I am still wondering to exactly differentiate both tools irrespective of their words' meaning. I have seen in literature that they are applying kinetic equations and heading it mathematical modeling. Same way, at many times applying mathematical models to estimate kinetic parameters. Are they same tools to describe any physical phenomena through mathematical or kinetic equations?
Elaboration will highly be appreciated.
Thanks,
Asim
A kinetic model is a set of elementary (ideally but could be uni- or bimolecular) reactions with values of rate constants. A mathematical model is set of mathematical (differential) equations is built based on this set of reactions (often called the reaction mechanism). Commonly, the solution of these differential equation can't be presented as a set of simple formulas describing the change of concentrations as a functions of time. A digitaal integration is used in this case.
If all reaction constants are known, then the model quantitatively describes all experimental kinetic data and can simulate the kinetics at different conditions. If some rate constants are not known, then they can be extracted by the mathematical procedure which is called a fitting. The, these rate constants can be used for a simulation of kinetics.
I don't understand what is a mathematical model without a kinetic model. A kinetic model is the reaction mechanism with all rate constants. Based on this model the reaction kinetics can be quantitatively described using certain mathematical algorithm. If some rate constants are not known, they can be extracted from experimental data by fitting. In other words, in order to simulate the reaction kinetics under different conditions you need to know the reaction mechanism.
I am not sure exactly what the question is but there are some "Expert System" process control systems that work completely independent of rigorous kinetic modelling. They simply regress all of the data accumulated during a run with a heavier weighting towards most recent data. This type of modelling approach can work well if you are only interested in staying very close to operating conditions you have already visited. I would not trust these methods to extrapolate to operating regions that the unit has never visited before. For that I would insist on a kinetic model and an abundance of caution.
I agree with Rick with his approach as a chemical engineer. To build a kinetic model of an industrial process is the Gargantuan job. Any kinetic model should be used with " an abundance of caution."
Kinetic models are formulated mainly by differential equations. It seems to me that kinetic models are one of the types of mathematical models.
Is it right to ask whether there is a difference between a linear model and a mathematical model. I think not, because the linear model is a class of a mathematical model. The external difference between mathematical models is that one model has an objective function, and the other does not have it. As I understood from sources, the kinetic model is found mainly in biophysical processes. As a rule, many processes are expressed in the form of mathematical models without goal functions. For example. known heat equation. I'm sorry if I misunderstood you.
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