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