Design equations for continuous stirred-tank reactors

Design Equations for Continuous Stirred-Tank Reactors 

When a series of stirred-tanks is used as a chemical reactor, and the reactants are fed at a constant rate, eventually the system reaches a steady state such that the concentrations in the individual tanks, although different, do not vary with time. When the general material balance of equation 1.19 is applied, the accumulation term is therefore zero. Considering first of all the most general case in which the mass density of the mixture is not necessarily constant, the material balance on the reactant A is made on the basis of FA moles of A per unit time fed to the first tank. Then a material balance for the rth tank of volume V (Fig. 1.17) is, in the steady state  

Assuming that the contents of the tank are well mixed, aAr is also the fractional conversion of the reactant A in tank r. 

Stirred tanks are usually employed for reactions in liquids and, in most cases, the mass density of the reaction mixture may be assumed constant. Material balances may then be taken on the basis of the volume rate of flow v which is constant throughout the system of tanks. The material balance on A over tank r may thus be written, in the steady state  

In these equations Vcr/v- rr, the residence time in tank r. Equation 1.46 may be compared with equation 1.37 for a tubular reactor. The difference between them is that, whereas 1.37 is an integral equation, 1.46 is a simple algebraic equation. If the reactor system consists of only one or two tanks the equations are fairly simple to solve. If a large number of tanks is employed, the equations whose general form is given by 1.46 constitute a set of finite-difference equations and must be solved accordingly. If there is more than one reactant involved, in general a set of material balance equations must be written for each reactant. 

---