End-Point Prediction of Granule Moisture in a ConsiGmaTM-25 Segmented Fluid Bed Dryer

. 2020 May 14;12(5):452. doi: 10.3390/pharmaceutics12050452

$c_{p, a}$	$J / (kg \cdot K)$	specific heat capacity of dry air: $c_{p, a} = 1005 J / (kg \cdot K)$ [12] (p. 289)
$c_{p, v}$	$J / (kg \cdot K)$	specific heat capacity of water vapor: $c_{p, v} = 1863 J / (kg \cdot K)$ [12] (p. 289)
$c_{w}$	$J / (kg \cdot K)$	specific heat capacity of water: $c_{w} = 4191 J / (kg \cdot K)$ [12] (p. 289)
$c_{g}$	$J / (kg \cdot K)$	specific heat capacity of granules (computed from specific heat of lactose [21] (p. 20), corn starch [22] (p. 10) and Povidon PVP [23] (p. 120)): $c_{g} = 1321 J / (kg \cdot K)$
$Δ h_{e}$	$J / kg$	evaporation enthalpy of water at $T = 0 ° C$ : $Δ h_{e} = 2501 \times 10^{3} J / kg$ [12] (p. 289)
$k_{1}$	-	factor used to obtain “mean” air temperature across cell height
$k_{a g}$	$J / (K \cdot s)$	proportional factor describing heat transfer from air to granules
$k_{m}$	$1 / kg$	proportional factor describing evaporation rate
$k_{l o s s}$	$J / (K \cdot s)$	proportional factor describing heat transfer from air to ambient
$k_{s e p}$	-	factor used to obtain cell temperature sensor value from ${\tilde{T}}_{a}^{i}$ and ${\hat{T}}_{g, k}$
$m_{a}$	$kg$	dry air mass in one dryer cell
$m_{g, k}$	$kg$	dry granule mass in dryer cell $k$
$m_{w, k}$	$kg$	water mass in granules in dryer cell $k$
${\dot{m}}_{a}^{e}$	$kg / s$	dryer emptying air mass flow
${\dot{m}}_{a}^{i}$	$kg / s$	dryer inlet mass flow of dry air into one dryer cell coming from AHU
${\dot{\tilde{m}}}_{a}^{i}$	$kg / s$	net inlet mass flow of dry air into one dryer cell
${\dot{m}}_{a}^{i, t}$	$kg / s$	total dryer inlet mass flow of dry air coming from AHU
${\dot{m}}_{a}^{f}$	$kg / s$	mass flow of dry air for filter blowback
${\dot{m}}_{a}^{o, t}$	$kg / s$	total dryer outlet mass flow of dry air
${\dot{m}}_{a}^{o, k}$	$kg / s$	dryer cell $k$ outlet mass flow of dry air
${\dot{m}}_{a}^{p}$	$kg / s$	mass flow of dry air for granule transport
${\dot{m}}_{p}$	$kg / s$	mass flow of pre-blend
${\dot{m}}_{g}^{i}$	$kg / s$	mass flow of dry granules during filling
${\dot{m}}_{w}^{i}$	$kg / s$	mass flow of water (in wet granules) during filling
${\dot{m}}_{g}^{e}$	$kg / s$	mass flow of dry granules during emptying
${\dot{m}}_{w}^{e}$	$kg / s$	mass flow of water (in wet granules) during emptying
${\dot{m}}_{l}$	$kg / s$	mass flow of granulation liquid
${\dot{m}}_{w}$	$kg / s$	mass flow of water from granules to air
$p$	$Pa$	air pressure
${\tilde{p}}_{}^{i}$	$Pa$	air pressure of inlet air into one dryer cell
$p_{v}$	$Pa$	partial pressure of water vapor
$p_{v, s}$	$Pa$	partial saturation pressure of water vapor
${\dot{Q}}_{l o s s}$	$J / s$	heat flow between dryer and surroundings (heat loss)
${\dot{Q}}_{a g}$	$J / s$	heat exchange between air and granules
$R_{v}$	$J / (kg \cdot K)$	specific gas constant of water vapor: $R_{v} = 461.53 J / (kg \cdot K)$ [12] (p. 286)
$φ_{a}$	$%$	relative humidity of air
$φ_{a}^{a}$	$%$	relative humidity of ambient air
$φ_{a}^{e}$	$%$	relative humidity of air while emptying
$φ_{a}^{i}$	$%$	relative humidity of air coming from the AHU
$φ_{a}^{o, t}$	$%$	relative humidity of total dryer outlet air
$φ_{a}^{o, k}$	$%$	relative humidity of cell $k$ outlet air
$T_{g, k}$	$° C$	temperature in one dryer cell k
$T_{a}$	$° C$	air temperature
$T_{a}^{a}$	$° C$	ambient air temperature
$T_{a}^{e}$	$° C$	air temperature emptying
$T_{a}^{i}$	$° C$	air temperature of air coming from AHU
${\tilde{T}}_{a}^{i}$	$° C$	air temperature of net air entering one dryer cell
$T_{a}^{o, k}$	$° C$	air temperature outlet of cell $k$
$T_{a}^{o, t}$	$° C$	air temperature dryer outlet
$T_{g}^{}$	$° C$	measured granule temperature
$T_{g}^{i}$	$° C$	granule temperature of granules being filled
$U_{a v}$	J	internal energy of humid air
$U_{g w}$	J	internal energy of wet granules
$w_{g, k}$	$%$	LOD of granules (wet basis) in dryer cell k ( $w_{g, k} = \frac{m_{w, k}}{m_{w, k} + m_{g, k}} \times 100 %$ )
$w_{p}$	$%$	initial LOD of pre-blend (wet basis)
$x_{a}$	$kg / kg$	water content based on dry air mass, i.e., $kg$ water per $kg$ dry air
$x_{a}^{i}$	$kg / kg$	water content of air coming from AHU
${\tilde{x}}_{a}^{i}$	$kg / kg$	water content of net air entering one dryer cell
${\dot{V}}_{a}$	$m^{3} / s$	volume flow of air