Nonlocal modeling of continuously stirred tank reactors with residence time distribution

Abstract The residence time distribution (RTD) has an important impact in the performance of chemical reacting systems. The segregated fluid assumption is commonly used to assess the analysis and design of chemical reactors. Models derived from the segregated fluid assumption for continuously stirred tank reactors (CSTR) rely on batch reactor models. A drawback of such assumption is that the CSTR model structure is not recovered in the limit when the RTD becomes very narrow (e.g., a Dirac delta). The aim of the present work is to propose a nonlocal modeling approach that is consistent with the CSTR model structure. The main idea is to represent the reactor as a continuum of tiny differential CSTRs determined by the RTD. The resulting nonlocal model is expressed as integrodifferential equations representing the interaction of reactive molecules of a given residence time with molecules of all residence times. By doing this, the nonlocal model is reduced to the usual CSTR model in the limit when the RTD is very narrow. The methodology was illustrated with three worked cases of dimerization, autocatalytic and series reaction schemes, and the results were compared with that obtained with the segregated fluid assumption. It was found that nonlocal models predict lower conversions than the segregated fluid models.