INTRODUCTION

A chemical reactor could be any vessel containing chemical reac-

tions. In general, a reactor is designed to maximize the yield of some

particular products while requiring the least amount of money to

purchase and operate. Normal operating expenses include energy in-

put, energy removal, raw material costs, labor, etc. Energy changes

can occur in the form of heating or cooling, or agitation. The latter

is quite important because an appropriate mixing has a large influ-

ence on the yield. Therefore, the design and operation of mixing

devices often determines the profitability of the whole plant.

In particular, in the widely developed continuous stirred tank reac-

tors (CSTR) one or more fluid reagents are introduced into a tank

equipped with an impeller while the reactor effluent is removed [1].

The impeller stirs the reagents to ensure proper mixing. Classical

CSTR dynamical models, based on coupled deterministic ordinary

differential equations (ODEs), are the usual approach to chemical

systems at the macroscopic scale. They have been demonstrated to

have considerable usefulness, but it should be mentioned that they

are based on the common assumption that spatial inhomogeneities

may be neglected. Thus, ODEs are a mean field approach and the 源自六-维+论\文"网*加7位QQ3249.114 重庆时时彩的规律 www.mamitama.com

analytical solutions of the ordinary differential equations (ODEs)

provide an accurate model only in this case.

When the system is not homogeneous, application of the above

assumption often yields a model that does not accurately represent

the system. This is the case, for example, of CSTRs with a highly

viscous medium where spatial heterogeneities exist in species con-

centrations, temperature, etc. Of course, the application of partial

differential equations (PDEs) to model spatial inhomogeneities such

as diffusion and hydrodynamic turbulence may produce accurate

models. However, their solution requires advanced numerical tech-

niques such as finite element methods. Moreover, the numerical

techniques for solving the PDEs could be computationally expensive

and do not account for localized stochastic phenomena. In particu-lar, chemical systems are discrete from the microstructure until the

molecular level and statistical fluctuations in concentration and tem-

perature occur at these local scales.

Cellular automata are an attractive alternative to PDEs to model

complex systems with inhomogeneities of this type. A cellular auto-

mata lattice is comprised of discrete cells whose states are func-

tions of the previous state of the cell and its neighbors. Rules are

used to update each cell by scanning the value of the cells in the

neighborhood. Seyborg [2] and Neuforth [3] have shown that sto-

chastic cellular automata models can be successfully applied to simu-

late first order chemical reactions. In their papers, they worked on a

squared lattice of cells, each of them having a chemical reactant.

The reactions are performed by considering a probability of change,

from reactant A to product B, proportional to the kinetics constant

that defines the chemical equation. However, this type of calculation 连续搅拌反应器的元胞自动机模拟英文文献和中文翻译:重庆时时彩的规律/a/fanyi/20171204/17371.html