Balance region

Choose the balance region such that the variables are constant or change little within the system. Draw boundaries around the balance region... 

If the tank is well-mixed, the concentrations and density of the tank contents are uniform throughout. This means that the outlet stream properties are identical with the tank properties, in this case concentration Ca and density p. The balance region can therefore be taken around the whole tank (Fig. 1.5). 

Figure 1.5. The balance region around the continuous reactor.

Figure 1.7. Choosing balance regions for lumped and distributed parameter systems.

Having defined the balance regions, the next task is to identify all the relevant inputs and outputs to the system (Fig. 1.10). These may be well-defined physical flow rates (convective streams), diffusive fluxes, but may also include interphase transfer rates. 

Figure 1.10. Balance region showing convective and diffusive flows in and out.

In this section the application of the total mass balance principles is presented. Consider some arbitrary balance region, as shown in Fig. 1.14 by the shaded area. Mass accumulates within the system at a rate dM/dt, owing to the competing effects of a convective flow input (mass flow rate in) and an output stream (mass flow rate out). 

Each chemical species, in the system, can be described by means of a component balance around an arbitrary, well-mixed, balance region, as shown in Fig. 1.16. 

I. Choose the Balance Region Such That the Variables Are Constant or Change Little Within the System. Draw Boundaries Around the Balance Region... 

Fig. 1 Chromatographic column showing a mass balance region.

It should be noted that taking the balance region over both the combined phases, as done in this example, is useful only for linear equilibrium. In general the best method is to use a transfer rate model, as described in Section 4.4.4, and to make balances for each component in each phase separately. 

Fig. 1 Balance regions for heavy metal transport for a lake in the Netherlands.

Kling H, Nachtnebel HP, Ftirst J (2005) Water balance regions, climatic water balance and runoff characteristics. Hydrological Atlas of Austria, Plate 7.1, Wien... 

In Ref. 139 a purely numerical approach to the solution of the considered complex RA problem was suggested. The liquid film is treated as an additional balance region, in which reaction and mass transfer occur simultaneously. Therefore, the reactions are considered both in the liquid-bulk-phase mass balances, Eq. (Al), and in the differential balances for the liquid film, Eq. (A10). 

The energy balance is available as a further equation. In order to set this up we will consider a balance region on the gas side, depicted by the dotted lines in Fig. 1.53, from the gas at the surface of the film to a point y. The energy balance... 

This volume integral only disappears for any chosen balance region if the integrand... 

As the balance region can be infinitely small, it holds that... 

The material balance around the dotted balance region, Fig. 2.60, yields... 

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