Tubular reactors dispersion coefficient correlation

The model is referred to as a dispersion model, and the value of the dispersion coefficient De is determined empirically based on correlations or experimental data. In a case where Eq. (19-21) is converted to dimensionless variables, the coefficient of the second derivative is referred to as the Peclet number (Pe = uL/De), where L is the reactor length and u is the linear velocity. For plug flow, De = 0 (Pe ) while for a CSTR, De = oo (Pe = 0). To solve Eq. (19-21), one initial condition and two boundary conditions are needed. The closed-ends boundary conditions are uC0 = (uC — DedC/dL)L=o and (dC/BL)i = i = 0 (e.g., see Wen and Fan, Models for Flow Systems in Chemical Reactors, Marcel Dekker, 1975). Figure 19-2 shows the performance of a tubular reactor with dispersion compared to that of a plug flow reactor. 

Results from the previous section in this chapter illustrate how and when interpellet axial dispersion plays an important role in the design of packed catalytic tubular reactors. When diffusion is important, more sophisticated numerical techniques are required to solve second-order ODEs with split boundary conditions to predict non-ideal reactor performance. Tubular reactor performance is nonideal when the mass transfer Peclet number is small enough such that interpellet axial dispersion cannot be neglected. The objectives of this section are to understand the correlations for effective axial dispersion coefficients in packed beds and porous media and calculate the mass transfer Peclet number based on axial dispersion. Before one can make predictions about the ideal vs. non-ideal performance of tubular reactors, steady-state mass balances with and without axial dispersion must be solved and the reactant concentration profiles from both solutions must be compared. If the difference between these profiles with and without interpellet axial dispersion is indistinguishable, then the reactor operates ideally. 

---