Henry C. Lim

The extended Graetz problem with Dirichlet wall boundary conditions

The extension of the Graetz problem to include axial conduction has been of interest in view of its application to a number of low Peclet number heat or mass transfer situations. Past efforts in dealing with this problem have been plagued with uncertainties arising from expansion in terms of “eigenfunctions” and “eigenvalues” belonging to a nonselfadjoint operator. The uncertainties spring from a lack of basis for the assumptions that no complex eigenvalues exist and that the calculated eigenvectors originate from a complete set. Other methods have been entirely numerical.

Yield optimization for multiple reactions

Abstract A heretofore unavailable systematic and unified analysis of the problem of yield optimization in complex reaction schemes is presented in this paper. Cyclic operation of a variable-volume, semi-batch, stirred tank reactor is examined within the framework of the optimal control theory in order to identify feasible operation modes and candidate optimal strategies. The optimal strategy is shown to be one of the following: (1) a continuous-flow stirred tank reactor; (2) a repeated batch operation (spatial dual: a plug flow reactor with/without recycle); (3) a repeated fed-batch operatio involving singular control (spatial dual: a plug flow reactor with recycle and distributed feed); or a specific combination of (1), (2) and (3). The admissibility of singular control is examined for reaction schemes obeying power law kinetics and Langmuir-Hinshelwood-type kinetics. The strength of the approach adopted here is well illustrated by analytical identification of optimal policies via phase-plane analysis for three specific reaction schemes: first-order consecutive parallel reactions, the Denbigh reaction scheme and Van de Vusse reaction scheme.

Optimal Control of Fed-Batch Bioreactors

Optimal feed rate profiles for fed-batch bioreactors have been characterized for the production of cell mass and metabolites using various kinetic forms. A complete nonlinear feedback control based on the state variables and a kinetic model may be realized for certain limiting cases.

Single-Cell Protein from C1 Compounds

Publisher Summary This chapter discusses single-cell protein (SCP) from C 1 compounds. The search for unconventional protein sources has turned to single-cell protein, a term so coined by Wilson to represent the cells of algae, bacteria, yeasts, and fungi grown for their protein content. These organisms convert inexpensive raw materials into protein quite rapidly and without putting additional burden on shrinking cropland. Availability of raw materials in commercial quantities and modern fermentation processes favor the commercial production of high grade protein in the form of SCP. The need for SCP as a source of animal feed and as a supplementary protein source has been well established, and research and development efforts on SCP production have been and are intensive worldwide, including USA, UK, France, Federal Republic of Germany, GDR, Italy, Japan, USSR, Rumania, Venezuela and elsewhere. The SCP that are formed from C 1 compounds are reviewed with a major emphasis on the aspects of carbon assimilation and energy generation particular to these microorganisms.

Optimal output feedback control for systems with inaccessible state variables

Optimal linear control laws require the measurement of each and every state variable. However, in practice it is difficult to measure every state variable, and thus the optimal control is not widely accepted. This paper is concerned with overcoming this difficulty by considering the design of optimal linear regulator systems with some inaccessible state variables. Two methods leading to dynamic feedback control laws in terms of measurable output alone are developed. One of these methods is extended to time-varying problems.

Sufficient conditions for uniqueness and local asymptotic stability for a class of distributed parameter systems: non-adiabatic plug-flow tubular reactors with recycle and feedback control

An analysis of the stability of a non-adiabatic tubular reactor with feedback control, modelled by a plug-flow reactor in which axial dispersion of heat and mass is accounted for by recycle, is presented, A sufficient condition for local stability is developed in terms of system parameters and steady-state profiles. This condition is extended to a condition which is in terms of system parameters and outlet temperature only. Also, a unique stable steady-state criterion, which is in terms of system parameters only, is obtained. These conditions show that under certain assumptions the stability can always be proved for a suitable choice of controller settings.