On modelling of three dimensional flow in extraction of biologically active substances from plants

The authors consider the process of extraction from heterogeneous plant material; a novel model offering 3D spatial resolution is proposed and simulation possibilities by applying several modern numerical methods for three dimensional problems are discussed. These types of problems naturally arise when one wishes to mathematically describe the processes of the extraction with solvents such as supercritical carbon dioxide (scCO2). The results of this process meet the demand of the functional foods, nutraceutical, pharmaceutical and cosmetic industries on bioactive compounds. The models used in typical simulations by the industry offer no spatial resolution of the extraction process, however, when novel designs of extractors are developed, the three dimensional flow of the solvent and its interaction with the plant material should be considered. We propose a coupled system of equations consisting of fluid dynamics equations describing the flow of the solvent and reaction advection-diffusion equations for the solute, plus equations describing the remaining concentration of solute in the biomass. The exchange of the active material between the solid and fluid is modelled by the Langmuir law. The initial distribution of solute in the plant material is not assumed to be homogeneous, nor are the extraction parameters, i.e. heterogeneous mixture of plant materials can be covered by this model. The equations are discretized by using finite volume techniques and currently implemented in Octave/Matlab environment. As a result, the temporal evolution of the three dimensional distribution of the solute is obtained along with the velocity field of the solvent, allowing detailed studies of the extraction process in a virtual design. The model is modular, allowing integrating tailor-made laws to describe various plant materials. The authors present simulation results and analyse the advantages and disadvantages of the proposed methods and approaches.