## Materials and Methods
### Fusel Oil Delhydration
#### 3.3.2 Calculation of External and Internal Mass Transfer Parameters  
In this study, mass transfer parameters were also estimated to elucidate the adsorption process. Initially, the external diffusion coefficient of lipase molecules in buffer solution (D\({}_{\mathrm{AB}}\)) was determined using the Wilke-Chang correlation (Equation (4)) [63]:  
\[\mathrm{D_{AB}}=\frac{7.4\times 10^{-8}(\varnothing\times\mathrm{M_{ solution}})^{0.5}\times\mathrm{T}}{\mathrm{\mu_{suspension}\times V_{M}^{0.6}}} \tag{4}\]  
where: D\({}_{\mathrm{AB}}\) is the external diffusion coefficient of the enzyme in the solution (cm\({}^{2}\cdot\)s\({}^{-1}\)); \(\mathrm{\psi}\) is the association factor of the enzyme solution (\(\mathrm{\phi}\) = 2.6, dimensionless); \(\mathrm{M_{solution}}\) is the molecular mass of the solvent--water (18 g\(\cdot\)mol\({}^{-1}\)); \(\mathrm{T}\) is the absolute temperature (298.15 K); \(\mathrm{\mu_{suspension}}\) is the dynamic viscosity of the solid-liquid suspension (g\(\cdot\)cm\({}^{-1}\cdot\)s\({}^{-1}\)); and \(\mathrm{V_{M}}\) is the molar volume of the lipase (cm\({}^{3}\cdot\)mol\({}^{-1}\)). The molar volume (V\({}_{\rm M}\)) of lipase from _T. lanuginosus_, a spherical enzyme with a size of 35 A \(\times\) 45 A \(\times\) 50 A that corresponds to 7.875 \(\times\) 10\({}^{-20}\) cm\({}^{3}\)[7], can be calculated according to Equation (5):  
\[\rm V_{M}=NA\times V_{enzyme} \tag{5}\]  
where: NA is the Avogrado constant (6.02 \(\times\) 10\({}^{23}\) molecules.mol\({}^{-1}\)) and V\({}_{\rm enzyme}\) is the volume of each lipase molecule (7.875 \(\times\) 10\({}^{-20}\) cm\({}^{3}\)). The specific mass (\(\rho_{\rm suspension}\)--g\(\cdot\)cm\({}^{-3}\)) and dynamic viscosity (\(\mu_{\rm suspension}\)--g\(\cdot\)cm\({}^{-1}\cdot\)s\({}^{-1}\)) values of the suspension solid-liquid with a solid concentration up to 20% v\(\cdot\)v\({}^{-1}\) were determined as described in Equations (6) and (7), respectively [64; 65]. \[\rm\rho_{\rm suspension}=\frac{100}{\left(\frac{C_{m}}{\rho_{S}}\right)+\left( \frac{100-C_{m}}{\rho_{solution}}\right)} \tag{6}\]  
\[\rm\mu_{\rm suspension}=\mu_{\rm solution}\times\left(1+2.5\times\varphi+14.1 \times\varphi^{2}\right)\ \ \therefore\ \varphi=\frac{C_{v}}{100} \tag{7}\]  
where: C\({}_{m}\) is the concentration of support in the suspension by unit of mass (5%); \(\rho_{S}\) is the solid specific mass of PSty-DVB beads (1.01 cm\({}^{3}\cdot\)g\({}^{-1}\)--Supelco Technical Information); \(\rm\rho_{\rm suspension}\) is the specific mass of the enzyme solution (1.007 cm\({}^{3}\cdot\)g\({}^{-1}\)); \(\rm\mu_{\rm solution}\) is the dynamic viscosity of the enzyme solution (9.3 \(\times\) 10\({}^{-3}\) g\(\cdot\)cm\({}^{-1}\cdot\)s\({}^{-1}\)); C\({}_{v}\) is the concentration of support in the suspension by unit of volume (\(\approx\)5%). Dimensionless numbers such Schmidt (Sc), Reynolds (Re), and Sherwood (Sh) were calculated according to Equations (8)-(10), respectively. The solid-liquid external mass transfer coefficient (k\({}_{\rm SL}\)) was then determined as shown in Equation (11) [45; 66; 67]:  
\[\rm Sc=\frac{\rm\mu_{\rm suspension}}{\rm\rho_{\rm suspension}\times D_{AB}} \tag{8}\]  
\[\rm Re=\frac{\rm\rho_{\rm suspension}\times n\times d_{T}^{2}}{\rm\mu_{\rm suspension}} \tag{9}\]  
\[\rm Sh=2+0.6(Re)^{0.5}\times(Sc)^{0.33} \tag{10}\]  
\[\rm k_{\rm SL}=\frac{\rm Sh\times D_{AB}}{D_{P}} \tag{11}\]  
where: n is the mechanical stirring frequency (200 rpm or 3.3 revolutions per second); \(\rm d_{T}\) is the inner diameter of the cylindrical flasks (5 cm), k\({}_{\rm SL}\) is the solid-liquid mass transfer coefficient (cm\(\cdot\)s\({}^{-1}\)); and D\({}_{P}\) is the average diameter of PSty-DVB beads (5.5 \(\times\) 10\({}^{-2}\) cm--Supelco Technical Information). The intraparticle diffusion of molecules in porous adsorbents can be due to Fick diffusion [45; 68]. Therefore, the effective diffusivity of lipase molecules inside the pores of the support (D\({}_{\rm eff.