Fluxes in Reactor Mass Balances

The expressions that we obtained for the molar flux of very slow, slow, normal, fast, and infinitely fast reactions are inserted into the mass balances of the ideal reactor models. The molar flux at the gas-liquid interface was derived for ideal reactor models for plug flow column reactors (Equations 7.15 and 7.16), for stirred tank reactors (Equations 7.22,7.25, and 7.26), and for BRs (Equations 7.33 and 7.34)  

The expression for molar flux, N[j, was derived for different kinds of reactions. The flux from the liquid film to the liquid bulk (required for the mass balances) is equal to the flux from the liquid film to the solid surface, Nlj, for very slow reactions (no reaction in the liquid film). For other types of reactions, the flux is obtained from the concentration profile of the liquid bulk cla(z) by calculating the derivative dcLA/dz and inserting it into Equation 7.36. 

In its most general form, the problem can be solved with N + 2 N = number of reactions) differential equations (column reactor and BRs) or algebraic equations (CSTR). If the column reactor operates in a countercurrent mode, the mass balances pose a boundary value problem. For concurrent column reactors and BRs, the mass balances are solved as initial value problems. 

The same numerical methods as those used to solve the homogeneous reactor models (PFR, BR, and stirred tank reactor) as well as the heterogeneous catalytic packed bed reactor models are used for gas-Uquid reactor problems. For the solution of a countercurrent column reactor, an iterative procedure must be applied in case the initial value solvers are used (Adams-Moulton, BD, explicit, or semi-implicit Runge-Kutta). A better alternative is to solve the problem as a true boundary value problem and to take advantage of a suitable method such as orthogonal collocation. If it is impossible to obtain an analytical solution for the liquid film diffusion Equation 7.52, it can be solved numerically as a boundary value problem. This increases the numerical complexity considerably. For coupled reactions, it is known that no analytical solutions exist for Equation 7.52 and, therefore, the bulk-phase mass balances and Equation 7.52 must be solved numerically. 

For systems with only one reaction, the number of necessary balance equations can be reduced by setting up a total balance both at the reactor inlet (i.e., liquid feed inlet) and at an arbitrary location in the reactor. This is illustrated for the concurrent case, for components 

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