Supercritical Fluid Extraction - Simple Model of SFE

Simple Model of SFE

There are two essential steps to SFE, transport (by diffusion or otherwise) from with the solid particles to the surface, and dissolution in the supercritical fluid. Other factors, such as diffusion into the particle by the SF and reversible release such as desorption from an active site are sometimes significant, but not dealt with in detail here. Figure 2 shows the stages during extraction from a spherical particle where at the start of the extraction the level of extractant is equal across the whole sphere (Fig. 2a). As extraction commences, material is initially extracted from the edge of the sphere, and the concentration in the center is unchanged (Fig 2b). As the extraction progresses, the concentration in the center of the sphere drops as the extractant diffuses towards the edge of the sphere (Figure 2c).

The relative rates of diffusion and dissolution are illustrated by two extreme cases in Figure 3. Figure 3a shows a case where dissolution is fast relative to diffusion. The material is carried away from the edge faster than it can diffuse from the center, so the concentration at the edge drops to zero. The material is carried away as fast as it arrives at the surface, and the extraction is completely diffusion limited. Here the rate of extraction can be increased by increasing diffusion rate, for example raising the temperature, but not by increasing the flow rate of the solvent. Figure 3b shows a case where solubility is low relative to diffusion. The extractant is able to diffuse to the edge faster than it can be carried away by the solvent, and the concentration profile is flat. In this case, the extraction rate can be increased by increasing the rate of dissolution, for example by increasing flow rate of the solvent.

The extraction curve of % recovery against time can be used to elucidate the type of extraction occurring. Figure 4(a) shows a typical diffusion controlled curve. The extraction is initially rapid, until the concentration at the surface drops to zero, and the rate then becomes much slower. The % extracted eventually approaches 100%. Figure 4(b) shows a curve for a solubility limited extraction. The extraction rate is almost constant, and only flattens off towards the end of the extraction. Figure 4(c) shows a curve where there are significant matrix effects, where there is some sort of reversible interaction with the matrix, such as desorption from an active site. The recovery flattens off, and if the 100% value is not known, then it is hard to tell that extraction is less than complete.