*Article* **The Response Surface Optimization of Supercritical CO2 Modified with Ethanol Extraction of** *p***-Anisic Acid from** *Acacia mearnsii* **Flowers and Mathematical Modeling of the Mass Transfer**

**Graciane Fabiela da Silva, Edgar Teixeira de Souza Júnior, Rafael Nolibos Almeida , Ana Luisa Butelli Fianco, Alexandre Timm do Espirito Santo, Aline Machado Lucas, Rubem Mário Figueiró Vargas and Eduardo Cassel \***

> Unit Operations Laboratory (LOPE), School of Technology, Pontifical Catholic University of Rio Grande do Sul, Av Ipiranga 6681, Building 30, Block F, Room 208, Porto Alegre ZC 90619-900, RS, Brazil; gracianenh@gmail.com (G.F.d.S.); edgar.souza@edu.pucrs.br (E.T.d.S.J.); rnolibos@gmail.com (R.N.A.); lu\_fianco@hotmail.com (A.L.B.F.); alexandre.santo@acad.pucrs.br (A.T.d.E.S.); aline.lucas@pucrs.br (A.M.L.); rvargas@pucrs.br (R.M.F.V.)

**\*** Correspondence: cassel@pucrs.br; Tel.: +55-51-3353-4585

**Abstract:** A widely disseminated native species from Australia, *Acacia mearnsii*, which is mainly cultivated in Brazil and South Africa, represents a rich source of natural tannins used in the tanning process. Many flowers of the *Acacia* species are used as sources of compounds of interest for the cosmetic industry, such as phenolic compounds. In this study, supercritical fluid extraction was used to obtain non-volatile compounds from *A. mearnsii* flowers for the first time. The extract showed antimicrobial activity and the presence of *p*-anisic acid, a substance with industrial and pharmaceutical applications. The fractionation of the extract was performed using a chromatographic column and the fraction containing *p*-anisic acid presented better minimum inhibitory concentration (MIC) results than the crude extract. Thus, the extraction process was optimized to maximize the *p*-anisic acid extraction. The response surface methodology and the Box–Behnken design was used to evaluate the pressure, temperature, the cosolvent, and the influence of the particle size on the extraction process. After the optimization process, the *p*-anisic acid yield was 2.51% *w*/*w* and the extraction curve was plotted as a function of time. The simulation of the extraction process was performed using the three models available in the literature.

**Keywords:** *Acacia mearnsii*; supercritical fluid extraction; *p*-anisic acid; response surface methodology; mathematical modeling
