Extended Definition of Conversion and Reaction Extent for a Systematic Development of the Design Equations for Reactor Networks
Abstract
:1. Introduction
Objectives and Motivations
2. Methodology of the General Design Approach
2.1. Reactor Networks
- {n, i} = {Number of Species, Related Index};
- {m, j} = {Number of Reactions, Related Index};
- {r, k} = {Number of Reactors, Related Index};
- {b, l} = {Number of Network Branches, Related Index}.
2.2. General Extension of the Definition of Conversion
2.3. Approach Validation Using Simple Reactor Networks
2.3.1. Series of Reactors in a Row
2.3.2. Reactors in Parallel
2.3.3. Adiabatic-Stage Reactors with Recycle (See Appendix A.2)
Geometrical Interpretation of Mass Balance
3. Application to Other Case Studies of Interest
- Adiabatic-Stage Reactors with Split;
- Adiabatic-Stage Reactors Intercooled/Interheated by Reactants;
- Adiabatic-Stage Reactors with Distributed Interstage Feed.
3.1. Adiabatic-Stage Reactors with Split (See Appendix A.3)
Geometrical Interpretation of Mass Balance
3.2. Adiabatic-Stage Reactors Intercooled/Interheated by Reactants (See Appendix A.4)
3.3. Adiabatic-Stage Reactors with Distributed Interstage Feed (See Appendix A.5)
4. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
Specific heat, J mol−1 K−1 | |
F | Flow rate, mol s−1 |
H | Molar enthalpy, J mol−1 K−1 |
{n, m, r, b} | Number of: {species, reactions, reactors, network branches} |
rA | Reaction rate (of the key-species A), mol s−1 m−3 |
Rk | Recycle ratio (at the k-th reactors) |
Sk | Split ratio (at the k-th reactors) |
T | Temperature, K |
V | Volume, m3 |
xA | Conversion (of the key-species) |
Greek Symbols | |
θi | Feed ratio, moli molA−1 |
νij | Stoichiometric coefficients |
ξj | Reaction extent for the jth reaction |
Subscripts/Superscripts | |
‘f’ | Final (with respect to a stage with recycle or split) |
{i, j, k, l} | Indices for: {species, reactions, reactors, network branches} |
‘r’ | Reaction (enthalpy of) or number of reactors |
‘r, A’ | Reaction enthalpy expressed per mole of A consumed |
‘ref’ | Reference (temperature) |
‘S’ | Summation (referred to specific heat) |
‘*’ | Refers to the network in the absence of a reaction |
‘0′ | Reference state (enthalpy) |
‘IG’ | Ideal gas |
‘Res’ | Residual quantity (with respect to the ideal-gas state) |
Appendix A. Detailed Development of Design Equations
Appendix A.1. Enthalpy and Flow Rate Expressions
Appendix A.2. Adiabatic-Stage Reactors with Recycle
Appendix A.2.1. Mass Balances
Mass Balance on the Mixing Nodes
Mass Balance on PFR
Mass Balance on CSTR
Appendix A.2.2. Energy Balances
Energy Balance on the Mixing Nodes
Energy Balance on PFR
Energy Balance on CSTR
Appendix A.3. Adiabatic-Stage Reactors with Split
Appendix A.3.1. Mass Balances
Mass Balance on the Mixing Nodes
Mass Balance on PFR
Mass Balance on CSTR
Appendix A.3.2. Energy Balances
Energy Balance on the Mixing Nodes
Energy Balance on PFR
Energy Balance on CSTR
Appendix A.4. Adiabatic-Stage Reactors Intercooled/Interheated by Reactants
Appendix A.4.1. Mass Balances
Mass Balance on the Mixing Nodes
Mass Balance on PFR
Mass Balance on CSTR
Appendix A.4.2. Energy Balances
Energy Balance on the Mixing Nodes
Energy Balance on PFR
Energy Balance on CSTR
Appendix A.5. Adiabatic-Stage Reactors with Distributed Interstage Feed
Appendix A.5.1. Mass Balances
Mass Balance on the Mixing Nodes
Mass Balance on PFR
Mass Balance on CSTR
Appendix A.5.2. Energy Balances
Energy Balance on the Mixing Nodes
Energy Balance on PFR
Energy Balance on CSTR
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Stoichiometric Table on the l-th Branch of the Network | ||
---|---|---|
Species i | Non-Reactive Case | Reactive Case |
A (limiting species) | ||
⁝ | ⁝ | ⁝ |
i | ||
⁝ | ⁝ | ⁝ |
Z |
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Caravella, A. Extended Definition of Conversion and Reaction Extent for a Systematic Development of the Design Equations for Reactor Networks. Processes 2024, 12, 107. https://doi.org/10.3390/pr12010107
Caravella A. Extended Definition of Conversion and Reaction Extent for a Systematic Development of the Design Equations for Reactor Networks. Processes. 2024; 12(1):107. https://doi.org/10.3390/pr12010107
Chicago/Turabian StyleCaravella, Alessio. 2024. "Extended Definition of Conversion and Reaction Extent for a Systematic Development of the Design Equations for Reactor Networks" Processes 12, no. 1: 107. https://doi.org/10.3390/pr12010107