On mutating autocatalytic reactions in a CSTR. I: Multiplicity of steady states

A conceptual model describing a mutating autocatalytic reaction in a continuous stirred tank reactor is analyzed. The mutant is assumed to compete with the original autocatalyst. The phenomenon of multiplicity of steady states is determined through the application of singularity theory. A mutant-containing feed and a mutant-free feed cases were considered. Eleven regions for the first case and at least 25 regions for the second case of qualitatively different bifurcation behavior were determined using only conditions for isola and hystersis variety. More subregions were identified when applying the double limit variety conditions. The maximum number of steady states which was found for the first case was five whereas the second case showed regions of seven steady states. The yield distribution of the main product and the mutant was briefly discussed for some cases.

Modeling, Simulation and Bifurcation Analysis of a Mutating Autocatalytic Reaction

In this paper, we present a conceptual model for autocatalytic reactions in which the autocatalyst undergoes a mutation process in a continuous stirred tank reactor. Three cases with different mutation coefficient (a) have been considered. The analysis of these cases shows the importance of this parameter and the qualitative and quantitative differences in the resulting bifurcation diagrams. Generally speaking, selectivity towards main product increases with decreasing substrate conversion. Co-existence of a mushroom and an isola has been determined for one of the cases. The isola portion is a low main product yield solution and is to be avoided. Keywords: Autocatalytic reactions, mutation, bifurcation, selectivit

Modeling, Simulation and Bifurcation Analysis of a Mutating Autocatalytic Reaction

In this paper, we present a conceptual model for autocatalytic reactions in which the autocatalyst undergoes a mutation process in a continuous stirred tank reactor. Three cases with different mutation coefficient (a) have been considered. The analysis of these cases shows the importance of this parameter and the qualitative and quantitative differences in the resulting bifurcation diagrams. Generally speaking, selectivity towards main product increases with decreasing substrate conversion. Co-existence of a mushroom and an isola has been determined for one of the cases. The isola portion is a low main product yield solution and is to be avoided. Keywords: Autocatalytic reactions, mutation, bifurcation, selectivit

Studies on the Method of Orthogonal Collocation: V. Multiple Steady States in Catalyst Particles

Efficient numerical schemes are developed in this paper to solve the boundary value problems of diffusion with chemical reaction in catalyst particles. These schemes are based on the fact the concentration profiles can be divided into reaction and dead zones. The reaction zone can be further divided into two zones at a defined critical point. New transformations are used to minimize the number of collocation points needed to obtain accurate solutions. With the help of the continuation package AUTO, the modified collocation schemes are used to obtain the multiple steady states and the locations of the concentration profiles zones for different values of Thiele modulus

Studies on the Method of Orthogonal Collocation: V. Multiple Steady States in Catalyst Particles

Efficient numerical schemes are developed in this paper to solve the boundary value problems of diffusion with chemical reaction in catalyst particles. These schemes are based on the fact the concentration profiles can be divided into reaction and dead zones. The reaction zone can be further divided into two zones at a defined critical point. New transformations are used to minimize the number of collocation points needed to obtain accurate solutions. With the help of the continuation package AUTO, the modified collocation schemes are used to obtain the multiple steady states and the locations of the concentration profiles zones for different values of Thiele modulus

Studies on the Method of Orthogonal Collocation VII: An Efficient Collocation Method for Diffusion-convection Problems with Chemical Reaction

In this work we present a new numerical scheme based on orthogonal collocation method to solve a reacting flow problem. The method is based on recasting the problem to become a larger set of first order differential equations and we show by numerical computation that the application of the method of orthogonal collocation to this new set of equations leads to a more efficient numerical scheme. Numerical simulation is carried out for steady state case. Keywords: Numerical solution, Orthogonal collocation, Diffusion, Convection, Reactio

Model reduction and robust control of multi-stage flash (MSF) desalination plants

Department of Chemical Engineering King Saud University P.O. Box 800, Riyadh 11421, Saudi Arabia Fax: (9661) 467-8770 Email: [email protected] orthogonal collocation method is used for the reduction of a large nonlinear model of a multi-stage flash (MSF) desalination plant. The real plant located in Saudi Arabia consists of nineteen stages in the heat recovery section and three in the heat rejection section. It is shown that three collocation points. i.e. two for the heat recovery section and one for the heat rejection section are sufficient for a good representation of the full order model for both steady state and dynamic behavior. The reduced model is then used for a robust controller design of the plant using a constrained non-linear model predictive control (NLMPC) strategy. Numerical simulations show that the controlled system obtained when the reduced model is used for output prediction yield the same performances as with the full order model but with a considerable reduction in the computational time and a much easier tuning of the controller