Optimum temperature gradients in tubular reactors—I: General theory and methods

Abstract

In this paper the mathematical techniques necessary for the determination of the optimum temperatures profile in a tubular reactor to insure maximum yields or minimum contact times are developed, and applications are made to reversible and consecutive reaction systems. The problem is shown to be reducible to a system of ordinary non-linear differential equations. The solution of these differential equations can be made by conventional numerical methods, and will allow the specification of the temperatures in the reactor. In a succeeding paper numerical calculations obtained with an analogue computer (REAC) will be presented. The problem of two consecutive reactions A → B → C, in which the reactions are of first or second order, is discussed in detail. The method of attack on more complicated problems is sketched. It is shown in general that appreciable gains in the yield may be obtained if the optimum temperature distribution is used.