Dimensionless equations, external mass transfer resistance

The important dimensionless parameter that determines the significance of external mass transfer resistance for nth-order irreversible chemical kinetics in packed catalytic tubular reactors was introduced in equation (30-63) as a = iS(CA.iniet)" Simple algebraic manipulation allows one to relate a to the interpellet Damkohler number, the effectiveness factor, the mass transfer Peclet number, and a few other dimensionless parameters. For example, let the coefficient of the chemical reaction term in the dimensionless mass transfer equation be defined as follows ... 

This mass transfer resistance and the reaction kinetics are usually compared using a dimensionless ratio, Damkohler number. Da, as in Equation 4.49. If Da is greater than unity, then the mass transfer resistance is significant and the reaction of the external diffusion is limited. On the other hand, when Da is less than unity, the reaction, in this case, is surface reaction limited. 

For the nonisothermal catalyst pellet with negligible external mass and heat transfer resistances, i.e., with Sh —> 00 and Nu —> 00 and for a first-order reaction, the dimensionless concentration and temperature are governed by the following couple of boundary value differential equations... 

The effectiveness factor E is evaluated for the appropriate kinetic rate law and catalyst geometry at the corresponding value of the intrapellet Damkohler number of reactant A. When the resistance to mass transfer within the boundary layer external to the catalytic pellet is very small relative to intrapellet resistances, the dimensionless molar density of component i near the external surface of the catalyst (4, surface) IS Very similar to the dimensionless molar density of component i in the bulk gas stream that moves through the reactor ( I, ). Under these conditions, the kinetic rate law is evaluated at bulk gas-phase molar densities, 4, . This is convenient because the convective mass transfer term on the left side of the plug-flow differential design equation d p /di ) is based on the bulk gas-phase molar density of reactant A. The one-dimensional mass transfer equation which includes the effectiveness factor. 

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