A model can be looked at as an abstraction of reality, a simplified representation of the complex workings of a real world system. The model should be simple but at the same time be adequate for the purposes of modelling. It is important to remember that a model no matter how good cannot capture all the factors of a system, as Dr George Box puts it “All models are wrong but some are useful”.
The Systematic Modelling Approach is a seven stage processes, described as “more art than science”. It provides some key rules to follow for modelling, in my case process modelling. Initially the “problem definition statement” needs to be analysed, specifically to identify the process, modelling goal and the validation criteria. A system in which chemical and physical process are taking place is known as a process system. It is important to specify the boundaries, inputs, outputs and the physico-chemical process taking place within the system. I found one of the more important things to define properly is the modelling goal. It is important to remember that a modelling goal impacts not only the level of detail attained but also the mathematical form of the model, it is therefore vital to set an appropriate goal. To familiarise yourself with the different models check out: System Identification
1. Define the problem
The objective of this step is to set the degree of details relevant to your modelling goal. To achieve this, the following will need to be specified: inputs, outputs, hierarchy level, distributed or lumped model (spatial distribution), time characteristics, required range and accuracy of the model.
2. Identifying the controlling factors
To find the controlling factors an investigation must be carried out on the system to identify the physico-chemical processes and phenomena taking place. It is important to understand that as the modeller you will not be able to identify all the process characteristics and that a few will be incorrectly identified, it will never be perfect – unless you’re superhuman. Some of the most common controlling factors are chemical reactions, heat transfer (conduction, convection, radiation), evaporation, type of mixing, heat/mass transfer over boundary (boundary, see step 1) and fluid flow.
3. Evaluate the problem data
We need to determine or set the value of the data presented. It is quite common to find that the parameter values or measured data is not suitable for the model at this step, if this does happen we must go back and revise. Also remember to set the default precision values when evaluating, as this can affect the accuracy of the model.
4. Construct the model
You will need to identify the balance (Conservation) and Constitutive equations that usually take the form of differential and algebraic equations respectively. The model is then constructed from these to give a mathematical model.
5. Solve the model
Firstly we must ensure that the degrees of freedom are satisfied and then set up a solution procedure for the mathematical form that originates from the mathematical model. It is also a good idea to avoid high index systems as this can be time consuming even with computer aid.
6. Verify the model solution
It is important to make sure the model is implemented correctly and that it is producing the desired result. If you are programming the model, it might be a good idea to develop a verification procedure – depending on the complexity of your system.
7. Validate the model
There are many different ways to validate a model. Probably the most common are experimentally, analytically, comparisons between model & process behavior, compare with other models and comparing the process data directly with the model. Validation is important to ensure the quality of the model, if however the validation shows the model is not suitable, the modeller must return to step 2 and repeat the process.
It is good practice to maintain a sequence of events when designing a model. The systematic approach provides a simple seven step layout that has wide engineering applications not just for processing. Model building can get frustrating at times but keep in mind that no one gets it right the first time.
Bergman, T., Lavine, A., Incropera, F. (2011).Fundamentals of Heat and Mass Transfer 7Ed. John Wiley.
Green, D. W., & Perry, R. H. (2008). Perry’s Chemical Engineer’s Handbook. McGraw-Hill.
Hangos, K.M. and Cameron, I.T. (2001). Process Modelling and Model Analysis.California: Academic Press.