Axial Flow Operations with Longitudinal Dispersion and Chemical Reaction

Abstract

Methods of predicting the extent of chemical reaction or mass transfer are presented for onedimensionalaxial flow systems accompanying longitudinal dispersion, chemical reaction and othertransport phenomena. Four typical cases are treated as follows.Case 1 Two-phase mass-transfer operation with fast irreversible second-order reaction:Basic differential equation, Eq.(4), for the column operation are reduced to those for simplemass-transfer case by defining the nondimensional terms included in Eq.(5) as Eq.(6). Previoustheoretical analysis is indicated entirely applicable to this new situation by defining those terms inthis manner.Case 2 Two-phase mass-transfer operation with slow first-order irreversible reaction:With negligible reactant concentration in the liquid bulk of phase Y this case is indicatedequivalent to that of one-dimensional homogeneous phase reactor accompanying simple first-orderreaction. When the reactant concentration in phase Y has a finite value, analytical solution of thebasic rate equation is complicated in its form and not convenient for design purpose (see appendix).Case 3 Homogeneous-phase nonisothermal chemical reactor of back-flow model type:Chemical reactors of the type of back-flow model, which assumes multi-cell type column withinterstage mixing of fluid between adjacent perfectly mixed cells, is treated in this section and thenext following.For homogeneous case the operation is shown in Fig. 2. Eq.(11)-(16) are obtained for heat andmass balances, and used to calculate the values at the 1st stage from the values of the N-th stage, which must be fixed at first. Sample calculations for the case of first order reaction are shown in Fig. 3 to 6; Fig. 3 and 4 show the effect of interstage mixing, reaction rate, and wall heat transfer; Fig. 5, 6 show the effect of the number of division. These are calculated by a digital computerHIPAC-101. Solutions by this method are exact, when interstage mixing really exists, and are goodapproximate solution for the diffusion model with enough higher number of division, because thedifferential equations of the diffusion model (Eq.(17), (18)) can be written in a finite differenceform same as Eq.(11)-(16). P-B has a relation expressed by Eq.(19) for heat and mass.Case 4 Two-phase nonisothermal cell-model reactor with interstage mixing:Operation is shown in Fig. 7. When the rate processes taking place in the dispersed phase isfirst order, this phase can be regarded as the second continuous phase under some restriction. Therefore the basic equations are Eq.(22)-(30), where interstage mixing flow of phase Y (dispersed)is neglected, since usually the hold-up of this phase is rather small. As an example, countercurrent nitration of toluene by mixed acids is treated and shown in Fig. 8. In this case, 6 stages are enough to convert 90% of toluene to mononitrotoluene. These methods are enoughuseful for design purposes in such complicated cases.