Combination of PAT andmechanistic modeling tools in a fully continuous powder to granule line: Rapid and deep process understanding

a Budapest University of Technology and Economics, Organic Chemistry and Technology Department, H-1111 Budapest, Hungary b Budapest University of Technology and Economics, Department of Chemical and Environmental Process Engineering, H-1111 Budapest, Hungary c Department of Pharmaceutical Technology and Biopharmacy, “Iuliu Hatieganu” University of Medicine and Pharmacy, 400012 Cluj-Napoca, Romania d Budapest University of Technology and Economics, Faculty of Chemical Technology and Biotechnology, H-1111 Budapest, Hungary


Introduction
Continuous manufacturing (CM) has gained significant attention in the pharmaceutical industry in the recent years [1][2][3]. Technology transfer from batch to continuous faces dosage (e.g. tablets, injectables, etc.) and unit-operation specific challenges as well. Regarding the product form, approximately 80% of the pharmaceuticals are solid dosage formulations, the majority of them being tablets [4]. Within the solid form production, granulation is critical for the improvement of powder properties e.g. flowability required for the tableting process operation [5,6]. Several process variant is known in the literature [7], among which wet granulation (when a liquid is applied to help stick the small particles of the starting powder blend together) has become the most common approach due to the very good controllability and reproducibility [8]. Thus, implementing wet granulation in a continuous manner recently gained significant attention [9]. Numerous papers investigate continuous twin-screw wet granulation (TSWG) and the effect of process parameters on product quality [10][11][12][13][14][15][16][17][18][19][20][21][22].
Wet granulation is inherently followed by drying to eliminate the residual granulating liquid from the granule product [23]. The challenge of drying is that high operating temperatures might result in thermal decomposition of the API, conversely, low-temperature drying might fail to meet the established limit with reasonable drying time. Various dryer constructions are available to overcome these issues. Fluidized bed drying (FBD) is a frequently applied technology, which applies heated air flowing through the wet granules [24]. The continuous implementation of FBD is represented in the literature mainly by segmented, semi-continuous FBDs developed by GEA [25][26][27], Glatt [24,28,29], or Bohle [30]. In these systems, the wet granules are collected and dried in separated compartments in small batches, and the residence time and batch size are defined by the rotation frequency of the compartments. Truly continuous horizontal bed dryers have long been known in the food industry [31,32]. In these systems, the vibration of the perforated bed triggers forward particle movement, meanwhile the drying air flows through the mesh enabling significantly more control over the process, translating to reduced quality variability. Bohle presented such a continuous dryer for pharmaceutical materials, which was integrated with continuous TSWG as well [33].
Continuous manufacturing is a promising alternative for the pharmaceutical industry and offer great overall benefits. However, in order to identify and remove the off-spec products effectively from the stream and to improve the safety and quality tight, realtime monitoring is required by Process Analytical Technologies (PATs) [34][35][36]. Various PAT tools can be applied to monitor the critical quality attributes (CQA) of the TSWG and FBD products, such as particle size and shape [37], blend uniformity [38,39], polymorphism [40], or the moisture content of the granules [4,30,[41][42][43][44]. The importance of a comprehensive PAT network is even higher in integrated systems, where the disturbances can propagate through the production line, sometimes generating complex and delayed effects [45] Only a handful of examples can be found in the literature for integrated TSWG-FBD systems with incorporated PAT tools for realtime CQA monitoring. NIR spectroscopy was utilized for real-time moisture content measurement in the Consigma™ system by Chablani et al. [42] and by Fonteyne et al. [4,41,43], in the Glatt GPCG2 CM system by Pauli et al. [24] and in the Bohle BCD 25 system by Peters et al. [30]. The first fully continuous powder-to-granule line was published recently by the authors for the production of ultra-low dose granules, in which however no PAT tools were incorporated for real-time monitoring yet [46].
Besides PAT-based monitoring, another tool for getting new traction in the process design, operation and analysis is mathematical modeling and numerical simulations [44,47]. Traditionally, the models were used for numerical experimentation, model-based analysis, design and predictive control or execution of in-silico Design of Experiment (DoE) studies, resulting in cost and considerable material savings [48]. With the quick spread of PAT tools combined with the ongoing crossindustry digitalization efforts, novel applications for the simulations were also found, such as the digital twins [49], when the simulation utilizes real-time process data. Digital twins can be used for on-line fault diagnosis or as soft-sensor granting access to a high amount of realtime process-and product-related information. Model calibration and validation with quantified parametric uncertainty are critical to ensure reliable predictions in those applications [50]. Several pharmaceutical drying processes were modeled successfully, e.g. the Consigma™ line [51] or the continuous vibrated FBD of Bohle [50].
As it was presented, deep process understanding of integrated continuous technologies is possible through the implementation of PAT tools and model-based digital twins. However, no example was found for such a process design in the case of fully continuous TSWG-FBD lines. Hence, in this work our aim was to extend the investigations of the system presented in [46], aiming for a detailed, systematic and comprehensive modeling-experimental analysis of product moisture content. To achieve this, firstly, a PLS-based NIR technique was developed for real-time moisture content monitoring. Then, the effects of process parameters on the product moisture content were systematically analyzed by a full factorial split-plot experimental design. Furthermore, a mechanistic drying model was developed, which was able to predict the moisture content generally within the measurement uncertainty and enabled to carry out simulation studies. Since very few examples can be found in the literature about truly continuous TSWG-FBD-milling lines, the presented PAT-and model-based approach of system performance evaluation can be very useful for the deeper understanding of these processes.

Materials
For the granulation experiments, α-lactose monohydrate (Granu-Lac® 70) and corn starch were applied in the starting powder blend. The α-lactose was supplied by Meggle Pharma (Wasserburg, Germany) and corn starch was provided by Roquette Pharma (Lestrem, France). Purified water was used as granulating liquid with Kollidon® 30 (Povidone, PVPK30) as a binder, shipped by BASF (Ludwigshafen, Germany).

Granulation experiments
The continuous production of granules was carried out in an integrated TSWG-FBD-milling manufacturing line. A continuous twinscrew multipurpose equipment, TS16 QuickExtruder® (Quick 2000 Ltd., Hungary) was applied for wet granulation. A screw with 16 mm diameter (25 L/D ratio) was used with a set screw configuration consisting of conveying and two kneading zones (Fig. S 1). The kneading zones comprised individual elements set up at a 45°angle with a forward configuration (first zone: 5 elements; second zone: 5 elements).
A pre-blend of α-lactose and corn starch was applied as a starting powder. Pre-blending was carried out via manual mixing in plastic bags for 5 min. The pre-blend was fed into the system by a gravimetric feeder (Brabender Technologie, Duisburg, Germany) at the first zone of the granulator. The granulating liquid was prepared by dissolving PVPK30 in purified water (ratio: 75 g in 200 mL) and was dosed into the second zone (upstream of the first kneading zone) using a peristaltic pump (Watson-Marlow 120 U, Wilmington, MA, US) with silicone tubing (inner diameter: 3.1 mm). The mass flow rate of the pre-blend was varied between 1 and 3 kg/h, while the liquid dosing was set in a range of 1.33-4.67 g/min, according to the liquid to solid ration (L/S) setting of the actual experiment (0.08-0.14). The peristaltic pump was calibrated with the granulation liquid prior to the experiments. The screw speed was set according to the mass flow of the pre-blend: 200 rpm for 1 kg/h, 300 rpm for 1.5 kg/h and 400 rpm for 2 kg/h. The setup of TSWG is shown in Fig. S 2 with the pre-blend and granulation liquid feeders, the twin-screw device and the inlet of the continuous dryer right under the screw tips.

Continuous drying
The continuous drying of the wet granules was carried out in a horizontal FBD (Quick 2000 Ltd., Hungary) (Fig. 1). The main element of the device was a perforated metal mesh, which was vibrated by vibromotors with a constant frequency of 50 Hz. The wet granules fell from the screw tips directly onto this bed and started moving towards the other end of the apparatus as a result of the vibration. Drying took place during this movement, as heated air was flowing upwards from the metal mesh and through the granules. The vibrating bed was divided into 4 drying zones, each with its corresponding filter bag above the granules. Heating could be applied on the inlet air in the first 3 zones individually, while the last, 4th zone was only for conditioning with room temperature air flow. The air flow rate could be set independently for all of the 4 zones. It is important to note that real fluidization did not take place in the applied air flow range of the device. Automatic filter bag dedusting happened once in a minute. The temperature of the drying air was varied between 30 and 90°C, while the applied range of the flow rate was 60-120 L/min per zones. The schematic drawing of the continuous dryer is presented in Fig. 1.

Milling
A continuous mill (Quick 2000 Ltd., Hungary) was placed under the outlet of the continuous dryer, which could be operated either with a co-mill or an oscillatory mill tool (Fig. S 3). The dried granules fell directly into the mill. Oscillatory milling with 1 mm sieve size was applied in all experiments. Milling intensity was set to 200 oscillations/min in all cases.

Granule characterizationresidual moisture content
The amount of remaining water in the dried and milled product was determined by loss on drying (LOD, % w/w) measurements. Samples were taken from the material exiting the continuous mill, and were put in an oven for 60 min at 105°C. The sample mass was measured using an analytical scale before and right after the 60 min of drying, and the LOD was calculated from the difference.

NIR spectroscopy and spectral evaluation
A Bruker MPA FT-NIR (Bruker Optik GmbH, Ettlingen, Germany) spectrometer, equipped with a Solvias fiberoptic probe was used for real-time moisture content measurement of the dried and milled material. A vibratory conveying feeder (Fritsch Laborette 24, Idar-Oberstein, Germany) with a U-shaped channel was positioned under the outlet of the milling device, and the NIR probe was fixed above the channel of the vibratory feeder (Fig. 2). Thus, the NIR spectra was collected from the continuously moving material. Spectra collection was carried out in reflection mode, and each NIR spectrum was collected by accumulating 8 scans with 8 cm −1 resolution in the range of 4000-12,500 cm −1 . Spectrum accumulation was completed using OPUS® 7.5 software (Bruker), while the real-time evaluation of the spectra was carried out using MATLAB 9.7. (MathWorks, USA) and PLS Toolbox 8.7.1.
(Eigenvector Research, USA). A Matlab script and an interface have been developed to import the spectra to Matlab in real-time. After that, another script was used for the chemometric moisture content determination using a Partial Least Squares (PLS) model developed in PLS Toolbox (also in real-time). During building of the PLS model, the preprocessing of the spectra consisted of Savitzky-Golay smoothing (2nd order polynomial, 15-point window), Standard Normal Variation (SNV) correction and mean centering. Venetian blinds cross-validation method was applied with 10 data splits and 1 left-out sample per blind.

Design of experiments with the integrated continuous system
The previously described three stages of the continuous system were operated in an integrated fashion: the wet granules produced during TSWG fell directly into the continuous FBD, and the continuous mill was connected to the outlet of the drier as well. Then, the dried and milled material was conveyed with a vibratory feeder, and by fixing the NIR probe above the channel of the feeder in-line spectra were collected for real-time moisture content analysis.
A Split-Plot DoE study was created for the systematical evaluation of the effect of different process parameters on the moisture content of the produced granules. The examined parameters were the mass flow rate of the pre-blend, the liquid to solid ratio (L/S), and the temperature and flow rate of the drying air. Each factor was varied on two levels, and with multiple repeats at the central point. The temperature of the drier was a so-called "hard-to-change factor" since quite a long time was required for a new setting to stabilize. Thus, executing the experiments with the temperature settings in randomized order would have resulted in a drastically elongated measurement time. Instead, the DoE was split up into blocks according to the temperature levels (split-plot design). Each block was repeated twice to separate the variability of the change of temperature from the variability originating from the restricted randomization. Central point experiments were conducted between the blocks, resulting in a total of 4 central point repeats. The set levels of the process parameters are listed in Table 1, while the order of the experiments executed in the final DoE is presented in Appendix 1 in Table S1.
The temperature of the granulator was kept constant at 25°C in all cases. The temperature and the flow rate of the drying air in the continuous dryer could be set for each of the 4 zones individually (except for the temperature of the 4th zone as detailed in Section 2.3), which would have increased the number of parameters significantly. Thus, in  this study, the first 3 drying zones were handled together by setting the air temperature and flow rate to the same level between 30 and 50°C and 60 and 120 L/min. In the case of the 4th zone, the air flow rate was set to 60 L/min in each experiment. The results were evaluated with analysis of variance (ANOVA) using the TIBCO Statistica (Version 13.5) software. The experimental design was carried out in one long operational run. The system was initiated with the central point settings (1.5 kg/h, 0.11 L/S, 40°C, 90 L/min), and the in-line NIR measurement was started simultaneously. The recorded spectra were analyzed in real-time, thus the moisture content trend could be followed accurately. At the beginning of the experiment, the system was operated for ca. 20 min to reach steady the state in all units (the stabilization of the drying temperature took most of this time, a few minutes was enough for the other units and parameters). When the in-line signal stabilized, the actual moisture content was noted, and we moved on to the next setting within the first temperature block. The system was operated at each setting for approximately 5-10 min to reach the steady state, which was determined based on visual observation and the in-line NIR measurement. In each setting, 5 spectra were marked to determine the actual residual solvent content level. After finishing a temperature block, a slightly longer settling time was required to reach the steady temperature of the next block (20-30 min). An overall operating time of ca. 5 h was required to execute the experimental design, which was quite impressive taking into account the number of settings [36].
After evaluating the results of the presented experimental design, the temperature factor was found to be statistically not significant (see later in Section 3.2). As temperature has an important role in drying mechanism [48], the experimental plan presented in Table 1 was supplemented with subsequent levels for drying temperature at 70 and 90°C as new blocks in order to gain more insight into the effect of this parameter. The investigated range of the rest of parameters was identical to the previously presented DoE setup. The exact settings are listed in Appendix 1 in Table S 2.

Modeling of the continuous drying process
The drying models can be divided into two major categories: the equilibrium and the Arrhenius concepts [52]. The former assumes heat transfer limitation between the drying air and the particles [53], whereas the latter considers that the drying process is governed by the evaporation rate. In this work, the Arrhenius approach is employed. The developed model distinguishes a gas and a solid phase. Although there is also liquid in the system in the form of moisture, this is handled as an intrinsic property of the pseudo-solid phase. The sub-processes considered in the drying model are illustrated in Fig. 3, where it seems that the particles are not separated from each other. Instead, there are channels in the air flow, reducing the overall solid surface area and making the liquid diffusion from the pores to the surface a macroscopically significant step.
Under such conditions, two drying regimes exist: above a critical moisture content (X C ) the drying rate (R V ) is independent of the actual moisture (X). Below X C , the liquid is transferred to the surface of the particles from the inner pores first and then is evaporated, which translates to a moisture content-dependent drying rate. These are described with the semi-empirical Eq. [54]: Table 1 The set levels of process parameters in the DoE study for the evaluation of the effect of process parameters on the moisture content of the product.  k is the temperature-dependent rate constant (T K, s : solid temperature in Kelvin), expressed as: In Eq. (1) H r denotes the relative humidity, accounting that the drying rate is negatively proportional to the relative humidity. H r is expressed as the ratio of actual partial pressure (P A ) and saturation pressure at the given temperature (P A * ): The evaporation is accompanied by the release of evaporation heat, resulting in the decrease of solid temperature (T s ) as well as the increase of the relative humidity of the air. The solid-gas heat transfer compensates evaporation heat, described as a function of temperatures, heat transfer coefficient (U) and apparent heat transfer area (A): where T a is the air temperature in the bed. The developed process model assumes that the gas phase is wellmixed, and the heat of evaporation is completely absorbed by the solids. Then, a differential equation system with four states, namely the air temperature (T a ), partial pressure of water (P A ), the solid temperature (T s ) and moisture content (X), is derived, which is described in detail in Appendix 2. The numerical solution of the model-equations was performed in MATLAB R2019a using an explicit Runge-Kutta method by calling the ode23 function.
The heat transfer coefficient (U), activation energy (E A ) and evaporation rate constant (k) are unknowns for this system, hence, has to be determined based on the experimental data. The parameter identification is carried out by optimization, with the decision variable vector of θ = (U,E A , k) as: where φ denotes the objective function, depending on the experimentally measured (X e ) and simulated (X s ) steady state moisture contents of the product of the N calibration experiments.
90% of the experiments were randomly selected for model calibration, the remaining 10% was used for validation. 10% of experiments translated to 3 validation experiments, which is in the commonly used range of pharmaceutical model validations [55][56][57]. Maximizing the number of calibration experiments is known to contribute to the mitigation of parameter uncertainties and inter-correlations.The optimization was solved using the covariance matrix adaptation-evolution strategy (CMA-ES) global optimization algorithm [58], and the statistics (parameter covariance matrix and the 95% confidence intervals) were calculated by executing a nonlinear regression using the lsqnonlin function, started from the point returned by the global optimization. The confidence intervals were calculated by nlparci function, using the decision variable vector, vector of residuals and the Jacobian matrix returned by the lsqnonlin. To quantify the effects of uncertainties, firstly, 2000 random kinetic parameter combinations were generated by Monte-Carlo sampling from the uncertainty space. Then, the process was simulated using these random parameters, which not only allows the calculation of the mean and the standard deviation (SD) of the simulated outputs but also permits the construction of a full probability distribution [59].

Development of PLS model for in-line moisture content measurement by NIR
An NIR probe was positioned above the channel of the vibratory feeder, which conveyed the dried and milled material produced in the integrated continuous system. Spectra were collected continuously every 8 s from the moving material, and by taking samples for off-line LOD measurements, the relationship between the spectra and the moisture content of the product could be determined. The spectra taken during the sampling were marked to be used for calibration. The calibration was carried out by varying the L/S ratio (0.07-0.16) and the drying air flow rate (45 L/min-140 L/min) to cover a wide range of moisture content for calibration. The mass feeding rate was set to 1 kg/h, the temperature to 25°C (no heating was applied). This way, a residual solvent content range of approximately from 0.5% to 7% could be covered. The spectra of the completely dry material were also obtained from samples just taken out of the drying oven, which were used as 0% calibration samples.
After preliminary studies of the optimal spectral range and preprocessing methods, the spectral range of 8000-4250 cm −1 was selected for calibration. The raw and pre-processed spectra are shown in Fig. 4a and b. As it can be seen, the spectral regions of 5300-4900 cm −1 and 7200-6700 cm −1 contained the majority of information about the amount of residual granulating liquid in the product, which was in good agreement with the main NIR absorption regions of water [60]. A PLS model was built using the preprocessed NIR spectra and the reference off-line LOD measurements. Altogether 70 spectra were included in the final model, and 4 latent variables were applied, which explained 98.39% of the variation. An experiment was executed independently from the calibration to generate data for validation, from which 9 samples were used (Fig. 5). With these settings, the error of calibration (RMSEC) and cross-validation (RMSECV) were 0.278 and 0.334, respectively. The error of prediction in the validation experiment was RMSEP = 0.168, which showed the robustness of the model and the applicability for in-line monitoring of the continuous process.
In order to test the developed in-line measurement tool, experiments were carried out using the continuous system with the incorporated NIR probe. The process parameters were changed within the range of the calibration and the product moisture content was monitored in real-time. The parameter settings of the experiment are shown in Table 2, and the moisture content results with the corresponding settings are shown in Fig. 6.
It was found that the start-up period was approximately 10 min, followed by the steady state, where a low fluctuation of the moisture content was observed. At 20 min the malfunction of the gravimetric feeder (used for the pre-blend feeding) caused a disturbance, but the signal stabilized quickly after the restart of the device. The parameter settings were changed shortly after reaching the steady state again (at 34 min in Fig. 6). The system response was found to be sharp, and the signal stabilized quickly. Then, the remaining settings detailed in Table 2 were tested in the system having ca. 20 min at each setup. Another accidental stoppage of the gravimetric feeder could be detected in the moisture content signal (at~70 min), followed by rapid restabilization.
Based on the result of the experiments, the developed in-line NIR method was suitable for real-time system monitoring by detecting the varying moisture content associated with the changes of the operating parameters, and even minor fluctuations could be detected. Thus, the in-line method was suitable to be applied as measurement tool during the execution of the split-plot experimental design.

Evaluation of the system performance by DoE
The split-plot experimental design detailed in Table 1 (Section 2.7) was used to assess the effect of the mass flow rate of the pre-blend, the L/S, and the temperature and the flow rate of drying air on the moisture content of the granules. The results are shown in a variability plot in Fig. 7.
In Fig. 7 a small triangle marks an individual setting, the corresponding parameter levels can be found beneath the figure (the data are not arranged according to the execution order of the experiments, which is shown in Table S 1). As it can be seen, each setting was repeated twice, whereas four central point repeats were conducted. The repeatability of the experiments was found to be good according to these central point measurements, carried out at the beginning of the operation and between the temperature blocks (visible on the first column of Fig. 7). Based on the visual evaluation, the L/S ratio has the greatest influence on the moisture content, which results are shown within the yellow, dash-dotted rectangles. Substantial differences can be observed in the measured moisture content between the lower (1.42%) and higher (3.09%) L/S levels. Moreover, in a few cases, the results of the two repeats were not as close as at the central point, which was observed mainly at the higher L/S level (0.14). This phenomenon can be explained by the disturbances in the feeding flow rate of the preblend due to the inaccuracies of the gravimetric feeder. At this high level of moisture content, a small variation in the pre-blend mass flow could have resulted in hardly processable over-wetted particles, which showed different drying behavior.
The mass flow rate and the drying air flow rate were also found to be important. The effect of these variables is shown within the green (dotted line) and red (dashed line) rectangles in Fig. 7, respectively. The lower level of mass flow rate and the higher level of drying air flow rate resulted in notably dryer material. In Fig. 7, the blue (solid line) rectangles include the repeats on the two temperature levels. The results obtained at the higher and lower levels of this factor did not differ as much as in the case of the other three factors. The residual solvent content was reduced below 1% even with 30°C (1 kg/h, 0.08 L/S, 120  L/min), but 50°C could not decrease moisture content below 4% with 2 kg/h, 0.14 L/S and 60 L/min. The statistical analysis of the results is shown in Table 3. In order to determine the appropriate comparisons of the test statistics (F-test), the expected mean squares were derived based on the general algorithm [61]. The type of the effects, sum of squares, degree of freedoms, mean squares, the applied comparisons and p values are given in Table 3. The expected mean squares are summarized in Table S 3 (Appendix 1).
Based on the p values listed in Table 3, the effect of flow rate of the drying air, the mass flow rate and the L/S were significant factors (p < 0.05). Furthermore, the interaction between the flow rate of the drying air and the mass flow rate, the flow rate of the drying air and L/S, and the mass flow rate and the L/S were statistically significant. In this analysis, the higher-order interactions were neglected due to their presumably negligible effects on the response variable.
In order to facilitate the interpretation of the results of the DoE study, the response surfaces of the experiments are presented in Fig. 8a-d. As it can be observed, the increase of the flow rate of the drying air and the L/S resulted in higher levels of moisture content in the product in all cases. Similar surfaces were obtained on the different mass flow rate levels, only the scale of attainable moisture content differed. Examining the response surfaces from the different drying air temperature levels reveals that in this temperature range the attainable moisture content level was less dependent on this factor than on the others. The interaction of L/S and the flow rate of drying air was found to be significant during the statistical analysis of the results (Table 2), which is also visible in Fig. 8a-d as the surface is slightly curved.
As the ANOVA table shows (Table 3), the temperature of the drying air appeared to not have a significant effect on the measured moisture content at 0.05 significance level. Although, it should be noted that the p value of the effect of the temperature was very close to 0.05, thus this situation has not been fully clarified, yet. The sensitivity of the F-test concerning the temperature can be increased by greater sample size. To have a more detailed picture about this effect further experiments are planned in the future.
Since the temperature is known to play a fundamental role in the drying process [48], the first experimental design was extended with additional levels of drying air temperature as detailed in Section 2.7 by  Table 3 Results from ANOVA (split-plot design) for moisture content (%). creating two new smaller 2 3 experimental designs at 70°C and 90°C. We did not include the results of these new blocks into the statistical analysis and DoE evaluation, since they were executed a longer period of time after the first DoE setup, leaving a possibility for additional variation. The results of the additional experiments are shown in Fig. 9. Fig. 9 depicts that the measured moisture content is decreasing with the increasing temperature, dropping below 1% when ca. at 70°C is reached. However, high moisture content was measured when the combination of the other three factors reduced the drying efficiency (high L/S and mass flow rate at both levels of drying air flow rate). This showed that the temperature alone could not decrease the residual moisture content level effectively even at this temperature level, however, it was possible to reach lower moisture contents than what was obtained at 50°C. At 90°C, the amount of remaining water was reduced below 1% in all cases; hence no effect could be observed for the other three factors. This result shows the importance of further evaluation of drying temperature on these higher levels.

Drying model
The unknown kinetic parameters of the mathematical model were determined based on the result of the DoE study. The obtained parameters and objective function values calculated for the calibration and validation datasets are listed in Table 4. As expected, the validation provides higher error than the calibration, however, there is no major difference, indicating that there is no substantial overfitting. This is also underlined by the relatively narrow confidence intervals of the estimated parameters. For further details about the parameter estimation procedure, the reader is directed to Appendix 2.3.
The parity plot presenting the calibration and validation data is depicted in Fig. 10a. In addition to the nominal values, the simulated and measured SDs are plotted. There is a clear correlation between the measurements and the simulations, and the diagonal predominantly falls within the SD. Thus, the model is able to predict the product moisture content reasonably, and the SDs resulting from the parametric uncertainty are in the range of measurement SDs.
The validated model can provide detailed insight into the process. For example, Fig. 10b depicts the steady state temperature and moisture content profile along the dryer in a representative simulation. The drying air temperature is generally between 50 and 60°C or 10-20°C below its inlet temperature. The mean solid temperature remains well under the air temperature, due to the cooling effect of the evaporation. As expected, the moisture content decreases monotonically. The effects of the low temperature air stream in the last segment is clearly observable on both temperature curves that exhibit a sudden decrease, and on the slowing moisture content decrease, too. T s shows higher SD than the moisture content, being influenced both by the uncertainties of evaporation rate and heat transfer parameters. The lower SD of T a is explained by the higher air mass flow rate, which reduces the impact of the parameter uncertainty-caused heat uptake. Such simulations could be performed in real-time, based on PAT sensor data, in which case numerous un-measured states become available from the simulation for process control and product property prediction. There are several ways to improve the presented model, both in terms of estimated parameter accuracy and model structure. Some of the basic assumptions could be replaced with direct measurements e.g. the air pressure at the flow rate measurement; the relative humidity and temperature of the drying air leaving the dryer. Coupled with the temperature measurement of the solid material along the belt, this  would allow not only to de-couple the heat transfer coefficient and the drying rate (reducing the SD of T s ) but also to estimate more model parameters, such as X c . The specific surface area of the powder belonging to various twin-screw granulator operating conditions could be determined, enabling more accurate gas-solid heat and mass transfer calculation. From a model structure perspective, one may describe the evaporation rate as a two-step process, accounting for the kinetics of water diffusion from the pores to the surface of particles. From a mathematical perspective, dynamic information could easily be obtained, which is alluring but it would also require dynamic model calibration.
Once a model with quantified prediction capability and uncertainty becomes available, it can be used for various purposes. In this work, the achievable product moisture content domains are investigated for three characteristic L/S ratios and solid mass flow rates. The operating conditions were varied in the region of experimental conditions, with slight extrapolation (50-130 L/min in the simulation study vs. 60-120 L/min in the experiments, and 20-100°C in the simulation study vs. 30-90°C in the experiments). The results are depicted in Fig. 11a-c. When both the initial moisture and mass flow rate are high, significantly higher product moistures are realized than in the mid-, and low-level cases (2-10%,~1-6% and~0-3%, respectively). Unsurprisingly, the lowest product moisture content was predicted at the highest drying air temperature and flow rate in all cases, and vice-versa. It is noteworthy that at sufficiently high drying air flow rates, regardless its temperature, sufficiently low moisture contents can be achieved (<2%) (Fig. 11c). This observation aligns with the outcomes of the experimental design and has great significance in the drying of heat-sensitive APIs.

Conclusions
In this work a deep and thorough process understanding approach was presented for integrated continuous pharmaceutical technologies. The process performance of a TSWG-FBD-milling line was evaluated rapidly by means of mechanistic modeling and design of experiments using real-time PAT monitoring. A PLS model was built using NIR spectroscopy for the real-time monitoring of the moisture content of the dried and milled product. The NIR calibration model was found to be accurate and reliable, with a 0.168% prediction error RMSEP. A full factorial split-plot experimental design was executed within just a few hours to assess the effect of process parameters on the residual water content of the granules. It was found that the mass flow rate of the starting preblend, the L/S and the flow rate of the drying air are statistically significant variables. The temperature of the drying air was also important; however, the p value was close but did not reach the 0.05 significance criteria. This was the motivation to extend the studied temperature range. These experiments revealed that at a high drying air temperature, the moisture content falls below 1% regardless of any other parameters, but sufficiently high drying air flow rates could result in low moisture contents even at low air temperatures. This is an important observation for the drying of thermolabile APIs. A mechanistic process model was developed and calibrated based on the experimental data recorded as a part of the DoE. The simulation results reinforced the experimental observations. Using the developed model, the number of experiments required for process understanding can be decreased in future works, but it also paves the way for the process optimizations and applications of digital twins. In conclusion, it was presented in this study that comprehensive and thorough process understanding can be achieved within a short time by PAT-supported DoE studies supported by digital twin-based simulations, which could bring QbD-based process development to a new level.

Declaration of Competing Interest
The authors declare no conflict of interest.