Applied Parameter Estimation for Chemical Engineers

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ISBN: 9780824795610 | 082479561X
Cover: Hardcover
Copyright: 10/12/2000

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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.

Preface

Introduction

(6)

Formulation of the Parameter Estimation Problem

(16)

Structure of the Mathematical Model

(6)

Algebraic Equation Models

(4)

Differential Equation Models

(2)

The Objective Function

(9)

Explicit Estimation

(1)

Simple or Unweighted Least Squares (LS) Estimation

(1)

Weighted Least Squares (WLS) Estimation

(1)

Generalized Least Squares (GLS) Estimation

(1)

Maximum Likelihood (ML) Estimation

(4)

The Determinant Criterion

(1)

Incorporation of Prior Information About the Parameters

(1)

Implicit Estimation

(3)

Parameter Estimation Subject to Constraints

(1)

Computation of Parameters in Linear Models-Linear Regression

(26)

The Linear Regression Model

(3)

The Linear Least Squares Objective Function

(1)

Linear Least Squares Estimation

(2)

Polynomial Curve Fitting

(3)

Statistical Inferences

(3)

Inference on the Parameters

(1)

Inference on the Expected Response Variables

(2)

Solution of Multiple Linear Regression Problems

(11)

Procedure for Using Microsoft Excel™ for Windows

(7)

Procedure for Using SigmaPlot™ for Windows

(4)

Solution of Multiresponse Linear Regression Problems

(1)

Problems on Linear Regression

(3)

Vapor Pressure Data for Pyridine and Piperidine

(1)

Vapor Pressure Data for R142b and R152a

(2)

Gauss-Newton Method for Algebraic Models

(18)

Formulation of the Problem

(1)

The Gauss-Newton Method

(5)

Bisection Rule

(1)

Convergence Criteria

(1)

Formulation of the Solution Steps for the Gauss-Newton Method: Two Consecutive Chemical Reactions

(2)

Notes on the Gauss-Newton Method

(1)

Examples

(9)

Chemical Kinetics: Catalytic Oxidation of 3-Hexanol

(1)

Biological Oxygen Demand (BOD)

(1)

Numerical Example 1

(1)

Chemical Kinetics: Isomerization of Bicyclo [2,1,1] Hexane

(2)

Enzyme Kinetics

(1)

Catalytic Reduction of Nitric Oxide

(1)

Numerical Example 2

(2)

Solutions

(3)

Numerical Example 1

(1)

Numerical Example 2

(1)

Other Nonlinear Regression Methods for Algebraic Models

(17)

Gradient Minimization Methods

(11)

Steepest Descent Method

(2)

Newton's Method

(5)

Modified Newton's Method

(1)

Conjugate Gradient Methods

(1)

Quasi-Newton or Variable Metric or Secant Methods

(1)

Direct Search or Derivative Free Methods

(5)

LJ Optimization Procedure

(2)

Simplex Method

(2)

Exercises

(1)

Gauss-Newton Method for Ordinary Differential Equation (ODE) Models

(31)

Formulation of the Problem

(1)

The Gauss-Newton Method

(7)

Gauss-Newton Algorithm for ODE Models

(1)

Implementation Guidelines for ODE Models

(4)

The Gauss-Newton Method-Nonlinear Output Relationship

(1)

The Gauss-Newton Method-Systems with Unknown Initial Conditions

(3)

Examples

(15)

A Homogeneous Gas Phase Reaction

(2)

Pyrolytic Dehydrogenation of Benzene to Diphenyl and Triphenyl

(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

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Applied Parameter Estimation for Chemical Engineers

Summary

Author Biography

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Applied Parameter Estimation for Chemical Engineers

Summary

Author Biography

Table of Contents

Supplemental Materials

Digital License