Applied Parameter Estimation for Chemical Engineers

by Englezos; Peter

• ISBN13: 9780824795610
• ISBN10: 082479561X
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-10-12
• Publisher: CRC Press

Summary

A reference and textbook providing readers with the most important optimization methods for parameter estimation in chemical engineering. The CD-ROM features Fortran computer programs for solving equation systems and other problems with Microsoft Excel and Sigma Plot. Contains over 900 equations in all.

Author Biography

Peter Englezos is Professor in the Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, Canada Nicolas Kalogerakis is Professor of Biochemical Engineering and Director of the Laboratory of Biochemical Engineering and Environmental Biotechnology, Department of Environmental Engineering, Technical University of Crete, Chania, Greece

Table of Contents

Preface	v
Introduction	1	(6)
Formulation of the Parameter Estimation Problem	7	(16)
Structure of the Mathematical Model	7	(6)
Algebraic Equation Models	7	(4)
Differential Equation Models	11	(2)
The Objective Function	13	(9)
Explicit Estimation	14	(1)
Simple or Unweighted Least Squares (LS) Estimation	15	(1)
Weighted Least Squares (WLS) Estimation	15	(1)
Generalized Least Squares (GLS) Estimation	15	(1)
Maximum Likelihood (ML) Estimation	15	(4)
The Determinant Criterion	19	(1)
Incorporation of Prior Information About the Parameters	19	(1)
Implicit Estimation	19	(3)
Parameter Estimation Subject to Constraints	22	(1)
Computation of Parameters in Linear Models-Linear Regression	23	(26)
The Linear Regression Model	23	(3)
The Linear Least Squares Objective Function	26	(1)
Linear Least Squares Estimation	27	(2)
Polynomial Curve Fitting	29	(3)
Statistical Inferences	32	(3)
Inference on the Parameters	32	(1)
Inference on the Expected Response Variables	33	(2)
Solution of Multiple Linear Regression Problems	35	(11)
Procedure for Using Microsoft Excel™ for Windows	35	(7)
Procedure for Using SigmaPlot™ for Windows	42	(4)
Solution of Multiresponse Linear Regression Problems	46	(1)
Problems on Linear Regression	46	(3)
Vapor Pressure Data for Pyridine and Piperidine	46	(1)
Vapor Pressure Data for R142b and R152a	47	(2)
Gauss-Newton Method for Algebraic Models	49	(18)
Formulation of the Problem	49	(1)
The Gauss-Newton Method	50	(5)
Bisection Rule	52	(1)
Convergence Criteria	52	(1)
Formulation of the Solution Steps for the Gauss-Newton Method: Two Consecutive Chemical Reactions	53	(2)
Notes on the Gauss-Newton Method	55	(1)
Examples	55	(9)
Chemical Kinetics: Catalytic Oxidation of 3-Hexanol	55	(1)
Biological Oxygen Demand (BOD)	56	(1)
Numerical Example 1	57	(1)
Chemical Kinetics: Isomerization of Bicyclo [2,1,1] Hexane	58	(2)
Enzyme Kinetics	60	(1)
Catalytic Reduction of Nitric Oxide	61	(1)
Numerical Example 2	62	(2)
Solutions	64	(3)
Numerical Example 1	65	(1)
Numerical Example 2	66	(1)
Other Nonlinear Regression Methods for Algebraic Models	67	(17)
Gradient Minimization Methods	67	(11)
Steepest Descent Method	69	(2)
Newton's Method	71	(5)
Modified Newton's Method	76	(1)
Conjugate Gradient Methods	76	(1)
Quasi-Newton or Variable Metric or Secant Methods	77	(1)
Direct Search or Derivative Free Methods	78	(5)
LJ Optimization Procedure	79	(2)
Simplex Method	81	(2)
Exercises	83	(1)
Gauss-Newton Method for Ordinary Differential Equation (ODE) Models	84	(31)
Formulation of the Problem	84	(1)
The Gauss-Newton Method	85	(7)
Gauss-Newton Algorithm for ODE Models	88	(1)
Implementation Guidelines for ODE Models	88	(4)
The Gauss-Newton Method-Nonlinear Output Relationship	92	(1)
The Gauss-Newton Method-Systems with Unknown Initial Conditions	93	(3)
Examples	96	(15)
A Homogeneous Gas Phase Reaction	96	(2)
Pyrolytic Dehydrogenation of Benzene to Diphenyl and Triphenyl	98	(4)
Catalytic Hydrogenation of 3-Hydroxypropanal (HPA) to 1,3-Propanediol (PD)	102	(9)
Equivalence of Gauss-Newton with Quasilinearization Method	111	(4)
The Quasilinearization Method and its Simplification	111	(3)
Equivalence to Gauss-Newton Method	114	(1)
Nonlinear Output Relationship	114	(1)
Shortcut Estimation Methods for ODE Models	115	(18)
ODE Models with Linear Dependence on the Parameters	115	(4)
Derivative Approach	116	(2)
Integral Approach	118	(1)
Generalization to ODE Models with Nonlinear Dependence on the Parameters	119	(1)
Estimation of Apparent Rates in Biological Systems	120	(9)
Derivative Approach	122	(1)
Integral Approach	123	(6)
Examples	129	(4)
Derivative Approach-Pyrolytic Dehydrogenation of Benzene	129	(4)
Practical Guidelines for Algorithm Implementation	133	(25)
Inspection of the Data	133	(2)
Generation of Initial Guesses	135	(4)
Nature and Structure of the Model	135	(1)
Asymptotic Behavior of the Model Equations	135	(1)
Transformation of the Model Equations	136	(2)
Conditionally Linear Systems	138	(1)
Direct Search Approach	139	(1)
Overstepping	139	(2)
An Optimal Step-Size Policy	140	(1)
III-Conditioning of Matrix A and Partial Remedies	141	(5)
Pseudoinverse	143	(1)
Marquardt's Modification	144	(1)
Scaling of Matrix A	145	(1)
Use of ``Prior'' Information	146	(1)
Selection of Weighting Matrix Q in Least Squares Estimation	147	(1)
Implementation Guidelines for ODE Models	148	(8)
Stiff ODE Models	148	(2)
Increasing the Region of Convergence	150	(1)
An Optimal Step-Size Policy	150	(2)
Use of the Information Index	152	(3)
Use of Direct Search Methods	155	(1)
Autocorrelation in Dynamic Systems	156	(2)
Constrained Parameter Estimation	158	(9)
Equality Constraints	158	(4)
Lagrange Multipliers	159	(3)
Inequality Constraints	162	(5)
Optimum Is Internal Point	162	(1)
Reparameterization	162	(1)
Penalty Function	163	(2)
Bisection Rule	165	(1)
The Kuhn-Tucker Conditions	165	(2)
Gauss-Newton Method for Partial Differential Equation (PDE) Models	167	(10)
Formulation of the Problem	167	(2)
The Gauss-Newton Method for PDE Models	169	(3)
The Gauss-Newton Method for Discretized PDE Models	172	(5)
Efficient Computation of the Sensitivity Coefficients	173	(4)
Statistical Inferences	177	(8)
Inferences on the Parameters	177	(2)
Inferences on the Expected Response Variables	179	(3)
Model Adequacy Tests	182	(3)
Single Response Models	182	(2)
Multivariate Models	184	(1)
Design of Experiments	185	(33)
Preliminary Experimental Design	185	(2)
Sequential Experimental Design for Precise Parameter Estimation	187	(4)
The Volume Design Criterion	188	(1)
The Shape Design Criterion	189	(1)
Implementation Steps	190	(1)
Sequential Experimental Design for Model Discrimination	191	(5)
The Divergence Design Criterion	192	(1)
Model Adequacy Tests for Model Discrimination	193	(2)
Implementation Steps for Model Discrimination	195	(1)
Sequential Experimental Design for ODE Systems	196	(6)
Selection of Optimal Sampling Interval and Initial State for Precise Parameter Estimation	196	(4)
Selection of Optimal Sampling Interval and Initial State for Model Discrimination	200	(1)
Determination of Optimal Inputs for Precise Parameter Estimation and Model Discrimination	200	(2)
Examples	202	(16)
Consecutive Chemical Reactions	202	(5)
Fed-batch Bioreactor	207	(6)
Chemostat Growth Kinetics	213	(5)
Recursive Parameter Estimation	218	(8)
Discrete Input-Output Models	218	(1)
Recursive Least Squares (RLS)	219	(2)
Recursive Extended Least Squares (RELS)	221	(2)
Recursive Generalized Least Squares (RGLS)	223	(3)
Parameter Estimation in Nonlinear Thermodynamic Models: Cubic Equations of State	226	(42)
Equations of State	226	(5)
Cubic Equations of State	227	(2)
Estimation of Interaction Parameters	229	(1)
Fugacity Expressions Using the Peng-Robinson EoS	230	(1)
Fugacity Expressions Using the Trebble-Bishnoi EoS	231	(1)
Parameter Estimation Using Binary VLE Data	231	(24)
Maximum Likelihood Parameter and State Estimation	232	(1)
Explicit Least Squares Estimation	233	(1)
Implicit Maximum Likelihood Parameter Estimation	234	(2)
Implicit Least Squares Estimation	236	(1)
Constrained Least Squares Estimation	236	(1)
Simplified Constrained Least Squares Estimation	237	(1)
A Potential Problem with Sparse or Not Well Distributed Data	238	(2)
Constrained Gauss-Newton Method for Regression of Binary VLE Data	240	(2)
A Systematic Approach for Regression of Binary VLE Data	242	(2)
Numerical Results	244	(1)
The n-Pentane-Acetone System	244	(1)
The Methane-Acetone System	245	(1)
The Nitrogen-Ethane System	246	(1)
The Methane-Methanol System	246	(1)
The Carbon Dioxide-Methanol System	246	(1)
The Carbon Dioxide-n-Hexane System	247	(1)
The Propane-Methanol System	248	(2)
The Diethylamine-Water System	250	(5)
Parameter Estimation Using the Entire Binary Phase Equilibrium Data	255	(6)
The Objective Function	255	(2)
Covariance Matrix of the Parameters	257	(1)
Numerical Results	258	(1)
The Hydrogen Sulfide-Water System	258	(1)
The Methane-n-Hexane System	259	(2)
Parameter Estimation Using Binary Critical Point Data	261	(5)
The Objective Function	261	(3)
Numerical Results	264	(2)
Problems	266	(2)
Data for the Methanol-Isobutane System	266	(1)
Data for the Carbon Dioxide-Cyclohexane System	266	(2)
Parameter Estimation in Nonlinear Thermodynamic Models: Activity Coefficients	268	(17)
Electrolyte Solutions	268	(6)
Pitzer's Model Parameters for Aqueous Na2SiO3 Solutions	268	(2)
Pitzer's Model Parameters for Aqueous Na2SiO3-NaOH Solutions	270	(3)
Numerical Results	273	(1)
Non-Electrolyte Solutions	274	(5)
The Two-Parameter Wilson Model	276	(1)
The Three-Parameter NRTL Model	276	(1)
The Two-Parameter UNIQUAC Model	277	(1)
Parameter Estimation: The Objective Function	278	(1)
Problems	279	(6)
Osmotic Coefficients for Aqueous Solutions of KCI Obtained by the Isopiestic Method	279	(1)
Osmotic Coefficients for Aqueous Solutions of High-Purity NiCl2	280	(1)
The Benzene (1)-i-Propyl Alcohol (2) System	281	(1)
Vapor-Liquid Equilibria of Coal-Derived Liquids: Binary Systems with Tetralin	282	(1)
Vapor-Liquid Equilibria of Ethylbenzene (1)-o-Xylene (2) at 26.66 kPa	283	(2)
Parameter Estimation in Chemical Reaction Kinetic Models	285	(37)
Algebraic Equation Models	285	(10)
Chemical Kinetics: Catalytic Oxidation of 3-Hexanol	285	(2)
Chemical Kinetics: Isomerization of Bicyclo [2,1,1] Hexane	287	(1)
Catalytic Reduction of Nitric Oxide	288	(7)
Problems with Algebraic Models	295	(7)
Catalytic Dehydrogenation of sec-butyl Alcohol	295	(2)
Oxidation of Propylene	297	(3)
Model Reduction Through Parameter Estimation in the s-Domain	300	(2)
Ordinary Differential Equation Models	302	(14)
A Homogeneous Gas Phase Reaction	302	(1)
Pyrolytic Dehydrogenation of Benzene to Diphenyl and Triphenyl	303	(4)
Catalytic Hydrogenation of 3-Hydroxypropanal (HPA) to 1,3-Propanediol (PD)	307	(7)
Gas Hydrate Formation Kinetics	314	(2)
Problems with ODE Models	316	(6)
Toluene Hydrogenation	317	(1)
Methylester Hydrogenation	318	(2)
Catalytic Hydrogenation of 3-Hydroxypropanal (HPA) to 1,3-Propanediol (PD)-Nonisothermal Data	320	(2)
Parameter Estimation in Biochemical Engineering Models	322	(31)
Algebraic Equation Models	322	(16)
Biological Oxygen Demand	322	(1)
Enzyme Kinetics	323	(4)
Determination of Mass Transfer Coefficient (kLa) in a Municipal Wastewater Treatment Plant (with PULSAR aerators)	327	(3)
Determination of Monoclonal Antibody Productivity in a Dialyzed Chemostat	330	(8)
Problems with Algebraic Equation Models	338	(6)
Effect of Glucose to Glutamine Ratio on MAb Productivity in a Chemostat	338	(2)
Enzyme Inhibition Kinetics	340	(1)
Determination of kLa in Bubble-free Bioreactors	341	(3)
Ordinary Differential Equation Models	344	(3)
Contact Inhibition in Microcarrier Cultures of MRC-5 Cells	344	(3)
Problems with ODE Models	347	(6)
Vero Cells Grown on Microcarriers (Contact Inhibition)	347	(1)
Effect of Temperature on Insect Cell Growth Kinetics	348	(5)
Parameter Estimation in Petroleum Engineering	353	(38)
Modeling of Drilling Rate Using Canadian Offshore Well Data	353	(5)
Application to Canadian Offshore Well Data	355	(3)
Modeling of Bitumen Oxidation and Cracking Kinetics Using Data from Alberta Oil Sands	358	(13)
Two-Component Models	358	(1)
Three-Component Models	359	(3)
Four-Component Models	362	(2)
Results and Discussion	364	(7)
Automatic History Matching in Reservoir Engineering	371	(20)
A Fully Implicit, Three Dimensional, Three-Phase Simulator with Automatic History-Matching Capability	371	(2)
Application to a Radial Coning Problem (Second SPE Comparative Solution Problem)	373	(1)
Matching Reservoir Pressure	373	(1)
Matching Water-Oil Ratio, Gas-Oil Ratio or Bottom Hole Pressure	374	(1)
Matching All Observed Data	374	(2)
A Three-Dimensional, Three-Phase Automatic History-Matching Model: Reliability of Parameter Estimates	376	(2)
Implementation and Numerical Results	378	(2)
Improved Reservoir Characterization Through Automatic History Matching	380	(2)
Incorporation of Prior Information and Constraints on the Parameters	382	(2)
Reservoir Characterization Using Automatic History Matching	384	(1)
Reliability of Predicted Well Performance Through Automatic History Matching	385	(3)
Quantification of Risk	388	(1)
Multiple Reservoir Descriptions	388	(1)
Case Study-Reliability of a Horizontal Well Performance	389	(2)
References	391	(12)
Appendix 1	403	(7)
A.1.1 The Trebble-Bishnoi Equation of State	403	(1)
A.1.2 Derivation of the Fugacity Expression	403	(2)
A.1.3 Derivation of the Expression for (∂lnfj/∂xj) T,P,x	405	(5)
Appendix 2	410	(24)
A.2.1 Listings of Computer Programs	410	(1)
A.2.2 Contents of Accompanying CD	411	(1)
A.2.3 Computer Program for Example 16.1.2	412	(8)
A.2.4 Computer Program for Example 16.3.2	420	(14)
Index	434