and Methanol-Ethanol; Vapor-Liquid Equilibrium.
Introduction

          Distillation is a separation technique utilizing the difference in composition of a liquid and the vapor in equilibrium with that liquid.  Simple, or differential, distillation employs a single equilibrium stage to effect that separation.  A batch distillation operates on an unreplenished charge of material being boiled off from a still pot and then condensed as product in another vessel.  It is an unsteady-state process, where the amount and composition of feed and product vary with time.  In a two-component (binary) system, the charge of feed material boils away and gradually becomes richer in the less volatile / higher-boiling / heavy component.  The condensed vapor product (distillate) increases in volume and is enhanced in the more volatile / lower-boiling / light component.  This paper discusses the simple, differential batch distillation of a two-component (binary) system, in which none of the condensed vapor is returned, or refluxed, to the still pot.    A typical laboratory setup is shown in Figure 1. 

            Simple batch distillation is not practiced extensively in industry.  It is used commercially for separating small quantities of high-value chemicals, when high purities are not required, as a preliminary step to be followed by further processing, for separations where the equipment requires frequent cleanout, or where the feed mixture is very easy to separate.  A rule of thumb for ease of separation is that the feed components differ in atmospheric boiling point by at least 25°C, 30-40°C, or 75°C, depending on the source.  Whatever the precise numerical value, the intent is that the lighter component be much more easily vaporized in preference to the heavier component in order to distill a decent amount of high-purity product before too much of the feed material boils away.  

Figure1.  Typical Laboratory Setup for Batch Distillation

Reference

1. Kunz, R.G., "The Rayleigh Equation Revisited: What to Do When Alpha (a) Isn’t Constant,” Paper 118b presented at the 2012 A.I.Ch.E. Spring Meeting, Houston, TX (April 1 - 5, 2012).