Energy Optimization in Process Systems (eBook)

Front cover 1
Energy Optimization in Process Systems 4
Copyright 5
Contents 6
Preface 12
Acknowledgements 20
Chapter 1: Brief review of static optimization methods 21
1.1. Introduction: Signifi cance of Mathematical Models 21
1.2. Unconstrained Problems 24
1.3. Equality Constraints and Lagrange Multipliers 27
1.4. Methods of Mathematical Programming 31
1.5. Iterative Search Methods 33
1.6. On Some Stochastic Optimization Techniques 37
Chapter 2: Dynamic optimization problems 65
2.1. Discrete Representations and Dynamic Programming Algorithms 65
2.2. Recurrence Equations 67
2.3. Discrete Processes Linear with Respect to the Time Interval 71
2.4. Discrete Algorithm of the Pontryagin's Type for Processes Linear in èN 75
2.5. Hamilton-Jacobi-Bellman Equations for Continuous Systems 78
2.6. Continuous Maximum Principle 90
2.7. Calculus of Variations 93
2.8. Viscosity Solutions and Non-smooth Analyses 96
2.9. Stochastic Control and Stochastic Maximum Principle 104
Chapter 3: Energy limits for thermal engines and heat-pumps at steady states 105
3.1. Introduction: Role of Optimization in Determining Thermodynamic Limits 105
3.2. Classical Problem of Thermal Engine Driven by Heat Flux 110
3.3. Toward Work Limits in Sequential Systems 129
3.4. Energy Utilization and Heat-pumps 132
3.5. Thermal Separation Processes 136
3.6. Steady Chemical, Electrochemical and Other Systems 137
3.7. Limits in Living Systems 143
3.8. Final Remarks 144
Chapter 4: Hamiltonian optimization of imperfect cascades 147
4.1. Basic Properties of Irreversible Cascade Operations with a Work Flux 147
4.2. Description of Imperfect Units in Terms of Carnot Temperature Control 152
4.3. Single-stage Formulae in a Model of Cascade Operation 158
4.4. Work Optimization in Cascade by Discrete Maximum Principle 161
4.5. Example 175
4.6. Continuous Imperfect System with Two Finite Reservoirs 177
4.7. Final Remarks 184
Chapter 5: Maximum power from solar energy 187
5.1. Introducing Carnot Controls for Modeling Solar-assisted Operations 187
5.2. Thermodynamics of Radiation 195
5.3. Classical Exergy of Radiation 200
5.4. Flux of Classical Exergy 204
5.5. Effi ciencies of Energy Conversion 206
5.6. Towards a Dissipative Exergy of Radiation at Flow 207
5.7. Basic Analytical Formulae of Steady Pseudo-Newtonian Model 210
5.8. Steady Non-Linear Models applying Stefan-Boltzmann Equation 212
5.9. Dynamical Theory for Pseudo-Newtonian Models 215
5.10. Dynamical Models using the Stefan-Boltzmann Equation 224
5.11. Towards the Hamilton-Jacobi-Bellman Approaches 231
5.12. Final Remarks 232
Chapter 6: Hamilton-Jacobi-Bellman theory of energy systems 235
6.1. Introduction 235
6.2. Dynamic Optimization of Power in a Finite-resource Process 236
6.3. Two Different Works and Finite-Rate Exergies 239
6.4. Some Aspects of Classical Analytical HJB Theory for Continuous Systems 243
6.5. HJB Equations for Non-Linear Power Generation Systems 245
6.6. Analytical Solutions in Systems with Linear Kinetics 247
6.7. Extensions for Systems with Non-Linear Kinetics and Internal Dissipation 250
6.8. Generalized Exergies for Non-Linear Systems with Minimum Dissipation 252
6.9. Final Remarks 255
Chapter 7: Numerical optimization in allocation, storage and recovery of thermal energy and resources 257
7.1. Introduction 257
7.2. A Discrete Model for a Non-Linear Problem of Maximum Power from Radiation 259
7.3. Non-Constant Hamiltonians and Convergence of Discrete DP Algorithms to Viscosity Solutions of HJB Equations 260
7.4. Dynamic Programming Equation for Maximum Power From Radiation 269
7.5. Discrete Approximations and Time Adjoint as a Lagrange Multiplier 270
7.6. Mean and Local Intensities in Discrete Processes 277
7.7. Legendre Transform and Original Work Function 279
7.8. Numerical Approaches Applying Dynamic Programming 281
7.9. Dimensionality Reduction in Dynamic Programming Algorithms 285
7.10. Concluding Remarks 287
Chapter 8: Optimal control of separation processes 291
8.1. General Thermokinetic Issues 291
8.2. Thermodynamic Balances toward Minimum Heat or Work 293
8.3. Results for Irreversible Separations Driven by Work or Heat 299
8.4. Thermoeconomic Optimization of Thermal Drying with Fluidizing Solids 302
8.5. Solar Energy Application to Work-Assisted Drying 332
8.6. Concluding Remarks 340
Chapter 9: Optimal decisions for chemical and electrochemical reactors 341
9.1. Introduction 341
9.2. Driving Forces in Transport Processes and Chemical Reactions 341
9.3. General Non-Linear Equations of Macrokinetics 344
9.4. Classical Chemical and Electrochemical Kinetics 345
9.5. Inclusion of Non-Linear Transport Phenomena 347
9.6. Continuous Description of Chemical (Electrochemical) Kinetics and Transport Phenomena 349
9.7. Towards Power Production in Chemical Systems 351
9.8. Thermodynamics of Power Generation in Non-Isothermal Chemical Engines 354
9.9. Non-Isothermal Engines in Terms of Carnot Variables 358
9.10. Entropy Production in Steady Systems 360
9.11. Dissipative Availabilities in Dynamical Systems 361
9.12. Characteristics of Steady Isothermal Engines 363
9.13. Sequential Models for Dynamic Power Generators 371
9.14. A Computational Algorithm for Dynamical Process with Power Maximization 375
9.15. Results of Computations 378
9.16. Some Additional Comments 379
9.17. Comparison of Chemical and Thermal Operations of Power Production 380
9.18. Fuel Cell Application 381
9.19. Final Remarks 385
Chapter 10: Energy limits and evolution in biological systems 387
10.1. Introduction 387
10.2. Energy and Size Limits 388
10.3. Toward a Quantitative Description of Development and Evolution of Species 395
10.4. Signifi cance of Complexity and Entropy 398
10.5. Evolutions of Multiple Organs without Mutations 401
10.6. Organisms with Mutations or Specializations of Organs 403
10.7. A Variational Approach to the Dynamics of Evolution 404
10.8. Concluding Remarks 408
Chapter 11: Systems theory in thermal & chemical engineering
11.1. Introduction 411
11.2. System Energy Analyses 412
11.3. Mathematical Modeling of Industrial Energy Management 412
11.4. Linear Model of the Energy Balance for an Industrial Plant and its Applications 415
11.5. Non-Linear Mathematical Model of a Short-Term Balance of Industrial Energy System 419
11.6. Mathematical Optimization Model for the Preliminary Design of Industrial Energy Systems 421
11.7. Remarks on Diverse Methodologies and Link with Ecological Criteria 426
11.8. Control Thermodynamics for Explicitly Dynamical Systems 432
11.9. Interface of Energy Limits, Structure Design, Thermoeconomics and Ecology 434
11.10. Towards the Thermoeconomics and Integration of Heat Energy 445
Chapter 12: Heat integration within process integration 447
Chapter 13: Maximum heat recovery and its consequences for process system design 457
13.1. Introduction and Problem Formulation 457
13.2. Composite Curve (CC) Plot 459
13.3. Problem Table (PR-T) Method 466
13.4. Grand Composite Curve (GCC) Plot 470
13.5. Special Topics in MER/MUC Calculations 474
13.6. Summary and Further Reading 478
Chapter 14: Targeting and supertargeting in heat exchanger network design 481
14.1. Targeting Stage in Overall Design Process 481
14.2. Basis of Sequential Approaches for HEN Targeting 482
14.3. Basis of Simultaneous Approaches for HEN Targeting 487
Chapter 15: Minimum utility cost (MUC) target by optimization approaches 489
15.1. Introduction and MER Problem Solution by Mathematical Programming 489
15.2. MUC Problem Solution Methods 492
15.3. Dual Matches 505
15.4. Minimum Utility Cost under Disturbances 508
Chapter 16: Minimum number of units (MNU) and minimum total surface area (MTA) targets 515
16.1. Introduction 515
16.2. Minimum Number of Matches (MNM) Target 516
16.3. Minimum Total Area for Matches (MTA-M) Target 535
16.4. Minimum Number of Shells (MNS) Target 541
16.5. Minimum Total Area for Shells (MTA-S) Target 545
Chapter 17: Simultaneous HEN targeting for total annual cost 553
Chapter 18: Heat exchanger network synthesis 567
18.1. Introduction 567
18.2. Sequential Approaches 568
18.3. Simultaneous Approaches to HEN Synthesis 586
Chapter 19: Heat exchanger network retrofi t 603
19.1. Introduction 603
19.2. Network Pinch Method 606
19.3. Simultaneous Approaches for HEN Retrofi t 616
Chapter 20: Approaches to water network design 633
20.1. Introduction 633
20.2. Mathematical Models and Data for Water Network Problem 637
20.3. Overview of Approaches in the Literature 641
References 679
Glossary of symbols 745
Index 755