Modelling simulation of chemical processes

Under isothermal/isobaric conditions the transformation processes of a chemical reaction can be modelled depending on the behaviour of the concentrations in time given a certain temperature. To get an idea, assume the simple splitting reaction 

Assuming a constant volume of the reactants and processing the reaction in a stirred-tank reactor one important question is to determine the time needed to achieve a desired turnover rate. To answer this question, (2.15) is solved exactly to f = -jln(l - X) for a given turnover ratio X. Normalizing this result by the reaction constant k leads to the 

In general, Damkohler numbers approximate the reaction time necessary to achieve a desired concentration/turnover rate. To calculate the Damkohler numbers for nth-order reactions, the concentration differential equation can be derived directly by the following 

For more complex reactions the derivation of Damkohler numbers is much more complicated.  

Under adiabatic conditions heat flows have to be modelled accordingly with respect to the mass balances. For exothermic reactions usually a stimulation of the chemical reaction is required due to the higher energy level at the beginning of the reaction. In general, the interactions between heat and mass balances are more difficult to model. More complicated cases occur when both conditions are mixed, i.e. under polytropic conditions. Here, solutions for heat and mass balances are hardly available analytically. Instead, 

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