A cellular automata approach to chemical reactions; 1 Reaction controlled systems

doi:10.1016/j.cej.2013.04.084

Chemical Engineering Journal

Volume 228, 15 July 2013, Pages 172-178

https://doi.org/10.1016/j.cej.2013.04.084 Get rights and content

Highlights

•
Cellular automata approach is suitable to simulate the chemical controlled reactions.
•
Therefore a modification of dissolution routine of CEMHYD3D has been introduced.
•
A general and original linear relation between time and cycles was derived.

Abstract

A direct link between the chemical reaction controlled (shrinking core) model and cellular automata, to study the dissolution of particles, is derived in this paper. Previous research on first and second order reactions is based on the concentration of the reactant. The present paper describes the reaction kinetics based on particles and takes into account the shape and specific surface of these particles.

As a vehicle for the present study of cellular automata, a simplified version of the CEMHYD3D model is used. During the research it was found that during the dissolution of particles, additional reactive surface was created due to the dissolution of voxels in the middle of the top-surfaces. Therefore a modification of the dissolution routine within CEMHYD3D was introduced. This modification introduced the preference of the system to dissolve voxels on the outside of the particles rather than the middle of the top-surfaces of the particles. In this way the increase of reactive surface is prohibited and a spherical shape maintained.

Using this modification, it is proven that the dissolution of digitized particle can be describe based on the chemical reaction controlled system. Based on 165 simulations a general linear relation between cycles and time was derived. The derived model can describe the reaction sufficient up to 99.9%. Therefore it can be concluded that the single ‘cellular automata’ particle unambiguously related to the chemical controlled reactions.

Introduction

Chemical reactions are studied since centuries. Reactions can be described based either on concentration or on particle geometry. Levenspiel [1], [2] and Szekely et al. [3], besides others, describe the progression of chemical reactions based on the particle geometry. From the described reactions, the chemical reaction controlled shrinking core model is the most simple reaction [2]. This reaction is relevant for particles and used for instance to describe the burning of carbon in air. The reaction kinetics are usually analyzed using numerical and analytical models. Besides these models also other methods have become available such as cellular automata (CA).

Cellular automata are already commonly used for the modeling of chemical systems [4], [5]. Cellular automata systems are among others applied for studying biology, cement reaction, population growth, computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. Kier et al. [6] uses cellular automata to describe the percolation within chemical systems. Furthermore Kier and co-authors described a broad range of chemical systems and processes in which the cellular automata approach can be applied, ranging from aqueous systems (water), dissociation of organic acid in solutions and bond interactions [7], [8], [9], [10], [11], [12], [13], [14]. Berryman and Franceschetti [15] described the simulation of diffusion controlled reaction kinetics using cellular automata. Kier and Cheng [13] gave a cellular automata model for dissolution. Goetz and Seetharaman [16] used cellular automata to describe the static recrystallization kinetics with homogeneous and heterogeneous nucleation. Liu et al. [17] and Raghavan and Sahay [18], [19] simulated grain growth using cellular automata. Dab et al. [20] used a cellular-automaton for reactive systems containing particles. Zahedi Sohi and Khoshandam [21] used 2D cellular automata to describe non-catalytic gas–solid reactions of pellets consisting out of agglomerated grains with diffusion through a porous product layer and reaction on the surface of grains. In their work the cells were the grains and the conversion per cell was considered. This paper considers spheres in 3D which consists of several cells, being either product, reactant or void. Kier and Seybold and their co-authors [22], [23], [24], [25], [26], [27] did research to the application of cellular automaton systems to describe chemical reactions. Their work describes first and second order reactions as well thermodynamically controlled reactions [26] and is closely related to our work. Their research on first and second order reactions is based on the concentration of the reactant, while in this research the shape is taking in account as well as the specific surface of the dissolving particle. Hence, this article considers the reaction as surface-based rather than volume-based.

A rigorous link between the (mathematical) chemical reaction models, like chemical reaction (shrinking core) model and the cellular automata approach to study the dissolution of particle has, to the authors’ knowledge, not been achieved yet.

Section snippets

Chemical reaction kinetics

Within the chemical reaction kinetics literature, two main reaction model families are distinguished the progressive-conversion model (PCM) and the shrinking unreacted core model (SCM). Within the progressive-conversion model (sometimes referred to as the zone reaction model [28]), the solid reactant is converted continuously and progressively throughout the particle, while within the shrinking core model, the reactions take place on the outer skin of the particle and the zone of reaction is

Cellular automata

Cellular automata (CA) were first proposed by Ulam [34], [35] and Von Neumann [36], based on ideas of Zuse [25]. The first full comprehensive description of cellular automata was made by Wolfram [37]. Cellular automata are ‘simple mathematical idealizations of natural systems. They consist of a lattice of discrete identical sites, each site taking on a finite set of integer values. The values of the sites evolve in discrete time steps according to deterministic rules that specify the value of

Simulation results

Using simulations, the cycle in a certain α is reached has been determined for a dissolution probability (P₀) of 0.003–0.09 with steps of 0.003 and d = 7, 13, 21, 25 and 35. Analysis of the simulation data shows that the reaction rate depends on the available surface area of the reactant. Based on the description in the previous section, the chemical reaction controlled (CRC) model is most appropriate to describe a chemical system without precipitation of reaction products and the existence of a

Coupling cellular automata and reaction kinetics

Since the resemblance between the reaction curves obtained from the CEMHYD3D and the reaction controlled curves as, in this section a correlation between simulations and theoretical model is researched. Therefore a linear regression between cycle number (C-2) and (1 − (1 − α)^1/3) is tested, since according to the chemical reaction controlled model a linear relation between time and (1 − (1 − α)^1/3) exists and linear relation between cycle and time is assumed here. The relation with C-2 rather with C is

Conclusions

In this paper, the relation between the theoretical shrinking core reaction kinetic equations, as presented by Levenspiel [1], [2], Szekely et al. [3] and others, and a cellular automata reaction approach has been investigated. As cellular automata tool CEMHYD3D was employed. In order to derive this relation a major improvement/modification was introduced. This modification introduced the preference of the system to dissolve voxels on the outside of the particles rather than the middle of the

Acknowledgements

The authors wish to express their sincere thanks to the European Commission (I-SSB Project, Proposal No. 026661-2) and the following sponsors of the research group: Bouwdienst Rijkswaterstaat, Graniet-Import Benelux, Kijlstra Betonmortel, Struyk Verwo, Attero, Enci, Provincie Overijssel, Rijkswaterstaat Directie Zeeland, A&G Maasvlakte, BTE, Alvon Bouwsystemen, V.d. Bosch Beton, Selor, Twee “R” Recyling, GMB, Schenk Concrete Consultancy, Geochem Research, Icopal, BN International, APP All

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A cellular automata approach to chemical reactions; 1 Reaction controlled systems

Highlights

Abstract

Introduction

Section snippets

Chemical reaction kinetics

Cellular automata

Simulation results

Coupling cellular automata and reaction kinetics

Conclusions

Acknowledgements

Scripta Mater.

Comput. Mater. Sci.

Mater. Sci. Eng.: A

Chem. Eng. J.

Chem. Eng. Sci.

Chem. Eng. Sci.

Chem. Eng. Sci.

Chem. Eng. Sci.

Chem. Eng. Sci.

Chem. Eng. Sci.

Phys. D: Nonlinear Phenom.

Chemical Reaction Engineering

The Chemical Reactor Omnibook +

Gas-Solid Reactions

Cellular Automata Modeling of Physical Systems

Cellular Automata Modeling of Chemical Systems: A Textbook and Laboratory Manual

A cellular automata model of the percolation process

J. Chem. Inf. Comput. Sci.

A cellular automata model of bond interactions among molecules

J. Chem. Inf. Comput. Sci.

A cellular automata model of acid dissociation

J. Chem. Inf. Comput. Sci.

A cellular automata model of oil–water partitioning

J. Chem. Inf. Comput. Sci.

A cellular automata model of water structuring by a chiral solute

J. Chem. Inf. Comput. Sci.

A cellular automata model of water

J. Chem. Inf. Comput. Sci.