Parametric Sensitivity in Chemical Systems

by Arvind Varma , Massimo Morbidelli , Hua Wu

• ISBN13: 9780521019842
• ISBN10: 0521019842
• Format: Paperback
• Copyright: 2005-09-15
• Publisher: Cambridge University Press

Summary

The behavior of a chemical system is affected by many physicochemical parameters. The sensitivity of the system's behavior to changes in parameters is known as parametric sensitivity. When a system operates in a parametrically sensitive region, its performance becomes unreliable and changes sharply with small variations in parameters. Thus, it would be of great value to predict sensitivity behavior in chemical systems. This book is the first to provide a thorough treatment of the concept of parametric sensitivity and the mathematical tool it generated, sensitivity analysis. The emphasis is on applications to real situations. The book begins with definitions of various sensitivity indices and describes the numerical techniques used for their evaluation. Extensively illustrated chapters discuss sensitivity analysis in a variety of chemical reactors - batch, tubular, continuous-flow, fixed-bed - and in combustion systems, air pollution, and metabolic processes. Chemical engineers, chemists, graduate students, and researchers will welcome this valuable resource.

Table of Contents

Preface	xv
Introduction	1	(8)
The Concept of Sensitivity	1	(4)
Uses of the Sensitivity Concept	5	(2)
Overview of the Book Contents	7	(2)
References	8	(1)
Introduction to Sensitivity Analysis	9	(27)
Sensitivity Indices	9	(8)
Local Sensitivity	9	(2)
Example 2.1 Conversion sensitivity in a batch reactor	11	(2)
Objective Sensitivity	13	(1)
Example 2.2 Sensitivity of the maximum yield in an isothermal batch reactor with consecutive reactions	14	(2)
Global Sensitivity	16	(1)
Computation of Sensitivity Indices	17	(19)
Local Sensitivity	17	(1)
Example 2.3 Sensitivity analysis of an isothermal batch reactor with consecutive reactions of arbitrary order	18	(6)
Global Sensitivity	24	(8)
Nomenclature	32	(1)
References	33	(3)
Thermal Explosion in Batch Reactors	36	(44)
Basic Equations	37	(1)
Geometry-Based Criteria for Thermal Runaway	38	(17)
The Case of Negligible Reactant Consumption: Semenov Theory	38	(5)
Example 3.1 Application of Semenov criterion to thermal explosion of methyl nitrate	43	(1)
Criteria Accounting for Reactant Consumption	44	(9)
Example 3.2 Application of AE and VF criteria to thermal explosion of methyl nitrate	53	(2)
Sensitivity-Based Criteria for Thermal Runaway	55	(15)
The Morbidelli and Varma (MV) Criterion	56	(7)
Example 3.3 Application of the MV criterion to catalytic hydrolysis of acetic anhydride	63	(1)
The Vajda and Rabitz (VR) Criterion	64	(3)
Example 3.4 A comparison between various criteria in predicting explosion limits in azomethane decomposition	67	(2)
The Strozzi and Zaldivar (SZ) Criterion	69	(1)
Explicit Criteria for Thermal Runaway	70	(10)
Nomenclature	76	(1)
References	77	(3)
Runaway in Tubular Reactors	80	(63)
Basic Equations for Tubular Plug-Flow Reactors	81	(2)
Plug-Flow Reactors with Constant External Cooling	83	(18)
Runaway Criteria	83	(2)
Example 4.1 Runaway behavior in the naphthalene oxidation reactor	85	(4)
The Region of Pseudo-Adiabatic Operation (PAO)	89	(5)
Influence of PAO on the Runaway Region	94	(6)
Example 4.2 Runaway behavior in a naphthalene oxidation reactor operating in the pseudo-adiabatic operation region	100	(1)
Plug-Flow Reactors Varying Coolant Temperature	101	(10)
The Regions of Pseudo-Adiabatic Operation	101	(3)
Influence of PAO on Runaway Regions	104	(7)
Role of Radial Temperature and Concentration Gradients	111	(5)
Complex Kinetic Schemes	116	(27)
The Case of Two Consecutive Reactions (A → B → C)	119	(11)
Example 4.3 Reactor operation diagram for naphthalene oxidation process	130	(2)
The Case of Two Parallel Reactions (A → B → C)	132	(3)
Example 4.4 Reactor operation diagram for ethylene epoxidation process	135	(3)
Nomenclature	138	(2)
References	140	(3)
Parametric Sensitivity in Continuous-Flow Stirred Tank Reactors	143	(26)
Sensitivity Analysis	144	(8)
Regions of Parametrically Sensitive Behavior	152	(7)
Role of the Involved Physicochemical Parameters	152	(5)
Relation between Multiplicity and Sensitivity Behavior	157	(2)
Role of Mixing on Reactor Parametric Sensitivity	159	(4)
Explicit Criteria for Parametric Sensitivity	163	(6)
Nomenclature	166	(1)
References	167	(2)
Runaway in Fixed-Bed Catalytic Reactors	169	(51)
The Heterogeneous Model of a Fixed-Bed Catalytic Reactor	170	(2)
Runaway of a Single Catalyst Particle: Local Runaway	172	(17)
Critical Conditions for Local Runaway of Particle Temperature	173	(6)
Runaway Regions	179	(10)
Runaway of Fixed-Bed Reactors: Global Runaway	189	(24)
Critical Conditions for Global Runaway of Particle Temperature	189	(3)
Runaway Regions	192	(4)
Example 6.1 Experimental analysis of runaway in a fixed-bed reactor for vinyl acetate synthesis	196	(7)
Example 6.2 Experimental analysis of runaway in a fixed-bed reactor for carbon monoxide oxidation	203	(2)
Limiting Behavior	205	(1)
Example 6.3 Runaway regions in the case of severe intraparticle mass transfer resistance	206	(2)
Effect of Pseudo-Adiabatic Operation on Runaway Regions	208	(5)
Explicit Criteria for Runaway	213	(7)
Nomenclature	216	(2)
References	218	(2)
Parametric Sensitivity and Ignition Phenomena in Combustion Systems	220	(27)
General Definition of Ignition Limits	221	(3)
Explosion Limits in Hydrogen-Oxygen Mixtures	224	(10)
Application of the Sensitivity Criterion	224	(7)
Comparison between Experimental and Calculated Explosion Limits	231	(3)
Further Insight into Explosion Behavior in Hydrogen-Oxygen Mixtures	234	(13)
Explosion in the Low Pressure Region	235	(8)
Explosion in the High Pressure Region	243	(1)
References	244	(3)
Sensitivity Analysis in Mechanistic Study and Model Reduction	247	(40)
Sensitivity Analysis in Mechanistic Studies	248	(25)
Applications of the Green's Function Method	249	(1)
Example 8.1 Oxidation of wet carbon monoxide	250	(4)
Example 8.2 Sensitivity analysis of the Belousov-Zhabotinsky oscillating reaction	254	(5)
Applications of the Finite Difference Method	259	(1)
Example 8.3 Explosion mechanism in hydrogen-oxygen systems: The first limit	260	(5)
Example 8.4 Explosion mechanism in hydrogen-oxygen systems: The second limit	265	(4)
Example 8.5 Explosion mechanism in hydrogen-oxygen systems: The third limit	269	(2)
Example 8.6 Explosion mechanism in hydrogen-oxygen systems: The weak-strong explosion boundaries (WSEB)	271	(2)
Reduction of Detailed Kinetic Models	273	(14)
Example 8.7 Minimum reduced kinetic model for the explosion limits of hydrogen-oxygen systems	274	(6)
Example 8.8 Reduced kinetic model for the combustion of methane-ethane systems	280	(4)
References	284	(3)
Sensitivity Analysis in Air Pollution	287	(25)
Basic Equations	288	(2)
Sensitivity Analysis of Regional Air Quality with Respect to Emission Sources	290	(12)
Definition of Sensitivities	290	(2)
A Case Study: Emissions of NOx and SO2 in the Eastern United States	292	(10)
Global Sensitivity Analysis of Trajectory Model for Photochemical Air Pollution	302	(10)
Global Sensitivities and the FAST Method	302	(1)
A Case Study: Emissions of NO, NO2, Reactive Hydrocarbons and O3	303	(7)
References	310	(2)
Sensitivity Analysis in Metabolic Processes	312	(23)
The General Approach for Sensitivity Analysis	313	(7)
Mathematical Framework	313	(4)
A Case Study: The Yeast Glycolytic Pathway	317	(3)
The Matrix Method from Metabolic Control Theory	320	(15)
Model Framework	322	(2)
A Case Study: The Metabolic Pathway of Gluconeogenesis from Lactate	324	(4)
Some Useful Theorems for Sensitivity Analysis	328	(2)
Nomenclature	330	(1)
References	331	(4)
Author Index	335	(4)
Subject Index	339