Steady State Models for Isothermal Heterogeneous Distributed Systems

3 The Design Equations (Steady-State Models) for Isothermal Heterogeneous Distributed Systems 

As explained in detail for homogeneous systems in Chapter 4, a distributed system includes variations in the space direction. Therefore for a distributed system we can not use the overall rate of reaction, i.e., the rate of reaction per unit volume multiplied by the total volume, nor the overall rate of mass transfer, i.e., the mass transfer per unit area multiplied by the area of mass transfer. For lumped systems the area of mass transfer is treated as the multiple of the area per unit volume of the process multiplied by the volume of the process for the design equations. 

As an illustration, let us consider a system with the single reaction 

Here the-balance equation for phase I, or the first design equation is 

Rearranging equation (6.50) and taking the difference quotient limit as Ay — 0 gives us 

---