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This 11-volume encyclopedia provides both an easy introduction to all topics related to modern electrochemistry as well as a comprehensive overview of the subject. Unrivalled in its breadth and depth, this standard reference has been created and written by renowned scientists, covering everything from fundamental research to areas of application.
1 Why Modelling?
1.1 Process and Process Modelling.
1.2 Observations on Some General Aspects of ModellingMethodology.
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 AnalogousComputers.
2 On the Classification of Models.
2.1 Fields of Modelling and Simulation in ChemicalEngineering.
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 andMethods.
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.
2.2 Some Observations on the Practical Use of Modelling andSimulation.
2.2.1 Reliability of Models and Simulations.
2.2.2 The Role of Industry as Final User of Modelling andSimulation.
2.2.3 Modelling and Simulation in Innovations.
2.2.4 Role of Modelling in Technology Transfer and KnowledgeManagement.
2.2.5 Role of the Universities in Modelling and SimulationDevelopment.
3 Mathematical Modelling Based on TransportPhenomena.
3.1 Algorithm for the Development of a Mathematical Model of aProcess.
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 FlowModels.
3.3.2 Combined Flow Models.
3.3.3 The Slip Flow Effect on the Efficiency of a MechanicallyMixed Reactor in a Permanent Regime.
3.3.4 Dispersion Flow Model.
220.127.116.11 Mechanically Mixed Reactor for Reactions in LiquidMedia.
18.104.22.168 Gas Flow in a Fluidized Bed Reactor.
22.214.171.124 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 MassTransfer.
3.5 Some Aspects of Parameters Identification in MathematicalModelling.
3.5.1 The Analytical Method for Identifying the Parameters of aModel.
126.96.36.199 The Pore Radius and Tortuosity of a Porous Membrane forGas Permeation.
3.5.2 The Method of Lagrange Multiplicators.
188.8.131.52 One Geometrical Problem.
3.5.3 The Use of Gradient Methods for the Identification ofParameters.
184.108.40.206 Identification of the Parameters of a Model by theSteepest Slope Method.
220.127.116.11 Identifying the Parameters of an Unsteady StatePerfectly Mixed Reactor.
3.5.4 The Gauss–Newton Gradient Technique.
18.104.22.168 The Identification of Thermal Parameters for the Case ofthe Cooling of a Cylindrical Body.
22.214.171.124 Complex Models with One Unknown Parameter.
3.5.5 Identification of the Parameters of a Model by the MaximumLikelihood Method.
126.96.36.199 The Kalman Filter Equations.
188.8.131.52 Example of the Use of the Kalman Filter.
3.6 Some Conclusions.
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 DiscretePolystochastic Processes.
4.3.1 Polystochastic Chains and Their Models.
184.108.40.206 Random Chains and Systems with Complete Connections.
4.3.2 Continuous Polystochastic Process.
4.3.3 The Similarity between theFokker–Plank–Kolmogorov Equation and the PropertyTransport Equation.
220.127.116.11 Stochastic Differential Equation Systems for Heat andMass Molecular Transport.
4.4 Methods for Solving Stochastic Models.
4.4.1 The Resolution of Stochastic Models by Means of AsymptoticModels.
18.104.22.168 Stochastic Models Based on Asymptotic PolystochasticChains.
22.214.171.124 Stochastic Models Based on Asymptotic PolystochasticProcesses.
126.96.36.199 Asymptotic Models Derived from Stochastic Models withDifferential Equations.
4.4.2 Numerical Methods for Solving Stochastic Models.
4.4.3 The Solution of Stochastic Models with AnalyticalMethods.
4.5 Use of Stochastic Algorithms to Solve OptimizationProblems.
4.6 Stochastic Models for Chemical Engineering Processes.
4.6.1 Liquid and Gas Flow in a Column with a Mobile PackedBed.
188.8.131.52 Gas Hold-up in a MWPB.
184.108.40.206 Axial Mixing of Liquid in a MWPB.
220.127.116.11 The Gas Fraction in a Mobile Flooded Packed Bed.
4.6.2 Species Movement and Transfer in a Porous Medium.
18.104.22.168 Liquid Motion Inside a Porous Medium.
22.214.171.124 Molecular Species Transfer in a Porous Solid.
4.6.3 Stochastic Models for Processes with DiscreteDisplacement.
126.96.36.199 The Computation of the Temperature State of a HeatExchanger.
188.8.131.52 Cellular Stochastic Model for a Countercurrent Flow withRecycling.
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.
184.108.40.206 A Particular Application of the Confidence Interval to aMean Value.
220.127.116.11 An Actual Example of the Calculation of the ConfidenceInterval for the Variance.
5.2.3 Statistical Hypotheses and Their Checking.
5.3 Correlation Analysis.
5.4 Regression Analysis.
5.4.1 Linear Regression.
18.104.22.168 Application to the Relationship between the ReactantConversion and the Input Concentration for a CSR.
5.4.2 Parabolic Regression.
5.4.3 Transcendental Regression.
5.4.4 Multiple Linear Regression.
22.214.171.124 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 theResponse Surface: Sequential Experimental Planning.
5.5.4 Second Order Orthogonal Plan.
126.96.36.199 Second Order Orthogonal Plan, Example of the Nitrationof an Aromatic Hydrocarbon.
5.5.5 Second Order Complete Plan.
5.5.6 Use of Simplex Regular Plan for Experimental Research.
188.8.131.52 SRP Investigation of a Liquid–Solid Extraction inBatch.
5.5.7 On-line Process Analysis by the EVOP Method.
184.108.40.206 EVOP Analysis of an Organic Synthesis.
220.127.116.11 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.
18.104.22.168 Interaction Analysis for a CFE 2n Plan.
22.214.171.124 Interaction Analysis Using a High Level FactorialPlan.
126.96.36.199 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.
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 DimensionalAnalysis.
6.3.1 Dimensional Analysis for Mass Transfer by NaturalConvection 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.
188.8.131.52 Variables Imposed by the Geometry of the System.
184.108.40.206 Variables Imposed by the Properties of theMaterials.
220.127.116.11 Dynamic Internal Effects.
18.104.22.168 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 InterfaceProperty Transfer Relationship.
6.6.3 Physical Interpretation of the Nu, Pr, Sh and ScNumbers.
6.6.4 Dimensionless Groups for Interactive Processes.
6.6.5 Common Dimensionless Groups in Chemical Engineering.
6.7 Particularization of the Relationship of DimensionlessGroups Using Experimental Data.
6.7.1 One Dimensionless Group Problem.
6.7.2 Data Correlation for Problems with Two DimensionlessGroups.
6.7.3 Data Correlation for Problems with More than TwoDimensionless 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 forSignificant Model Uncertainties.
22.214.171.124 Impact of Uncertainties and the Necessity for a ControlSystem Design.
6.9 Some Important Particularities of Chemical EngineeringLaboratory Models.