## 2 Experimental Section
### Modelling of Fractionated Condensation Step  
A mathematical model is necessary to simulate the capture of each aroma in the two inseries condensers to achieve successful fractionated condensation and remove off-flavours from potentially important target aromas. Such a model should also allow users to identify the best operating temperatures in each condenser to separate off-flavours from desirable aromas. Supported by the work carried out by [PERSON] et al. (2015), a simple mathematical model for designing a fractionated condensation system, comprised of a set of condensers, can be established to achieve off-flavour removal ([PERSON] et al., 2016). The model is built on the assumption that the vapour stream in a series of condensers (non-total condensation) is in thermodynamic equilibrium with the liquid condensate phase in each condenser. This model uses the feed composition and feed flow operating parameters as well as the temperature of the first condenser as input variables (see Figure 4). The second condenser was assumed to achieve total condensation due to the low temperature of operation. The model simulation predicts the mass and composition of the condensate in each condenser. It is possible to simulate the composition of the condensates obtained in the condensers by starting with inputs such as: (i) the permeate flux of each aroma under study, (ii) thermodynamic parameters (saturation vapour pressure and activity coefficient at infinite dilution), and (iii) the operating conditions of pressure and temperature applied in upstream and downstream compartments. This is a very effective model for determining the optimal operating parameters for achieving the desired separation of valuable aromas from off-flavours. For aqueous systems, the model was extensively explained in a previous paper ([PERSON] et al., 2016). Through a system of equations that constitute the model, we were able to select the best operating conditions to achieve the best separation of valuable flavours from off-flavours. Equations (2) and (3) allow the determination of the percentage of water and aroma(s) condensation of in the first condenser, respectively:  
\[\%condens_{w1}=1-\frac{n_{inert}}{n_{w0}}.\frac{P_{vw(T1,\,condens)}}{p_{perm }-p_{vw(T1,\,condens)}} \tag{2}\]  
\[\%condens_{aroma1}\cong 1-\frac{n_{inert}}{n_{aroma0}}.\frac{\chi_{aroma1} \cdot\gamma_{aroma1}^{\infty}\cdot P_{aroma(T1,\,condens)}}{p_{perm}-p_{vw( T1,\,condens)}} \tag{3}\]  
where \(n_{inert}\) is the inert gas (CO\({}_{2}\)) molar flow rate in the stream, \(P_{vw}\) is the saturation vapour pressure of water or aroma, \(p_{perm}\) is the permeate pressure applied to the system, \(n_{w}\) or aroma is the molar flow rate of each species before the first condenser, \(\varkappa_{w\,\,or\,  
It is important to highlight that this model can handle multicomponent aroma systems because the target aroma compounds are extremely diluted in the feed solutions in most real-case scenarios. Therefore, each aroma behaves independently under these highly diluted aroma concentration conditions, with no flow coupling between them [21]. Furthermore, diluted aroma compounds have no effect on water and ethanol transport [22]. This model was applied and experimentally validated for aqueous systems [16]. Following the strategy established for aqueous solutions, the model was developed for more complex solutions comprising ethanol and the presence of noncondensable gases. \[x_{w1}+x_{e1}=1 \tag{4}\]  
\[x_{w2}=\frac{n_{w1^{\prime}}}{n_{w1^{\prime}}+n_{e1^{\prime}}} \tag{5}\]  
\[n_{w0}+n_{e0}=n_{T1}+n_{T2} \tag{6}\]  
\[n_{w0}\cong x_{w1^{\prime}}n_{T1}+x_{w2^{\prime}}n_{T2} \tag{7}\]  
\[\%condens_{i1}=1-\frac{n_{intert}}{n_{0}}.\frac{x_{i1}\cdot\gamma_{i1}\cdot p _{ii}(T_{i,condens})}{p_{perm}-x_{w1}\cdot\gamma_{w1}\cdot p_{iw}(T_{i,condens })-x_{ei1}\cdot\gamma_{e1^{\prime}}\cdot p_{iw}(T_{i,condens})} \tag{8}\]  
\(i=w\), \(et\), \( aroma\)  
With Equations (2) and (3), it is possible to calculate the percentage of water and aroma(s) obtained in the first condenser.