A new approach for studying the particle dynamics and RTD (residence time distribution) in processes is to formulate stochastic
models. A common question to all models for RTD is whether Danckwerts’ law for mean residence time holds. In this paper we
revisit a Markov process that has been proposed by Dehling et al. (1999) as a stochastic model for particle transport in fluidized
bed reactors. Under the volumetric flow balance conditions, we deduce different boundary conditions at the entrance and the
exit of the reactor, and in both discrete model and continuous model we show that processes satisfy Danckwerts’ law, stating
that the mean residence time of particle transport in fluidized bed reactors equals V/v, where V denotes the volume of the reactor occupied by the fluid and v the volumetric inflow rate. 相似文献
The dynamics of the activity and polymer growth in Ziegler-Natta catalysts has been well established in the literature. 1 , 2 The corresponding dynamic behaviour of the reactor system is predicted using a segregation model approach and the unsteady state model of residence time distribution previously developed. 3 The model is therefore able to predict reactor performance for a time-varying catalyst flow rate through the reactor, as well as time-varying concentrations of monomer, co-catalyst and chain termination agent. A method of determining grade transition policies by the use of the developed reactor models is then presented. It is demonstrated that the reactor productivity, catalyst efficiency, average chain length and polydispersity can be controlled by the catalyst flow rate and reactor monomer and hydrogen concentrations. The relationship between the required polymer product properties and the system flow rates is determined. Case studies are presented that evaluate various transition strategies for a specific polymer grades. 相似文献
Free‐radical polymerization that involves the polymer transfer reactions leading to both long‐chain branching and scission, as in the cases of high‐pressure olefin polymerization, is considered. In CSTR, the residence time distribution is broad and the primary polymer chain, whose residence time is large, is subjected to polymer transfer reaction for a longer time, leading to a larger number of branching and scission points. The distributions of both branching and scission density are much broader in a CSTR than in a batch, or equivalently, a PFR. The radius of gyration for larger sized polymers formed in a CSTR tends to be much smaller than that for randomly branched polymers.
The efficiency of chemical reactors can be analysed using the residence time distribution. This research focusses on flat-sheet geometries applied in membrane-based systems. The residence time distribution depends mainly on the 2D velocity field, parallel to the membrane. The velocity average over the transversal direction is calculated using potential flow theory. A combination of real and virtual sources and sinks are used to model the internal inlets and outlets. Furthermore, a novel method is presented to calculate the residence time distribution. By ignoring diffusion and dispersion, every streamline is modelled to have a fixed residence time, which can be calculated with a simple quadrature based on a coordinate transformation. The model predicts the impact of the two-dimensional geometry on the residence time distribution, but it is demonstrated that large zones of nearly stagnant flow have only a limited impact on the residence time distribution. The new model can predict the travelling time from the inlet to each interior location, providing a better tool to analyse spatially distributed chemical reactions. The models agreed highly with pressure measurements (R2 = 0.94–0.98) and they agreed well with tracer experiments for the residence time (R2 = 0.73–0.99). 相似文献
A millimeter scale butterfly-shaped reactor was proposed based on sizing-up strategy and fabricated via femtosecond laser engraving. An improvement of mixing performance and residence time distribution was realized by means of contraction and expansion of the reaction channel. The liquid holdup was greatly increased through connection of multiple mixing units. Structure optimization of the reactor was carried out by computational fluid dynamics simulation, from which the effect of reactor internals on mixing and the influence of parallel branching structure on heat transfer were discussed. The UV–vis absorption spectroscopy was used to determine the residence time distribution in the reactor, and characteristic parameters such as skewness and dimensionless variance were obtained. Further, a chained stagnant flow model was proposed to precisely describe the trailing phenomenon caused by fluid stagnation and laminar flow in small scale reactors, which enables a better fit for the experimental results of the asymmetric residence time distribution. In addition, the heat transfer performance of the reactor was investigated, and the overall heat transfer coefficient was 110–600 W m-2 K-1 in the flow rate range of 10–40 mL/min. 相似文献
Thermal degradation at processing temperature and the effect on the rheological properties for poly(3-hydroxybutyrate) have been studied by means of oscillatory shear modulus and capillary extrusion properties, with the aid of molecular weight measurements. Thermal history at processing temperature depresses the viscosity because of random chain scission. As a result, gross melt fracture hardly takes place with increasing the residence time in a capillary rheometer. Moreover, it was also found that the molecular weight distribution is independent of the residence time, whereas the inverse of the average molecular weight is proportional to the residence time. Prediction of average molecular weight with a constant molecular weight distribution makes it possible to calculate the flow curve following generalized Newtonian fluid equation proposed by Carreau as a function of temperature as well as the residence time. 相似文献