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2010-10-16 13:38 |
Applied Parameter Estimation for Chemical Engineers
Hardcover: 462 pages Publisher: CRC Press; 1st edition (December 15, 2000) Language: English IN-10: 082479561X IN-13: 978-0824795610
Contents Preface v 1 Introduction 1 2 Formulation of the Parameter Estimation Problem 7 2.1 Structure of the Mathematical Model 7 2.1.1 Algebraic Equation Models 7 2.1.2 Differential Equation Models 11 2.2 The Objective Function 13 2.2.1 Explicit Estimation 14 2.2.1.1 Simple or Unweighted Least Squares (LS) Estimation 15 2.2.1.2 Weighted Least Squares (WLS) Estimation 15 2.2.1.3 Generalized Least Squares (GLS) Estimation 15 2.2.1.4 Maximum Likelihood (ML) Estimation 15 2.2.1.5 The Determinant Criterion 19 2.2.1.6 Incorporation of Prior Information About the Parameters 19 2.2.2 Implicit Estimation 19 2.3 Parameter Estimation Subject to Constraints 22 3 Computation of Parameters in Linear Models - Linear Regression 23 3.1 The Linear Regression Model 23 3.2 The Linear Least Squares Objective Function 26 3.3 Linear Least Squares Estimation 27 3.4 Polynomial Curve Fitting 29 3.5 Statistical Inferences 32 3.5.1 Inference on the Parameters 3 2 3.5.2 Inference on the Expected Response Variables 33 3.6 Solution of Multiple Linear Regression Problems 35 3.6.1 Procedure for Using Microsoft Excel™ for Windows 35 3.6.2 Procedure for Using SigmaPlot™ for Windows 42 3.7 Solution of Multiresponse Linear Regression Problems 46 3.8 Problems on Linear Regression 46 3.8.1 Vapor Pressure Data for Pyridine and Piperidine 46 3.8.2 Vapor Pressure Data for R142b and R152a 47 4.Gauss-Newton Method for Algebraic Models 49 4.1 Formulation of the Problem 49 4.2 The Gauss-Newton Method 50 4.2.1 Bisection Rule 52 4.2.2 Convergence Criteria 52 4.2.3 Formulation of the Solution Steps for the Gauss-Newton Method: Two Consecutive Chemical Reactions 53 4.2.4 Notes on the Gauss-Newton Method 55 4.3 Examples 55 4.3.1 Chemical Kinetics: Catalytic Oxidation of 3-Hexanol 55 4.3.2 Biological Oxygen Demand (BOD) 56 4.3.3 Numerical Example 1 57 4.3.4 Chemical Kinetics: Isomerization of Bicyclo [2,1,1] Hexane 58 4.3.5 Enzyme Kinetics 60 4.3.6 Catalytic Reduction of Nitric Oxide 61 4.3.7 Numerical Example 2 62 4.4 Solutions 64 4.4.1 Numerical Example 1 65 4.4.2 Numerical Example 2 66 5.Other Nonlinear Regression Methods for Algebraic Models 67 5.1 Gradient Minimization Methods 67 5.1.1 Steepest Descent Method 69 5.1.2 Newton's Method 71 5.1.3 Modified Newton's Method 76 5.1.4 Conjugate Gradient Methods 76 5.1.5 Quasi-Newton or Variable Metric or Secant Methods 77 5.2 Direct Search or Derivative Free Methods 78 5.2.1 LJ Optimization Procedure 79 5.2.2 Simplex Method 81 5.3 Exercises 83 6. Gauss-Newton Method for Ordinary Differential Equation (ODE) Models 84 6.1 Formulation of the Problem 84 6.2 The Gauss-Newton Method 85 6.2.1 Gauss-Newton Algorithm for ODE Models 88 6.2.2 Implementation Guidelines for ODE Models 88 6.3 The Gauss-Newton Method - Nonlinear Output Relationship 92 6.4 The Gauss-Newton Method - Systems with Unknown Initial Conditions 93 6.5 Examples 96 6.5.1 A Homogeneous Gas Phase Reaction 96 6.5.2 Pyrolytic Dehydrogenation of Benzene to Diphenyl and Triphenyl 98 6.5.3 Catalytic Hydrogenation of 3 -Hydroxyprop (HPA) to l,3-Propanediol(PD) 102 6.6 Equivalence of Gauss-Newton with Quasilinearization Method 111 6.6.1 The Quasilinearization Method and its Simplification 111 6.6.2 Equivalence to Gauss-Newton Method 114 6.6.3 Nonlinear Output Relationship 114 7 Shortcut Estimation Methods for ODE Models 115 7.1 ODE Models with Linear Dependence on the Parameters 115 7.1.1 Derivative Approach 116 7.1.2 Integral Approach 118 7.2 Generalization to ODE Models with Nonlinear Dependence on the Parameters 119 7.3 Estimation of Apparent Rates in Biological Systems 120 7.3.1 Derivative Approach 122 7.3.2 Integral Approach 123 7.4 Examples 129 7.4.1 Derivative Approach - Pyrolytic Dehydrogenation of Benzene 129 8. Practical Guidelines for Algorithm Implementation 133 8.1 Inspection of the Data 133 8.2 Generation of Initial Guesses 135 8.2.1 Nature and Structure of the Model 135 8.2.2 Asymptotic Behavior of the Model Equations 135 8.2.3 Transformation of the Model Equations 136 8.2.4 Conditionally Linear Systems 138 8.2.5 Direct Search Approach 139 8.3 Overstepping 139 8.3.1 An Optimal Step-Size Policy 140 8.4 Ill-Conditioning of Matrix A and Partial Remedies 141 8.4.1 Pseudoinverse 143 8.4.2 Marquardt's Modification 144 8.4.3 Scaling of Matrix A 145 8.5 Use of "Prior" Information 146 8.6 Selection of Weighting Matrix Q in Least Squares Estimation 147 8.7 Implementation Guidelines for ODE Models 148 8.7.1 Stiff ODE Models 148 8.7.2 Increasing the Region of Convergence 150 8.7.2.1 An Optimal Step-Size Policy 150 8.7.2.2 Use of the Information Index 152 8.7.2.3 Use of Direct Search Methods 155 8.8 Autocorrelation in Dynamic Systems 156 9. Constrained Parameter Estimation 158 9.1 Equality Constraints 158 9.1.1 Lagrange Multipliers 159 9.2 Inequality Constraints 162 9.2.1 Optimum Is Internal Point 162 9.2.1.1 Reparameterization 162 9.2.1.2 Penalty Function 163 9.2.1.3 Bisection Rule 165 9.2.2 The Kuhn-Tucker Conditions 165 10 Gauss-Newton Method for Partial Differential Equation (PDE) Models 167 10.1 Formulation of the Problem 167 10.2 The Gauss-Newton Method for PDE Models 169 10.3 The Gauss-Newton Method for Discretized PDE Models 172 10.3.1 Efficient Computation of the Sensitivity Coefficients 173 11 Statistical Inferences 177 11.1 Inferences on the Parameters 177 11.2 Inferences on the Expected Response Variables 179 11.3 Model Adequacy Tests 182 11.3.1 Single Response Models 182 11.3.2 Multivariate Models 184 12 Design of Experiments 185 12.1 Preliminary Experimental Design 185 12.2 Sequential Experimental Design for Precise Parameter Estimation 187 12.2.1 The Volume Design Criterion 188 12.2.2 The Shape Design Criterion 189 12.2.3 Implementation Steps 190 12.3 Sequential Experimental Design for Model Discrimination 191 12.3.1 The Divergence Design Criterion 192 12.3.2 Model Adequacy Tests for Model Discrimination 193 12.3.3 Implementation Steps for Model Discrimination 195 12.4 Sequential Experimental Design for ODE Systems 196 12.4.1 Selection of Optimal Sampling Interval and Initial State for Precise Parameter Estimation 196 12.4.2 Selection of Optimal Sampling Interval and Initial State for Model Discrimination 200 12.4.3 Determination of Optimal Inputs for Precise Parameter Estimation and Model Discrimination 200 12.5 Examples 202 12.5.1 Consecutive Chemical Reactions 202 12.5.2 Fed-batch Bioreactor 207 12.5.3 Chemostat Growth Kinetics 213 13 Recursive Parameter Estimation 218 13.1 Discrete Input-Output Models 218 13.2 Recursive Least Squares (RLS) 219 13.3 Recursive Extended Least Squares (RELS) 221 13.4 Recursive Generalized Least Squares (RGLS) 223 14 Parameter Estimation in Nonlinear Thermodynamic Models: Cubic Equations of State 226 14.1 Equations of State 226 14.1.1 Cubic Equations of State 227 14.1.2 Estimation of Interaction Parameters 229 14.1.3 Fugacity Expressions Using the Peng-Robinson EoS 230 14.1.4 Fugacity Expressions Using the Trebble-Bishnoi EoS 231 14.2 Parameter Estimation Using Binary VLB Data 231 14.2.1 Maximum Likelihood Parameter and State Estimation 232 14.2.2 Explicit Least Squares Estimation 233 14.2.3 Implicit Maximum Likelihood Parameter Estimation 234 14.2.4 Implicit Least Squares Estimation 236 14.2.5 Constrained Least Squares Estimation 236 14.2.5.1 Simplified Constrained Least Squares Estimation 237 14.2.5.2 A Potential Problem with Sparse or Not Well Distributed Data 238 14.2.5.3 Constrained Gauss-Newton Method for Regression of Binary VLB Data 240 14.2.6 A Systematic Approach for Regression of Binary VLB Data 242 14.2.7 Numerical Results 244 14.2.7.1 The n-Pentane-Acetone System 244 14.2.7.2 The Methane-Acetone System 245 14.2.7.3 The Nitrogen-Ethane System 246 14.2.7.4 The Methane-Methanol System 246 14.2.7.5 The Carbon Dioxide-Methanol System 246 14.2.7.6 The Carbon Dioxide-n-Hexane System 247 14.2.7.7 The Propane-Methanol System 248 14.2.7.8 The Diethylamine-Water System 250 14.3 Parameter Estimation Using the Entire Binary Phase Equilibrium Data 255 14.3.1 The Objective Function 255 14.3.2 Covariance Matrix of the Parameters 257 14.3.3 Numerical Results 258 14.3.3.1 The Hydrogen Sulfide-Water System 258 14.3.3.2 The Methane-n-Hexane System 259 14.4 Parameter Estimation Using Binary Critical Point Data 261 14.4.1 The Objective Function 261 14.4.2 Numerical Results 264 14.5 Problems 266 14.5.1 Data for the Methanol-Isobutane System 266 14.5.2 Data for the Carbon Dioxide-Cyclohexane System 266 15 Parameter Estimation in Nonlinear Thermodynamic Models: Activity Coefficients 268 15.1 Electrolyte Solutions 268 15.1.1 Pitzer's Model Parameters for Aqueous Na2SiO3 Solutions 268 15.1.2 Pitzer's Model Parameters for Aqueous Na2SiO3 - NaOH Solutions 270 15.1.3 Numerical Results 273 15.2 Non-Electrolyte Solutions 274 15.2.1 The Two-Parameter Wilson Model 276 15.2.2 The Three-Parameter NRTL Model 276 15.2.3 The Two-Parameter UNIQUAC Model 277 15.2.4 Parameter Estimation: The Objective Function 278 15.3 Problems 279 15.3.1 Ootic Coefficients for Aqueous Solutions of KC1 Obtained by the Isopiestic Method 279 15.3.2 Ootic Coefficients for Aqueous Solutions of High-Purity NiCl2 280 15.3.3 The Benzene (l)-i-Propyl Alcohol (2) System 281 15.3.4 Vapor-Liquid Equilibria of Coal-Derived Liquids: Binary Systems with Terralin 282 15.3.5 Vapor-Liquid Equilibria of Ethylbenzene (l)-o-Xylene (2) at 26.66 kPa 283 16 Parameter Estimation in Chemical Reaction Kinetic Models 285 16.1 Algebraic Equation Models 285 16.1.1 Chemical Kinetics: Catalytic Oxidation of 3-Hexanol 285 16.1.2 Chemical Kinetics: Isomerization of Bicyclo [2,1,1] Hexane 287 16.1.3 Catalytic Reduction of Nitric Oxide 288 16.2 Problems with Algebraic Models 295 16.2.1 Catalytic Dehydrogenation of sec-butyl Alcohol 295 16.2.2 Oxidation of Propylene 297 16.2.3 Model Reduction Through Parameter Estimation in the s-Domain 300 16.3 Ordinary Differential Equation Models 302 16.3.1 A Homogeneous Gas Phase Reaction 302 16.3.2 Pyrolytic Dehydrogenation of Benzene to Diphenyl and Triphenyl 303 16.3.3 Catalytic Hydrogenation of 3-Hydroxyprop (HPA) to l,3-Propanediol(PD) 307 16.3.4 Gas Hydrate Formation Kinetics 314 16.4 Problems with ODE Models 316 16.4.1 Toluene Hydrogenation 317 16.4.2 Methylester Hydrogenation 318 16.4.3 Catalytic Hydrogenation of 3-Hydroxyprop (HPA) to 1,3-Propanediol (PD) - Nonisothermal Data 320 17 Parameter Estimation in Biochemical Engineering Models 322 17.1 Algebraic Equation Models 322 17.1.1 Biological Oxygen Demand 322 17.1.2 Enzyme Kinetics 323 17.1.3 Determination of Mass Transfer Coefficient (kLa) in a Municipal Wastewater Treatment Plant (with PULSAR aerators) 327 17.1.4 Determination of Monoclonal Antibody Productivity in a Dialyzed Chemostat 330 17.2 Problems with Algebraic Equation Models 338 17.2.1 Effect of Glucose to Glutamine Ratio on MAb Productivity in a Chemostat 338 17.2.2 Enzyme Inhibition Kinetics 340 17.2.3 Determination of kLa in Bubble-free Bioreactors 341 17.3 Ordinary Differential Equation Models 344 17.3.1 Contact Inhibition in Microcarrier Cultures of MRC-5 Cells 344 17.4 Problems with ODE Models 347 17.4.1 Vero Cells Grown on Microcarriers (Contact Inhibition) 347 17.4.2 Effect of Temperature on Insect Cell Growth Kinetics 348 18 Parameter Estimation in Petroleum Engineering 353 18.1 Modeling of Drilling Rate Using Canadian Offshore Well Data 353 18.1.1 Application to Canadian Offshore Well Data 355 18.2 Modeling of Bitumen Oxidation and Cracking Kinetics Using Data from Alberta Oil Sands 358 18.2.1 Two-Component Models 358 18.2.2 Three-Component Models 359 18.2.3 Four-Component Models 362 18.2.4 Results and Discussion 364 18.3 Automatic History Matching in Reservoir Engineering 371 18.3.1 A Fully Implicit, Three Dimensional, Three-Phase Simulator with Automatic History-Matching Capability 371 18.3.2 Application to a Radial Coning Problem (Second SPE Comparative Solution Problem) 373 18.3.2.1 Matching Reservoir Pressure 373 18.3.2.2 Matching Water-Oil Ratio, Gas-Oil Ratio or Bottom Hole Pressure 374 18.3.2.3 Matching All Observed Data 374 18.3.3 A Three-Dimensional, Three-Phase Automatic History-Matching Model: Reliability of Parameter Estimates 376 18.3.3.1 Implementation and Numerical Results 378 18.3.4 Improved Reservoir Characterization Through Automatic History Matching 380 18.3.4.1 Incorporation of Prior Information and Constraints on the Parameters 382 18.3.4.2 Reservoir Characterization Using Automatic History Matching 384 18.3.5 Reliability of Predicted Well Performance Through Automatic History Matching 385 18.3.5.1 Quantification of Risk 388 18.3.5.2 Multiple Reservoir Descriptions 388 18.3.5.3 Case Study-Reliability of a Horizontal Well Performance 389 References 391 Appendix 1 403 A. 1.1 The Trebble-Bishnoi Equation of State 403 A. 1.2 Derivation of the Fugacity Expression 403 A. 1.3 Derivation of the Expression for (91nfj/3xj)TiPjX 405 Appendix 2 410 A.2.1 Listings of Computer Programs 410 A.2.2 Contents of Accompanying CD 411 A.2.3 Computer Program for Example 16.1.2 412 A.2.4 Computer Program for Example 16.3.2
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