Chemical engineering : modelling, simulation and similitude

Preface. 1 Why Modelling? 1.1 Process and Process Modelling. 1.2 Observations on Some General Aspects of Modelling Methodology. 1.3 The Life-cycle of a Process and Modelling. 1.3.1 Modelling and Research and Development Stage. 1.3.2 Modelling and Conceptual Design Stage. 1.3.3 Modelling and Pilot Stage. 1.3.4 Modelling and Detailed Engineering Stage. 1.3.5 Modelling and Operating Stage. 1.4 Actual Objectives for Chemical Engineering Research. 1.5 Considerations About the Process Simulation. 1.5.1 The Simulation of a Physical Process and Analogous Computers. References. 2 On the Classification of Models. 2.1 Fields of Modelling and Simulation in Chemical Engineering. 2.1.1 Steady-state Flowsheet Modelling and Simulation. 2.1.2 Unsteady-state Process Modelling and Simulation. 2.1.3 Molecular Modelling and Computational Chemistry. 2.1.4 Computational Fluid Dynamics. 2.1.5 Optimisation and Some Associated Algorithms and Methods. 2.1.6 Artificial Intelligence and Neural Networks. 2.1.7 Environment, Health, Safety and Quality Models. 2.1.8 Detailed Design Models and Programs. 2.1.9 Process Control. 2.1.10 Estimation of Parameters. 2.1.11 Experimental Design. 2.1.12 Process Integration. 2.1.13 Process Synthesis. 2.1.14 Data Reconciliation. 2.1.15 Mathematical Computing Software. 2.1.16 Chemometrics. 2.2 Some Observations on the Practical Use of Modelling and Simulation. 2.2.1 Reliability of Models and Simulations. 2.2.2 The Role of Industry as Final User of Modelling and Simulation. 2.2.3 Modelling and Simulation in Innovations. 2.2.4 Role of Modelling in Technology Transfer and Knowledge Management. 2.2.5 Role of the Universities in Modelling and Simulation Development. References. 3 Mathematical Modelling Based on Transport Phenomena. 3.1 Algorithm for the Development of a Mathematical Model of a Process. 3.1.1 Some Observations about the Start of the Research. 3.1.2 The Limits of Modelling Based on Transport Phenomena. 3.2 An Example: From a Written Description to a Simulator. 3.3 Chemical Engineering Flow Models. 3.3.1 The Distribution Function and the Fundamental Flow Models. 3.3.2 Combined Flow Models. 3.3.3 The Slip Flow Effect on the Efficiency of a Mechanically Mixed Reactor in a Permanent Regime. 3.3.4 Dispersion Flow Model. 3.3.5 Examples. 3.3.5.1 Mechanically Mixed Reactor for Reactions in Liquid Media. 3.3.5.2 Gas Flow in a Fluidized Bed Reactor. 3.3.5.3 Flow in a Fixed Bed Catalytic Reactor. 3.3.6 Flow Modelling using Computational Fluid Dynamics. 3.4 Complex Models and Their Simulators. 3.4.1 Problem of Heating in a Zone Refining Process. 3.4.2 Heat Transfer in a Composite Medium. 3.4.3 Fast Chemical Reaction Accompanied by Heat and Mass Transfer. 3.5 Some Aspects of Parameters Identification in Mathematical Modelling. 3.5.1 The Analytical Method for Identifying the Parameters of a Model. 3.5.1.1 The Pore Radius and Tortuosity of a Porous Membrane for Gas Permeation. 3.5.2 The Method of Lagrange Multiplicators. 3.5.2.1 One Geometrical Problem. 3.5.3 The Use of Gradient Methods for the Identification of Parameters. 3.5.3.1 Identification of the Parameters of a Model by the Steepest Slope Method. 3.5.3.2 Identifying the Parameters of an Unsteady State Perfectly Mixed Reactor. 3.5.4 The Gauss-Newton Gradient Technique. 3.5.4.1 The Identification of Thermal Parameters for the Case of the Cooling of a Cylindrical Body. 3.5.4.2 Complex Models with One Unknown Parameter. 3.5.5 Identification of the Parameters of a Model by the Maximum Likelihood Method. 3.5.5.1 The Kalman Filter Equations. 3.5.5.2 Example of the Use of the Kalman Filter. 3.6 Some Conclusions. References. 4 Stochastic Mathematical Modelling. 4.1 Introduction to Stochastic Modelling. 4.1.1 Mechanical Stirring of a Liquid. 4.1.2 Numerical Application. 4.2 Stochastic Models by Probability Balance. 4.2.1 Solid Motion in a Liquid Fluidized Bed. 4.3 Mathematical Models of Continuous and Discrete Polystochastic Processes. 4.3.1 Polystochastic Chains and Their Models. 4.3.1.1 Random Chains and Systems with Complete Connections. 4.3.2 Continuous Polystochastic Process. 4.3.3 The Similarity between the Fokker-Plank-Kolmogorov Equation and the Property Transport Equation. 4.3.3.1 Stochastic Differential Equation Systems for Heat and Mass Molecular Transport. 4.4 Methods for Solving Stochastic Models. 4.4.1 The Resolution of Stochastic Models by Means of Asymptotic Models. 4.4.1.1 Stochastic Models Based on Asymptotic Polystochastic Chains. 4.4.1.2 Stochastic Models Based on Asymptotic Polystochastic Processes. 4.4.1.3 Asymptotic Models Derived from Stochastic Models with Differential Equations. 4.4.2 Numerical Methods for Solving Stochastic Models. 4.4.3 The Solution of Stochastic Models with Analytical Methods. 4.5 Use of Stochastic Algorithms to Solve Optimization Problems. 4.6 Stochastic Models for Chemical Engineering Processes. 4.6.1 Liquid and Gas Flow in a Column with a Mobile Packed Bed. 4.6.1.1 Gas Hold-up in a MWPB. 4.6.1.2 Axial Mixing of Liquid in a MWPB. 4.6.1.3 The Gas Fraction in a Mobile Flooded Packed Bed. 4.6.2 Species Movement and Transfer in a Porous Medium. 4.6.2.1 Liquid Motion Inside a Porous Medium. 4.6.2.2 Molecular Species Transfer in a Porous Solid. 4.6.3 Stochastic Models for Processes with Discrete Displacement. 4.6.3.1 The Computation of the Temperature State of a Heat Exchanger. 4.6.3.2 Cellular Stochastic Model for a Countercurrent Flow with Recycling. References. 5 Statistical Models in Chemical Engineering. 5.1 Basic Statistical Modelling. 5.2 Characteristics of the Statistical Selection. 5.2.1 The Distribution of Frequently Used Random Variables. 5.2.2 Intervals and Limits of Confidence. 5.2.2.1 A Particular Application of the Confidence Interval to a Mean Value. 5.2.2.2 An Actual Example of the Calculation of the Confidence Interval for the Variance. 5.2.3 Statistical Hypotheses and Their Checking. 5.3 Correlation Analysis. 5.4 Regression Analysis. 5.4.1 Linear Regression. 5.4.1.1 Application to the Relationship between the Reactant Conversion and the Input Concentration for a CSR. 5.4.2 Parabolic Regression. 5.4.3 Transcendental Regression. 5.4.4 Multiple Linear Regression. 5.4.4.1 Multiple Linear Regressions in Matrix Forms. 5.4.5 Multiple Regression with Monomial Functions. 5.5 Experimental Design Methods. 5.5.1 Experimental Design with Two Levels (2k Plan). 5.5.2 Two-level Experiment Plan with Fractionary Reply. 5.5.3 Investigation of the Great Curvature Domain of the Response Surface: Sequential Experimental Planning. 5.5.4 Second Order Orthogonal Plan. 5.5.4.1 Second Order Orthogonal Plan, Example of the Nitration of an Aromatic Hydrocarbon. 5.5.5 Second Order Complete Plan. 5.5.6 Use of Simplex Regular Plan for Experimental Research. 5.5.6.1 SRP Investigation of a Liquid-Solid Extraction in Batch. 5.5.7 On-line Process Analysis by the EVOP Method. 5.5.7.1 EVOP Analysis of an Organic Synthesis. 5.5.7.2 Some Supplementary Observations. 5.6 Analysis of Variances and Interaction of Factors. 5.6.1 Analysis of the Variances for a Monofactor Process. 5.6.2 Analysis of the Variances for Two Factors Processes. 5.6.3 Interactions Between the Factors of a Process. 5.6.3.1 Interaction Analysis for a CFE 2n Plan. 5.6.3.2 Interaction Analysis Using a High Level Factorial Plan. 5.6.3.3 Analysis of the Effects of Systematic Influences. 5.7 Use of Neural Net Computing Statistical Modelling. 5.7.1 Short Review of Artificial Neural Networks. 5.7.2 Structure and Threshold Functions for Neural Networks. 5.7.3 Back-propagation Algorithm. 5.7.4 Application of ANNs in Chemical Engineering. References. 6 Similitude, Dimensional Analysis and Modelling. 6.1 Dimensional Analysis in Chemical Engineering. 6.2 Vaschy-Buckingham Pi Theorem. 6.2.1 Determination of Pi Groups. 6.3 Chemical Engineering Problems Particularized by Dimensional Analysis. 6.3.1 Dimensional Analysis for Mass Transfer by Natural Convection in Finite Space. 6.3.2 Dimensional Analysis Applied to Mixing Liquids. 6.4 Supplementary Comments about Dimensional Analysis. 6.4.1 Selection of Variables. 6.4.1.1 Variables Imposed by the Geometry of the System. 6.4.1.2 Variables Imposed by the Properties of the Materials. 6.4.1.3 Dynamic Internal Effects. 6.4.1.4 Dynamic External Effects. 6.5 Uniqueness of Pi Terms. 6.6 Identification of Pi Groups Using the Inspection Method. 6.7 Common Dimensionless Groups and Their Relationships. 6.7.1 Physical Significance of Dimensionless Groups. 6.6.2 The Dimensionless Relationship as Kinetic Interface Property Transfer Relationship. 6.6.3 Physical Interpretation of the Nu, Pr, Sh and Sc Numbers. 6.6.4 Dimensionless Groups for Interactive Processes. 6.6.5 Common Dimensionless Groups in Chemical Engineering. 6.7 Particularization of the Relationship of Dimensionless Groups Using Experimental Data. 6.7.1 One Dimensionless Group Problem. 6.7.2 Data Correlation for Problems with Two Dimensionless Groups. 6.7.3 Data Correlation for Problems with More than Two Dimensionless Groups. 6.8 Physical Models and Similitude. 6.8.1 The Basis of the Similitude Theory. 6.8.2 Design Aspects: Role of CSD in Compensating for Significant Model Uncertainties. 6.8.2.1 Impact of Uncertainties and the Necessity for a Control System Design. 6.9 Some Important Particularities of Chemical Engineering Laboratory Models. References. Index.