A geometric approach to steady flow reactors: the attainable region and optimization in concentration space

Abstract

Experimental data for a fixed-bed reactor were obtained for the reaction of sucrose to give glucose plus fructose using the enzyme invertase which was immobilized by covalently binding it to a polymer matrix adsorbed in the pores of alumina. A mathematical model, which included external film mass transfer, internal pore diffusion, axial dispersion, and enzymatic reaction with both substrate and product inhibition, was used to predict the performance of the fixed-bed reactor over a wide range of operating variables. The tortuosity factor for pore diffusion was measured separately for use in the model. Hence, external and internal pore diffusion effects were known and it was necessary to obtain only the activity of the immobilized enzyme from the experimental reactor data. Comparisons of the experimental data and the theoretical predictions from the model indicated a 70% loss of the native invertase activity constant resulting from the immobilization and a 32% decrease for the Michaelis constant and the product and substrate inhibition constants.

Review of Mixed‐Integer Nonlinear and Generalized Disjunctive Programming Methods

“…Attainable region is the convex hull of concentrations for a given feed and reaction scheme. The geometrical concepts that allow the derivation of the attainable region, and further extensions to higher dimensions where developed mainly by Glasser, Hildebrandt, and Feinberg [127][128][129][130]. There are two main downsides of the "attainable region" technique.…”

Synthesis of Optimal Chemical Reactor Networks

“…The attainable region is the convex hull of concentrations that can be achieved starting from the feed point by reaction and mixing. Recently, Glasser et al (1987) and Hildebrandt et al (1990) developed geometric concepts for reaction and mixing to map the entire region in the concentration space that is attainable from a given feed concentration. Alternate plug flow reactor (PFR) and continuous stirred tank reactor (CSTR) trajectories were drawn to cover the attainable region and derive an optimal reactor network.…”

Reactor Network Synthesis Using Coupled Genetic Algorithm with the Quasi-linear Programming Method

“…The third method of design is based on the systematic generation of the process flow sheet or part of it. Here, the objective is to find all possible concentration domains resulting from various reactor systems, and to consider all defined reactions 10,11 . Therefore, a functional representation is used to model all reactions and mixing.…”

“…This method was first devised by Horn 10 . After Glasser et al 11 had defined a systematic graphical method, this method became popular in the field of design of reactor networks. The main characteristic of the two latter methods is that they can be considered as mathematical programming methods, and the problem can be solved to find the optimum process flow diagrams.…”