Modeling of Combustion Systems: A Practical Approach

by Colannino; Joseph

• ISBN13: 9780849333651
• ISBN10: 0849333652
• Format: Hardcover
• Copyright: 2006-03-24
• Publisher: CRC Press

Summary

Increasing competitive pressure for improved quality and efficiency on one hand and tightening emissions and operating requirements on the other leave the modern process engineer squeezed in the middle. While effective modeling can help balance these demands, the current literature offers overly theoretical treatments on modeling that do not translate quickly and easily to the immediate needs of the practicing engineer.Based on more than a quarter-century of experience, Modeling of Combustion Systems: A Practical Approach introduces an approach to semi-empirical combustion modeling for better control, optimization, prediction, and description of industrial combustion processes. First, the author provides an introduction to modeling, the basic model categories, and analytical methods followed by an introduction to combustion that includes equipment and mathematical modeling. Next, he introduces the concepts and procedures of experimental design and provides detailed discussion on how to analyze non-ideal data.The final chapter draws together the previous information to clearly demonstrate the construction of semi-empirical models. Fully worked examples and step-by-step derivations support the discussion along the way, and the book also includes a complete guide to nomenclature and supplies appendices for important physical and chemical properties, conversions, statistical tables, and much more.Modeling of Combustion Systems: A Practical Approach provides concrete answers to real problems and is tailor-made to suit the needs of practicing engineers.

Table of Contents

List of Tables
List of Figures
Concordance of Nomenclature
About the Author
Prologue
Introduction to Modeling	1	(100)
Model Categories	1	(3)
Model Validation	2	(1)
Fundamental Theoretical Models	2	(1)
Simulations	2	(1)
Semiempirical Models	3	(1)
Dimensionless Models	3	(1)
Empirical Models	3	(1)
Problems with Post Hoc Models	4	(1)
Kinds of Testing	4	(1)
No Physical Testing	4	(1)
Scale Testing	5	(1)
Full-Scale Testing	5	(1)
Analytical Methods	5	(18)
Qualitative Analysis	6	(2)
Dimensional Analysis	8	(1)
Raleigh's Method	9	(2)
Cautions Regarding Dimensional Analysis	11	(4)
Function Shape Analysis	15	(3)
The Method of Partial Fractions	18	(4)
Limitations of Function Shape Analysis	22	(1)
Perceiving Higher Dimensionality	23	(6)
A View from Flatland	23	(1)
Contour Surfaces	24	(2)
Orthogonal Directions	26	(1)
Visualization with Cubic Regions	26	(2)
The Use of Color	28	(1)
Basic Data Classifications	29	(6)
Level of Scale	29	(3)
Data Quality	32	(1)
Planned Experiments	32	(1)
Unplanned Experiments	33	(1)
Source Classifications	33	(1)
Functional Classifications	33	(2)
A Linear Algebra Primer	35	(20)
Matrix Addition	35	(1)
The Transpose Operator	36	(1)
Multiplication by a Constant	37	(1)
Matrix Multiplication	37	(1)
Distributive Property of Multiplication over Addition	38	(1)
Symmetric Matrices	39	(1)
The Identity Matrix	40	(1)
The Unity, Zero, and Constant Vectors	41	(1)
The Inverse	42	(1)
Elementary Row Operations	42	(3)
Solving for the Inverse	45	(1)
The Determinant	46	(1)
Orthogonality	47	(5)
Eigenvalues and Eigenvectors	52	(3)
Important Concepts and Notation	55	(7)
Summation and Matrix Notation	55	(1)
Converting between Summation and Matrix Notation	56	(1)
Averages: Mean, Mode, and Median	57	(1)
Various Means and the Generalized Mean	58	(4)
Least Squares	62	(31)
The Method of Least Squares	62	(3)
The Method of Least Squares: The Calculus	65	(4)
Least Squares for Continuous Intervals	69	(3)
Least Squares as a Filter	72	(3)
A Misconception about Least Squares	75	(1)
Transforming Equations for Least Squares Fitting of the Parameters	75	(2)
Constrained Polynomials	77	(3)
Orthogonal Polynomials	80	(3)
General Definition of Orthogonal Polynomials	83	(7)
Discrete MOPs and Real Data	90	(3)
Addendum	93	(8)
Proof That M0 Reduces to the Geometric Mean	93	(2)
Proof of the Monotonicity of Mp	95	(3)
Proof That Mp Approaches xmax as P → ∞	98	(1)
Proof That Mp Approaches xmin as P → ∞	99	(1)
Proof xmin ≤ Mp ≤ xmax for x > 0	99	(1)
Proof That Mp Increases with Increasing p and the Converse	99	(1)
References	100	(1)
Introduction to Combustion	101	(90)
General Overview	102	(21)
The Burner	102	(1)
The Fuel System	103	(1)
About Fuels	104	(1)
Fuel Metering	105	(1)
Turndown	105	(1)
The Air System	106	(2)
The Flame Holder	108	(1)
Stabilizing and Shaping the Flame	108	(1)
Controlling Emissions	109	(1)
Archetypical Burners	109	(2)
Round-Flame Gas Diffusion Burners	111	(1)
Round-Flame Gas Premix Burners	111	(2)
Flat-Flame Gas Diffusion Burners	113	(1)
Flat-Flame Premix Burners	114	(1)
Flashback	115	(1)
Use of Secondary Fuel and Air	115	(1)
Round Combination Burners	116	(3)
Burner Orientations	119	(1)
Upfired	119	(1)
Downfired	120	(1)
Side-Fired	121	(1)
Balcony Fired	121	(1)
Combination Side and Floor Firing	121	(2)
Archetypical Process Units	123	(4)
Boilers	123	(1)
Firetube Boilers	123	(1)
Watertube Boilers	123	(1)
Fired Heaters and Reactors	123	(1)
Vertical Cylindrical	124	(1)
Cabin Style	124	(2)
Fired Reactors	126	(1)
Hydrogen Reformers	126	(1)
Ammonia Reformers	126	(1)
Ethylene Cracking Units (ECUs)	127	(1)
Important Factors and Responses	127	(8)
The Traditional Test Protocol	127	(1)
Instability, Thermoacoustic and Otherwise	128	(1)
Quarter-Wave Behavior	129	(2)
Half-Wave Behavior	131	(1)
Helmholtz Resonator Behavior	131	(1)
Mechanism for Thermoacoustic Coupling	132	(1)
Comments Regarding Thermoacoustic Resonance	133	(1)
Resonance in the Field	134	(1)
Mass Balance for Combustion in Air	135	(29)
Wet vs. Dry Measurements	137	(1)
Flue Gas Relations for Hydrocarbons	137	(3)
Accounting for Moisture	140	(3)
Addition of Molecular Hydrogen to the Fuel	143	(2)
Addition of Flue Gas Components to Fuel	145	(3)
Substoichiometric Combustion	148	(1)
Lead-Lag Control	148	(1)
Substoichiometric Equations	148	(6)
Conservation of Mass for Flow in a Furnace	154	(1)
Simplifying Assumptions (SAs)	155	(3)
Ideal Gas Law	158	(1)
Dilution Correction	159	(5)
Conservation of Energy	164	(9)
Heat and Related Quantities	164	(1)
Work	165	(1)
Heating Value	166	(1)
Adiabatic Flame Temperature	167	(2)
Heat Capacity as a Function of Temperature	169	(2)
Adiabatic Flame Temperature with Preheated Air	171	(2)
Mechanical Energy Balance	173	(18)
Work Terms	173	(1)
Theoretical Mechanical Models	174	(1)
Units of Pressure	174	(1)
Natural Draft Model	175	(1)
Draft Pressure in a Furnace	175	(2)
Air Velocity Due to Natural Draft	177	(1)
Airflow through a Diffusion Burner	177	(5)
Airflow through Adjustable Dampers	182	(1)
Unknown Damper Characteristics	183	(1)
Fuel Flow as a Function of Pressure	184	(1)
Compressible Flow	185	(1)
The Fuel Capacity Curve Revisited	186	(2)
Airflow in Premix Burners	188	(1)
Gas Jets Entraining Flue Gas	189	(1)
References	189	(2)
Experimental Design and Analysis	191	(102)
Some Statistics	192	(11)
Statistics and Distributions	193	(1)
The Normal, Chi-Squared (X2), F, and t Distributions	194	(1)
The Normal Distribution	195	(1)
Probability Distribution for Galton's Board	196	(1)
Pascal's Triangle	197	(3)
The Chi-Squared Distribution	200	(1)
The F Distribution	201	(1)
The t Distribution	202	(1)
The Analysis of Variance (ANOVA)	203	(6)
Use of the F Distribution	206	(3)
Two-Level Factorial Designs	209	(25)
ANOVA for Several Model Effects	211	(1)
General Features of Factorial Designs	212	(1)
Construction Details of the Two-Level Factorial	213	(3)
Contrast of Factorial and Classical Experimentation	216	(3)
Statistical Properties of Classical Experimentation	219	(2)
How Factorial Designs Estimate Coefficients	221	(1)
The Sneaky Farmer	222	(7)
Interpretation of the Coefficients	229	(3)
Using Higher-Order Effects to Estimate Experimental Error	232	(1)
Normal Probability Plots for Estimating Residual Effects	232	(2)
Correspondence of Factor Space and Equation Form	234	(6)
Fractional Factorials	240	(5)
The Half Fraction	241	(1)
Quarter and Higher Fractions	242	(3)
ANOVA with Genuine Replicates	245	(15)
Bias Error	248	(2)
Center-Point Replicates	250	(1)
Degrees of Freedom Entries	251	(3)
Sum-of-Squares Entries	254	(3)
Standard Errors and the t Test	257	(1)
The Value of Orthogonal Designs with ANOVA	258	(1)
Rotatability	259	(1)
Randomization	260	(3)
Hysteresis	260	(1)
Lurking Factors	261	(2)
About Residuals	263	(6)
Residuals vs. Run Order	263	(1)
Other Residual Plots	263	(1)
Full and Block Randomization	264	(1)
Blocking	265	(1)
Random vs. Fixed Effects	265	(4)
Screening Designs	269	(6)
Simplex Designs	269	(3)
Highly Fractionated Factorials	272	(2)
Foldover	274	(1)
Second-Order Designs	275	(11)
Central Composites	275	(2)
Quadratic Bias Only	277	(1)
Orthogonal Components	278	(2)
Adjusting the Axial Component	280	(3)
Box--Behnken Designs	283	(1)
Multilevel Factorials	283	(3)
Sequential Experimental Design	286	(7)
Augmenting to Less Fractionated Factorials	287	(1)
Method of Steepest Ascent	287	(2)
Augmenting to Second-Order Designs	289	(2)
References	291	(2)
Analysis of Nonideal Data	293	(128)
Plant Data	294	(4)
Problem 1: Events Too Close in Time	294	(1)
Problem 2: Lurking Factors	295	(1)
Problem 3: Moving Average Processes	295	(2)
Some Diagnostics and Remedies	297	(1)
Historical Data and Serial Correlation	297	(1)
Empirical Models	298	(7)
Model Bias from an Incorrect Model Specification	301	(2)
Design Bias	303	(2)
Ways to Make Designs Orthogonal	305	(19)
Source and Target Matrices: Morphing Factor Space	306	(2)
Eigenvalues and Eigenvectors	308	(8)
Using Eigenvectors to Make Matrices Orthogonal	316	(2)
Canonical Forms	318	(1)
Derivation of A Canonical Form	318	(1)
Derivation of B Canonical Form	319	(1)
Canonical Form and Function Shape	320	(4)
Regression Statistics and Data Integrity	324	(24)
The Coefficient of Determination, r2	324	(1)
Overfit	325	(1)
Parsing Data into Model and Validation Sets	326	(1)
The Adjusted Coefficient of Determination, rA2	327	(1)
The PRESS Statistic	328	(1)
The Hat Matrix	329	(1)
The Coefficient of Determination, Predicted, r2p	330	(1)
Extrapolation	331	(5)
Failure to Detect Hidden Extrapolation	336	(1)
Collinearity	337	(2)
Reparameterization in Noncorrelated Factors	339	(3)
Variance Inflation Factor	342	(1)
Beta Coefficients	343	(3)
Confidence and Prediction Intervals	346	(2)
Residual Analyses	348	(1)
Categorical Factors	349	(34)
Multilevel Categorical Factors	349	(3)
Accounting for Multiple Blocks	352	(4)
Accounting for Hard-to-Change Factors	356	(1)
The Longest Duration Experimental Series	357	(1)
The Shortest Duration Experimental Series	358	(3)
Experimental Units	361	(1)
The Split-Plot Design	362	(5)
Expected Mean Squares (EMS)	367	(1)
Methodology for Deriving EMS for Balanced Data	367	(6)
EMS for the Factorial Design	373	(1)
EMS for a Split-Plot Design	374	(4)
Split-Plot Structure with Multiple Whole-Plot Factors	378	(5)
Nested Factors	383	(1)
Categorical Response Values	383	(3)
Conversion from Qualitative to Quantitative Measures	384	(1)
Using the Logit and Probit Functions to Categorize Flame Quality	385	(1)
Mixture Designs	386	(35)
Simplex-Centroid	388	(2)
Simplex-Lattice	390	(1)
Simplex-Axial	391	(1)
Generalizing to Higher Dimensions	392	(3)
Fuels of Many Components	395	(1)
Fuel Chemistry	395	(1)
Hydrogen	396	(1)
Hydrocarbon Chemistry	396	(1)
Bonding	397	(1)
Saturates	397	(2)
Olefins	399	(1)
Coke Formation	399	(1)
Mono-Olefins	400	(1)
Di-Olefins	400	(1)
Acetylenes	401	(1)
Aromatic Hydrocarbons	401	(1)
Cyclo Hydrocarbons	402	(1)
Representing Gaseous Fuel Blends	402	(1)
Chemical Bond Method	403	(4)
Equivalent Oxygen Method	407	(1)
Component Ranges	408	(2)
Pseudo-Components	410	(1)
Orthogonal Mixture Designs	410	(1)
Ratios of Mixture Fractions	411	(2)
Combining Mixture and Factorial Designs	413	(1)
Mixtures within Factorial	414	(1)
Mixture within Fractional Factorial	414	(1)
Fractionated Mixture within Fractional Factorial	415	(5)
References	420	(1)
Semiempirical Models	421	(110)
NOx and Kinetics	422	(21)
NOx: Some General Comments	422	(1)
The Thermal NOx Mechanism	422	(2)
The Fuel-Bound Nitrogen Mechanism	424	(2)
The Prompt NOx Mechanism	426	(1)
Chemical Kinetic Effects for NOx in Diffusion Flames	427	(1)
NOx Response to Air in Diffusion Flames	427	(5)
Dimensional Units for NOx	432	(2)
The Relation of Referent and Objective Forms	434	(1)
NOx Response to Temperature in Diffusion Flames	435	(3)
NOx Response to Fuel Composition	438	(1)
Chemical NOx When Prompt NOx Is Important	439	(1)
Chemical Kinetic Effects for NOx in Premixed Flames	440	(1)
NOx Response to Temperature in Premixed Flames	440	(1)
NOx Response to Air in Premixed Burners	440	(1)
Solving for δ as a Function of αw	441	(1)
Solving for T as a Function of αw	441	(1)
Log NOx as a Function of αw	442	(1)
Overview of NOx Reduction Strategies	443	(15)
Low Excess Air (LEA) Operation	443	(2)
Air Staging	445	(1)
Overfire Air	445	(1)
Burners out of Service (BOOS)	446	(1)
Fuel Staging	446	(1)
Fuel Blending	447	(1)
Flue Gas Recirculation	447	(1)
Mass-Based Relations	447	(3)
Molar and Volumetric Definitions	450	(3)
Fuel Dilution, Flue Gas Inducted Recirculation (FIR)	453	(3)
Steam or Water Injection	456	(1)
Selective Noncatalytic Reduction (SNCR)	456	(1)
Selective Catalytic Reduction (SCR)	457	(1)
NOx Models	458	(19)
Categorization of Emissions Reduction Strategies	460	(1)
Temperature Reduction Strategies	460	(1)
Fuel Blending or Fuel Dilution	460	(1)
Flue Gas Inducted Recirculation	460	(1)
Flue Gas Recirculation	461	(1)
Steam or Water Injection	462	(1)
Air Staging	462	(5)
Fuel Staging	467	(1)
Overfire Air	467	(2)
Burners out of Service	469	(1)
Concentration Reduction Strategies	469	(1)
Low Excess Air (LEA) Operation	469	(1)
Air Staging with Fuel-Bound Nitrogen	470	(1)
Fuel Staging with Fuel-Bound Nitrogen	471	(1)
Reagent Injection Strategies	471	(1)
Selective Noncatalytic Reduction (SNCR)	471	(5)
Selective Catalytic Reduction (SCR)	476	(1)
Limestone Injection	476	(1)
CO Models	477	(6)
Cold CO	478	(1)
Hot CO	479	(1)
General Behavior of Hot CO	479	(2)
Equilibrium Considerations	481	(2)
Arrested Oxidation of CO (via Ammoniacal Poisoning of OH Catalysis)	483	(1)
Response Transformations	483	(3)
Empirical Considerations for Transformation of the CO Response	483	(3)
Empirical Considerations for Transformation of NOx Response	486	(1)
Heat Flux	486	(29)
Heat Flux Profile	487	(2)
The Normalized Heat Flux Equation	489	(2)
Data Normalization	491	(1)
Data Smoothing	492	(5)
Renormalization	497	(3)
The Heat Flux Model	500	(1)
Heat Flux as a Function of Furnace Temperatures	500	(3)
Qualitative Behavior of zmax	503	(3)
The Effect of Air Preheat	506	(1)
The Effect of Air/Fuel Ratio	507	(1)
The Effect of Fuel Pressure	507	(2)
Heat Flux Profile in Terms of Fractional Heat Release	509	(2)
The Effect of the Heat Sink (Process)	511	(1)
Final Heat Flux and Process Efficiency	512	(1)
Run Length and Flux Profile Curvature	512	(1)
Factors Affecting the Initial Heat Flux	513	(2)
Similarity and Scaling of Heat Flux Curves	515	(1)
Flame Shape	515	(6)
Flame Measurements	516	(1)
Flame Length	517	(4)
Visible Plumes	521	(10)
Bisulfite Plumes	521	(1)
Ammonium Chloride Plumes	522	(2)
Sulfur Oxides	524	(1)
Equations for Dew Point Elevation	525	(3)
References	528	(3)
Epilogue	531	(1)
References	532	(87)
Appendices
A. Fuel and Combustion Properties	533	(22)
B. Mechanical Properties	555	(18)
C. Units Conversions	573	(4)
D. Properties of the Elements	577	(24)
E. Statistical Tables	601	(8)
F. Numbers in Binary, Octal, and Hexadecimal Representations	609	(4)
G. Kinetics Primer	613	(4)
H. Equilibrium Primer	617	(2)
Index	619