Mathematical Modeling of Supercritical Extraction of Valerenic Acid from Valeriana officinalis L

The dynamic behavior of supercritical fluid extraction (SFE) of valerenic acid (VA) from valerian (Valeriana officinalis L.) roots was studied by mathematical modeling. The extraction yield of VA was considered as the most desirable compound among the other extracted constituents. A two‐phase desorption model was developed by considering a diffusion controlled regime in the particle and axial dispersion in the bed. The mass transfer parameters, i.e., pore diffusivity, film mass transfer coefficient and axial dispersion, along with the solubility parameters were chosen as the model parameters. The first three mass transfer parameters were predicted using nondimensional equations from the literature. The solubility equation and the parameters were studied using different equilibrium models, i.e., Henry, Langmuir, Freundlich, Langmuir‐Freundlich (L‐F) and Toth isotherms. The equilibrium parameters were correlated by comparing the outlet results of the dynamic SFE model with experiments. The experimental yield of the VA extraction was obtained at a pressure of 15.0–36.0 MPa, temperature of 310–334 K, solvent flow rate of 0.50–1.10 · 10–6 m3/min and different particle sizes ranging from 0.18–2.00 · 10–3 m in diameter, at a 20 min constant static period, in the presence of 46.9 μL/g ethanol as the co‐solvent, followed by dynamic time extraction for up to 50 min. From the results, the mathematical model using the L‐F equation exhibited the best agreement with the experimental yield of VA extraction in the range of studied conditions. The present model can be applied to design and scale up the SFE process of VA from Valeriana officinalis L. roots. The dynamic behavior of a supercritical fluid extraction of valerenic acid from Valeriana officinalis L. is studied using a two‐phase desorption model with an appropriate solubility equation. The Langmuir‐Freundlich equation is shown to exhibit the best agreement with the experimental yield of VA extraction in the range of studied conditions.