Probability theory for inverse diffusion: Extracting the transport/kinetic time-dependence from transient experiments

Detailed kinetic data is an essential component of process and catalyst development. Transient experiments can provide abundant kinetic information describing the evolution of the reaction rate with respect to the gas concentration, but require more complex analysis than steady-state experiments as they must contend with the separation of transport and kinetic information as a function of time. With the Temporal Analysis of Products (TAP) reactor and Fourier domain based transformations via the Y-Procedure, kinetic information may be separated from transport without any mechanistic assumptions, but there is a strong influence of experimental noise, Yablonsky et al. [1] As an alternative, this work is focused on connecting steady-state reactor assumptions to the TAP experiment through the use of the residence time distribution. The proposed residence time distribution for the TAP reactor, and the following algorithm referred to as the G-Procedure, is shown to measure time-dependent rate and concentration information in the active zone of the reactor while being mechanistic and diffusional model free. We compare the differences of the Y- and G-procedure in the form of estimation of concentration and rate on synthetic and experimental data consisting of platinum oxidation and ammonia decomposition. The results show improved accuracy in the estimation of kinetic information using the G-Procedure as well as successfully maintaining an estimate of the reaction rate in the presence of large amounts of experimental noise. This is especially important in dealing with low-level response signals typical to that of minor products. Embodied in a probabilistic framework, we believe this methodology provides a useful tool for separating transport and kinetic processes in general and may be applied more broadly beyond the specialized configuration of the TAP reactor in the future.