KKEK 3152 MODELLING of CHEMICAL PROCESSES. Lumped vs Distributed parameter model.

Slides:

Advertisements

Similar presentations

Transient Conduction: The Lumped Capacitance Method

Advertisements

Topics to be covered in this module

FACTORIAL ANOVA Overview of Factorial ANOVA Factorial Designs Types of Effects Assumptions Analyzing the Variance Regression Equation Fixed and Random.

CHE 185 – PROCESS CONTROL AND DYNAMICS

Chapter 3 Dynamic Modeling.

FIRST AND SECOND-ORDER TRANSIENT CIRCUITS

Basic Mathematical Models; Direction Fields. A Falling Object.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Part Eight Partial Differential Equations.

Numerical Methods for Engineers MECH 300 Hong Kong University of Science and Technology.

Energy. Simple System Statistical mechanics applies to large sets of particles. Assume a system with a countable set of states.  Probability p n  Energy.

Development of Dynamic Models Illustrative Example: A Blending Process

1 MECH 221 FLUID MECHANICS (Fall 06/07) Tutorial 6 FLUID KINETMATICS.

9.1 Parametric Curves 9.2 Calculus with Parametric Curves.

1 6.3 Separation of Variables and the Logistic Equation Objective: Solve differential equations that can be solved by separation of variables.

LINEAR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

1 Chapter 9 Differential Equations: Classical Methods A differential equation (DE) may be defined as an equation involving one or more derivatives of an.

Transient Conduction: The Lumped Capacitance Method

Partial Differential Equation (PDE) An ordinary differential equation is a differential equation that has only one independent variable. For example, the.

Boyce/DiPrima 10th ed, Ch 10.5: Separation of Variables; Heat Conduction in a Rod Elementary Differential Equations and Boundary Value Problems, 10th.

THEORETICAL MODELS OF CHEMICAL PROCESSES

Basic Mechanical Engineering Courses

Scientific Computing Partial Differential Equations Introduction and

Analytical vs. Numerical Minimization Each experimental data point, l, has an error, ε l, associated with it ‣ Difference between the experimentally measured.

© 2014 Carl Lund, all rights reserved A First Course on Kinetics and Reaction Engineering Class 19.

© 2014 Carl Lund, all rights reserved A First Course on Kinetics and Reaction Engineering Class 26.

One model for the growth of a population is based on the assumption that the population grows at a rate proportional to the size of the population. That.

The complex exponential function REVIEW. Hyperbolic functions.

© 2014 Carl Lund, all rights reserved A First Course on Kinetics and Reaction Engineering Class 23.

FLUID PROPERTIES Independent variables SCALARS VECTORS TENSORS.

11/17/ Introduction to Partial Differential Equations Transforming Numerical.

3.1 Solving equations by Graphing System of equations Consistent vs. Inconsistent Independent vs. Dependent.

(1) The order of ODE: the order of the highest derivative e.g., Chapter 14 First-order ordinary differential equation (2) The degree of ODE: After the.

Differential Equations Brannan Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved. Chapter 09: Partial Differential Equations and Fourier.

PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences A Model Building Framework.

PROCESS MODELLING AND MODEL ANALYSIS © CAPE Centre, The University of Queensland Hungarian Academy of Sciences Modelling Lumped Parameter Systems C5A.

Chapter 1 Partial Differential Equations

Differential Equations Linear Equations with Variable Coefficients.

Differential Equations

CHAPTER VI BLOCK DIAGRAMS AND LINEARIZATION

ERT 210/4 Process Control & Dynamics DYNAMIC BEHAVIOR OF PROCESSES :

Team  Spatially distributed deterministic models  Many hydrological phenomena vary spatially and temporally in accordance with the conservation.

© 2016 Carl Lund, all rights reserved A First Course on Kinetics and Reaction Engineering Class 40.

Partial derivative b a. Let be defined on and let Define If has a derivative at we call its value the partial derivative of by at.

OBJECTIVES Students will able to Students will able to 1. define differential equation 1. define differential equation 2. identify types, order & degree.

Introduction to Differential Equations

Our task is to estimate the axial displacement u at any section x

CHE 354 Chemical Reactor Design

Solution to Homework 1 qi h1 h2 q1 qo a1 a2 v1 v2

Solution to Homework 2 Chapter 2

Introduction to Differential Equations

differential equations of heat transfer

Differential Equations

Chain Rules for Functions of Several Variables

3.2 Series of Continuous , constant-holdup Stirred-tank Reactors

CHAPTER VI BLOCK DIAGRAMS AND LINEARIZATION

MATH 270 Enthusiastic Studysnaptutorial.com

Simple Linear Regression - Introduction

FIRST AND SECOND-ORDER TRANSIENT CIRCUITS

Differential Equations Separation of Variables

Chapter 1:First order Partial Differential Equations

Sampling Distributions

Chapter One: Mole Balances

Chapter One: Mole Balances

Introduction to Ordinary Differential Equations

Linear Algebra Lecture 7.

Which cookie do you like?

Gradients and Tangents

Chemical Engineering Mathematics 1. Presentation Contents Chemical Engineering Mathematics2  Partial Differentiation Equation in long non-uniform rod.

State Equations: State determined system is a system in which the time derivatives of the variables describing the state (the state variables) are.

Chapter 1: First-Order Differential Equations

Presentation transcript:

KKEK 3152 MODELLING of CHEMICAL PROCESSES

Lumped vs Distributed parameter model

Lumped parameter model The model is homogeneous and consistent throughout the entire system Model is generally described by ordinary differential equation ◦ Varying only with one independent ◦ Eg: time

Example for lumped parameter model Stirred heating tank

With the suitable assumption the equation is derived to One independent variable

Distributed parameter model The model is heterogeneous and varying state within the system. The model is represented by partial differential equations. ◦ More than one independent variables ◦ Eg: spatial position and time

Example for distributed parameter model Shell and tube heat exchanger

With derivation and assuming delta t and delta z zero we get: More than one (two) independent variables