(201c) Characterizing Continuous Powder Mixing Using Residence Time Distribution
It is well known that continuous powder mixer smoothes out input fluctuations as well as locally mixes the initially segregated components in the radial directions (Pernenkil and Cooney 2006). However, little has been done towards the development of predictive models. As a result, the complicated relationship between the performance and the mixer geometry, material, flow rate, blade speed and other manipulating conditions (Laurent and Bridgwater 2002) is still unknown, thus hindering the design and optimization of continuous mixer.
In many of previous studies Residence Time Distribution (RTD) has been used as an index of the mixer performance. RTD is a probability distribution function that describes the amount of time a particle could spend inside the mixer. Several models are introduced in the literature to characterize the experimental RTD curve (Nauman 2008). For instance, delay and dead volume model that linked units of PFR and CSTR was widely used in the RTD simulation of cylinder rotating drum, single screw extrusion process and a twin-screw continuous mixer (Yeh and Jaw 1998; Ziegler and Aguilar 2003); dispersion model based on the Fokker-Planck equation with specified boundary conditions were detailed analyzed in different solid mixing processes (Sudah, Chester et al. 2002; Sherritt, Chaouki et al. 2003); Markov chains (Marikh, Berthiaux et al. 2006) and compartment model (Portillo, Muzzio et al. 2008) were developed to describe the solid mixing using a network of interconnected cells based on the flow structure inside the mixer.
In these studies, a boarder RTD is generally considered as an indication of better mixing performance (Danckwerts 1953) especially when the reproducibility of the RTD pulse test is verified (Williams and Rahman 1972; Ralf Weineköter 1995). An inverse finding is reported based on our prior work (Portillo, Ierapetritou et al. 2008) where we found that the most dispersed RTD corresponds to the worst continuous mixing mainly due to the local insufficient mixing between the mixture components.
In this work, we develop a general method using the residence time distribution measurement to predict the performance of a continuous mixer. Based on this method, the Taylor dispersion model is chosen as the RTD model in the curve fitting process due to the good adaptability in a wide range of operating conditions. In order to estimate the influence of the RTD reproducibility to the mixing performance, multiple RTD tests are performed. The final fitted curve to the multiple RTD tests is further used to calculate the variance reduction of the flow rate fluctuations, while the fitting error is utilized to evaluate the sum of the output variance components that are not introduced by the feed rate fluctuations. Due to the independence of the variance sources, the contributions to the output variance from the feed rate, RTD reproducibility, radial segregation and measurement error can be analyzed separately. Thus the main components of output variance can be distinguished and specially minimized in further design and control of the continuous mixing system.
To verify the proposed methodology, multiple RTDs and the corresponding output variances are measured experimentally for different flow rates, blade speeds, and blade angles. The RTD results are used to fit the Taylor dispersion model. The fitted curves are applied into the feed rate fluctuation samples to calculate all the variance components. The variance components due to measurement error are also estimated for different API concentrations. Compared with the overall output variance the variance contribution of the feed rate fluctuations and measurement error are not significant, indicating that these source of fluctuations are controlled in satisfactory level in this case study. A linear correlation between the fitted error of RTD and the component of radial mixing in the experimental output variance is established, suggesting that the fluctuations of the RTD measurement reflect the radial mixing process in the continuous mixing system. Further analysis indicates that the variance components of radial segregation and that of the RTD reproducibility increase with the decrease of the blade speed, thus is reversely proportional to the mean residence time.
In summary, the advantage of the proposed method is that it is independent of operating conditions, sampling detection method and mixer type. This feature makes it adaptable to investigate continuous mixing in a wide range of mixing conditions and mixer geometries. Moreover, the variance characterization applied in this work has the advantage that it can be used to further understand the different variance sources. This is the first step towards developing a reliable guideline in design and quality control of continuous mixer.
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