Component balance piston flow

While true, this result is not helpful. The derivation of Equation (1.6) used the entire reactor as the control volume and produced a result containing the average reaction rate, In piston flow, a varies with z so that the local reaction rate also varies with z, and there is no simple way of calculating a-Equation (1.6) is an overall balance applicable to the entire system. It is also called an integral balance. It just states that if more of a component leaves the reactor than entered it, then the difference had to have been formed inside the reactor. 

A differential balance written for a vanishingly small control volume, within which t A is approximately constant, is needed to analyze a piston flow reactor. See Figure 1.4. The differential volume element has volume AV, cross-sectional area A and length Az. The general component balance now gives... 

Piston Flow in Contact with a CSTR. A liquid-phase reaction in a spray tower is conceptually similar to the transpired-wall reactors in Section 3.3. The liquid drops are in piston flow but absorb components from a well-mixed gas phase. The rate of absorption is a function of as it can be in a transpired-wall reactor. The component balance for the piston flow phase is... 

Axial Dispersion. Enthusiastic modelers sometimes add axial dispersion terms to their two-phase, piston flow models. The component balances are... 

Unlike stirred tanks, piston flow reactors are distributed systems with one-dimensional gradients in composition and physical properties. Steady-state performance is governed by ordinary differential equations, and dynamic performance is governed by partial differential equations, albeit simple, first-order PDEs. Figure 14.6 illustrates a component balance for a differential volume element. 

Problems due to piston turnaround can often be relieved by proper output hose selection. Hose diameters should be selected so that the dynamic component pressures at the mixer will be equal. Hose line pressure drop is affected by viscosity, flow rate, and hose diameter. The hose diameter usually is the only one of these factors that the designer can change and in order to compensate for differences in flow rate or viscosity between components, hoses should be selected that will yield the desired balanced pressures. The formula for pressure drop in hoses is given by Eq. (1). 

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