Knopf - Modeling, Analysis and Optimization of Process and Energy Systems

Preface xiii

Conversion Factors xvii

List of Symbols xix

1. Introduction to Energy Usage, Cost, and Efficiency 1

1.1 Energy Utilization in the United States 1

1.2 The Cost of Energy 1

1.3 Energy Efficiency 4

1.4 The Cost of Self-Generated versus Purchased Electricity 10

1.5 The Cost of Fuel and Fuel Heating Value 11

1.6 Text Organization 12

1.7 Getting Started 15

1.8 Closing Comments 16

References 16

Problems 17

2. Engineering Economics with VBA Procedures 19

2.1 Introduction to Engineering Economics 19

2.2 The Time Value of Money: Present Value (PV) and Future Value (FV) 19

2.3 Annuities 22

2.4 Comparing Process Alternatives 29

2.4.1 Present Value 31

2.4.2 Rate of Return (ROR) 31

2.4.3 Equivalent Annual Cost/Annual Capital Recovery Factor (CRF) 32

2.5 Plant Design Economics 33

2.6 Formulating Economics-Based Energy Optimization Problems 34

2.7 Economic Analysis with Uncertainty: Monte Carlo Simulation 36

2.8 Closing Comments 38

References 39

Problems 39

3. Computer-Aided Solutions of Process Material Balances: The Sequential Modular Solution Approach 42

3.1 Elementary Material Balance Modules 42

3.1.1 Mixer 43

3.1.2 Separator 43

3.1.3 Splitter 44

3.1.4 Reactors 45

3.2 Sequential Modular Approach: Material Balances with Recycle 46

3.3 Understanding Tear Stream Iteration Methods 49

3.3.1 Single-Variable Successive Substitution Method 49

3.3.2 Multidimensional Successive Substitution Method 50

3.3.3 Single-Variable Wegstein Method 52

3.3.4 Multidimensional Wegstein Method 53

3.4 Material Balance Problems with Alternative Specifications 58

3.5 Single-Variable Optimization Problems 61

3.5.1 Forming the Objective Function for Single-Variable Constrained Material Balance Problems 61

3.5.2 Bounding Step or Bounding Phase: Swann’s Equation 61

3.5.3 Interval Refinement Phase: Interval Halving 65

3.6 Material Balance Problems with Local Nonlinear Specifications 66

3.7 Closing Comments 68

References 69

Problems 70

4. Computer-Aided Solutions of Process Material Balances: The Simultaneous Solution Approach 76

4.1 Solution of Linear Equation Sets: The Simultaneous Approach 76

4.1.1 The Gauss–Jordan Matrix Elimination Method 76

4.1.2 Gauss–Jordan Coding Strategy for Linear Equation Sets 78

4.1.3 Linear Material Balance Problems: Natural Specifi cations 78

4.1.4 Linear Material Balance Problems: Alternative Specifications 82

4.2 Solution of Nonlinear Equation Sets: The Newton–Raphson Method 82

4.2.1 Equation Linearization via Taylor’s Series Expansion 82

4.2.2 Nonlinear Equation Set Solution via the Newton–Raphson Method 83

4.2.3 Newton–Raphson Coding Strategy for Nonlinear Equation Sets 86

4.2.4 Nonlinear Material Balance Problems: The Simultaneous Approach 90

References 92

Problems 93

5. Process Energy Balances 98

5.1 Introduction 98

5.2 Separator: Equilibrium Flash 101

5.2.1 Equilibrium Flash with Recycle: Sequential Modular Approach 103

5.3 Equilibrium Flash with Recycle: Simultaneous Approach 109

5.4 Adiabatic Plug Flow Reactor (PFR) Material and Energy Balances Including Rate Expressions: Euler’s First-Order Method 112

5.4.1 Reactor Types 112

5.5 Styrene Process: Material and Energy Balances with Reaction Rate 117

5.6 Euler’s Method versus Fourth-Order Runge–Kutta Method for Numerical Integration 121

5.6.1 The Euler Method: First-Order ODEs 121

5.6.2 RK4 Method: First-Order ODEs 122

5.7 Closing Comments 124

References 125

Problems 125

6. Introduction to Data Reconciliation and Gross Error Detection 132

6.1 Standard Deviation and Probability Density Functions 133

6.2 Data Reconciliation: Excel Solver 136

6.2.1 Single-Unit Material Balance: Excel Solver 136

6.2.2 Multiple-Unit Material Balance: Excel Solver 138

6.3 Data Reconciliation: Redundancy and Variable Types 138

6.4 Data Reconciliation: Linear and Nonlinear Material and Energy Balances 143

6.5 Data Reconciliation: Lagrange Multipliers 149

6.5.1 Data Reconciliation: Lagrange Multiplier Compact Matrix Notation 152

6.6 Gross Error Detection and Identification 154

6.6.1 Gross Error Detection: The Global Test (GT) Method 154

6.6.2 Gross Error (Suspect Measurement) Identification: The Measurement Test (MT) Method: Linear Constraints 155

6.6.3 Gross Error (Suspect Measurement) Identification: The Measurement Test Method: Nonlinear Constraints 156

6.7 Closing Remarks 158

References 158

Problems 158

7. Gas Turbine Cogeneration System Performance, Design, and Off-Design Calculations: Ideal Gas Fluid Properties 164

7.1 Equilibrium State of a Simple Compressible Fluid: Development of the T ds Equations 165

7.1.1 Application of the T ds Equations to an Ideal Gas 166

7.1.2 Application of the T ds Equations to an Ideal Gas: Isentropic Process 166

7.2 General Energy Balance Equation for an Open System 167

7.3 Cogeneration Turbine System Performance Calculations: Ideal Gas Working Fluid 167

7.3.1 Compressor Performance Calculations 167

7.3.2 Turbine Performance Calculations 168

7.4 Air Basic Gas Turbine Performance Calculations 169

7.5 Energy Balance for the Combustion Chamber 172

7.5.1 Energy Balance for the Combustion Chamber: Ideal Gas Working Fluid 172

7.6 The HRSG: Design Performance Calculations 173

7.6.1 HRSG Design Calculations: Exhaust Gas Ideal and Water-Side Real Properties 176

7.7 Gas Turbine Cogeneration System Performance with Design HRSG 177

7.7.1 HRSG Material and Energy Balance Calculations Using Excel Callable Sheet Functions 179

7.8 HRSG Off-Design Calculations: Supplemental Firing 180

7.8.1 HRSG Off-Design Performance: Overall Energy Balance Approach 180

7.8.2 HRSG Off-Design Performance: Overall Heat Transfer Coefficient Approach 181

7.9 Gas Turbine Design and Off-Design Performance 185

7.9.1 Gas Turbines Types and Gas Turbine Design Conditions 185

7.9.2 Gas Turbine Design and Off-Design Using Performance Curves 186

7.9.3 Gas Turbine Internal Mass Flow Patterns 186

7.9.4 Industrial Gas Turbine Off-Design (Part Load) Control Algorithm 188

7.9.5 Aeroderivative Gas Turbine Off-Design (Part Load) Control Algorithm 189

7.9.6 Off-Design Performance Algorithm for Gas Turbines 189

7.10 Closing Remarks 193

References 194

Problems 194

8. Development of a Physical Properties Program for Cogeneration Calculations 198

8.1 Available Function Calls for Cogeneration Calculations 198

8.2 Pure Species Thermodynamic Properties 202

8.3 Derivation of Working Equations for Pure Species Thermodynamic Properties 207

8.4 Ideal Mixture Thermodynamic Properties: General Development and Combustion Reaction Considerations 209

8.4.1 Ideal Mixture 209

8.4.2 Changes in Enthalpy and Entropy 209

8.5 Ideal Mixture Thermodynamic Properties: Apparent Difficulties 211

8.6 Mixing Rules for EOS 213

8.7 Closing Remarks 215

References 216

Problems 216

9. Gas Turbine Cogeneration System Performance, Design, and Off-Design Calculations: Real Fluid Properties 222

9.1 Cogeneration Gas Turbine System Performance Calculations: Real Physical Properties 223

9.1.1 Air Compressor (AC) Performance Calculation 224

9.1.2 Energy Balance for the Combustion Chamber (CC) 224

9.1.3 C Functions for Combustion Temperature and Exhaust Gas Physical Properties 224

9.1.4 Gas and Power Turbine (G&PT) Performance Calculations 229

9.1.5 Air Preheater (APH) 230

9.2 HRSG: Design Performance Calculations 230

9.3 HRSG Off-Design Calculations: Supplemental Firing 232

9.3.1 HRSG Off-Design Performance: Overall Energy Balance Approach 233

9.3.2 HRSG Off-Design Performance: Overall Heat Transfer Coefficient Approach 234

9.4 Gas Turbine Design and Off-Design Performance 235

9.5 Closing Remarks 237

References 238

Problems 238

10. Gas Turbine Cogeneration System Economic Design Optimization and Heat Recovery Steam Generator Numerical Analysis 243

10.1 Cogeneration System: Economy of Scale 244

10.2 Cogeneration System Confi guration: Site Power-to-Heat Ratio 244

10.3 Economic Optimization of a Cogeneration System: The CGAM Problem 245

10.3.1 The Objective Function: Cogeneration System Capital and Operating Costs 246

10.3.2 Optimization: Variable Selection and Solution Strategy 248

10.3.3 Process Constraints 249

10.4 Economic Design Optimization of the CGAM Problem: Ideal Gas 249

10.4.1 Air Preheater (APH) Equations 249

10.4.2 CGAM Problem Physical Properties 249

10.5 The CGAM Cogeneration Design Problem: Real Physical Properties 250

10.6 Comparing CogenD and General Electric’s GateCycle™ 253

10.7 Numerical Solution of HRSG Heat Transfer Problems 254

10.7.1 Steady-State Heat Conduction in a One-Dimensional Wall 254

10.7.2 Unsteady-State Heat Conduction in a One-Dimensional Wall 255

10.7.3 Steady-State Heat Conduction in the HRSG 259

10.8 Closing Remarks 266

References 267

Problems 267

11. Data Reconciliation and Gross Error Detection in a Cogeneration System 272

11.1 Cogeneration System Data Reconciliation 272

11.2 Cogeneration System Gross Error Detection and Identification 278

11.3 Visual Display of Results 281

11.4 Closing Comments 281

References 282

Problems 283

12. Optimal Power Dispatch in a Cogeneration Facility 284

12.1 Developing the Optimal Dispatch Model 284

12.2 Overview of the Cogeneration System 286

12.3 General Operating Strategy Considerations 287

12.4 Equipment Energy Efficiency 287

12.4.1 Stand-Alone Boiler (Boiler 4) Performance (Based on Fuel Higher Heating Value (HHV)) 288

12.4.2 Electric Chiller Performance 289

12.4.3 Steam-Driven Chiller Performance 290

12.4.4 GE Air Cooler Chiller Performance 291

12.4.5 GE Gas Turbine Performance (Based on Fuel HHV) 294

12.4.6 GE Gas Turbine HRSG Boiler 8 Performance (Based on Fuel HHV) 295

12.4.7 GE Gas Turbine HRSG Boiler 8 Performance Supplemental Firing (Based on Fuel HHV) 296

12.4.8 Allison Gas Turbine Performance (Based on Fuel HHV) 296

12.4.9 Allison Gas Turbine HRSG Boiler 7 Performance (Based on Fuel HHV) 297

12.4.10 Allison Gas Turbine HRSG Boiler 7 Performance Supplemental Firing (Based on Fuel HHV) 297

12.5 Predicting the Cost of Natural Gas and Purchased Electricity 298

12.5.1 Natural Gas Cost 299

12.5.2 Purchased Electricity Cost 299

12.6 Development of a Multiperiod Dispatch Model for the Cogeneration Facility 302

12.7 Closing Comments 309

References 310

Problems 310

13. Process Energy Integration 314

13.1 Introduction to Process Energy Integration/Minimum Utilities 314

13.2 Temperature Interval/Problem Table Analysis with 0° Approach Temperature 316

13.3 The Grand Composite Curve (GCC) 317

13.4 Temperature Interval/Problem Table Analysis with “Real” Approach Temperature 318

13.5 Determining Hot and Cold Stream from the Process Flow Sheet 319

13.6 Heat Exchanger Network Design with Maximum Energy Recovery (MER) 324

13.6.1 Design above the Pinch 325

13.6.2 Design below the Pinch 327

13.7 Heat Exchanger Network Design with Stream Splitting 328

13.8 Heat Exchanger Network Design with Minimum Number of Units (MNU) 329

13.9 Software for Teaching the Basics of Heat Exchanger Network Design (Teaching Heat Exchanger Networks (THEN)) 331

13.10 Heat Exchanger Network Design: Distillation Columns 331

13.11 Closing Remarks 336

References 336

Problems 337

14. Process and Site Utility Integration 343

14.1 Gas Turbine-Based Cogeneration Utility System for a Processing Plant 343

14.2 Steam Turbine-Based Utility System for a Processing Plant 353

14.3 Site-Wide Utility System Considerations 356

14.4 Closing Remarks 362

References 363

Problems 363

15. Site Utility Emissions 368

15.1 Emissions from Stoichiometric Considerations 369

15.2 Emissions from Combustion Equilibrium Calculations 370

15.2.1 Equilibrium Reactions 371

15.2.2 Combustion Chamber Material Balances 371

15.2.3 Equilibrium Relations for Gas-Phase Reactions/Gas-Phase Combustors 372

15.2.4 Equilibrium Compositions from Equilibrium Constants 376

15.3 Emission Prediction Using Elementary Kinetics Rate Expressions 380

15.3.1 Combustion Chemical Kinetics 380

15.3.2 Compact Matrix Notation for the Species Net Generation (or Production) Rate 381

15.4 Models for Predicting Emissions from Gas Turbine Combustors 382

15.4.1 Perfectly Stirred Reactor for Combustion Processes: The Material Balance Problem 382

15.4.2 The Energy Balance for an Open System with Reaction (Combustion) 385

15.4.3 Perfectly Stirred Reactor Energy Balance 385

15.4.4 Solution of the Perfectly Stirred Reactor Material and Energy Balance Problem Using the Provided CVODE Code 386

15.4.5 Plug Flow Reactor for Combustion Processes: The Material Balance Problem 388

15.4.6 Plug Flow Reactor for Combustion Processes: The Energy Balance Problem 389

15.5 Closing Remarks 393

References 393

CVODE Tutorial 393

Problems 394

16. Coal-Fired Conventional Utility Plants with CO2 Capture (Design and Off-Design Steam Turbine Performance) 397

16.1 Power Plant Design Performance (Using Operational Data for Full-Load Operation) 398

16.1.1 Turbine System: Design Case (See Example 16.1.xls) 401

16.1.2 Extraction Flow Rates and Feedwater Heaters 402

16.1.3 Auxiliary Turbine/High-Pressure Feedwater Pump 402

16.1.4 Low-Pressure Feedwater Pump 403

16.1.5 Turbine Exhaust End Loss 403

16.1.6 Steam Turbine System Heat Rate and Performance Parameters 405

16.2 Power Plant Off-Design Performance (Part Load with Throttling Control Operation) 406

16.2.1 Initial Estimates for All Pressures and Effi ciencies: Sub Off_Design_Initial_Estimates ( ) 406

16.2.2 Modify Pressures: Sub Pressure_Iteration ( ) 406

16.2.3 Modify Effi ciencies: Sub Update Effi ciencies ( ) 408

16.3 Levelized Economics for Utility Pricing 409

16.4 CO2 Capture and Its Impact on a Conventional Utility Power Plant 413

16.5 Closing Comments 414

References 417

Problems 417

17. Alternative Energy Systems 419

17.1 Levelized Costs for Alternative Energy Systems 419

17.2 Organic Rankine Cycle (ORC): Determination of Levelized Cost 420

17.3 Nuclear Power Cycle 425

17.3.1 A High-Temperature Gas-Cooled Nuclear Reactor (HTGR) 425

References 427

Problems 427

Appendix. Bridging Excel and C Codes 429

A.1 Introduction 429

A.2 Working with Functions 431

A.3 Working with Vectors 434

A.4 Working with Matrices 442

A.4.1 Gauss–Jordan Matrix Elimination Method 442

A.4.2 Coding the Gauss–Jordan Matrix Elimination Method 443

A.5 Closing Comments 446

References 448

Tutorial 448

Microsoft C++ 2008 Express: Creating C Programs and DLLs 448

Index 458

Modeling, Analysis and Optimization of Process and Energy Systems

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