Experimental methods in chemical engineering: Residence time distribution—RTD

Statistical data treatment for residence time distribution studies in pharmaceutical manufacturing

Residence time distribution (RTD) method has been widely used in the pharmaceutical manufacturing for understanding powder dynamics within unit operations and continuous integrated manufacturing lines. The dynamics thus captured is then used to develop predictive models for unit operations and important RTD-based applications ensuring product quality assurance. Despite thorough efforts in tracer selection, data acquisition, and calibration model development to obtain tracer concentration profiles for RTD studies, there can exist significant noise in these profiles. This noise can make it challenging to identify the underlying signal and get a representative RTD of the system under study. Such concerns have previously indicated the importance of noise handling for RTD measurements in literature. However, the literature does not provide sufficient information on noise handling or data treatment strategies for RTD studies. To this end, we investigate the impact of varying levels of noise using different tracers on measurement of RTD profile and its applications. We quantify the impact of different denoising methods (time and frequency averaging methods). Through this investigation, we see that Savitsky Golay filtering turns out to a good method for denoising RTD profiles despite varying noise levels. The investigation is performed such that the key features of the RTD profile (which are important for RTD based applications) are preserved. Subsequently, we also investigate the impact of denoising on RTD-based applications such as out-of-specification (OOS) analysis and RTD modeling. The results show that the degree of noise levels considered in this work do not significantly impact the RTD-based applications.

Optimal quantification of residence time distribution profiles from a quality assurance perspective

Residence time distribution (RTD) has been widely applied across various fields of chemical engineering, including pharmaceutical manufacturing, for applications such as material traceability, quality assurance, system health monitoring, and fault detection. Determination of a representative RTD, in principle, requires an accurate process analytical technology (PAT) procedure capturing the entire range of tracer concentrations from zero to maximum. Such a wide concentration range creates at least two problems: i) decreased accuracy of the model across the entire range of concentrations, relating to limit of quantification, and ii) ambiguity associated with the detection of the tracer for low concentration levels, relating to limit of detection (LOD). These problems affect not only the RTD profile itself, but also RTD-based applications, which can potentially lead to erroneous conclusions. This article seeks to minimize the impact of these problems by understanding the relative importance of different features of RTD on the detection of out-of-specification (OOS) products. In this work, the RTD obtained experimentally was truncated at different levels, to investigate the impact of the truncation of RTD on funnel plots for OOS detection. The main finding is that the tail of the RTD can be truncated with no loss of accuracy in the determination of exclusion intervals. This enables the manufacturing scientist to focus entirely on the peak region, maximizing the accuracy of chemometric models.

Investigation of aqueous phase dynamics in a uranium stripping unit using radioactive tracer

Mixer-setters units are widely used in uranium purification processes. For efficient operations of mixer-settler units, it is essential to measure the hydrodynamics parameters of the different phases involved. The residence time distribution (RTD) measurement is commonly used method to estimate the hydrodynamics parameters of process reactors. In the present study, RTD of the aqueous phase was measured in different stages mixer-settler unit (mixers, settlers and mixer-settler units) used for stripping operation using Iodine-131 as a radiotracer. For the RTD measurements, radiotracer was injected as an impulse in aqueous phase feed line and its movement was monitored at different locations in the stripping unit using NaI(Tl) detectors. The mean residence times (MRTs) of the aqueous phase were estimated from measured RTD curves. For quantification of the degree of mixing, suitable flow models were proposed based on design and nature of the measured RTD curves and subsequently used for simulation. Based on the results of the RTD study, the mixing of aqueous phase was characterized and design of the stripping unit and its sub-units were validated. The optimum conditions were identified for efficient for the operation of the stripping unit.

Residence Time Distribution of Non-Spherical Particles in a Continuous Rotary Drum

The motion of non-spherical particles with sharp edges, as they are commonly involved in practice, was characterized by residence time distribution (RTD) measurement in a continuous drum. Particles with two sizes, 6 and 10 mm, and two densities, 750 and 2085 kg/m3, were used in the experiments. The effects of rotation speed (3–11 rpm), incline angle (2–4°), feed rate, and mixture composition were investigated and compared to the results of other researchers on particles without sharp edges. We also fitted the RTD with an axial dispersion model to obtain a better insight into the flow behavior. MRT of non-spherical particles with sharp edges depends on ω−α similar to other shapes, while the value of alpha is higher for particles with sharp edges (0.9 < α < 1.24), especially at high incline angles. The MRT depends on incline angle, β−b, where b varies between 0.81 (at low ω) and 1.34 (at high ω), while it is close to 1 for other shapes. Feed rate has a slight effect on the MRT of particles with sharp edges and the effect of particle size diminishes when rotation speed increases. The MRT linearly increases with volume fraction of light particles in a mixture of light and heavy particles (from pure heavy to pure light particles).

Using residence time distribution in pharmaceutical solid dose manufacturing - A critical review

While continuous manufacturing (CM) of pharmaceutical solid-based drug products has been shown to be advantageous for improving the product quality and process efficiency in alignment with FDA's support of the quality-by-design paradigm (Lee, 2015; Ierapetritou et al., 2016; Plumb, 2005; Schaber, 2011), it is critical to enable full utilization of CM technology for robust production and commercialization (Schaber, 2011; Byrn, 2015). To do so, an important prerequisite is to obtain a detailed understanding of overall process characteristics to develop cost-effective and accurate predictive models for unit operations and process flowsheets. These models are utilized to predict product quality and maintain desired manufacturing efficiency (Ierapetritou et al., 2016). Residence time distribution (RTD) has been a widely used tool to characterize the extent of mixing in pharmaceutical unit operations (Vanhoorne, 2020; Rogers and Ierapetritou, 2015; Teżyk et al., 2015) and manufacturing lines and develop computationally cheap predictive models. These models developed using RTD have been demonstrated to be crucial for various flowsheet applications (Kruisz, 2017; Martinetz, 2018; Tian, 2021). Though extensively used in the literature (Gao et al., 2012), the implementation, execution, evaluation, and assessment of RTD studies has not been standardized by regulatory agencies and can thus lead to ambiguity regarding their accurate implementation. To address this issue and subsequently prevent unforeseen errors in RTD implementation, the presented article aims to aid in developing standardized guidelines through a detailed review and critical discussion of RTD studies in the pharmaceutical manufacturing literature. The review article is divided into two main sections - 1) determination of RTD including different steps for RTD evaluation including experimental approach, data acquisition and pre-treatment, RTD modeling, and RTD metrics and, 2) applications of RTD for solid dose manufacturing. Critical considerations, pertaining to the limitations of RTDs for solid dose manufacturing, are also examined along with a perspective discussion of future avenues of improvement.

Residence time distribution (RTD) revisited

Residence Time Distribution (RTD) theory is revisited and tracer technology discussed. The background of RTD following Danckwerts ideas is presented by introducing "distribution" functions for residence time, internal age and intensity function and how to experimentally obtain them with tracer techniques (curves C and F of Danckwerts). Compartment models to describe fluid flow in real reactors are reviewed and progressive modeling of chromatographic processes discussed in some detail. The shortcomings of Standard Dispersion Model (SDM) are addressed, the Taylor-Aris model discussed and the Wave Model of Westerterp's group introduced. The contribution of Computational Fluid Dynamics (CFD) is highlighted to calculate RTD from momentum and mass transport equations and to access spatial age distribution and degree of mixing. Finally smart RTD and future challenges are discussed.