Advanced Reactor Modeling with MATLAB

Case Studies with Solved Examples

Riccardo Tesser, Vincenzo Russo

• Publisher: De Gruyter
• Year: 2020
• eBook ISBN: 9783110632316
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Chemical & Biochemical Engineering
• Index: Technology & Engineering

Offers the reader a modern approach to reactor description and modelling. Using the widely applied numerical language MATLAB, it provides the reader with categorized groups of general code for a wide variety of chemical reactors. Being designed as a tool for researchers and professionals, the code can easily be extended and adapted by the reader to their own specific problems.

Chapter 1 Introduction on chemical reactors modeling

1.1 Chemical reactors modeling

Modeling of chemical reactors is a specific sector of chemical reaction engineering (CRE), dedicated to the description of the chemical and physical phenomena occurring in a reactor. The number of reactor types is rather large; thus, each reactor needs a specific approach to be modeled [1, 2, 3, 4].

Focusing on the phenomena occurring in a chemical reactor, it is possible to develop a reactor model starting from a generic classification of the main types of these devices:

• Batch and fed batch
• Steady-state continuous tubular
  • Plug flow, laminar flow, nonideal flow
  • Packed bed, trickle bed
• Dynamic continuous tubular
• Continuous steady-state/dynamic stirred tank

Independent of the specific reactor type, the physical phenomena occurring can be always done writing down the conservation laws for mass, heat and momentum balances, that means defining the terms of: (i) reaction and (ii) mass/heat/momentum transfer.

The derivation of a unified approach to define differential mass/heat/momentum balances are given as follows [1]:

(1.1)$\frac{\mathrm{\partial }{C}_i}{\mathrm{\partial }t}=-\mathrm{\nabla }(C_{i}u)-\mathrm{\nabla }{J}_i+{\sum }_j{\nu }_{ij}{r}_j$

(1.2)${\sum }_i{M}_i{C}_i{c}_{p,i}\left(\frac{\mathrm{\partial }T}{\mathrm{\partial }t}+u\mathrm{\nabla }T\right)=\mathrm{\nabla }(\lambda \mathrm{\nabla }T)+{\sum }_j(-\mathrm{\Delta }{H}_j)r_j+{\sum }_i{J}_i\mathrm{\nabla }{H}_i+Q_{\mathrm{r}\mathrm{a}\mathrm{d}}$

(1.3)$\frac{\mathrm{\partial }({\rho }_{f}u)}{\mathrm{\partial }t}+\mathrm{\nabla }({\rho }_{f}uu)=-\mathrm{\nabla }P-\mathrm{\nabla }s+{\rho }_{f}g$

All the terms could be grouped as follows, showing a deep rationalization of the approach:

Accumulation: $\mathrm{\partial }{C}_i/\mathrm{\partial }t,\mathrm{\partial }T/\mathrm{\partial }t,\mathrm{\partial }({\rho }_{f}u)/\mathrm{\partial }t$

Convective flow: $\mathrm{\nabla }(C_{i}u),u\mathrm{\nabla }T,\mathrm{\nabla }({\rho }_{f}uu)$

Chemical reaction: ${\sum }_j{\nu }_{ij}{r}_j,{\sum }_j(-\mathrm{\Delta }{H}_j)r_j$

Flux given by molecular diffusion: $\mathrm{\nabla }{J}_i,{\sum }_i{J}_i\mathrm{\nabla }{H}_i$

Heat transfer by conduction: $\mathrm{\nabla }(\lambda \mathrm{\nabla }T)$

Radiation heat flux: $Q_{\mathrm{r}\mathrm{a}\mathrm{d}}$

Pressure gradient: $\mathrm{\nabla }P$

Shear stress: $\mathrm{\nabla }s$

Gravity: ${\rho }_{f}g$

Ideally, with these general equations, it would be impossible to model every kind of reactor. For example, for a batch reactor, the accumulation and the reaction rate are the only terms to be considered, while for a dynamic plug-flow reactor, it is necessary to introduce also the convective term. For multiphase systems, it is necessary to write a mass balance for each phase, including terms related to interfacial mass transfer.

Usually, the reactor models published in the literature are written simplifying the momentum balance equation, often omitted solving the velocity profiles with algebraic expressions (i.e., parabolic profile for laminar flow modeling) and the pressure drop is often calculated by using friction factor correlations [5].

Therefore, in selecting the terms to include in the conservation equations, several aspects must be considered. Some major issues are summarized in Table 1.1.

Table 1.1:Main aspects to be considered in reactor modeling.

	Batch/fed batch	Continuous reactor
Solid phase	Rate laws and temperature dependencies Adsorption/desorption phenomena Catalyst deactivation Intraparticle diffusion limitation Fluid–solid ...

Table of contents

• Title Page
• Copyright
• Contents
• Preface
• Chapter 1 Introduction on chemical reactors modeling
• Chapter 2 Batch reactors for homogeneous catalysis
• Chapter 3 Batch reactors for heterogeneous catalysis
• Chapter 4 Ideal single-phase continuous reactors for homogeneous catalysis
• Chapter 5 Real reactors for heterogeneous catalysis
• Chapter 6 Packed bed reactors
• Chapter 7 Parameters estimation
• Chapter 8 Statistical techniques applied to chemical processes
• Chapter 9 Case studies in chemical reaction engineering
• Word Index