modeling, analysis and

Modeling, Analysis and Optimization of Process and Energy Systems

Modeling, Analysis and Optimization of Process and Energy Systems

F. Carl KnopfLouisiana State UniversityBaton Rouge, LA

A JOHN WILEY & SONS, INC., PUBLICATION

Copyright © 2012 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Knopf, F. Carl, 1952- Modeling, analysis and optimization of process and energy systems / F. Carl Knopf. p. cm. Includes bibliographical references and index. ISBN 978-0-470-62421-0 (hardback) 1. Factories–Energy conservation. 2. Manufacturing industries–Energy conservation. 3. Industrial efficiency–Simulation methods. 4. Manufacturing processes–Evaluation. 5. Electric power-plants–Efficiency. I. Title. TJ163.5.F3K66 2012 658.2'6–dc23 2011015221

Printed in the United States of America.

10 9 8 7 6 5 4 3 2 1

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I dedicate this book to my wife Donna and our daughter Megan.

vii

Contents

Preface xiiiConversion Factors xviiList of Symbols xix

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

1.1 Energy Utilization in the United States 11.2 The Cost of Energy 11.3 Energy Efficiency 41.4 The Cost of Self-Generated versus Purchased

Electricity 101.5 The Cost of Fuel and Fuel Heating

Value 111.6 Text Organization 121.7 Getting Started 151.8 Closing Comments 16

References 16Problems 17

2. Engineering Economics with VBA Procedures 19

2.1 Introduction to Engineering Economics 192.2 The Time Value of Money: Present Value

(PV ) and Future Value (FV ) 192.3 Annuities 222.4 Comparing Process Alternatives 29

2.4.1 Present Value 312.4.2 Rate of Return (ROR) 312.4.3 Equivalent Annual Cost/Annual Capital

Recovery Factor (CRF) 322.5 Plant Design Economics 332.6 Formulating Economics-Based Energy

Optimization Problems 342.7 Economic Analysis with Uncertainty: Monte

Carlo Simulation 362.8 Closing Comments 38


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

3.1 Elementary Material Balance Modules 423.1.1 Mixer 433.1.2 Separator 433.1.3 Splitter 443.1.4 Reactors 45

3.2 Sequential Modular Approach: Material Balances with Recycle 46

3.3 Understanding Tear Stream Iteration Methods 493.3.1 Single-Variable Successive

Substitution Method 493.3.2 Multidimensional Successive

Substitution Method 503.3.3 Single-Variable Wegstein

Method 523.3.4 Multidimensional Wegstein

Method 533.4 Material Balance Problems with

Alternative Specifications 583.5 Single-Variable Optimization

Problems 613.5.1 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 68References 69Problems 70

viii Contents

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

4.1 Solution of Linear Equation Sets: The Simultaneous Approach 764.1.1 The Gauss–Jordan Matrix Elimination

Method 764.1.2 Gauss–Jordan Coding Strategy for Linear

Equation Sets 784.1.3 Linear Material Balance Problems:

Natural Specifications 784.1.4 Linear Material Balance Problems:

Alternative Specifications 824.2 Solution of Nonlinear Equation Sets: The

Newton–Raphson Method 824.2.1 Equation Linearization via Taylor’s Series

Expansion 824.2.2 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


5. Process Energy Balances 98

5.1 Introduction 985.2 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 1125.4.1 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 1215.6.1 The Euler Method: First-Order

ODEs 1215.6.2 RK4 Method: First-Order

ODEs 1225.7 Closing Comments 124


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 1366.2.1 Single-Unit Material Balance:

Excel Solver 1366.2.2 Multiple-Unit Material Balance: Excel

Solver 1386.3 Data Reconciliation: Redundancy and Variable

Types 1386.4 Data Reconciliation: Linear and Nonlinear

Material and Energy Balances 1436.5 Data Reconciliation: Lagrange

Multipliers 1496.5.1 Data Reconciliation: Lagrange

Multiplier Compact Matrix Notation 152

6.6 Gross Error Detection and Identification 1546.6.1 Gross Error Detection: The Global Test

(GT) Method 1546.6.2 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 158References 158Problems 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 1657.1.1 Application of the T ds Equations to an

Ideal Gas 1667.1.2 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 1677.3.1 Compressor Performance

Calculations 1677.3.2 Turbine Performance

Calculations 1687.4 Air Basic Gas Turbine Performance

Calculations 169

Contents ix

7.5 Energy Balance for the Combustion Chamber 1727.5.1 Energy Balance for the Combustion

Chamber: Ideal Gas Working Fluid 172

7.6 The HRSG: Design Performance Calculations 1737.6.1 HRSG Design Calculations: Exhaust Gas

Ideal and Water-Side Real Properties 176

7.7 Gas Turbine Cogeneration System Performance with Design HRSG 1777.7.1 HRSG Material and Energy Balance

Calculations Using Excel Callable Sheet Functions 179

7.8 HRSG Off-Design Calculations: Supplemental Firing 1807.8.1 HRSG Off-Design Performance: Overall

Energy Balance Approach 1807.8.2 HRSG Off-Design Performance: Overall

Heat Transfer Coefficient Approach 181

7.9 Gas Turbine Design and Off-Design Performance 1857.9.1 Gas Turbines Types and Gas Turbine

Design Conditions 1857.9.2 Gas Turbine Design and Off-Design

Using Performance Curves 1867.9.3 Gas Turbine Internal Mass Flow

Patterns 1867.9.4 Industrial Gas Turbine Off-Design (Part

Load) Control Algorithm 1887.9.5 Aeroderivative Gas Turbine Off-Design

(Part Load) Control Algorithm 1897.9.6 Off-Design Performance Algorithm for

Gas Turbines 1897.10 Closing Remarks 193


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

8.1 Available Function Calls

x Contents

10.4 Economic Design Optimization of the CGAM Problem: Ideal Gas 24910.4.1 Air Preheater (APH) Equations 24910.4.2 CGAM Problem Physical

Properties 24910.5 The CGAM Cogeneration Design Problem:

Real Physical Properties 25010.6 Comparing CogenD and General Electric’s

GateCycle™ 25310.7 Numerical Solution of HRSG Heat Transfer

Problems 25410.7.1 Steady-State Heat Conduction in a

One-Dimensional Wall 25410.7.2 Unsteady-State Heat Conduction in a

One-Dimensional Wall 25510.7.3 Steady-State Heat Conduction in the

HRSG 25910.8 Closing Remarks 266


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 28111.4 Closing Comments 281


12. Optimal Power Dispatch in a Cogeneration Facility 284

12.1 Developing the Optimal Dispatch Model 284

12.2 Overview of the Cogeneration System 28612.3 General Operating Strategy

Considerations 28712.4 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 28912.4.3 Steam-Driven Chiller

Performance 29012.4.4 GE Air Cooler Chiller

Performance 29112.4.5 GE Gas Turbine Performance (Based on

Fuel HHV) 29412.4.6 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 29812.5.1 Natural Gas Cost 29912.5.2 Purchased Electricity Cost 299

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


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) 31713.4 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) 32413.6.1 Design above the Pinch 32513.6.2 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


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

Contents xi

14.3 Site-Wide Utility System Considerations 356


15. Site Utility Emissions 368

15.1 Emissions from Stoichiometric Considerations 369

15.2 Emissions from Combustion Equilibrium Calculations 37015.2.1 Equilibrium Reactions 37115.2.2 Combustion Chamber Material

Balances 37115.2.3 Equilibrium Relations for Gas-Phase

Reactions/Gas-Phase Combustors 37215.2.4 Equilibrium Compositions from

Equilibrium Constants 37615.3 Emission Prediction Using Elementary

Kinetics Rate Expressions 38015.3.1 Combustion Chemical Kinetics 38015.3.2 Compact Matrix Notation for the Species

Net Generation (or Production) Rate 381

15.4 Models for Predicting Emissions from Gas Turbine Combustors 38215.4.1 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 393References 393CVODE Tutorial 393Problems 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) 39816.1.1 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 40316.1.5 Turbine Exhaust End Loss 40316.1.6 Steam Turbine System Heat Rate and

Performance Parameters 40516.2 Power Plant Off-Design Performance (Part

Load with Throttling Control Operation) 40616.2.1 Initial Estimates for All Pressures and

Efficiencies: Sub Off_Design_Initial_Estimates ( ) 406

16.2.2 Modify Pressures: Sub Pressure_ Iteration ( ) 406

16.2.3 Modify Efficiencies: Sub Update Efficiencies ( ) 408

16.3 Levelized Economics for Utility Pricing 409

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


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 42517.3.1 A High-Temperature Gas-Cooled

Nuclear Reactor (HTGR) 425References 427Problems 427

Appendix. Bridging Excel and C Codes 429

A.1 Introduction 429A.2 Working with Functions 431A.3 Working with Vectors 434A.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 446References 448

Tutorial 448Microsoft C++ 2008 Express: Creating C Programs

and DLLs 448

Index 458

xiii

Preface

Energy costs affect the profitability of virtually every process. This book provides a unified platform for process improvement through the analysis of both the energy demand side—the processing plant—and the energy supply side—available heat and power resources. Emphasis is placed on first quantifying the material and energy flows in a process. The energy needs of the process guide the optimal design of the utility system. Techniques are also presented to ensure that the most cost-effective operation of the utility system is maintained.

Both practicing engineers and engineering students can use the information presented here. For practicing engineers, the book provides a systematic and self-contained approach for minimizing energy use and cost at an operational facility. For chemical, mechanical, petroleum, and energy engineer-ing students, the book provides a detailed evaluation of energy analysis, design, and optimization.

FEATURES OF THE BOOK

There are a number of features of this book that we hope will encourage its use.

The installation of example files, problem solution files, and compiled and source versions of all developed software is detailed in Chapter 1, Section 1.7.

Energy costs, basic economic calculations, and eco-nomic uncertainty using Monte Carlo simulations are intro-duced in Chapters 1 and 2. Levelized utility costing is also developed (Chapter 16).

A systematic approach using either sequential modular (Chapters 3 and 5) or simultaneous-based (Chapters 4 and 5) methodologies is developed for the solution of process material and energy balances. Necessary numerical methods are developed naturally as part of the solution process.

Data reconciliation and gross error detection are intro-duced (Chapter 6) and applied to an actual cogeneration system (Chapter 11).

Cogeneration system performance and design and off-design calculations are developed using both ideal gas (Chapter 7) and real fluid (Chapter 9) properties.

An open source thermodynamics package (∼7000 lines of code) for cogeneration, combustion, and steam calcula-tions is provided in Chapter 8. Codes are provided for prob-lems with field or SI units. The code is used to solve cogeneration design, data reconciliation, and power dis-patching problems. Details are provided on how this or any code (written in C, C++, Fortran, etc.) can be seamlessly incorporated into Excel (Appendix A).

Optimal power dispatching for an actual cogeneration system is developed in Chapter 12.

A unified approach to process heat integration and site utility system integration is provided in Chapters 13 and 14. An open source software package is provided to help in the understanding of the basic concepts of heat exchanger network synthesis.

Site emissions are addressed and gas turbine systems are modeled as a series of stirred tank and plug flow reactors (Chapter 15). The ordinary differential equation solver CVODE (from Lawrence Livermore National Laboratory) is made available as a callable routine from Excel, and a reduced kinetics set based on GRI-Mech 3.0 is used to predict emissions from gas turbines.

The economics of carbon dioxide capture in conven-tional coal-fired utility plants, including steam turbine design and off-design calculations, is addressed in Chapter 16.

Many of the concepts used throughout the text are brought together for the economic analysis of an organic Rankine cycle in Chapter 17.

For several of the heat and power generation topics discussed in the text, “self-contained” Web-based down-loadable videos (∼30 minutes) with self-study guides and additional problems are available at our Web site, www.cogened.lsu.edu. This site also provides real-time data from the Louisiana State University (LSU) cogeneration system; these data can be used to enhance cogeneration problems and discussions.

http://www.cogened.lsu.edu


xiv Preface

There are over 160 completely worked chapter exam-ples. Virtually every example includes a computer-aided (Excel-based) solution. The chapter problems provide an additional 140 problems, with most having computer-aided solutions. A detailed solution manual for the chapter prob-lems is available at the Wiley Web site. A faculty member or practicing engineer can request a copy by sending a letter on a company letterhead.

BACKGROUND

I have assumed that the reader has some knowledge of Excel and programming and has been introduced to basic material and energy balance calculations. Enough detail is provided to help a reader without detailed knowledge of Visual Basic for Applications (VBA) and C.

Throughout this text, a “just in time” approach has been taken to the development of the necessary solution tech-niques. Developing needed solution techniques often pro-vides the opportunity to improve engineering computer skills. Excel was used as the starting platform for problem solution; however, enhancements made possible by the use of VBA and C programs within Excel are emphasized. The reader is shown, step-by-step, how VBA and C programs can be incor-porated into Excel sheets as callable functions and subrou-tines. The user is given access to all source codes used in this text, which will promote improvements and widespread use.

In the text, I often use both field and SI units. I appreci-ate that many faculty prefer the sole use of SI units; however, too often I have found that starting engineers make unit mistakes. One solution is practice, which this text provides. As virtually all examples and problems are solved using computer-aided techniques, it is straightforward for the user to change units in the provided solutions. Several examples carry extra significant figures in intermediate calculations to allow direct comparison with Excel sheet values. Some chapter problems are especially important for reinforcing and extending presented materials; for these problems, detailed solutions are provided as part of the text. A detailed solution manual is available for chapter problems.

The optimal design and operation of energy systems can involve the solution of linear programming (LP), nonlinear programming (NLP), mixed-integer linear programming (MILP), or mixed-integer nonlinear programming (MINLP) problems. We utilize both Excel Solver and What’s Best for the solution of these problems. What’s Best is an Excel add-in for solving optimization problems; a version of What’s Best has been supplied by LINDO Systems for use with this text.

USE OF THE BOOK

For engineering students, this book provides a logical progression to allow a better understanding of energy flows

in a processing plant. Topics of importance to energy engi-neering calculations occur naturally. This should prove to be an interesting way of improving skills in coding, using numerical methods to solve engineering problems, and for-mulating and solving process and utility energy optimization problems.

The book can be integrated into engineering curricula by following one of the following paths.

ENERGY SUSTAINABILITY COURSE

This book can be used in a one-semester special topic course to introduce energy sustainability to third- and fourth-year engineering students. Here the first three-quarters of the course focuses on understanding energy flows in processing plants and how cogeneration and energy efficiency are important aspects of a national energy portfolio; these topics are directly covered in this text. Then using this text as a basis, and combined with outside reading materials, the final quarter of the course can be devoted to detailed analysis of key emerging energy technologies—I suggest including biomass gasification, solar thermal/organic Rankine power plants, and integrated gasification combined cycle and other advanced clean coal processes. A reasonable question is, Why study these topics when there are so many emerging energy technologies? There are several answers to this ques-tion: First, biomass and solar thermal/organic Rankine plants represent the breadth of the emerging technologies; second, the best currently available large-scale conservation technol-ogy is cogeneration; and finally, coal usage must be addressed since ∼50% of the electricity generation in the United States is from coal. In addition, these technologies all share several process units. The energy inputs to these processes (from chemicals, fuel, or radiation from the sun) can be used to produce steam (or to vaporize an organic compound) in a Rankine power cycle; chemical energy can be converted into a synthesis gas and can be used in gas turbines; or some combination of these may be used. This allows the students to see the common features of these processes and allows for a discussion of optimal process designs dependent on the energy source. Students can explore other alternative energy technologies through team-oriented term projects that are suggested in the text.

NUMERICAL METHODS AND CAPSTONE DESIGN COURSES: ESTABLISHING AN “ENERGY THREAD”

Another alternative is to use ∼50% of this text in an applied numerical analysis course and to use the remaining chapters as part of a capstone design sequence and within other

Preface xv

courses in the curriculum. This is actually how I originally developed the text; we wanted to establish an “energy thread” in our engineering courses without adding a new course. For a sophomore-level applied numerical method course, topics included engineering programming (Chapter 2), solution of linear and nonlinear equations (Chapter 3), solution of linear and nonlinear equation sets (Chapter 4), data analysis and curve fitting (Chapter 6), ordinary differ-ential equations (Chapter 5, Sections 5.4–5.6, and Chapter 15, Sections 15.3 and 15.4), partial differential equations (Chapter 10, Section 10.7), and advanced engineering pro-gramming (Appendix A). As part of the capstone design sequence taught to fourth-year engineering students, Chap-ters 3–5 were quickly reviewed, highlighting the structure of computer-aided solutions to material and energy balances, and then emphasis was placed on optimizing energy resources in processing plants using material from Chapters 13 and 14. Chapters 16 and 17 were used to detail levelized economics. Data reconciliation and gross error detection (Chapters 6 and 11) were used as a lab for third-year engi-neering students. The chapters on determining gas turbine performance (Chapters 7 and 9) and developing physical property packages (Chapter 8) were used within engineering thermodynamics courses. Modeling gas turbine combustors (Chapter 15, Sections 15.2–15.4) was used within our kinet-ics and reactor design course.

PROCESS SYSTEMS COURSE (ENGINEERING CURRICULUM)

In an engineering curriculum, this book can be used to help provide an integrated introduction to process synthesis. Fol-lowing the introductory material and energy balance course, a process perspective of energy costs and basic economics, data reconciliation, gross error detection, heat and power systems, utility system dispatch, heat integration, and cogen-eration can be taught using the materials in this book.

INDUSTRIAL USE

One strength of this book will be its use for practicing engi-neers. Heat and power systems involve large flows that can magnify inaccuracies in physical properties. A major coding effort in the text has been the development of accurate physi-cal properties for utility systems. In Appendix A, we show the user how these thermodynamic codes, or any user-writ-ten code, can be seamlessly incorporated into Excel. The thermodynamic properties (∼7000 lines of code) for cogen-eration, combustion, and steam calculations are described in Chapter 8. Emphasis is also placed on data reconciliation and gross error detection, cogeneration system design and off-design operation, utility system dispatching, heat

exchanger network synthesis and site energy integration, and predicting emissions.

SUPPLEMENTARY MATERIALS

For several heat and power generation topics discussed in the text, Web-based downloadable videos (∼30 minutes) with documentation and additional problems are available at our Web site, www.cogened.lsu.edu. These materials have been designed for student use and have been tested at LSU, Florida A&M University–Florida State University (FAMU-FSU) (Dr. John Telotte), University of Alabama (Dr. Heath Turner), and University of Florida (Dr. Peng Jiang).

ACKNOWLEDGMENTS

The codes provided here would not have been possible without the efforts of graduate students and postdoctoral research associates with whom I have been fortunate to work. The cogeneration thermodynamics code (Chapter 8) was initially developed by Dr. Shane Stafford and was later modified and completed by Dr. Derya B. Orzyurt. There has been a long collaboration with Dr. Janardhana R. Punuru in developing techniques that allow bridging between Excel and C/C++ code. Dr. Punuru developed the Excel interface for CVODE, which is provided in Chapter 15 (CVODE is the ordinary differential equation solver available from Law-rence Livermore National Laboratory). The initial version of the heat exchanger network synthesis program THEN (Chapter 13) was developed by Sanjay P. Bhargava, Sanjay G. Pethe, and Rajiv Singh and was later coupled to Excel with the help of Dr. Punuru. Lina M. Bustami worked on the heat recovery steam generator problem and Robert Buckley worked on both the initial cogeneration data recon-ciliation problem and the energy dispatching model.

I also want to thank my colleagues who have made significant contributions to this book. I especially thank Dr. Kerry M. Dooley (LSU) who read and provided corrections for the first draft of each chapter in this text. I have had many discussions about energy systems and the cost of energy generation with Louis Braquet (LB Services) and Dr. David Dismukes (LSU), both of whom reviewed Chapter 1. Dr. Dismukes prepared the table of levelized costs for alterna-tive energy systems in Chapter 17. Richard McKinney reviewed Appendix A and helped provide the needed modi-fications to move from Microsoft Visual C++ 6.0 to Visual C++ 2008 Express Edition. Peter Davidson and Tony Cupit (LSU Facility Services) helped provide data and cogenera-tion operational strategies for the optimal energy dispatching model. Dr. Oscar Jimenez Cabeza (GEPROP) and Dr. Roger Nordman (SP Technical Research Institute of Sweden) pro-vided critical reviews of the energy integration chapters.


xvi Preface

Dr. John Telotte (FAMU-FSU) reviewed the thermodynamic aspects of Chapters 8 and 15.

I am especially indebted to Dr. Frank Madron (ChemP-lant) and Dr. Michael Erbes (Enginomix). Dr. Madron pro-vided many corrections and clarifications to the chapters on data reconciliation. Dr. Erbes provided his expertise on energy sustainability and modeling, cogeneration systems, and turbine performance in both design and off-design oper-ation, and also reviewed Chapters 7, 9, 10, and 16.

Dr. Ralph Pike (LSU) and Dr. G.V. Reklaitis (Purdue University) helped focus the goals of the text and provided suggestions for improvement. Mohammed Syed read the final draft of the text and Vamshi Kandula helped assemble all the materials in the text.

I would especially like to thank Professor Don Fresh-water for his suggestion for the cover painting ICI Wilton Works by Tom Gamble. I would also like to thank Professor Chris D. Rielly of Loughborough University in Leicester-shire, United Kingdom, for allowing its use and for provid-ing the copy.

I acknowledge the financial assistance of the National Science Foundation Phase I and Phase II grants, “Inte-grating a Cogeneration Facility into Engineering Educa-tion,” NSF Awards 0535560 (Phase I) and 0716303 (Phase II).

F. Carl KnopfBaton Rouge, Louisiana

To view color versions of the figures in this book, please visit: ftp://ftp.wiley.com/public/sci_tech_med/energy_system.

ftp://ftp.wiley.com/public/sci_tech_med/energy_system

xvii

Conversion Factors

Mass and Density 1 kg = 2.2046 lb 1 lb = 0.4536 kg1 g/cm3 = 103 kg/m3 1 lb/ft3 = 0.016018 g/cm3

1 g/cm3 = 62.428 lb/ft3 1 lb/ft3 = 16.018 kg/m3

Length 1 cm = 0.3937 in. 1 in = 2.54 cm1 m = 3.2808 ft 1 ft = 0.3048 m

Velocity 1 km/h = 0.62137 mile/h 1 mile/h = 1.6093 km/hVolume 1 cm3 = 0.061024 in.3 1 in3 = 16.387 cm3

1 m3 = 35.315 ft3 1 ft3 = 0.028317 m3

1 L = 10−3 m3 1 gal = 0.13368 ft3

1 L = 0.0353 ft3 1 gal = 3.7854 × 10−3 m3

Force 1 N = 1 kg-m/s2 1 lbf = 32.174 lb-ft/s2

1 N = 0.22481 lbf 1 lbf = 4.4482 NPressure 1 Pa = 1 N/m2 = 1 kg/m-s2 1 lbf/in2 = 6894.757 Pa

1 Pa = 1.4504 × 10−4 lbf/in2 1 lbf/in2 = 144 lbf/ft2

1 bar = 105 N/m2 = 105 Pa 1 atm = 14.696 lbf/in.2

1 atm = 1.01325 barsEnergy and Specific Energy 1 J = 1 N-m = 0.73756 ft-lbf 1 ft-lbf = 1.35582 J

1 kJ = 737.56 ft-lbf 1 Btu = 778.17 ft-lbf1 kJ = 0.9478 Btu 1 Btu = 1.0551 kJ1 kJ/kg = 0.42992 Btu/lb 1 Btu/lb = 2.326 kJ/kg1 kcal = 4.1868 kJ

Energy Transfer Rate or Power 1 W = 1 J/s = 3.4121 Btu/h 1 Btu/h = 0.29307 W1 kW = 1.341 hp 1 hp = 2544.4 Btu/h

1 hp = 550 ft-lbf/s1 hp = 0.7457 kW

Specific Heat or Entropy 1 kJ/kg-K = 0.238846 Btu/lb-R 1 Btu/lb-R = 4.1868 kJ/kg-K1 kcal/kg-K = 1 Btu/lb-R

(Continued)

xviii Conversion Factors

Temperature K = °C + 273.15 R = °F + 459.67K = (5/9) R R = (9/5) K = (1.8) K°C = (5/9) (°F − 32) °F = (1.8) °C + 32Δ K = Δ°C Δ R = Δ°FΔ K = (5/9) Δ R Δ R = (1.8) Δ K

Notation Common to the U.S. Power Industry

k (kilo) = 103; kW (kilowatt)m = 103; mSCF (1000 standard cubic feet)M (mega) = 106 ; MW (megawatt)MM = 106 ; MMBtu (million British thermal unit)

Universal Gas Constant, R 8.314 J/mol-K0.082057 L-atm/mol-K1.987 cal/mol-K1.987 Btu/(lb-mol-R)82.06 cm3-atm/mol-K

xix

List of Symbols

ae,i number of atoms of element e in species i, Chapter 3Ac plug flow reactor (PFR) tube cross-sectional areaCp,i isobaric molar heat capacity of species iˆ

,CP i isobaric heat capacity of species i per unit mass (specific heat capacity)ˆ

,CP j isobaric specific heat capacity of stream j (Btu/lb-R, kJ/kg-K)C C CP P P

igvapor liquid, , isobaric molar heat capacity vapor phase, liquid phase, ideal gasCTotal total cost rate ($/time), Chapter 10CV isochoric molar heat capacityd0, di tube diameter outside, inside, Chapter 10e escalation rate for economics calculation, Chapter 16fi fugacity of species i, Chapter 15fi

0 standard state fugacity of species i, Chapter 15f friction factor, Chapter 16Fj mass flow rate of stream jFi

j, Ft,j mass flow rate of species i in stream jF j

unitmass flow rate stream j in given unit, Chapter 16

G molar Gibbs free energy, Chapter 15Gi

0 standard molar Gibbs free energy of pure species i, Chapter 15Gj gas mass velocity of stream j, Chapter 10hi molar enthalpy of species ih h h T Pj T P j jj j

, , ,,( ) ( ) molar enthalpy of specific stream j

h h hj j jvapor liquid sat liquid, , molar enthalpy of stream j with state indicated: vapor, liquid, saturated liquid

h h hj j j a, ,, ,isenisen , hj

a molar enthalpy of stream with thermodynamic path indicated: isentropic, actualhi,j molar enthalpy of species i in stream j

Δh change in molar enthalpy, ∆h h hT P T P= −( , ) ( , )out out in in

href, h0 reference molar enthalpy for stream, generally for field units (77°F or 535.67 R, 14.696 psia) and for SI units (25°C or 298.15 K, 0.101326 MPa)

h0, hgas side heat transfer coefficient outside, gas side , Chapter 10ˆ , ˆh hi j, ˆ

,hi j enthalpy per unit mass of species i; enthalpy per unit mass of stream j (specific enthalpy) (Btu/lb, kJ/kg)

hLPsat vapor, hHPT out

Real specific enthalpy of low pressure (steam) at saturated vapor conditions, high-pressure turbine out at actual conditions

ˆ , ˆ , ,, , , ,h h h hi j i jref ref ref ref reference specific enthalpy for species i or stream j, molar enthalpy, generally for field units (77°F or 535.67 R, 14.696 psia) and for SI units (25°C or 298.15 K, 0.101326 MPa)

∆ ∆ˆ , ˆh hMP Steam LP Steam change in specific molar enthalpy for medium pressure, low-pressure steamH total enthalpy (Btu, kJ)H total enthalpy rate (Btu/s, kW)

xx List of Symbols

ΔHr, ΔHcombustion, ΔHvaporization heat of reaction, combustion, vaporizationi′ equivalent discount rate with escalation for economic calculations, Chapters 16 and 17i, ieff discount rate or interest rate per period or time value of money, effective interest ratekf, kb reaction rate constant forward, backward (reverse)k reaction rate constant, thermal conductivity of the material[k] kth iteration; brackets indicate iterationkc water/steam thermal conductivity, Chapter 10Ki equilibrium distribution coefficient for species iKeq equilibrium constant of chemical reactionKh exhaust gas thermal conductivity, Chapter 10L(x, λ) Lagrangian functionLtube tube length, Chapter 10MWi molecular weight of species in, ni number of periods (economics), number of moles of species iNtubes_wide number of tubes in the selected width, Chapter 10Nj molar flow rate of stream jNi,j, Ni

j molar flow rate of species i in stream jNi

k molar flow rate of species i at iteration k, Runge–Kutta method, Chapter 5

NiZ j molar flow rate of species i at position Zj, Euler’s method or Runge–Kutta method,

Chapter 5Pj, Pref pressure stream j, reference pressure∆PUnit

species, ∆PUnitstream pressure drop in given unit , stream side

q heat quantity per moleq heat quantity per unit massq q1 1

Isentropic real, steam quality isentropic, realQ variance–covariance matrix, Chapters 6 and 11Q

dQ

dt≡ rate of heat transfer (Btu/s, kW)

QUnit rate of heat transfer in specified unit (Btu/s, kW)QMP

Process, QLPProcess process heat load satisfied by medium pressure (MP), low pressure (LP) steam, Chapter 14

r, ri rate of reaction, rate of reaction species i (single reaction)rm rate of reaction for reaction m, Chapter 15R universal gas constant per mole

R universal gas constant per unit mass = R/MWi

Ri production or generation rate of species iRThermal thermal resistance, Chapter 10si molar entropy of species isj, s(Tj,Pj), s(Tj, Pj) molar entropy of stream jsi

0 molar entropy of species i, at reference T and PΔs change in molar entropyˆ , ˆs si j entropy per unit mass of species i, entropy per unit mass of stream j (specific entropy)ˆ , ˆ , ˆs s sj j j

isentropic real sat vapor entropy per unit mass stream j at isentropic, real, and saturated vapor conditionsS species column vector, Chapter 15Stube tube spacing, Chapter 10Tj temperature stream jTj,location temperature stream j, at specific locationTref, Tisen, Tactual, Ta reference temperature, isentropic temperature, actual temperature, acrtual temperatureTj

isen, Tjsat vap temperature stream j, isentropic thermodynamic path, saturated vapor condition

Tzj temperature at position Zj, Euler’s method or Runge–Kutta method, Chapter 5ΔTPinch, ΔTapproach, ΔTLMTD,Evaporater pinch temperature difference, approach temperature difference, log mean temperature

difference, unitˆ , ˆu uin out specific internal energyuj estimates of nonmeasured process variables for data reconciliation, Chapters 6 and 11U overall heat transfer coefficient

List of Symbols xxi

υ molar volumeυ, υ j volume per unit mass (specific volume), of stream jνc water velocity in tube (ft/s), Chapter 10V, Vr total volume, volume of the reactorVan annulus velocity (ft/s), Chapter 16wi

j weight fraction of species i in stream jw work per molew work per unit mass (Btu/lb)wc water/steam flow rate in the single tube (lb/h), Chapter 10WGT, WPT gas turbine work, power turbine work W WT , Flow , Wshaft rate of work total, rate of work due to fluid flow, rate of shaft work

x[k] kth iteration; brackets indicate iterationxi,j mole fraction of species i in stream jx xi i

+ , measured value, reconciled value in data reconciliation, Chapters 6 and 11Δx insulation thickness, Chapter 10yi

j, yi,j mole fraction of species i in stream jzj purchase cost of the ith component ($) in economic calculations, Chapter 10

GREEK LETTERS

αij, αi,j species i split fraction in separator output stream j = Ni,j/Ni,in, Chapters 3 and 5

αj species split fraction in splitter output stream j = Nj/Nin, Chapter 3αsite_PHR,αcogen_PHR base power to base heat ratio, Chapter 10

α ρ= k Cpˆ thermal diffusivity, Chapter 10

δi denotes whether equipment i is on = 1/off = 0ε convergence parameter or toleranceγ, γi ratio of heat capacities γ = CP/CV, ratio of heat capacities for species iη, ηunit efficiency, efficiency of given unitηunit

isentropic isentropic efficiency of given unit, Chapter 16λk Lagrange multipliersμi chemical potentialμh exhaust gas viscosity, Chapter 10νi, νm,i stoichiometric coefficient for species i (single reaction), stoichiometric coefficient for species i

in reaction mν ′ reactant stoichiometric coefficient matrix, Chapter 15ν″ product stoichiometric coefficient matrix, Chapter 15ξ, ξm extent of reaction (single reaction), extent of reaction for reaction mρ molar density, mole per unit volumeρ specific density, mass per unit volumeσi standard deviation, Chapters 6 and 11τ mean residence timeϕi fugacity coefficient for species iχ α( ) ( )1

2− v chi-squared distribution, Chapters 6 and 11

1

22ϑ kinetic energy

1

Modeling, Analysis and Optimization of Process and Energy Systems, First Edition. F. Carl Knopf.© 2012 John Wiley & Sons, Inc. Published 2012 by John Wiley & Sons, Inc.

1.1 ENERGY UTILIZATION IN THE UNITED STATES

Let us begin by examining energy use in the United States. Figures 1.1 and 1.2 are U.S. energy utilization in 2000 and 2008 as determined by the Energy Information Administra-tion (EIA) and Lawrence Livermore National Laboratory (LLNL). Here, the energy unit used in the figures is quadril-lion or quad, and 1 quad = 1015 Btu.

Key results from Figures 1.1 and 1.2 as well as energy utilization data from 2000–2008 are summarized in Table 1.1.

Table 1.1 indicates that total energy use in the United States has remained relatively flat for the years 2000–2008. Also, our reliance on “traditional” hydrocarbon energy sources (natural gas, coal, and petroleum) has remained little changed over this near decade. In the future, there is every expectation that alternative energy technologies will grow in importance. For example, wind energy use has increased some fivefold from 2003 to 2008. But in the near term, we should give renewed consideration to the most efficient use of existing energy resources, especially our traditional hydrocarbons. Based on LLNL estimates, Figures 1.1 and 1.2 indicate that overall U.S. energy efficiency is ∼42%. The ∼58% rejected energy is primarily waste heat from combus-tion. A motivation for this book is to support existing and planned processing sites and energy facilities to help ensure energy is being used as efficiently as possible.

1.2 THE COST OF ENERGY

We next ask the following question, “Just how important are process energy costs?” Energy costs are often one of the

largest single expenses at an industrial processing site along with labor and raw materials. These industrial processing sites would include chemicals and petrochemicals, agro-chemicals, pharmaceuticals, plastics, paper and pulp, metal and mining. In these industries, energy costs typically range from about 10% to over 50% of the operating expenses for the site.

To assign an actual dollar cost, we need to pick a price for energy and to estimate a typical process energy load. For the price of energy, we can use the cost of natural gas to industry as a benchmark. Many industries in the United States were built on “$2” natural gas—this “$2” refers to $2 per million British thermal unit (MMBtu) or $2 per thousand standard cubic foot (mSCF). Roughly 1 mSCF of natural gas contains 1 MMBtu. Figure 1.3 shows the average annual industrial price for natural gas from 1973 until 2009. Figure 1.4 shows the average monthly industrial price for natural gas from January 2000 to November 2010 (EIA). Costs in Figures 1.3 and 1.4 are not adjusted for inflation. Starting in about 2000, there has been an upward trend in natural gas price coupled with large short-term price swings. For example, in 2005, Hurricanes Katrina and Rita contributed to spot market natural gas prices climbing to $15+ per MMBtu for short periods of time.

Next, we can address, “What is a typical process energy load?” A large industrial (chemical plant or refinery) may use 50–100 × 109 Btu/day for heating and power generation. This is the energy required to produce steam and electricity for process use. A medium-sized industrial or a large uni-versity may use 10–20 × 109 Btu/day for heating and power generation.

Using a long-term projected price of $8 natural gas ($8 per MMBtu) as a fuel cost, the utility cost for a large indus-trial may be on the order of $200 × 106 per year, and a

Chapter 1

Introduction to Energy Usage, Cost, and Efficiency

Figure 1.1 Energy use in the United States (EIA and LLNL; see the References for the Web site) in 2000. In this figure, nonfuel from petroleum feed is, for example, petroleum used as a chemical feedstock.

25.70

Rejected Energy58.47


ElectricalGeneration

40.40


40.40Nuclear8.0

Nuclear8.0

Hydro2.83

Hydro2.83

Natural Gas23.70

Natural Gas23.70

Coal21.00Coal21.00

Petroleum38.10

Petroleum38.10

Biomass andOther**

3.70

Biomass andOther**

3.70

Useful Energy43.04

Useful Energy43.04

Residential andCommercial

11.43

Residential andCommercial

11.43

Industrial24.84

Industrial24.84

Nonfuel6.4

Nonfuel6.4

Transportation26.60

Transportation26.60 7.257.25

19.8719.87

2.00

0.660.66

0.500.50

1.001.003.303.30

9.419.41

28.1028.10

2.832.83

6.506.50

8.418.41

20.5020.50

8.508.50

0.600.60

3.433.43

4.744.74

2.282.28

4.964.968.008.00

21.7721.77

0.02

0.100.10

5.705.70

2.202.201.201.20

2

Figure 1.2 Energy use in the United States in 2008 (EIA and LLNL).

2.43

1.79

0.42

4.99

1.17

0.02

0.51

0.31

0.08

0.02

0.01

0.83

2.03

0.10

0.660.06

1.71

2.29

0.02

0.01

0.46




39.97


39.97

Solar0.09Solar0.09

Nuclear8.45

Nuclear8.45

Hydro2.45

Hydro2.45

Wind0.51Wind0.51

Geothermal0.35

Geothermal0.35

Natural Gas23.84

Natural Gas23.84

Coal22.42Coal22.42

Biomass3.88

Biomass3.88

Petroleum37.13

Petroleum37.13

Useful Energy42.15

Useful Energy42.15

Industrial23.94

Industrial23.94

Transportation27.86

Transportation27.86

Commercial8.58

Commercial8.58

Residential11.48

Residential11.48

9.189.18

4.744.74

4.584.58

0.490.49

6.866.86

4.784.78

19.1519.15

20.9020.90

6.966.9626.3326.33

8.588.58

8.148.14

3.433.43

0.570.573.203.20

27.3927.39

12.6812.6820.5420.54

6.826.82

8.458.45

3

4 Chapter 1 Introduction to Energy Usage, Cost, and Efficiency

Figure 1.3 Industrial price for delivered natural gas (dollar per MMBtu) and yearly average price from 1970 to 2009 (EIA).

Year

0

2

4

6

8

10

12

$ pe

r M

MB

tu

1980 1990 2000 2010

Figure 1.4 Industrial price for delivered natural gas (dollar per MMBtu) and monthly average price from January 2000 to November 2010 (EIA).

2

4

6

8

10

12

14$

per

MM

Btu

Month/Year

01/00 01/01 01/02 01/03 01/04 01/05 01/06 01/07 01/08 01/09 01/10 01/11

Table 1.1 Summary of Energy Use (Quadrillion British Thermal Unit) in the United States from 2000 to 2008 (EIA)

2000 2001 2002 2003 2004 2005 2006 2007 2008

Total energy use 98.5 97.0 97.0 98.1 100.2 100.4 99.8 101.5 99.2Energy fromSolar 0.06 0.06 0.06 0.07 0.08 0.09Nuclear 8.0 8.0 8.10 7.95 8.22 8.16 8.21 8.41 8.45Hydro 2.83 2.30 2.60 2.82 2.69 2.70 2.86 2.46 2.45Wind 0.11 0.14 0.17 0.26 0.31 0.51Geothermal 0.33 0.34 0.34 0.34 0.35 0.35Natural gas 23.70 23.20 23.20 22.90 22.93 22.50 22.19 23.63 23.84Coal 21.0 21.90 22.30 22.32 22.46 22.79 22.44 22.76 22.42Biomass 3.7* 3.3* 3.2* 2.81 3.02 3.15 3.37 3.61 3.88Petroleum 38.10 38.0 38.10 38.80 40.29 40.39 39.95 39.81 37.13Energy from natural gas, coal, and petroleum 82.28 83.10 83.60 84.05 85.68 85.68 84.58 86.30 83.39

*The biomass data for 2000–2002 include wood and waste, geothermal, solar, and wind.

medium-sized industrial or large university may see utility costs near $40 × 106 per year. Utility costs may be higher if electricity is purchased from the local utility and steam is generated in boilers, as opposed to taking advantage of com-bined heat and power generation opportunities.

We can see that energy costs are a significant consider-ation in most processes. Increasing worldwide demand for energy is expected to keep utility costs on a positive slope. There is a need for careful assessment of the energy cur-rently being used in a process coupled with a systematic approach for reducing this energy use. In many processing plants, electricity is both purchased and generated, and in deregulated areas, plants may sell electricity to the open market. Fluctuating energy costs (see Figure 1.4) necessitate

a careful coupling of process energy needs with utility pro-duction planning and utility purchase.

1.3 ENERGY EFFICIENCY

There are two commonly used definitions of efficiency, η, one based on the first law of thermodynamics and a second definition based on the second law of thermodynamics. From the first law of thermodynamics, we can write

η1stUsable energy output from the system

Energy supplied to the sys=

ttem. (1.1)

1.3 Energy Efficiency 5

Here, we account for the energy supplied to the system and the usable energy from the system. From the second law of thermodynamics, we can write

η2ndMinimum theoretical energy required

Energy actually used= . (1.2)

Both definitions will find use in the energy and power calculations performed in this text. As Equation (1.2) requires additional development, examples and problems in this chapter will just focus on Equation (1.1).

In many efficiency calculations, Equation (1.1) can be directly used. In some cases, especially when a specific operation is using or producing electricity (e.g., a turbine), Equation (1.2) proves more beneficial. For power (electric-ity) generating systems, overall performance is often pro-vided by an alterative form of Equation (1.1)—the plant net heat rate,

Plant net heat rate

Energy supplied to the system Btu

Usable electr=

,

iical energy output from the system kW-h,.

(1.3)

EXAMPLE 1.1 Utility Company Power Plant Energy Efficiency

A coal-fired utility company power plant is shown in Figure 1.5. Here, time is not considered—we are just looking at the energy flows resulting from 1000 lb of coal being added to the boiler. The values provided in Figure 1.5 represent energy inputs to each operation; for example, energy to the boiler from the coal feed is 12,720,000 Btu. Part of this 12,720,000 Btu will be sent to the turbine (as steam) and part will be lost to the stack. Of the 11,194,000 Btu sent to the turbine, 5,261,000 Btu is used for elec-tricity generation. The turbine here is a “condensing steam turbine.” This is also typically referred to as a bottoming cycle as all the available energy in the steam for power generation is extracted in the turbine and then the steam is condensed. The 4,933,000 Btu of thermal energy rejected to the environment is required to condense low-pressure steam from the turbine. This condensing allows the boiler feedwater to be recycled as it allows the boiler feedwater pressure to be increased using a pump. The return boiler feedwater contains 1,000,000 Btu.

It is possible to directly convert the energy flows in Figure 1.5 to energy transfer rates, for example, 1000 lb of coal per hour would generate 12,720,000 Btu/h. It is also possible to consider the energy flows in Figure 1.5 to be directly scalable; for example, 2000 lb of coal would generate 25,440,000 Btu. For now, we can use the energy values in Figure 1.5 to determine the efficiency of the boiler, the turbine, and the generator and also the overall process thermal efficiency (sometimes termed the plant net thermal efficiency) and the power plant net heat rate (British thermal unit per kilowatt-hour).

In this example, we are just accounting for energy flow within the utility plant fence line. We are not accounting for transportation and distribution losses. Exported power to the grid often experiences 5–8% transmission and distribution losses before that power can be utilized at the end application (see Problem 1.5).

SOLUTION It can sometimes be confusing trying to consistently determine unit by unit and overall system efficiencies using Equations (1.1) and (1.3). It can be helpful to think of each unit (or system) as a cost center. For example, the boiler “purchases” 12,720,000 Btu of coal and “sells” 11,194,000 Btu to the turbine and takes back “credit” 1,000,000 Btu as condensate return. The efficiency of the boiler is

ηBoiler =−( ) =

11 194 000 1 000 000

12 720 00080 1

, , , ,

, ,. %.

The turbine is needed to generate electricity, and here the turbine purchases 11,194,000 Btu and “delivers” 5,261,000 Btu for electricity generation. The efficiency of the turbine is

ηTurbine = =5 261 000

11 194 00047 01

, ,

, ,. %.

For the overall thermal efficiency, 12,720,000 Btu of coal is supplied to the plant, and 4,844,000 Btu of electricity is delivered for transmission and sale. Here 365,000 Btu of electricity for coal handling, including coal conveyors and coal crushers or pulveriz-ers, is used internally and is not available for “sale”—internal use of electricity is often termed a parasitic load. The utility plant net heat rate is defined as the British thermal unit supplied to the plant divided by the kilowatt-hour of electricity delivered for transmission:

12 720 000

14208957 7

, ,. .

Btu

kW-h

Btu

kW-h=

Efficiency results for the coal utility plant are summarized in Table 1.2.

It is often convenient to represent the energy flows in Figure 1.5 on a Sankey diagram, which is shown in Figure 1.6a. From the Sankey diagram, where the energy flow is normalized to 100 input units (Figure 1.6b), it is easy to see the overall plant thermal effi-ciency is 38.08%, here

4 844 000

12 720 00038 08

, ,

, ,. %.

Btu

Btu=

EXAMPLE 1.2 Topping Cycle Cogeneration Plant Energy Efficiency

A natural gas-fired topping cycle cogeneration facility is shown in Figure 1.7. It is termed a topping cycle because electricity is gener-ated from the steam before the steam is used by the process. The topping cycle uses a back-pressure or “let-down” steam turbine. Unlike the condensing steam turbine of Example 1.1, steam exhaust from a back-pressure turbine still has energy that can be useful in

6 Chapter 1 Introduction to Energy Usage, Cost, and Efficiency

Figure 1.5 Coal-fired electric power plant (adapted from Priest, 1973).

GeneratorBoiler

12,720,000 Btufrom fuel

Smokestack

Turbine

Energy into turbine11,194,000 Btu

EmissionsSulfur oxides = 97 lb

Fly ash = 1.1 lbHeat energy = 2,526,000 Btu

1000-lb fuel

Condenser

Thermal energy rejected to environment:4,933,000 Btu

Energy into generator5,261,000 Btu

Electric energyfor transmission4,844,000 Btuor 1420 kW-h

Energy into boiler from condensate return

1,000,000 Btu

Electric energyfor internal use

365,000 Btuor 107 kW-h

Energy from generator5,209,000 Btu or

1527 kW-h

the process. The thermal energy (steam) from the turbine is used for heating within the processing plant and the condensate is returned to the boiler. In a topping cycle cogeneration facility, the ratio of the process steam demand to the process electricity demand is generally large; this is typical of the needs found in a brewery or distillery. The values provided in Figure 1.7 again represent the energy input to each operation. Determine the efficiency of the boiler, the turbine, the generator, and also the overall process thermal efficiency and the cogeneration plant heat rate (British thermal unit per kilowatt-hour). Finally, draw the Sankey diagram with energy flows normal-ized to 100 input units (British thermal unit).

SOLUTION The efficiencies for the topping cycle are provided in Table 1.2. For the overall thermal efficiency, 12,720,000 Btu of natural gas is supplied to the system, 1,720,000 Btu is available for transmission as electricity (to the process), and 8,439,000 Btu is used as heat in the process. The Sankey diagram is shown in Figure 1.8.

and natural gas are mixed and combusted in the turbine system. The hot-pressurized exhaust gas loses pressure as it drives the turbine. Part of the energy from the turbine is used to compress the incoming air; part is used to generate electricity; and the remainder used for steam generation. The figure shows that the turbine shaft (here a single shaft) turns both the generator and the air compressor. The energy from the turbine that drives the air compressor (6,400,000 Btu) will add to the energy of the incoming air stream. In later chapters, we will account for energy losses in the compression process. If we examine the mechanical energy from the turbine (6,400,000-Btu compression + 4,250,000-Btu electricity), ∼60% of this mechanical energy is used to drive the compressor. The com-pression process can be viewed as a recycle energy stream—this energy (6,400,000 Btu) from the turbine is actually returned to the turbine by increasing the air feed stream pressure and temperature.

The hot and nearly atmospheric pressure exhaust gas from the turbine (8,470,000 Btu) passes to a waste heat boiler (WHB), which recovers energy, as steam, for use in the process. The steam from the boiler is used for heating within the processing plant and the condensate is returned to the boiler. Determine the efficiency of the boiler, the turbine, and the generator in this power plant. Also determine the overall plant thermal efficiency and the cogen-eration plant net heat rate (British thermal unit per kilowatt-hour). Finally, draw the Sankey diagram with energy flows normalized to 100 input units (British thermal unit).

EXAMPLE 1.3 Gas Turbine Cogeneration Plant Energy Efficiency

A natural gas-fired turbine cogeneration facility typical of a process-ing plant or university is shown in Figure 1.9. The values provided in Figure 1.9 are the energy input to each operation. Compressed air

modeling, analysis and

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