The Rates of a Bioprocess

The concentration-time profile for the six process variables shown schematically in Fig. 2.3 is shown in Fig. 2.4. This is for the case of a discontinuous process with constant reactor volume Conditions that can be observed and 

Varible concentration (g-r ) Absolute rate (g-l -h- ) specific rates [h ]  

The flow of mass = d N/A)/dt can be due to various kinds of transport phenomena, and it is described by various terms (for example, the convective flow velocity v or conduction through a gradient, that is, diffusion, D or dispersion, or interfacial transport, /cjr (see Fig. 2.3). 

A change in the concentration Cj with time is expressed in Equ. 2.3. In general, the equation can be written using a vector operator V (grad = partial derivative with respect to a direction coordinate) as follows  

Separating the various transport terms with n- = Cj u and v = F/A, this equation can be written in vector notation as 

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