Systematic Approach for Developing Dynamical Models
1. State the modelling objectives. This is to determine the model accuracy.
2. Sketch streams of the process.3. Define the accuracy of the model.4. Define is the process is on steady state or transient
state.5. Define is the model is on 1, 2 or 3D.
Definition of the problem
Systematic Approach for Developing Dynamical Models
Definition of the problem
Define the limiting factors of the process
Chemical
Reaction
Diffusion
Heat transfe
rMass Transfe
rMixing
Fluid dynami
cs
Systematic Approach for Developing Dynamical Models
Define the limiting factors of the process
Systematic Approach for Developing Dynamical Models
Cold stream
Hot OilCan you find the limiting factors here?
Define the limiting factors of the process
Systematic Approach for Developing Dynamical Models
Cold stream
Hot Oil
Can you find the limiting factors here?
Flows in and out Heat transfer between the jacket and the
vessel Work Heat lost through the jacket Heat lost on the liquid surface Evaporation
Define the limiting factors of the process
Systematic Approach for Developing Dynamical Models
Definition of the problem
Define the limiting factors of the process Developing the model
Systematic Approach for Developing Dynamical Models
Develop model equations.• T
ransport phenomena (differential equation).
• Global mass and energy balances (algebraic equations).
Verify the model:• D
egree of Freedom analysis.
Double check units and dimensions
Developing the model
Systematic Approach for Developing Dynamical Models
Developing the model
Define the system where the analysis is performed
Define variables of the momentum, material and energy balances such as flows in and out and accumulation.
Develop the necessary balances.
Use the different models for the transport mechanism of momentum, mass and energy
Develop other equations to model the behaviour of the system such as EoS.
Developing the model’s equations
Systematic Approach for Developing Dynamical Models
Developing the model
Verifying the model
𝐷𝑂𝐹=N umber of variables – N umberof equations
A system is completely defined ONLY when DOF = 0
Underspecified system
There are more unknowns that equations. - Reduce the number
of specified variables
- Find more equations
Over specified system
There are two types
Redundant•Equations are not independent from each other
Inconsistent•The system cannot be solve.
Always CHECK the DOF of the model
Systematic Approach for Developing Dynamical Models
Definition of the problem
Define the limiting factors of the process Developing the model
Solve the model
Systematic Approach for Developing Dynamical Models
Solving the model
Define the type of equations to solve
Select a solution method of the system- Analytical solution- Numerical methods
When possible avoid ill posed problems where the system can have conversion problems
Systematic Approach for Developing Dynamical Models
Definition of the problem
Define the limiting factors of the process Developing the model
Solve the model
Validation of the model
Systematic Approach for Developing Dynamical Models
Validation of the model
Compare the behaviour of the model with expected results. Is the model giving reasonable data?
Compare results with some experimental data. Use statistics to verify your data.
Fix the model if the data are not reflecting the expected values.
Experimental verification.
Compare the model against the real process.
Compare the model against some reported data.
Workshop 2
Now you have 30 min to solve the following questions