Temperature-Dependent Kinetic Prediction for Reactions Described by Isothermal Mathematics

Abstract

Most kinetic models are expressed in isothermal mathematics. This may lead unaware scientists either to the misconception that classical isothermal kinetic models cannot be used for any chemical process in an environment with a time-dependent temperature profile or, even worse, to a misuse of them. In reality, classical isothermal models can be employed to make kinetic predictions for reactions in environments with time-dependent temperature profiles, provided that there is a continuity/conservation in the reaction extent at every temperature-time step. In this article, fundamental analyses, illustrations, guiding tables, and examples are given to help the interested readers using either conventional isothermal reacted fraction curves or rate equations to make proper kinetic predictions for chemical reactions in environments with temperature profiles that vary, even arbitrarily, with time simply by the requirement of continuity/conservation of reaction extent whenever there is an external temperature change.

Hydrogen Uptake Kinetics of 1,4-Bis(phenylethynyl)benzene (DEB) Rubberized Coating on Silicone Foam Substrate

“…The kinetic prediction model presented here can also be applied to cases in which even the macroscopic temperature varies with time, as long as a history of environmental temperature change exists and the continuity in the cumulative reacted fraction is kept under check during modeling. 31 Effects of the Rubber Components and the Polymer Support on the H 2 Uptake. The differences between the current DEB-Pd/C rubber composite on silicone foam and the pressed DEB-Pd/C pellets 7 are that the DEB-Pd/C pellets are porous in structure and have no rubber in their composition and no silicone foam support.…”

“…Despite the complex uptake mechanism, the overall agreements between the dynamic uptake curves and prediction models based on isothermal isobaric data confirm that kinetic parameters extracted by the isoconversional analysis as employed in eq can be used to make reliable uptake kinetic predictions under a variety of complex vacuum or H 2 pressure situations. The kinetic prediction model presented here can also be applied to cases in which even the macroscopic temperature varies with time, as long as a history of environmental temperature change exists and the continuity in the cumulative reacted fraction is kept under check during modeling …”

General H2O Outgassing Model Applicable to Silica-Filled Silicones

“…In reality, the reaction conversion level, once achieved at a temperature, should not decrease because of a drop in the temperature. Thus, the "time correction" method 36 (discussed in the Modeling section) has been adapted here to estimate the conversion profile for dynamic temperature scenarios. One such scenario has been taken here as an example to predict the long-term moisture outgassing behavior from TR55.…”

“…Instead, time correction can be estimated for the temperature variation during the reaction to estimate the conversion level accurately. For a temperature change condition (from T o to T 1 ) during a time step (Δ t o + Δ t 1 ), the corrected time (using previous conversion α Δ t o ) and the new conversion (with corrected time) can be calculated as where F –1 is the inverse function of time-dependent function F of the conversion equation. For the first-order reaction (as in eq ), time correction can be computed as and for the second-order reaction (as in eq )­ …”

Continuous Stirred Tank Reactor: A Process Design for Interesterification of Macauba (Acrocomia aculeata) palm oil

“…Previous kinetic evaluation of carotenoids degradation in vegetable oil importantly indicates a first-order reaction kinetic mechanism (Aparicio-Ruiz, Isabel Minguez-Mosquera & Gandul-Rojas, 2011;Knockaert et al, 2012). Through mathematical and predictive modelling and simulation, industries can benefit from the use of kinetic data and procedures to enhance knowledge and understanding of thermal food processing (Dinh, Sun & McLean, 2016;Singh, Singh & Ramaswamy, 2015). The present study was undertaken primarily to develop a continuous version of the kinetic treatment of total carotenoids degradation reactions, through mathematical and predictive modelling, considering the thermal effects of conventional processes conditions usually applied for the interesterification of vegetable oils.…”