Aspects of Mass, Heat and Momentum Balances

The first step toward the calculation of the conversion of feed component A in the reactor consists of applying the law of conservation of mass on a volume element of the reactor, fixed in space  

In mathematical terms (7.2-1) is nothing but the so-called continuity equation for A. If A reacts in more than one phase, such an equation is needed for each of these phases. 

In a plug flow reactor all fluid elements move with equal velocity along parallel streamlines. The plug flow is the only mechanism for mass transport, and there is no mixing between fluid elements. The reaction, therefore, leads to a 

Reactors with complete mixing may be subdivided into batch and continuous types. In a batch-type reactor with complete mixing, the composition is uniform throughout the reactor. Consequently, the continuity equations may be written for the entire contents, not only over a volume element. The composition varies with time, however, so that a first-order ordinary differential equation is obtained, with time as variable. The form of this equation is analogous with that for the plug flow case. In the continuous flow type, an entering fluid element is instantaneously mixed with the contents of the reactor so that it loses its identity. This type also operates at a uniform concentration level. In the steady state, the continuity equations are algebraic equations. 

In an energy balance over a volume element of a chemical reactor, kinetic, potential, and work terms may usually be neglected relative to the heat of reaction and other heat transfer terms, so that the balance reduces to 

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