introduction to modelling in egineering
DESCRIPTION
University lecture note on general chemical engineering modelling. "Chapter 1"TRANSCRIPT
ModelRepresents the physical world
𝑢
𝑡𝑖𝑒𝑚𝑝𝑜
𝑦
𝑡𝑖𝑒𝑚𝑝𝑜
𝑦𝑚
𝑡𝑖𝑒𝑚𝑝𝑜
Model
It includes only the important aspects of the phenomena
“All models are wrong, but some are useful”
Models
Assumptions define the context in where the model is used.
¿Does the model predict the behaviour of the system at the level that is required?
A model is ONLY valid in the context and under the assumptions made during its development.
Using a model to calculate some behaviour far from its assumptions is wrong.
A model needs to be always verified.
There are a lot of models that can be use to describe a system. Each of these models show different aspects of the system.
Important details of modelling
Why do we use models?
Frequently to
• Design• Training• Take decisions …
To predict and understand the behaviour of the system
• What actually happens during the process?• What would happen if?• How can the process be optimum?
Develop control systems
• How to keep the system close to a desired value?
Classification of Models• They are:
• Heuristic• Intuitive• Not too accurate
Mental model
• They are:• Linguistic => they describe the process• QualitativeSymbolic
• They are:• A set of equations that shows the relationship
between process’ variables
Mathematical models
• They are:• Expensive,• Complicated to build up and use
Physical models
Mathematical modelsDiscreet and continuous
• Discrete: particulate system, system made of states
• Continuous: fluid flow, vector fieldTime dependent
• Dynamic: it accounts for time dependent changes in the system.
• Static: the system is at the equilibrium and it is time invariant.Spatial distribution
• Lumped parameters: • Distributed parameters
Linear and non linear
• Linear• Non linear
Theoretical and empirical
• Theoretical:• Empirical
General info click here
Discrete and continuous models
Continuous models• Variables change with time and can have any value. • Example: Temperature• These models are described from transport phenomena, momentum,
mass and energy balances.
Discrete models• Variables change in discrete manner and they have a limited number of
values• These modes describe processes that follow sequences of steps.
Static and dynamic models
• Variables are at the equilibrium state
Static models:
• Variables change with time
Dynamic models:
𝑡𝑖𝑚𝑒
𝐹 𝐸
h
Lumped and distributed parameters models
Lumped parameters)• A variable is a function of time but no position
• Stirred tank (Ordinary differential equations)
Distributed parameters• A variable is a function of time and at least one space variable (Partial
differential equations).• Tubular reactor [CA = f(L, r, t)]• Heat exchangers
Linear and non linear models
• They are represented by linear differential equations (Superposition principle)
Linear models:
• They are represented by non linear differential equations. – Chaos Theory -
Non linear models:
𝑥1(𝑡) System 𝑦 1(𝑡)𝑥2(𝑡) System 𝑦 2(𝑡)
𝑎𝑥 1(𝑡)+𝑏𝑥2(𝑡) System 𝑎𝑦 1(𝑡)+𝑏𝑦 2(𝑡 )
Theoretical and empirical models
Theoretical model• Physical insight of the process behaviour.• Applicable in a wide range of conditions.• Good understanding of the process.• Expensive and time consuming to develop.• Include some information difficult to obtain.
Empirical models• Inexpensive to develop.• Easy to develop.• Do not extrapolate well.
What does it make a good model?
Accuracy
• The most accurate model some time is not the best
Applicability
• Range of application• Conditions of use
Complexity
• Simple (macroscopic)• Detailed (microscopic)
Easy to use
Accurate
Occam’s Razor
• The principle states that among competing hypotheses that predict equally well, the one with the fewest assumptions should be selected. http://en.wikipedia.org/wiki/Occam%27s_razor
Workshop 1
Now you have 30 min to solve this questions
1. Search on the web for three models that are usually use in your engineering field. You need to A. Describe de models. If it is a mathematical model you need to develop
mental model that describes it. B. Indicate the assumptions and limitations of the model.C. Classify the models according to the classifications given in class.