Ross Taylor

COMPOSITION DERIVATIVES OF ACTIVITY COEFFICIENT MODELS (FOR THE ESTIMATION OF THERMODYNAMIC FACTORS IN DIFFUSION)

ABSTRACT Derivatives of activity coefficient models are needed for the evaluation of the thermodynamic factors that arise in the equations that describe diffusion in multicomponent systems. A general framework for the evaluation of these thermodynamic factors is presented together with specific results for the Margules, Van Laar, Wilson, NRTL and UNIQUAC activity coefficient models.

Distillation pinch points and more

Abstract Rising energy costs have spawned renewed interest in improving methodologies for the synthesis, design and/or retrofitting of separation processes. It is well known that energy use in many process industries is dominated by separation tasks—particularly distillation. In this work, the shortest stripping line approach recently proposed by Lucia, Amale, & Taylor (2006) is used to find minimum energy requirements in distillation. The new aspects of this work show that this shortest stripping line approach can find minimum energy requirements for (1) Distillations with feed pinch, saddle pinch, and tangent pinch points. (2) Distillations for which the minimum energy solutions do not correspond to a pinch point. (3) Processes with multiple units (e.g., reactive distillation, extraction/distillation, etc.). Other novel features of this work also shows that the shortest stripping line approach (4) Can be used to identify correct processing targets in multi-unit processes. (5) Encompasses longstanding methods for finding minimum energy requirements including the McCabe-Thiele method and boundary value methods. A back-to-front design approach based on shortest stripping lines is used so that correct processing targets can be identified so that all tasks can be synthesized simultaneously in such a way that the most energy efficient designs are achieved. New problem formulations that take the general form of nonlinear programming (NLP) and mixed integer nonlinear programming (MINLP) problems are given and a novel global optimization algorithm is presented for obtaining energy efficient process designs. A variety of ideal and nonideal distillations, including examples with four or more components, are used to demonstrate the efficacy of the shortest stripping line approach. The examples with more than three components are particularly significant because they clearly illustrate that the proposed approach can be readily used to find minimum energy requirements for distillation problems involving any number of components. Many geometric illustrations are used to highlight the key ideas of the method where appropriate.

Modeling of a reactive separation process using a nonequilibrium stage model

A nonequilibrium model for simulation of homogeneous reactive distillation has been developed. Mass transfer accompanied by simultaneous chemical reaction is described by the Maxwell Stefan equations. Calculations were done for the process to produce ethyl acetate that has been treated extensively in literature. It was found that reactions could, under certain conditions, have a significant impact on component effeciencies, thus emphasizing the need for rate-based models for reactive distillation. By means of parametric sensitivity studies it is shown that the effects of operational and design parameters on column behavior can be very complicated.

Film models for multicomponent mass transfer: computational methods—II: The linearised theory

Abstract The approximate solution of the linearised multicomponent diffusion equations for a film model is examined from the standpoint of computational efficiency. An alternative formulation of the mass transfer coefficients facilitates the development of stable and efficient algorithms for computing the rates of mass transfer.

Modelling mass transfer in multicomponent distillation

Abstract This paper highlights inconsistencies in the modelling of mass transfer in multicomponent distillation columns. Models of flow and mass transfer are developed that seek to avoid these inconsistencies based on the usual assumptions of plug flow of vapor and of plug flow or axial dispersion of the liquid. These models are used together with a nonequilibrium model of trayed distillation columns. It is shown that the revised models are capable of sensible predictions of column performance. Methods of evaluating binary (Maxwell—Stefan) mass transfer coefficients are evaluated and it is found that mass transfer on sieve trays is best modelled with the Chan and Fair correlation. Mass transfer is multicomponent distillation should be modelled using the Maxwell-Stefan equations; simpler approaches may be significantly less demanding of computer time but columns designs based on such methods can be very different from those obtained using the more rigorous approach.

A collection of 10 numerical problems in chemical engineering solved by various mathematical software packages

Current personal computers provide exceptional computing capabilities to engineering students that can greatly improve speed and accuracy during sophisticated problem solving. The need to actually create programs for mathematical problem solving has been reduced if not eliminated by available mathematical software packages. This article summarizes a collection of 10 typical problems from throughout the chemical engineering curriculum that require numerical solutions. These problems involve most of the standard numerical methods familiar to undergraduate engineering students. Complete problem solution sets have been generated by experienced users in six of the leading mathematical software packages. These detailed solutions including a writeup, and theelectronic files for each package are available through the Internet at www.che.utexas.edu/cache, and via FTP from ftp.engr.uconn.edu/pub/ASEE/. The written materials illustrate the differences in these mathematical software packages. The electronic files allow hands‐on experience with the packages during execution of the actual software packages. This article and the provided resources should be of considerable value during mathematical problem solving and/or the selection of a package for classroom or personal use.

Automatic derivation of thermodynamic property functions using computer algebra

Abstract The commercial computer algebra system known as Maple has been extended in order to make possible the automatic symbolic derivation and differentiation of thermodynamic property functions of mixtures with arbitrary numbers of components. The tools described here could be useful in the rapid development of new models for thermodynamic properties (and their derivatives).

A NONEQUILIBRIUM STAGE MODEL OF MULTICOMPONENT SEPARATION PROCESSES VI: SIMULATION OF LIQUID-LIQUID EXTRACTION

Abstract A nonequilibrium stage model of liquid-liquid extraction processes is described. The mass conservation equations for each phase are solved simultaneously with properly formulated mass transfer rate equations for multicomponent systems and phase equilibrium relationships to represent the phase interface. The model is used to simulate a number of extraction operations in sieve tray columns and the results compared to experimental data.

Maple and the art of thermodynamics

Maple is a computer algebra system that has the potential to be the tool of choice for many computational problems in science and engineering. In this article, we show how Maple can be used to develop graphical images of thermodynamic functions. We also describe ThermoView, a standalone program that can display Maple‐based images and animations. The visual images and tools described here can be used to enhance thermodynamics courses and give students an improved perspective on the relationships between thermodynamic state variables.

Chemical Engineering with Maple

Chemical engineering students are required (by accreditation agencies) to make appropriate use of computers throughout their program. Appropriate use is defined as including most of the following: (1) programming in a high level language; (2) use of software packages for analysis and design; (3) use of appropriate utilities; (4) simulation of engineering problems. Maple (Char, 1991) is a powerful and flexible computing tool that has the potential of becoming the software of choice for much scientific and engineering work, perhaps replacing, at least in part, other computer based methods such as traditional programming languages and special purpose analysis and design programs. The fact that Maple is designed for symbolic manipulation should not be taken to imply that it is unsuitable for the numerical calculations that dominate engineering computing today. Maple’ s symbolic mathematical abilities combined with numerical capabilities and sophisticated graphics allow new approaches to the teaching of traditional materials. In this paper we focus on a few ways in which Maple can be used in selected courses in the chemical engineering curriculum.