Correct Use of the Bhatia and Perlmutter Random Pore Model under Nonisothermal Conditions

The classic random pore model (RPM) of Bhatia and Perlmutter [A random pore model for fluid-solid reactions: I. Isothermal, kinetic control. AIChE J.1980, 26, 379-386], which has been used in the kinetic analysis of numerous gas-solid processes involving porous materials under reaction control, was originally derived only for isothermal conditions. This has not prevented many researchers from using it in nonisothermal conditions, a frequent procedure whose validity has not been demonstrated until now. In this work, different questions are answered: Are the isothermal equations of the RPM valid under nonisothermal conditions? And, related to this question, is the commonly used conversion function correct? This work provides the scientific basis that was missing until now for the use of the RPM in nonisothermal conditions, as well as the correct conversion function for such use over the entire particle size range. The said RPM conversion function has been obtained from the exact formulation of the reaction rate equation, and as it should have been originally, it has the grain model function as one of its particular solutions. In this way, the gap that prevented the use of the random pore model for very low particle size values has finally been closed.