Analytical Models for the Basic System

The analytical models developed in this part of the study describe the performance of the basic system and allow one to predict the output signal produced by the system when its operational parameters are known. Unlike previous work [76-86], these models explicitly take into account the operational mode of the system (i.e., the reactor type in which the reactions involved take place). This approach was taken in order not only to use these analytical models for numerical simulations, but also to allow us to interpret the experimental results obtained using real systems (Section 4.3) and to assess the validity of the analytical models employed. The models developed are based on mass balances of the components involved and on the characteristics related to the particular reactor used. Unless otherwise indicated, the simulations described below were carried out using these types of input signals with variations of the parameters defined above. 

In the fed-batch (semicontinuous) operation mode, substrates are fed into the reactor but no material is removed from the reactor. Therefore, the total volume of the material within the reactor increases as a function of time. For this reactor type the mass balance for each component of the reaction mixture is given by 

Cjfi = concentration of component j in the feed stream t = time 

Qj = volumetric flow rate of the inlet stream feeding component j Tj = rate of production of component j by reaction 

Assuming that the density of the reaction mixture is not affected by the inlet streams, equation (4) can be simplified  

---