Extraction Kinetics and Modeling

To design and evaluate scale-up feasibility, the development of a reliable mathematical model to describe the process is important. In a packed bed extraction, the extraction fluid first penetrates and diffuses into the solid matrix. Then the solute solubilizes and moves from the solid matrix to the pores where diffusion inside the pores takes place. At the end, the fluid with the dissolved extract axially diffuses back along the extraction bed and leaves the extractor. 

The most commonly used mass transfer models, however, are those based on a differential mass balance of the solnte over a control volume in the packed bed. 

Several differential mass balance models have been proposed to characterize mass transfer kinetics. Among them, the model proposed by Sovova (1994), based on extraction from broken and intact cells (BICs), has been widely used. In this model, the solutes are stored in particle cells and protected by the cell wall. During the pretreatment step, to reduce the particle size and increase the surface area between the solute and fluid, some of the cells are broken and solutes become accessible to the fluid. These easily accessible solutes are denoted as x. The remaining solutes retained in unbroken cells are referred to as intact cells and defined as x. Thus, internal and external resistance control the extraction. Sovova (2005) also proposed a more complete model with additional parameters to consider equilibrium relationships. However, this modified model has not been widely used, due to its complexity, and most published work continues to use the older BIC model with mass transfer coefficients in the fluid (k ) and solid (k) phases, and x as the main parameter. The following assumptions are usually considered  

Uniform initial solute content and particle size distribution 

The extraction of solutes from solid samples, according to the BIC model, can be divided into three periods the constant extraction rate, falling extraction rate, and diffusion (Sovova, 1994). In the first period, the easily accessible solutes are extracted at a constant rate until the particles at the bed entrance lose all their accessible solutes. At this time, the diffusion extraction of the entrance of the bed begins, combined with convection extraction of the rest of the bed. This results in a continuation of the extraction for broken cells, beyond the bed entrance, and at the same time the extraction of cells begins at the bed entrance and the rate of extraction decreases. At the end of this stage, all of the broken cells are extracted and only the intact cells are left. Thus the extraction becomes diffusion controlled. According to this, the simplified mass balances of the fluid and solid phases are described by Equations 5.1 and 5.2, respectively  

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