Generalization of the integral and differential method for analysis of rate data by means of the fractional calculus

Abstract

AbstractThe kinetic study of chemical reactions is usually carried out by means of analysis of experimental rate data obtained during the evolution of a reaction in a batch reactor. The methods for analysis of rate data obtained in a batch reactor include the classical integral methods (CIM) and classical differential methods (CDM), which use temporal derivatives of the unit‐order concentration, dCA/dt, in the mass balance equation. The present study proposes these two methods of analysis in a generalized formulation that makes use of non‐integer order temporal derivatives, dαCA/dtα, 0<α ≤ 1, called generalized integral method (GIM) and generalized differential method (GDM) in the present work. The solutions of the fractional ordinary differential equations (FODE) of GIM are presented using the Laplace transform technique and numerical fractional derivative evaluation methods for GDM application. The proposed generalized methods allow for the determination of the order and the specific reaction rate in the same way as the classical methods, that is, of integer order (α = 1); however, generalized methods have the additional advantage of determining the fractional order of the temporal derivative.