Investigation of Empty Dryer

A previous study showed a difference between the set \(_\) and \(_\) in empty state [21]. As the stainless-steel dryer and sieve bottom are heated, there is a loss in thermal energy due to heat conduction. This loss of thermal energy is not associated with the evaporation of water during drying. Therefore, a model for \(_\) was set up from the DoE in the empty state. Table 3 gives an overview of the observed responses used to build the following model. Correlating \(_\) against \(_\) and \(_\) enables the prediction of the conductive energy loss between \(_\) and \(_\). According to Pauli et al. [24], the predicted \(_\) based on \(_\) and \(_\) equals the theoretical granule temperature (\(_\)) as predicted by the temperature of the air that leaves the sieve bottom. Thus, in empty state, the \(_\) ideally equals \(_\) as well as \(_\). During drying of granules, the \(_\) is higher than \(_\) and consequently \(_\) or \(_\). Hence, the observed response \(_\) was applied as a factor for predicting \(_\) as this temperature is closer to \(_\) due to evaporation compared to \(_\). Figure 2 displays the evaluation of the set model for predicting \(_\) using a summary of fit. R2, which is a measure of fit, and Q2, which is the prediction ability, were close to 1.0 (> 0.98). The high value in reproducibility resulted in lower model validity. The observed versus predicted values using the model are also shown in Fig. 2. Equation (5) was used further in the MEB to predict the \(_\) at the conducted drying conditions.

Table 3 Observed responses of DoE in an empty dryerFig. 2

Summary of fit and observed versus predicted plot for the model of \(}_}\)

$$_\left[\mathrm\right]=-0.87*_+2.00*_-282.87$$

(5)

Derivation of Mass BalancePlacement of Sensors

The derivation of MEB is based on the sensors installed in QbCon® 1, which are displayed in Fig. 3. The temperature of the compressed air (\(_\)) and relative humidity (\(_\)) is measured before the air is heated to the set \(_\). \(_\) is converted into the absolute humidity of the inlet air (\(_).\) Before the hot air enters the drying chamber, the \(_\), \(_\) and inlet pressure (\(_\)) are recorded. The ambient pressure (\(_\)) is recorded by the equipment. Hot and dry air exits the drying chamber by passing through the product filter. At the outlet, the pressure (\(_\)) and \(_\) are measured. After passing the exhaust filter, the outlet temperature (\(_\)) and outlet relative humidity (\(_\)) are recorded and used for the calculation of the absolute humidity (\(_\)). The outlet air flow (\(_\)) is obtained after exiting the exhaust fan. The black arrows represent the flow of air, whereas the dashed arrows show the material flow. During granulation, the \(\dot\) and liquid feed rate (\(\dot\)) are recorded and the barrel temperature at three positions. The third position (\(_\)) was used for the calculations of the energy balance as it is close to the outlet of the TSG and closely represents the temperature of the granules entering the drying chamber.

Fig. 3

Sensor positions of the measured process parameters for the MEB

Derivation of Mass Balance—Empty Dryer

The mass balance calculation assumed that the amount of mass entering a system equals the amount of mass exiting a system. In the used VFBD, the mass balance was first calculated under empty conditions. Therefore, the water and dry air which enters the drying unit via the inlet air should equal the mass of water and dry air leaving the dryer through the outlet air. Table 4 lists the parameters used to demonstrate the mass balance in the empty state.

Table 4 Process parameters used to demonstrate the MEB of derivation at a certain time point in an empty dryer

\(_\) and \(_\) are indicated as the norm volumetric flow (\(}_\)) for a norm pressure (\(_\)) of 101,325 Pa and norm temperature (\(_\)) of 273.15 K. Therefore, the norm conditions are calculated for the operating volume flow for inlet (\(}_\)) and outlet air flow (\(}_\)) derived from the universal gas equation according to Eq. (6) [40]. Consequently, \(}_\) and \(}_\) are calculated as follows:

$$}_\left[\frac}^}}\right]=\frac_*}_*T}_*p}$$

(6)

$$}_=\frac*18.01 \frac}^}}*296.45\,\mathrm}*102780\,\mathrm}=19.27 \frac}^}}$$

$$}_=\frac*18.22 \frac}^}}*304.75\,\mathrm}*101240\,\mathrm}=20.34 \frac}^}}$$

To determine the mass flow of wet air (\(}_\)) through \(}_\), the density of wet air (\(_\)) is calculated according to Eq. (7) with the specific gas constant of wet air (\(_\)) which is calculated using Eq. (8) [40]. Where \(_\) is the specific gas constant of dry air, defined as \(287.0 \frac}*\mathrm}\), and \(_\) of water vapour defined as \(461.5 \frac}*\mathrm}\). \(\varphi\) is the relative humidity and \(_\) the saturation vapour pressure.

$$_ \left[\frac}}^}\right]=\frac_*T}$$

(7)

$$_ \left[\frac}*\mathrm}\right]=\frac_}_}*\left(1-\frac_}_}\right)}$$

(8)

Thus, the calculated densities are \(1.207 \frac}}^}\) of inlet air (\(_)\) and \(1.157 \frac}}^}\) of the outlet air (\(_)\). \(}_\) of inlet (\(}_\)) and outlet air (\(}_\)) is calculated using Eq. (9):

$$}_ \left[\frac}}\right]=_*}_$$

(9)

$$}_=1.207 \frac}}^}*19.27 \frac}^}}=23.26 \frac}}$$

$$}_=1.157 \frac}}^}*20.34 \frac}^}}=23.53 \frac}}$$

By using \(}_\) and X, the mass flow of dry air (\(}_\)) and water through the air (\(}_\)) is calculated using Eqs. (10) and (11):

$$}_ \left[\frac}}\right]=\frac}_}$$

(10)

$$}_ \left[\frac}}\right]=}_*X$$

(11)

$$}_=\frac}}}^ \frac}}}=23.24 \frac}}$$

$$}_=23.24\frac}}*0.944*^\frac}}=0.0219 \frac}}$$

$$}_=\frac}}}^ \frac}}}=23.51 \frac}}$$

$$}_=23.51\frac}}*0.696*^\frac}}=0.0164 \frac}}$$

There is a deviation between the incoming and outgoing \(}_\) and \(}_\). \(0.0055 \frac}}\) more water enters the drying chamber through the air but not exiting. At the same time, \(0.27 \frac}}\) more dry air leaves the system. Vacuum is applied in the drying chamber at the outlet of the TSG and thus ambient air can enter the drying chamber by attraction. In addition, through the rubber seals around the drying chamber, ambient air could have entered, which has a higher relative humidity. Therefore, the assumption was made that the difference between the supply and exhaust dry air is equal to the \(}_\) from the environment (\(}_\)). Thus, the \(}_\) is determined by converting Eq. (12) and the water entering the drying chamber through the environment (\(}_\)) is calculated using Eq. (11).

$$}_=23.51 \frac}}-23.24 \frac}}=0.27 \frac}}$$

$$}_=0.27\frac}}*7.67*^\frac}}=0.0021 \frac}}$$

Despite this, the mass balance of inlet and outlet water is not in balance and due to the ambient air an even higher amount of water entering but not leaving the system. The same phenomenon was observed by Mortier et al. [26] for the investigated datasets using the six segmented FBD of the ConsiGma™ from GEA. The authors had no explanation for the difference in the empty state. Thus, each sensor has an uncertainty that is considered in the calculations as described in the “Propagation of Uncertainty” section. The existing difference in water in the empty state is defined in the following study as \(}_\) according to Eq. (13).

$$}_=\left(}_+}_\right)-}_$$

(13)

For the shown example, the \(}_\) corresponds to \(0.0076 \frac}}\) and needs to be added to the amount of water leaving through the outlet air (\(}_)\) while drying the granules for the prediction of the LOD. To determine \(}_\), a heating phase before starting the granulation and drying process is required. In contrast to Mortier et al. [26], no correlation was found between the difference in \(}_\) and inlet air temperature. The authors used a linear regression with all taken data points and added the “offset” in their publication to the mass balance. With this correlation, they had a good agreement between the measured LOD and the predicted LOD. Figure 4 displays the \(}_\) over the time including the sensor uncertainty. Therefore, the heating phase starting from zero is included. Considering the sensor uncertainty, the calculated value covers a large range. As pressurised air is used as inlet air, which cannot be controlled, some fluctuations are possible.

Fig. 4

Heating phase in empty dryer at 48 °C–18 Nm3/h–7.5 m/s2 over 80 min, n = 1 with 4800 measuring points, \(}_ \pm\) uncertainty

Derivation of Mass Balance—Drying of Granules

The mass balance while processing in an empty state considered only entering and exiting air. With granulation and drying, more factors are involved in the balance. Figure 5 shows an overview of the factors involved in the setup of a MEB for drying after TSG using a VFBD. The blue arrows show the flow path of air, whereas the black arrows show the transportation path of the granules. Water enters the drying system via the granules, inlet air and ambient air and leaves via the outlet air, with dried granules and gets lost due to fines that remain trapped in the product filter. The loss of granules (\(}_\)) and hence the loss of water in the granules (\(}_\)) were neglected in the further calculations. While drying, energy enters the system via heated air (\(}_\)), ambient air (\(}_\)) and granules (\(}_\)) and exits the dryer through the outlet air (\(}_\)), conduction of the dryer (\(}_\)) and energy applied for evaporation (\(}_\)) of water from the wet granules. The energy flux during drying is presented in orange.

Fig. 5

Overview of factors involved in the MEB during drying via VFBD

The stepwise derivation of the mass balance for the dryer in the empty state is demonstrated in the “Derivation of Mass Balance—Empty Dryer” section. The derivation of the mass balance during the drying of granules is shown using an exemplary timepoint from the same drying process as in the demonstration of the empty dryer only after the heating phase, where now granules of lactose-MCC formulation were dried. The process parameters used for the calculations are listed in Table 5.

Table 5 Process parameters used for the demonstrating the MEB derivation at a certain time point during drying and granulation of the lactose-MCC formulation

Based on Fig. 5, the following mass balance for water while drying and neglecting the loss of granules through the filter can be set up as shown in Eq. (14). In addition to air, the water entering the system through the granules (\(}_\)) and water leaving the system through the dried granules (\(}_\)) is involved in the balance. After rearranging Eq. (14) according to \(}_\), the LOD can be calculated.

$$}_+}_+}_=}_+}_+}_$$

(14)

First, the mass flow of the solid into the dryer (\(}_\)) is calculated by excluding the water content of the starting material (\(_)\) using Eq. (15):

$$}_ \left[\frac}}\right]=\dot*\left(1-\frac_}\right)$$

(15)

$$}_=1.196\frac}}*\left(1-\frac\right)=1.185 \frac}}$$

Next, the theoretical liquid mass flow entering as \(}_\) is calculated using the \(\dot\) and \(_\) according to Eq. (16):

$$}_ \left[\frac}}\right]=\dot*\left(\frac_}*\dot\right)$$

(16)

$$}_=0.24 \frac}}*\left(\frac*1.196 \frac}}\right)=0.251 \frac}}$$

The incoming and outgoing mass of water were calculated as described in the empty state using Eqs. (4) to (10). Based on this, the calculated mass flows are as follows: \(}_= 0.0229\frac}}\); \(}_= 0.0073\frac}}\); \(}_= 0.228\frac}}\). The \(}_\) is used from the heating phase of the dryer and corresponds to \(0.0076 \frac}}\). Equation (14) was converted to \(}_\) and is described in Eq. (17) as follows:

$$}_ \left[\frac}}\right]=}_+}_+}_-}_-}_$$

(17)

$$}_=0.0229 \frac}}+0.0073 \frac}}+0.251 \frac}}-0.228 \frac}}-0.0076 \frac}}=0.0462 \frac}}$$

Consequently, the difference between the \(}_\) and the \(}_\) corresponds to the mass flow rate of evaporating water (\(}_\)) while drying described in Eq. (18):

$$}_\left[\frac}}\right]=}_-}_$$

(18)

$$}_=0.251 \frac}}-0.0462 \frac}}=0.205 \frac}}$$

With the assumption that no granules are lost while drying, the inlet mass flow rate of the powder \(}_\) equals the outlet mass of the dried granules (\(}_\)). Equation (19) describes the calculation of the LOD.

$$LOD \left[\%\right]=\frac}_}}_+}_}*100$$

(19)

$$LOD =\frac}}}}}+0.0462 \frac}}}*100=3.75\%$$

In comparison, the measured LOD at 130 min was 3.73%, which is close to the predicted LOD for this example of 3.75%. The demonstration does not include the uncertainty of the sensors used for the prediction. Figure 6 displays the predicted and measured LOD over time, including the model uncertainty. Thereby, the prediction with uncertainty covered a range of 3–4% for the LOD over the process of 150 min. The high fluctuations reached a steady state after 90 min of processing. Thus, a higher precision of the prediction is reached at the same time when \(_\) also achieves equilibrium. While production, longer processing times are obtained, and thereby, higher precision of the predicted LOD is obtained. Nevertheless, the prediction via mass balance showed good agreement with the measured LOD. The measured LOD increased in certain time periods, which is also covered by the predicted LOD values. An RMSE of 0.54% was obtained.

Fig. 6

Predicted LOD with n = 1 with 9000 measuring points, predicted \(\pm\) uncertainty and measured LOD with n = 1 over 150 min

Prediction of LOD by Mass Balance

The application of the mass balance for prediction is displayed for the two formulations (mannitol and lactose-MCC). Each formulation was processed under three different drying conditions to cover different ranges of LOD. Figure 7 displays the prediction vs. measured LOD while drying mannitol and Fig. 8 shows the lactose-MCC with the related heating phase. The water difference through incoming and outgoing air \(}_\) was determined for each run using the heating phase and is displayed in Figs. 7a and 8a. Thereby, the \(}_\) showed different values and fluctuations as the experiments were not conducted on the same day except for the granulation and drying for the first and third drying process (\(M1\) and \(M3).\) The \(}_\) showed a similar value compared to the drying conditions at M2. The conditions of the compressed supply air cannot be controlled, which might be a reason for the different obtained \(}_\) values at different drying parameters and thus days. Applying higher \(_\) or \(_\) resulted decrease in LOD. Decreasing Vib might lead to lower LOD depending on \(_\) as the residence time of the granules is affected. The measured LOD over time lies within the predicted values (Fig. 7b). The predicted LOD showed high fluctuations, which can be attributed to the variation in absolute humidity during drying. The \(_\) is measured at the outlet. The granules enter the drying chamber in a wet state at low temperature, and along the dryer, they are dried, and water is evaporated. The sensor itself covered all different drying stages at one position, which might explain the fluctuations in the absolute humidity of the outlet air. By changing the drying parameters from left to right (Fig. 7b), the obtained LOD decreased and the predicted LOD fluctuations decreased. The RMSE showed a smaller value and thus corresponded better at lower LOD or higher drying efficiency. While drying the mannitol granules at \(M1\), the predicted LOD exhibited the highest fluctuations. It might be that the drying capacity was not high enough to remove water from the granules compared with the higher drying temperature. Thus, resulting in an uneven evaporation of the water.

Fig. 7

\(}}_-\mathrm.}\) while heating phase in empty dryer over 30 min (a), n = 1 with 1800 measuring points, \(}}_-\mathrm} \pm\) uncertainty and LOD prediction (b) during drying of mannitol granules with n = 1 with 3600 measuring points, predicted \(\pm\) uncertainty and measured LOD with n = 3, mean \(\pm\) standard deviation

Fig. 8

\(}}_-\mathrm.}\) while heating phase in empty dryer over 30 min (a), n = 1 with 1800 measuring points, \(}}_-\mathrm} \pm\) uncertainty and LOD prediction (b) during drying of lactose-MCC granules with n = 1 with 3600 measuring points, predicted \(\pm\) uncertainty and measured LOD with n = 3, mean \(\pm\) standard deviation

Comparing Figs. 7b and 8b, drying of lactose-MCC showed a lower fluctuation of the predicted LOD values. This indicates that the fluctuation of the absolute humidity is less, and uniform drying is obtained. Drying of lactose-MCC at \(L3\) showed the highest variation in the prediction of the LOD over time. In addition, the obtained \(}_\) with uncertainty is the highest (Fig. 8a). At higher \(_\) and \(_\), the uncertainty of the sensor is higher. Drying at \(L1\) showed good agreement between the prediction and the measured LOD. After 45 min, a higher LOD was measured by using the mass balance. An increased LOD was also observed in the measurement. Finally, the predicted results for the two formulations using the established mass balance exhibit a good correspondence between the prediction and measured LOD.

Derivation of Energy BalanceDerivation of Energy Balance—Empty Dryer

The surfaces of the VFBD consisting of stainless steel were heated via convection, resulting in additional heat loss in addition to the evaporation of water while drying. Therefore, the energy entering and leaving the system was determined. In the heating phase, the energy balance considers the ambient air, inlet air and outlet air. This estimates the heat loss due to convection and thus the heating of the dryer surfaces. The specific enthalpy of humid air or energy flux (\(\dot\)) is calculated according to Eq. (20) with the specific enthalpy of dry air (\(_\)) and water vapour (\(_\)) [40].

$$\dot \left[\frac}}\right]=}_*_+}_*_$$

(20)

The calculation of \(_\) is determined using the simplified Eq. (21) using the specific heat capacity of air (\(_\)) with the value of \(1.006 \frac}*\mathrm}\). \(T\) is the temperature of the air and \(_\) is the triple point of water at \(273.16\,\mathrm\) [40].

$$_\left[\frac}}\right]=_*(T-_)$$

(21)

The calculation of \(_\) is done according to Eq. (22) where \(\Delta _\) is the specific evaporation enthalpy of water at \(_\) applied with the value of \(\Delta _=2500.9 \frac}}\) and \(_\) is the specific heat capacity of water vapour with \(1.888 \frac}*\mathrm}\) [40].

$$_\left[\frac}}\right]=_+c}_*(T-_)$$

(22)

According to Eqs. (20)–(22), the specific enthalpy respectively \(\dot\) of the inlet, ambient and outlet air are calculated for the empty dryer as follows:

$$}_ =23.24\frac}}*1.006\frac}*\mathrm}*\left(321.15-273.16\right)+\left(0.0219\frac}}*\left(2500.9\frac}}+1.888\frac}*\mathrm}*\left(321.15-273.16\right)\right)\right)=1178.7\frac}}=327.4\,\mathrm$$

$$}_ =0.27\frac}}*1.006\frac}*\mathrm}*\left(297.15-273.16\right)+\left(0.0021\frac}}*\left(2500.9\frac}}+1.888\frac}*\mathrm}*\left(297.15-273.16\right)\right)\right)=14.0 \frac}}=3.9\,\mathrm$$

$$}_ =23.51\frac}}*1.006\frac}*\mathrm}*\left(308.15-273.16\right)+\left(0.0164\frac}}*\left(2500.9\frac}}+1.888\frac}*\mathrm}*\left(308.15-273.16\right)\right)\right)=869.7 \frac}}=241.6\,\mathrm$$

For the heating phase, the energy balance can be calculated according to Eq. (23). The difference between the incoming and outgoing energy flux corresponds to the heat loss (\(}_\)) which is in empty dryer due to convection from the air to the dryer surface. The percentage \(}_\) is determined according to Eq. (24) resulting 27.1% heat loss during the heating phase due to the heating of the stainless-steel parts of the drying chamber.

$$}_=\left(}_+}_\right)-}_=\left(327.4\,W+3.9\,\mathrm\right)-241.6\,\mathrm=89.7\,\mathrm$$

$$}_\left[\%\right]=\frac}_}}_+}_}*100$$

(24)

$$}_\left[\%\right]=\frac}+3.9\,\mathrm}*100=27.1\%$$

Derivation of Energy Balance—Drying of Granules

In addition to the air, granules entering and leaving the drying system at a certain temperature are included to set the energy balance in Eq. (23) resulting in Eq. (25). The wet and dried granules consist of a specific enthalpy, which is calculated using Eq. (26). The specific heat capacity of each formulation was determined using differential scanning calorimetry and resulted for lactose-MCC in \(_=1.841 \frac}*\mathrm}\) and for mannitol in \(_=1.758 \frac}*\mathrm}\). \(_\) is the specific heat capacity of water with a value of \(4.22 \frac}*\mathrm}\).

$$}_+}_+}_=}_+}_+}_$$

(25)

$$}_=}_*_*\left(T-_\right)+}_*_*\left(T-_\right)$$

(26)

For the entering granules, the \(_\) is used as the temperature, and for the leaving granules the temperature \(_\) is predicted according to Eq. (5). Thus, the energy flux of the granules is determined as follows:

$$_=-0.87*18.01 \frac}}+2.00*298.45\,\mathrm-282.87=298.36\,\mathrm$$

$$}_=1.185\frac}}*1.841\frac}*\mathrm}*\left(298.85\,\mathrm-273.16\,\mathrm\right)+0.251\frac}}*4.22\frac}*\mathrm}*\left(298.85\,\mathrm-273.16\,\mathrm\right)=83.26 \frac}}=23.1\,\mathrm$$

$$}_=1.185\frac}}*1.841\frac}*\mathrm}*\left(298.36\,\mathrm-273.16\,\mathrm\right)+0.0462\frac}}*4.22\frac}*\mathrm}*\left(298.36\,\mathrm-273.16\,\mathrm\right)=59.89 \frac}}=16.6\,\mathrm$$

The energy flux of the air while drying is calculated as for the heating phase and resulted in the example in \(}_ =328.1\,\mathrm\), \(}_ =12.3\,\mathrm\) and \(}_ = 332.3\,\mathrm\). Thus, the \(}_\) is determined by converting Eq. (25):

$$}_=328.1\,\mathrm+12.3\,\mathrm+23.1\,\mathrm-332.3\,\mathrm-16.6\,\mathrm=14.6\,\mathrm$$

$$}_=\frac}+12.3\,\mathrm+23.1\,\mathrm)}*100=4.02\%$$

\(}_\), \(}_\) and \(}_\) are calculated over time for the heating phase and drying of the granules displayed in Fig. 9. \(}_\) and \(}_\) represent the sum of the entering, respectively, leaving \(\dot\). Figure 9b shows the energy balance over a longer drying time for the same experiment used for the stepwise deviation of the MEB. The heating phase includes the complete heating of the system (Fig. 9b). During the heating phase, the \(_\) increases and thus the \(}_\). The lower the temperature difference between \(_\) and \(_\), the lower \(}_\) as \(}_\) becomes higher. During this phase, the entire device is heated, including the sieve plate and dryer walls (Fig. 9b). For experiments shown in Fig. 9a and c, the system was already heated as previous runs were conducted before indicating constant values for \(}_\), \(}_\), \(_\) and \(}_\). As soon as wet granules enter the drying chamber, \(_\) is decreasing as water evaporates and the granules are dried. In addition, the pipes were heated up and it takes time till the \(_\) is reaching an equilibrium. At the beginning of drying, \(}_\) is low because the granules are also dried by the heated surfaces via conduction. As the surfaces are cooled down over time, the \(}_\) is decreasing as the temperature of the exhaust air reduces and thus the \(}_\) is increasing. Nevertheless, the \(}_\) is lower during drying compared to the heating phase. \(}_\) especially the \(}_\) is higher during drying because it also consists of the evaporated water and thus more energy.

Fig. 9

\(\dot}\) of incoming and leaving energy, \(}}_}\) and \(}_}\) during the heating phase and drying at M1 (a), L1 condition with longer time (b) and L3 (c), n = 1, value \(\pm\) uncertainty

The energy flux rates \(\dot\) for the different drying conditions are summarised for the drying of mannitol granules in Table 6 and lactose-MCC granules in Table 7. For the shown drying processes, the \(}_\) is around 30% due to conduction through the dryer walls and the sieve plate. The heating phase for mannitol granules (Table 6) showed a slightly lower \(}_\) by drying at higher air flow, indicating that the walls were not equally heated. The higher the evaporated amount of water, the higher the \(}_\) while drying the granules. During the drying of mannitol granules at \(M1\) drying conditions, a negative \(}_\) was observed. The change of \(}_\) and \(}_\) is shown in Fig. 9a, where it is observed that \(_\) is not reaching an equilibrium through 1 h of drying. \(}_\) is therefore lower compared to \(}_\) resulting in a negative \(}_\). A higher \(_\) was used for drying in Fig. 9b compared to Fig. 9a, which might be the reason for the difference. Higher \(_\) improved the heat distribution and resulted in an earlier onset of temperature equilibrium. \(}_\) is less during drying of granules compared to the heating because the walls of the dryer are cooled down due to evaporation cooling. Increasing \(_\) or \(_\), the \(}_\) which is entering the system also increases. \(}_\) is also dependent on the absolute humidity of the pressured air, which is not controlled. In a previous publication [21], the second drying stage was reached earlier with a lower LOD and the obtained \(_\) is also higher, as shown in Tables 6 and 7.

Table 6 \(\dot\) of incoming and leaving energy in [W], \(}_\) [%] and \(_\) [K] during the heating phase and drying of mannitol granules under different drying conditions, n = 1 with 300 measuring points (heating phase) and 600 measuring points (drying of granules), mean \(\pm\) uncertainty Table 7 \(\dot\) of incoming and leaving energy in [W], \(}_\) [%] and \(_\) [K] during the heating phase and drying of lactose-MCC granules under different drying conditions, n = 1 with 300 measuring points (heating phase) and 600 measuring points (drying of granules), mean \(\pm\) uncertainty

Based on the literature, the \(}_\) is only defined by the difference in \(}_\) and \(}_.\) Mortier et al. [