Solutions of partial differential equations (PDE) that describe mass transfer in conventional continuous, countercurrent solid-liquid extraction systems also successfully describe mass transfer in nearly continuous, contercurrent extraction systems where supercritical fluid (SF) is used to extract solutes from moist solids. These solutions can also be used to describe mass-transfer behavior in absorbers where solutes are transferred from SF to showers of liquid drops if information about drop diameters and velocities, effects of circulation in drops and, most important, axial dispersion is available. The variables involved include : dimensionless concentrations, Ficks number, F = D(s)t/a(2), the stripping factor, alpha the Peclet number, UL/D-a, and the mass-transfer Biot number, Bi. In extractors, alpha slightly greater than 1.0 are needed to provided efficient extraction without excessive circulation of solvent; in absorbers, ac should be < 1.0. alpha, P-e and Bi are used in PDE solutions to determine F and extraction or absorption times needed to achieve specified extents of solute transfer. Use of these solutions is illustrated by analysis of a patented, nearly continuous extractor in which moist, caffeine-containing, green coffee beans move countercurrent to supercritical CO2 which extracts the caffeine. The caffeine is recovered from the CO2 by absorption in water and the CO2 is recycled.