Strategies for simplifying mathematical models

A simulation may contain both errors and uncertainties. An error is defined as a recognizable deficiency that is not due to lack of knowledge, and an uncertainty is a potential deficiency that is due to lack of knowledge. All simulations must be validated and verified in order to avoid errors and imcertainties. Validation and verification are two important concepts in dealing with errors and uncertainties. Validation means making sure that the model describes die real world correctly, and verification is a procedure to ensure that the model has been solved in a correct way. 

Poor simulation results are due to many different reasons  

It is always recoimnended diat you do simple by-hand calculations to define the properties of die system prior to formulating the final model. The objective of this chapter is to present strategies for simphfying given mathematical models and for reducing the models already in the formulation. 

Many models in chemical engineering are derived from four basic balance equations, as seen in Chapter 4, but now we have also included the source terms for chemical reactions and heat formation. 

There are general programs that can solve these equations for simple systems, e.g. computational fluid dynamics, CFD. However, the equations can easily become very difficult if they include stiff non-linear equations and complex geometry that call for a structured approach. 

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In a commercial methanol plant, it is economicafly desirable to maintain a constant methanol production rate as the catalyst ages. With conventional, fixed-bed reactors, the feed temperature is raised gradually with time to compensate for catalyst deactivation. The mathematical model of catalyst deactivation developed in the previous section was used to test the feasibility of this strategy for a single slurry methanol reactor operating with CO-Rich Gas. The reactor was assumed to be completely backmixed, which simplifies the mathematics of the analysis [ref. 7]. 

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