For the fixed-bed reactors such as adiabatic multistage reactors, autothermic reactors and externally cooled reactors, the authors studied on the process optimum condition. which means the condition where the necessary amount of catalyst in VR/F is minimized when the conversion is specified.
Considering the reaction whose rate at a given composition of the reaction mixture have maximum at a temperature, as in the ammonia synthesis and the catalytic oxidation in sulphur dioxide, the authors extended Konoki's treatment for the adiabatic multistage reactor^{3, 4)} in whose operation maximum temperature is fixed, into the more general form, Eq. (18) through Eq. (21). These results were sucessfully applied to the sulphur dioxide convertor of adiabatic 3-stage.
For the autothermic process with two flow paths (Fig. 5), the authors using the simpler design equation (30) instead of Eq.(24), proposed a graphical method of solution based on Picard's method.¹⁰⁾ By this method we can easily determine optimum Γ and T₁₀ As an example the authors showed the result of trial and error for the determination of T and T₁₀ for the autothermic ammonia synthesis process. The basic equations (32) for the externally cooled reactor can be also reduced to the simpler form, Eq. (35), and so the same method above described will be employed.