Shehzaad Kauchali

Linear programming formulations for attainable region analysis

We propose linear programming (LP) models for attainable region (AR) analysis by considering a rate vector field in concentration space with an arbitrarily large number of points. One model provides a method to construct candidate ARs using a fully connected network of continuously stirred tank reactors (CSTRs) of arbitrary volume. More importantly, these methods are extended to derive linear programming conditions that are stronger necessary conditions than have proposed previously by Glasser and Hildebrandt. We state the LP condition as: No combination of nonzero volume CSTRs, operating at discretized points in the complement of the candidate AR, can extend the region. We demonstrate these proposed linear programming techniques on several two-dimensional reaction mechanisms and then apply the LP methods to verify extensions for a previously published three-dimensional candidate AR.

An experimental simulation of distillation column concentration profiles using a batch apparatus

Abstract There has been a growing interest in the use of residue curves for the preliminary design and sequencing of distillation columns. Residue curves are used not only to predict composition changes in separation processes, but also to determine the feasibility of proposed separations, and flowsheet development (Chem. Eng. Sci. 33 (1977) 281). An experimental technique has been developed for the measurement of these residue curves. (Distillation & absorption ’97, Inst. Chem. Eng. 1 (1997) 187). It can be shown that the time-dependent composition profiles obtained in a modified form of this apparatus are mathematically equivalent to the position-dependent profiles in a continuous distillation column. Hence, it is possible to experimentally simulate a distillation column profile in a small batch apparatus using only small quantities of material. The modified apparatus consists of a still immersed in a heated oil bath so that a liquid feed is continuously supplied to the still. Samples of liquid are then analysed over time using a gas chromatograph. The results from an experimental system have been compared to available information and simulations to determine the accuracy of the apparatus. This technique has several advantages over working with distillation columns, firstly in the sample size required, and secondly in the ease of operation. The method allows quick and low-cost measurements of the concentration variables that model a distillation column. The information obtained this way could prove useful for the selection of feasible systems and for finding minimum reflux requirements. It could also be very valuable for screening of complex systems where only small amounts of material are available and simulations may be very difficult.

Automating reactor network synthesis: finding a candidate attainable region for the water–gas shift (WGS) reaction

Abstract We use the attainable region (AR) technique to generate reactor network synthesis solutions to the WGS reaction system that is overall adiabatic. We first do this using the conventional method, as described by Nicol et al. (Comp. Chem. Eng. 21 (1001) 1997, s35), to generate the candidate AR (ARc) for exothermic reversible reactions in three dimensions. We then numerically generate the ARc using the iso-state algorithm and find the region to be within a percent of that found using the classical AR technique. We further use a linear programming model to show that no substantial extension to the ARc is possible. These latter two methods are shown to be simple enough such that they could, in principle, be incorporated in automated software. Generating the ARc using reaction and mixing processes for the WGS reaction provides the user with a benchmark for what can be attained in this system.

Binary distillation re-visited using the attainable region theory

Abstract An attainable region (AR) analysis is a geometrically-based method of optimisation that has mainly been used for performing optimal reactor synthesis. The objective of the analysis is to find the complete set of all possible outcomes, a system can achieve from a given feed set using a given number of fundamental physical processes such as chemical reaction, mixing and heat transfer. From such an analysis one can find optimal pathways that can be used to obtain a desired product from a given feed. More importantly, these pathways can be interpreted to represent optimised process equipment. In a previous paper (Kauchali, S., McGregor, C., & Hildebrandt, D., 1999), we applied the AR theory to binary distillation where we constructed a constrained attainable region. We considered the optimum policy for the reflux ratio along the column where there was no cost associated with the processes used to control the reflux ratio. In this paper, we would like to investigate the effect of including costs for the processes used to control the reflux ratio on the operating policy and structure of column. The attainable region, subject to the conditions discussed above, has been determined and the behaviour shown graphically in a composition, cost and reflux/reboil space. We discuss the effects of changing the reflux/reboil ratio along the length of the column and examine the implications of the results obtained from the construction of the constrained AR for the design of conventional distillation columns.

Membrane Process Design Using Residue Curve Maps: Peters/Membrane Process Design

MARK PETERS graduated with both undergraduate and PhD degrees in chemical engineering from the University of the Witwatersrand in Johannesburg, South Africa. He has previously worked at Sasol Technology, where he focused on lowtemperature Fischer-Tropsch gas-to-liquids conversion. He is currently a separations consultant at the Centre of Material and Process Synthesis (COMPS), based at the University of the Witwatersrand.

Automating Reactor Network Synthesis: Finding a Candidate Attainable Region for Water-Gas Shift(WGS) Reaction

We use the Attainable Region (AR) technique to generate reactor network synthesis solutions to the WGS system. We first do this using the conventional method as described by Nicol et al. (1999) to generate the AR for exothermic reversible reactions. We then generate the AR using the new iso-state algorithm and show the answers are essentially the same. We further use a linear programming model to show that no substantial extension to the candidate AR is possible at the level of resolution of the grid. These latter two methods are shown to be simple enough such that they could, in principle, be incorporated in software and be implemented by users who have a fair understanding of reactor system design. Generating candidate regions will provide the users with benchmarks for what can be attained for the WGS system.

DSR algorithm for construction of Attainable Region structure

Abstract A new Differential Side-stream Reactor (DSR) Algorithm is proposed for Attainable Region (AR) construction. For fundamental processes of reaction and mixing, the candidate AR can be constructed using constant intermediate mixing policy DSR, which fully describes the fundamental processes. Feinberg (2000) derived the mixing policy that governs the existence of a DSR on the AR boundary; he called that DSR a critical DSR. Here we show that the mixing policy can, in the limit, be approximated by constant values.