Energy Optimization in Process Systems and Fuel Cells

1. Brief review of static optimization methods

1.1 Introduction: significance of mathematical models

1.2 Unconstrained problems

1.3 Equality constraints and lagrange multipliers

1.4 Methods of mathematical programming

1.5 Iterative search methods

1.6 On some stochastic optimization techniques

2. Dynamic optimization problems

2.1 Discrete representations and dynamic programming algorithms

2.2 Recurrence equations

2.3 Discrete processes linear with respect to the time interval

2.4 Discrete algorithm of Pontryagin’s type for processes linear in θN

2.5 Hamilton–Jacobi–Bellman equations for continuous systems

2.6 Continuous Maximum Principle

2.7 Calculus of variations

2.8 Viscosity solutions and nonsmooth analyses

2.9 Stochastic control and stochastic Maximum Principle

3. Energy limits for thermal engines and heat pumps at steady states

3.1 Introduction: role of optimization in determining thermodynamic limits

3.2 Classical problem of thermal engine driven by heat flux

3.3 Toward work limits in sequential systems

3.4 Energy utilization and heat pumps

3.5 Thermal separation processes

3.6 Steady chemical, electrochemical, and other systems

3.7 Limits in living systems

3.8 Final remarks

4. Hamiltonian optimization of imperfect cascades

4.1 Basic properties of irreversible cascade operations with a work flux

4.2 Description of imperfect units in terms of carnot temperature control

4.3 Single-stage formulae in a model of cascade operation

4.4 Work optimization in cascade by discrete maximum principle

4.5 Example

4.6 Continuous imperfect system with two finite reservoirs

4.7 Final remarks

5. Maximum power from solar energy

5.1 Introducing Carnot controls for modeling solar-assisted operations

5.2 Thermodynamics of radiation

5.3 Classical exergy of radiation

5.4 Flux of classical exergy

5.5 Efficiencies of energy conversion

5.6 Towards a dissipative exergy of radiation at flow

5.7 Basic analytical formulae of steady pseudo-Newtonian model

5.8 Steady nonlinear models applying Stefan–Boltzmann equation

5.9 Dynamical theory for pseudo-Newtonian models

5.10 Dynamical models using the Stefan–Boltzmann equation

5.11 Towards the Hamilton–Jacobi–Bellman approaches

5.12 Final remarks

6. Hamilton–Jacobi–Bellman theory of energy systems

6.1 Introduction

6.2 Dynamic optimization of power in a finite-resource process

6.3 Two different works and finite-rate exergies

6.4 Some aspects of classical analytical HJB theory for continuous systems

6.5 HJB equations for nonlinear power generation systems

6.6 Analytical solutions in systems with linear kinetics

6.7 Extensions for systems with nonlinear kinetics and internal dissipation

6.8 Generalized exergies for nonlinear systems with minimum dissipation

6.9 Final remarks

7. Numerical optimization in allocation, storage and recovery of thermal energy and resources

7.1 Introduction

7.2 A discrete model for a nonlinear problem of maximum power from radiation

7.3 Nonconstant Hamiltonians and convergence of discrete DP algorithms to viscosity solutions of HJB equations

7.4 Dynamic programming equation for maximum power from radiation

7.5 Discrete approximations and time adjoint as a Lagrange multiplier

7.6 Mean and local intensities in discrete processes

7.7 Legendre transform and original work function

7.8 Numerical approaches applying dynamic programming

7.9 Dimensionality reduction in dynamic programming algorithms

7.10 Concluding remarks

8. Optimal control of separation processes

8.1 General thermokinetic issues

8.2 Thermodynamic balances toward minimum heat or work

8.3 Results for irreversible separations driven by work or heat

8.4 Thermoeconomic optimization of thermal drying with fluidizing solids

8.5 Solar energy application to work-assisted drying

8.6 Concluding Remarks

9. Optimal decisions for chemical reactors

9.1 Introduction

9.2 Driving forces in transport processes and chemical reactions

9.3 General nonlinear equations of macrokinetics

9.4 Classical chemical and electrochemical kinetics

9.5 Inclusion of nonlinear transport phenomena

9.6 Continuous description of chemical (electrochemical) kinetics and transport phenomena

9.7 Toward power production in chemical systems

9.8 Thermodynamics of power generation in nonisothermal chemical engines

9.9 Nonisothermal engines in terms of carnot variables

9.10 Entropy production in steady systems

9.11 Dissipative availabilities in dynamic systems

9.12 Characteristics of steady isothermal engines

9.13 Sequential models for dynamic power generators

9.14 A computational algorithm for dynamic process with power maximization

9.15 Results of computations

9.16 Some additional comments

9.17 Complex chemical power systems with internal dissipation

10. Fuel cells and limiting performance of electrochemobiological systems

10.1 Introduction

10.2 Electrochemical engines

10.3 Thermodynamics of entropy production and power limits in fuel cells

10.4 Calculation of operational voltage

10.5 Thermodynamic account of current-dependent and current-independent imperfections

10.6 Evaluation of mass flows, power output, and efficiency

10.7 Quality characteristics and feasibility criteria

10.8 Some experimental results

10.9 Assessing power limits in steady thermoelectrochemical engines

10.10 Hybrid systems

10.11 Unsteady states, dynamic units, and control problems

10.12 Biological fuel cells and biological sources of hydrogen

10.13 Energy and size limits for living organisms in biological systems

10.14 A brief commentary on development and evolution of species

11. Systems theory in thermal and chemical engineering

11.1 Introduction

11.2 System energy analyses

11.3 Mathematical modeling of industrial energy management

11.4 Linear model of the energy balance for an industrial plant and its applications

11.5 Nonlinear mathematical model of short-term balance of industrial energy system

11.6 Mathematical optimization model for the preliminary design of industrial energy systems

11.7 Remarks on diverse methodologies and link with ecological criteria

11.8 Control thermodynamics for explicitly dynamical systems

11.9 Interface of energy limits, structure design, thermoeconomics and ecology

11.10 Towards the thermoeconomics and integration of heat energy

12. Heat integration within process integration

13. Maximum heat recovery and its consequences for process system design

13.1 Introduction and problem formulation

13.2 Composite curve (CC) plot

13.3 Problem table (Pr-T) method

13.4 Grand composite curve (GCC) plot

13.5 Special topics in MER/MUC calculations

13.6 Summary and further reading

14. Targeting and supertargeting in heat exchanger network design

14.1 Targeting stage in overall design process

14.2 Basis of sequential approaches for HEN targeting

14.3 Basis of simultaneous approaches for HEN targeting

15. Minimum utility cost (MUC) target by optimization approaches

15.1 Introduction and MER problem solution by mathematical programming

15.2 MUC problem solution methods

15.3 Dual matches

15.4 Minimum utility cost under disturbances

16. Minimum number of units (MNU) and minimum total surface area (MTA) targets

16.1 Introduction

16.2 Minimum number of matches (MNM) target

16.3 Minimum total area for matches (MTA-m) target

16.4 Minimum number of shells (MNS) target

16.5 Minimum total area for shells (MTA-s) target

17. Simultaneous HEN targeting for total annual cost

TAC-Transp model

18. Heat exchanger network synthesis

18.1 Introduction

18.2 Sequential approaches

18.3 Simultaneous approaches to HEN synthesis

19. Heat exchanger network retrofit

19.1 Introduction

19.2 Network pinch method

19.3 Simultaneous approaches for HEN retrofit

20. Approaches to water network design

20.1 Introduction

20.2 Mathematical models and data for water network problem

20.3 Overview of approaches in the literature