Analytical and Numerical Solutions of Balance Equations for Three-Phase Reactors

4 ANALYTICAL AND NUMERICAL SOLUTIONS OF BALANCE EQUATIONS FOR THREE-PHASE REACTORS 

An analytical solution of the mass balance equations for three-phase reactors is possible in the case of isothermal reactors and reactions of first-order only. Analytical solutions [1,8] are rather cumbersome even in these cases. Some analytical solutions for effectiveness factors are listed in Table 6.4. This is why a numerical solution is preferred. Case studies will briefly 

The balance equations for column reactors that operate in a concurrent mode as well as for semibatch reactors are mathematically described by ordinary differential equations. Basically, it is an initial value problem, which can be solved by, for example, Runge-Kutta, Adams-Moulton, or BD methods (Appendix 2). Countercurrent column reactor models result in boundary value problems, and they can be solved, for example, by orthogonal collocation [3]. The backmixed model consists of an algebraic equation system that is solved by the Newton-Raphson method (Appendix 1). 

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