This survey presents the theoretical methods of chemical engineering for modeling and simulation of industrial processes. On this base it is possible to formulate correct experimental conditions and to under-stand rightly the experimental results.The book uses the mechanics of continuous media approach for modeling of the simple processes as hydrodynamic processes, mass and heat transfer processes. The theory of the scalar, vector and tensor fields permit to create the basic equa-tions and boundary conditions. The problems of rheology, turbulence, turbulent diffusion and turbulent mass transfer are examined too.The book incorporates a lot of fundamental knowledge, but it is assumed that the readers are familiar with the mathematics at engineer-ing level and that they thought some special topics in usual university courses. It includes examples at the end of all chapters using the author’s investigations. Therefore, it is highly valuable for scientists as well as graduate and PhD students.

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Theoretical Chem

ical Engineering

Theoretical Chemical

EngineeringModeling and Simulation

123

C. BoyadjievTheoretical Chemical Engineering

Boyadjiev

Christo Boyadjiev

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Christo B. Boyadjiev

Theoretical Chemical Engineering

Modeling & Simulation

Abstract

The theoretical methods of chemical engineering for modeling and simulation of

industrial processes are surveyed in this book. On this basis it is possible to formulate correct

experimental conditions and to understand correctly the experimental results.

The continuous media approach is used for modeling simple processes such as

hydrodynamic processes, mass transfer processes, and heat transfer processes. The theory of

scalar, vector, and tensor fields permits one to create the basic equations and boundary

conditions. Problems of rheology, turbulence, turbulent diffusion, and turbulent mass transfer

are examined too.

The chemical processes and adsorption models and especially the stoichiometry,

reaction mechanism, reaction route, kinetics of simple and complex chemical reactions,

physical and chemical adsorption, and heterogeneous reactions are discussed.

Different types of complex process models are presented depending on the process

mechanism. The relation between the mechanism and the mathematical description is shown

in the case of physical absorption. Characteristic scales, generalized variables, and

dimensionless parameters are used for analysis of the process mechanism. Full information

about this mechanism permits the creation of theoretical models. Mass transfer in film flows

is an example of such models, where the effects of a chemical reaction and gas motion and

absorption of slightly and highly soluble gases are considered.

The very complicated hydrodynamic behavior in column apparatuses is a reason for

using diffusion-type models in the cases of mass transfer with a chemical reaction and

interphase mass transfer. An average concentration model of an airlift reactor is presented.

Similarity theory models are demonstrated in the case of absorption in packed-bed

columns. Generalized (dimensionless) variables and generalized individual cases are used for

formulation of the similarity conditions and similarity criteria. The dimension analysis,

mathematical structure of the models, and some errors in criteria models are discussed.

Regression models are preferred when there is complete absence of information about

the process mechanism and the least-squares method is used for parameter identification.

A theoretical analysis of models of the mass transfer theories is presented in the cases of

linear and nonlinear mass transfer. The model theories, boundary layer theory, mass transfer

in countercurrent flows, influence of the intensive mass transfer on the hydrodynamics,

boundary conditions of the nonlinear mass transfer problem, nonlinear mass transfer in the

boundary layer, and the Marangoni effect are examined.

A qualitative theoretical analysis is presented as a generalized analysis. The use of

generalized variables permits the analysis of the models of mass transfer with a chemical

reaction, nonstationary processes, and stationary processes and the effect of the chemical

reaction rate.

The generalized analysis permits the analysis of the mechanism of gas–liquid chemical

reactions in the cases of irreversible chemical reactions, homogenous catalytic reactions, and

reversible chemical reactions and the relationships between the chemical and physical

equilibria during absorption.

A comparative qualitative analysis for process mechanism identification is presented in

the cases of different nonlinear effects, nonstationary absorption mechanisms, and

nonstationary evaporation kinetics.

A quantitative theoretical analysis is presented for solution of the scale-up problems and

statistical analysis of the models. The similarity and scale-up, scale effect and scale effect

modeling, scale-up theory and hydrodynamic modeling, and scale effect and scale-up of

column apparatuses are discussed. The statistical analysis ranges over basic terms, statistical

treatment of experimental data, testing of hypotheses, significance of parameters, and model

adequacy of different types of models.

The stability analysis of the models examines the general theory of stability (evolution

equations, bifurcation theory), hydrodynamic stability (fundamental equations, power theory,

linear theory, stability, bifurcations, and turbulence), the Orr–Sommerfeld equation (parallel

flows, almost parallel flows, linear stability, and nonlinear mass transfer), and self-organizing

dissipative structures (interphase heat and mass transfer between gas–liquid immovable

layers, Oberbeck–Boussinesq equations, gas absorption, and liquid evaporation).

The calculation problems in chemical engineering theory are related to the solutions of

differential equations and identification of the model parameters (estimation). Different

analytical methods, such as the similarity variables method, Green’s functions, Laplace

transforms, the Sturm–Liouville problem, the eigenvalue problem, and perturbation methods,

are presented. Numerical methods (finite differences method, finite elements method) are

examined on the basis of commercial software. Iterative solution methods are considered too.

Parameter estimation methods are discussed in the case of incorrect (ill-posed) inverse

problems. An iterative method for parameter identification is presented for solution of correct,

incorrect, and essentially incorrect problems. The optimization methods are examined as a

basis of the least squares function minimization.

Models of chemical plant systems are presented as a set of process models and the

relations between them. An algorithm for simulation of chemical plants is proposed. The

methods of optimal synthesis of chemical plants are considered in the case of optimal

synthesis of heat recuperation systems. The renovation of chemical plants is formulated as a

mathematical model. The main problems are the renovation by optimal synthesis, renovation

by introduction of new equipment, and renovation by introduction of new processes.

Examples from the author’s investigations are presented at the end of all chapters.

Motto

Experimenters are the striking force of science. The experiment is a question which

science puts to nature. The measurement is the registration of nature’s answer. But before

the question is put to nature, it must be formulated. Before the measurement result is used, it

must be explained, i.e., the answer must be understood correctly. These two problems are

obligations of the theoreticians.

Max Planck

Contents

Preface XX

Introduction XXIV

0.1 Quantitative Description XXIV

0.2 Modeling and Simulation XXIV

0.3 Chemical Engineering and Chemical Technology XXVI

0.4 Theoretical Problems and Methods XXVII

0.5 Physical Fundamentals of Theoretical Chemical Engineering XXVIII

Part 1

Model Construction Problems

Chapter 1 Simple Process Models 1

1.1 Mechanics of Continuous Media 2

1.1.1 Scalar and Vector Fields (3)

1.1.2 Stress Tensor and Tensor Field (5)

1.2 Hydrodynamic Processes 9

1.2.1 Basic Equations (10)

1.2.2 Cylindrical Coordinates (13)

1.2.3 Boundary Conditions (14)

1.2.4 Laminar Boundary Layer (15)

1.2.5 Two-Phase Boundary Layers (17)

1.2.6 Particular Processes (20)

1.2.7 Generalized Variables (21)

1.2.8 Basic Parameters (24)

1.2.9 Rheology (25)

1.2.10 Turbulence (28)

1.3 Mass and Heat Transfer Processes 38

1.3.1 Basic Equations (38)

1.3.2 Boundary Conditions (41)

1.3.3 Transfer Process Rate (41)

1.3.4 Diffusion Boundary Layer (43)

1.3.5 Turbulent Diffusion (44)

1.3.6 Turbulent Mass Transfer (46)

1.4 Chemical Processes and Adsorption 48

1.4.1 Stoichiometry (49)

1.4.2 Mechanism and Reaction Route (49)

1.4.3 Kinetics of Simple Chemical Reactions (50)

1.4.4 Kinetics of Complex Reactions (52)

1.4.5 Adsorption Processes (53)

1.4.6 Physical Adsorption (53)

1.4.7 Chemical Adsorption (54)

1.4.8 Heterogeneous Reactions (55)

1.5 Examples 56

1.5.1 Dissolution of a Solid Particle (56)

1.5.1.1 Particle Radius is Constant (56)

1.5.1.2 Particle Radius Decreases (57)

1.5.2 Contemporary Approach of Turbulence Modeling (57)

References 59

Chapter 2 Complex Process Models 61

2.1 Mechanism and Mathematical Description 61

2.1.1 Mechanism of Physical Absorption (61)

2.1.2 Mathematical Description (62)

2.1.3 Generalized Variables and Characteristic Scales (63)

2.1.4 Dimensionless Parameters and Process Mechanism (63)

2.1.5 Boundary Conditions and Mechanism (65)

2.1.6 Kinetics and Mechanism (65)

2.2 Theoretical Models. Mass Transfer in Film Flows 67

2.2.1 Film with a Free Interface (67)

2.2.2 Effect of a Chemical Reaction (69)

2.2.3 Effect of Gas Motion (69)

2.2.4 Absorption of Slightly Soluble Gas (74)

2.2.5 Absorption of Highly Soluble Gas (76)

2.3 Diffusion-Type Models 78

2.3.1 Mass Transfer with a Chemical Reaction (79)

2.3.2 Interphase Mass Transfer (79)

2.3.3 Average Concentration Models (80)

2.3.4 Airlift Reactor (83)

2.4 Similarity Theory Models 88

2.4.1 Absorption in a Packed-Bed Column (88)

2.4.2 Generalized (Dimensionless) Variables (89)

2.4.3 Generalized Individual Case and Similarity (90)

2.4.4 Mathematical Structure of the Models (91)

2.4.5 Dimension Analysis (94)

2.4.6 Some Errors in Criteria Models (96)

2.5 Regression Models 99

2.5.1 Regression Equations (99)

2.5.2 Parameter Identification (100)

2.5.3 Least-Squares Method (100)

2.6 Examples 101

2.6.1 Effect of Surfactants (101)

2.6.2 Effect of Interface Waves (107)

2.6.3 Photobioreactor Model (110)

References 119

Chapter 3 Mass Transfer Theories 122

3.1 Linear Mass Transfer Theory 122

3.1.1 Model Theories (123)

3.1.2 Boundary Layer Theory (125)

3.1.3 Two-Phase Boundary Layers (126)

3.2 Mass Transfer in Countercurrent Flows 128

3.2.1 Velocity Distribution (129)

3.2.2 Concentration Distribution (131)

3.2.3 Comparison Between Co-current and Countercurrent Flows (132)

3.3 Nonlinear Mass Transfer 133

3.3.1 Influence of Intensive Mass Transfer on the Hydrodynamics (135)

3.3.2 Boundary Conditions of the Nonlinear Mass Transfer Problem (136)

3.3.3 Nonlinear Mass Transfer in the Boundary Layer (138)

3.3.4 Two-Phase Systems (142)

3.3.5 Nonlinear Mass Transfer and the Marangoni Effect (149)

3.4 Examples 155

3.4.1 Heat Transfer in the Conditions of Nonlinear Mass Transfer (155)

3.4.2 Multicomponent Mass Transfer (158)

3.4.3 Concentration Effects (160)

3.4.4 Influence of High Concentration on the Mass Transfer Rate (166)

3.4.5 Nonlinear Mass Transfer in Countercurrent Flows (172)

References 173

Part 2

Theoretical Analysis of Models

Chapter 4 Qualitative Analysis 178

4.1 Generalized Analysis 178

4.1.1 Generalized Variables (178)

4.1.2 Mass Transfer with a Chemical Reaction (179)

4.1.3 Nonstationary Processes (181)

4.1.4 Steady-State Processes (181)

4.1.5 Effect of the Chemical Reaction Rate (182)

4.2 Mechanism of Gas–Liquid Chemical Reactions 183

4.2.1 Irreversible Chemical Reactions (183)

4.2.1 Homogenous Catalytic Reactions (193)

4.2.3 Reversible Chemical Reactions (196)

4.2.4 Relationships Between the Chemical Equilibrium and the Physical Equilibrium

During Absorption (199)

4.3 Comparative Qualitative Analysis for Process Mechanism Identification 201

4.3.1 Comparison of the Nonlinear Effects (201)

4.3.2 Nonstationary Absorption Mechanism (211)

4.3.3 Nonstationary Evaporation Kinetics (218)

4.4 Example 225

4.4.1 Sulfuric Acid Alkylation Process in a Film Flow Reactor (225)

References 229

Chapter 5 Quantitative Analysis 232

5.1 Scale-up 232

5.1.1 Similarity and Scale-up (233)

5.1.2 Scale Effect (238)

5.1.3 Diffusion Model (240)

5.1.4 Scale-up Theory (242)

5.1.5 Axial Mixing (243)

5.1.6 Evaluation of the Scale Effect (245)

5.1.7 Hydrodynamic Modeling (245).

5.2 Average Concentration Model and Scale-up 247

5.2.1 Diffusion-Type Model (248)

5.2.2 Influence of the Radial Nonuniformity of the Velocity Distribution on the Process

Efficiency (249)

5.2.3 Scale Effect (252)

5.2.4 Average Concentration Model (252)

5.2.5 Scale Effect Modeling (255)

5.2.6 Scale-up Parameter Identification (256)

5.3 Statistical Analysis 257

5.3.1 Basic Terms (258)

5.3.2 Statistical Treatment of Experimental Data (270)

5.3.3 Estimates of the Expectation and the Dispersion (270)

5.3.4 Tests of Hypotheses (272)

5.3.5 Dispersion Analysis (275)

5.3.6 Significance of Parameter Estimates and Model Adequacy (277)

5.3.7 Model Suitability (280)

5.3.8 Adequacy of the Theoretical Models and Model Theories (281).

5.4 Example 283

5.4.1 Statistical Analysis of Diffusion-Type Models (283)

References 284

Chapter 6 Stability Analysis 285

6.1 Stability Theory 285

6.1.1 Evolution Equations (285)

6.1.2 Bifurcation Theory (289)

6.1.3 Eigenvalue Problem (292)

6.2 Hydrodynamic Stability 294

6.2.1 Fundamental Equations (294)

6.2.2 Power Theory (295)

6.2.3 Linear Theory (297)

6.2.4 Stability, Bifurcations, and Turbulence (299)

6.2.5 Stability of Parallel Flows (301)

6.3 Orr–Sommerfeld Equation 302

6.3.1 Parallel Flows (303)

6.3.2 Almost Parallel Flows (303)

6.3.3 Linear Stability and Nonlinear Mass Transfer (304)

6.4 Self-Organizing Dissipative Structures 314

6.4.1 Nonlinear Mass Transfer in the Boundary Layer (317)

6.4.2 Gas Absorption (326)

6.4.3 Liquid Evaporation (354)

6.5 Examples 366

6.5.1 Gas–Liquid System (366)

6.5.2 Liquid–Liquid System (370)

6.5.3 Effect of Concentration (374).

6.5.4 Effect of Temperature (378)

References 380

Part 3

Calculation Problems

Chapter 7 Solution of Differential Equations 384

7.1 Analytical Methods 384

7.1.1 Green’s Functions (384)

7.1.2 Similarity Variables Method (388)

7.1.3 Eigenvalue Problem (388)

7.1.4 Laplace Transformation (390)

7.2 Perturbation Methods 392

7.2.1 Expansions with Respect to a Parameter (392)

7.2.2 Expansions with Respect to a Coordinate (395)

7.2.3 Nonuniform Expansions (Poincaret–Lighthill–Ho method) (396)

7.3 Numerical Methods 399

7.3.1 Finite Differences Method (399)

7.3.2 Finite Elements Method (400)

7.4 Examples 401

7.4.1 Application of Green’s Functions (401)

7.4.2 Sturm–Liouville Problem (402)

References 403

Chapter 8 Parameter Identification (Estimation) 405

8.1 Inverse Problems 405

8.1.1 Direct and Inverse Problems (405)

8.1.2 Types of Inverse Problems (406)

8.1.3 Incorrectness of the Inverse Problems (407)

8.2 Sets and Metric Spaces 409

8.2.1 Metrics (409)

8.2.2 Linear Spaces (410)

8.2.3 Functional (411)

8.2.4 Operator (412)

8.2.5 Functional of the Misfit (413)

8.2.6 Some Properties of the Direct and Inverse Operators (414)

8.3 Incorrectness of the Inverse Problems 415

8.3.1 Correctness After Hadamard (416)

8.3.2 Correctness After Tikhonov (417)

8.4 Methods for Solving Incorrect (Ill-Posed) Problems 417

8.4.1 Method of Selection (419)

8.4.2 Method of Quasi-Solutions (420)

8.4.3 Method of Substitution of Equations (420)

8.4.4 Method of the Quasi-Reverse (420)

8.4.5 Summary (420)

8.5 Methods for Solving Essentially Ill-Posed Problems 420

8.5.1 Regularization Operator (421)

8.5.2 Variational Approach (422)

8.5.2.1 Stabilizing Functional (423)

8.5.2.2 Smoothing Functional (423)

8.5.3 Iterative Approach (424)

8.5.3.1 Gradient Methods (424)

8.5.3.2 Uniqueness of the Solution (426)

8.5.3.3 Approximate Equations (427)

8.5.3.4 Criteria for Stopping the Iterations (428)

8.6 Parameter Identification in Different Types of Models 431

8.6.1 Regression Models (431)

8.6.2 Selection Methods (432)

8.6.3 Variational Regularization (434)

8.6.4 Similarity Theory Models (435)

8.6.5 Diffusion-Type Models (436)

8.6.5.1 Determination of the Heat Conductivity Coefficients in Inverse Heat Transfer

Problems (436)

8.6.5.2 Iterative Algorithm (437)

8.6.6 Theoretical Models and Model Theories (439)

8.7 Minimum of the Least-Squares Function 439

8.7.1 Incorrectness of the Inverse Problem (440)

8.7.2 Incorrectness of the Least Squares Function Method (441)

8.7.3 Regularization of the Iterative Method for Parameter Identification (442)

8.7.4 Iteration Step Determination and Iteration Stop Criterion (444)

8.7.5 Iterative Algorithm (445)

8.7.6 Correct Problem Solution (446)

8.7.7 Effect of the Regularization Parameter (447)

8.7.8 Incorrect Problem Solution (447)

8.7.9 Essentially Incorrect Problem Solution (449)

8.7.10 General Case (450)

8.7.11 Statistical Analysis of Model Adequacy (452)

8.7.12 Comparison Between Correct and Incorrect Problems (454)

8.8 Multiequation Models 456

8.8.1 Problem Formulation (457)

8.8.2 Fermentation System Modeling (460)

8.8.2.1 Experimental Data (461)

8.8.2.2 Zeroth-Order Approximations of the Model Parameters (462)

8.8.2.3 First-Order Approximations of the Parameters (463)

8.9 Experiment Design 466

8.9.1 Experimental Plans of Modeling (467)

8.9.2 Parameter Identification (468)

8.9.3 Significance of Parameters (470)

8.9.4 Adequacy of Models (471)

8.9.5 Randomized Plans (471)

8.9.6 Full and Fractional Factor Experiment (473)

8.9.7 Compositional Plans (477)

8.10 Examples 478

8.10.1 Regression Models (478)

8.10.2 Statistical Analysis of the Parameter Significance and Model Adequacy of the

Regression Models (484)

8.10.3 Clapeyron and Antoan Models (485)

8.10.4 Incorrectness Criterion (488)

8.10.5 Increase of the Exactness of the Identification Problem Solution (490)

8.10.6 Incomplete Experimental Data Cases (490)

References 502

Chapter 9 Optimization 507

9.1 Analytical Methods 506

9.1.1 Unconstraints Minimization (506)

9.1.2 Constraints Minimization (507)

9.1.3 Calculus of Variations (507)

9.1.4 Solution of a Set of Nonlinear Equations (510)

9.2 Numerical Methods 511

9.2.1 Linear Programming (511)

9.2.2 Nonlinear Programming (512)

9.3 Dynamic Programming and the Principle of the Maximum 516

9.3.1 Functional Equations (516)

9.3.2 Principle of Optimality (517)

9.3.3 Principle of the Maximum (517)

9.4 Examples 519

9.4.1 Problem of Optimal Equipment Change (519)

9.4.2 A Calculus of Variations Problem (521)

References 523

Part 4

Chemical Plant Systems

Chapter 10 Systems Analysis 524

10.1 Simulation of Chemical Plant Systems 524

10.1.1 Model of Chemical Plant Systems (524)

10.1.2 Simulation Methods (525)

10.1.3 Sequential Module (Hierarchical) Approach (526)

10.1.4 Acyclic Chemical Plant Systems (526)

10.1.5 Cyclic Chemical Plant Systems (528)

10.1.6 Independent Contours (530)

10.1.7 Breaking Sets (532)

10.1.8 Optimal Order (534)

10.2 Simulation for Specified Outlet Variables 535

10.2.1 Zone of Influence (536)

10.2.2 Absolutely Independent Influence (537)

10.2.3 Independent Influence (538)

10.2.4 Combined Zones (540)

10.3 Models of Separate Blocks 540

10.3.1 Types of Modules (541)

10.3.2 Heat Transfer (542)

10.3.3 Separation (543)

10.3.4 Chemical Processes (545)

References 546

Chapter 11 Synthesis of Systems 547

11.1 Optimal Synthesis of Chemical Plants 547

11.1.1 Optimization (547)

11.1.2 Optimal Synthesis (547)

11.1.3 Main Problems (548)

11.1.4 Methods of Synthesis (548)

11.1.5 Optimal Synthesis of a System for Recuperative Heat Transfer (550)

11.2 Renovation of Chemical Plant Systems 553

11.2.1 Mathematical Description (553)

11.2.2 Mathematical Models (555)

11.2.3 Main Problems (556)

11.2.4 Renovation by Optimal Synthesis of Chemical Plant Systems (557)

11.2.5 Renovation by Introduction of Highly Intensive Equipment (558)

11.2.6 Renovation by Introduction of Highly Effective Processes (558)

References 559

Conclusion 561

Index 563

Preface

The role of theory in science was formulated very brilliantly by Max Planck:

“Experimenters are the striking force of science. The experiment is a question which

science puts to nature. The measurement is the registration of nature’s answer. But before

the question is put to nature, it must be formulated. Before the measurement result is used, it

must be explained, i.e., the answer must be understood correctly. These two problems are

obligations of the theoreticians.”

Chemical engineering is an experimental science, but theory permits us to formulate

correct experimental conditions and to understand correctly the experimental results. The

theoretical methods of chemical engineering for modeling and simulation of industrial

processes are surveyed in this book.

Theoretical chemical engineering solves the problems that spring up from the necessity

for a quantitative description of the processes in the chemical industry. They are quite

different at the different stages of the quantitative description, i.e., a wide circle of theoretical

methods are required for their solutions.

Modeling and simulation are a united approach to obtain a quantitative description of

the processes and systems in chemical engineering and chemical technology, which is

necessary to clarify the process mechanism or for optimal process design, process control, and

plant renovation.

Modeling is the creation of the mathematical model, i.e., construction of the

mathematical description (on the basis of the process mechanism), calculation of the model

parameters (using experimental data), and statistical analysis of the model adequacy.

Simulation is a quantitative description of the processes by means of algorithms and

software for the solution of the model equations and numerical (mathematical) experiments.

The processes in chemical engineering are composed of many simple processes, such as

hydrodynamic, diffusion, heat conduction, and chemical processes. The models are created in

the approximations of continuous media mechanics.

The complex process model is constructed on the basis of the physical mechanism

hypothesis. In cases where full information is available, it is possible to create a theoretical

type of model. If the information is insufficient (it is not possible to formulate the

hydrodynamic influence on the heat and mass transfer), the model is pattern theory, diffusion

type or similarity criteria type. The absence of information leads to the regression model.

The theoretical analysis of the models solves qualitative, quantitative, and stability

problems. The qualitative analysis clarifies the process mechanism or similarity conditions.

The quantitative analysis solves the problems related to the scale-up and model adequacy. The

stability analysis explains the increase of the process efficiency as a result of self-organizing

dissipative structures.

All theoretical methods are related to calculation problems. The solutions of the model

equations use analytical and numerical methods. The identification (estimation) of the model

parameters leads to the solutions of the inverse problems, but very often they are incorrect

(ill-posed) and need the application of regularization methods, using a variational or an

iterative approach. The solutions of many chemical engineering problems (especially

parameter identification) use minimization methods.

The book ideology briefly described above addresses the theoretical foundation of

chemical engineering modeling and simulations. It is concerned with building, developing,

and applying the mathematical models that can be applied successfully for the solution of

chemical engineering problems. Our emphasis is on the description and evaluation of models

and simulations. The theory selected reflects our own interests and the needs of models

employed in chemical and process engineering. We hope that the problems covered in this

book will provide the readers (Ph.D. students, researchers, and teachers) with the tools to

permit the solution of various problems in modern chemical engineering, applied science, and

other fields through modeling and simulations.

The solutions of the theoretical problems of modeling and simulations employ a number

of mathematical methods (exact, asymptotic, numerical, etc.) whose adoption by engineers

will permit the optimal process design, process control, and plant renovation.

The modeling and the simulations of chemical systems and plants can be achieved very

often through a hierarchical modeling. This approach uses the structural analysis of the

process systems. The result of the structural analysis is a quantitative description allowing

further optimal process design, process control, and plant renovation. The effectiveness of the

optimal solutions can be enhanced if they are combined with suitable methods of optimal

synthesis. The latter is a methodical basis and a guide for process system renovations.

The book incorporates a lot of fundamental knowledge, but it is assumed that the

readers are familiar with the mathematics at engineering level of usual university courses.

The above comments are the main reasons determining the structure of this book.

Part 1 concerns model construction problems. The mechanics of the continuum

approach is used for modeling hydrodynamic, diffusion, and heat conduction processes as

basic (elementary) processes in chemical engineering. The modeling of complex processes in

chemical engineering is presented on the basis of the relation between the process mechanism

and the mathematical description. The models are classified in accordance with the

knowledge available concerning the process mechanisms. This means a situation when a

theoretical model is available, i.e., sufficient knowledge of the process mechanism as well as

the opposite situation of knowledge deficiency, which leads to regression models. Theoretical

diffusion, dimensionless, and regression types of models are illustrated. The linear, nonlinear,

and pattern mass transfer theories are considered too.

Part 2 focuses on theoretical analysis of chemical engineering process models. The

qualitative analysis uses generalized (dimensionless) variables and shows the degree to which

the different physical effects participate in a complex process. On this basis, similarity criteria

and physical modeling conditions are shown. The quantitative analysis concerns the scale-up

problems and statistical analysis of the models. The stability analysis of the models permits

the nonlinear mass transfer effects to be obtained and the creation of the self-organizing

dissipative structures with very intensive mass transfer.

Part 3 addresses the calculation problems in modeling and simulation. Different

analytical and numerical methods for the solution of differential equations are considered. The

estimation of the model parameters is related to the solutions of the ill-posed inverse

problems. An iterative method for incorrect problem solutions is presented. Different methods

for function minimization are shown for the purposes of process optimization and model

parameter identification.

Part 4 examines modeling and simulation of the chemical plant systems. The

simulation of the systems on the basis of structure system analysis is presented. The optimal

synthesis of chemical plants is considered in the case of the optimal synthesis of heat

recuperation systems.

This book can be used as a basis for theoretical and experimental investigations in the

field of the chemical engineering. The methods and analyses presented permit theoretical

problems to be solved, the experimental conditions to be correctly formulated, and the

experimental results to be interpreted correctly.

The fundamental suggestion in this book is the necessity for full correspondence (direct

and inverse) between the separated physical effect in the process and the mathematical

(differential) operator in the model equation.

The main part of this book has a monographic character and the examples are from the

author’s papers. The book uses the author’s lectures “Course of modeling and optimization”

(subject chemical cybernetics in the Faculty of Chemistry of Sofia University “St. Kliment

Ohridski”), “Course of modeling and simulation of chemical plant systems” (Bourgas

University “Prof. Asen Zlatarov”), and “Master’s classes of theoretical chemical engineering”

(Bourgas University “Prof. Asen Zlatarov”). That is why, as a whole, it is possible for it to be

used as teaching material for modeling and simulation. This book proposes an exact

formulation and the correct solution of quantitatively described problems in chemical

engineering. It may be useful for scientists, Ph.D. students, and undergraduate students.

Some of the results presented in the book were obtained with financial support from the

National Fund “Scientific Researches” of the Republic of Bulgaria (contracts no. TH-154/87,

TH-162/87, TH-89/91, TH-127/91, TH-508/95, TH-4/99, TH-1001/00, TH-1506/05).

The author would like to thank Assoc. Prof. Jordan Hristov, Assoc. Prof. Natasha

Vaklieva-Bancheva, Assoc. Prof. Boyan Ivanov, Assist. Prof. Maria Doichinova,, Assist.

Prof. Petya Popova, Assist. Prof. Elisaveta Shopova and Dipl. Eng., M. Sc. Boyan Boyadjiev

for their help in the preparation of this book.

Ch