. 2023 Apr 23;12(9):1750. doi: 10.3390/foods12091750

Table 1.

Overview of the models established for MAE in the present work and for UAE in the previous work [18].

Output Modelled	MAE Model (Present Work)	UAE Model (Previous Work [18])
t_b breaking time (min) (time when ultrasound generation switch from continuous to the discontinuous mode)	Not applicable	$t_{b} = V (ρ_{w} + X_{1} (ρ_{e} - ρ_{w})) ({C p}_{w} + X_{1} ({C p}_{e} - {C p}_{w})) ∆ T (\frac{1}{{y \cdot X}_{3}})$ where V is the solvent volume, ρ_w and ρ_e are water and ethanol densities, respectively, Cp_w and Cp_e are water and ethanol calorific capacities, respectively, and y is the efficiency of heat transmission to the solvent
TP or AA TP is the total polyphenol concentration (g.L⁻¹ GAE) and AA is the antioxidant activity (mM TEAC): one equation of the same type was used for TP and for AA	$\begin{matrix} T P \\ o r \\ A A \end{matrix}\} = \frac{1}{X_{2}} (A (1 - e^{(- K_{1} t)}) + B (1 - e^{(- K_{2} t)}))$ where t is the extraction time; A, B, K₁ and K₂ are coefficients expressed as second order polynomial functions of input parameters (solvent composition X₁, liquid/solid ratio X₂ and MW power density X₃)	$\begin{matrix} T P \\ o r \\ A A \end{matrix}\} = \frac{1}{X_{2}} (A (1 - e^{(- K_{1} t)}) + \{\begin{array}{l} B (1 - e^{(- K_{2} t)}) & i f t \leq t_{b} \\ C (1 - e^{(- K_{3} (t - t_{b}))}) + D & i f t > t_{b} \end{array})$ with $D = B (1 - e^{(- K_{2} t_{b})})$ where t is the extraction time; t_b is the breaking time; A, B, C, K₁, K₂ and K₃ are coefficients expressed as second order polynomial functions of input parameters (solvent composition X₁, liquid/solid ratio X₂ and US power density X₃)
EC Energy consumption (kWh)	$E C = P_{s} \cdot t + P_{c} \cdot t + P_{m w} \cdot t + E_{c e n t r}$ whereP_s is the electric power consumed by the stirrer; t is the extraction time; P_s is the electric power consumed by the water chiller; P_mw is the power consumed for MW generation; E_centr is the energy consumed for centrifugation	$E C = {E_{c e n t r} + P}_{s} \cdot t + \{\begin{array}{l} P_{u s} \cdot t & i f t \leq t_{b} \\ P_{u s} \cdot t_{b} + P_{u s}^{} (t - t_{b}) & i f t > t_{b} \end{array}$ where E_centr* is the energy consumed for centrifugation; P_s is the electric power consumed by the stirrer; t is the extraction time; t_b is the breaking time; P_us is the power consumed for US generation in the continuous mode and $P_{u s}^{*}$ the average power consumed for US generation in the discontinuous mode
EI 16 environmental impact categories with respective unit as defined in the ILCD Handbook, 2010 [23]: one equation of the same type was used for each of the 16 categories of impact	$E I = \overset{e q u i p m e n t s}{\overset{⏞}{(A_{e q} \cdot t + B_{e q})}} + \overset{t r a n s p o r t s}{\overset{⏞}{(A_{t} \cdot X_{1} + \frac{B_{t}}{X_{2}})}} + \overset{r a w m a t e r i a l s}{\overset{⏞}{(A_{r m} \cdot X_{1} + B_{r m})}} + \overset{e x t r a c t i o n}{\overset{⏞}{(A_{e x} \cdot E C + B_{e x})}} + \overset{e n d o f l i f e}{\overset{⏞}{\frac{A_{e o f}}{X_{2}}}}$ where t is the extraction time; X₁ and X₂ are the coded values for the solvent composition and the liquid/solid ratio, respectively; A_eq, B_eq, A_t, B_t, A_rm, B_rm, A_ex, B_ex, A_eof are coefficients associated to each life cycle stage (equipment, transports, raw materials, extraction, end of life)