Unformatted text preview: on can be made with the Kremser method based on
stripping factors for ethanol and water, and an absorption factor for carbon dioxide.
For ethanol, the stripping factor is S = KV/L = 0.115(3)/1 = 0.345. From the Kremser plot in
Fig. 5.9, the fraction extracted is approximately 35%, independent of the number of stages above
3. For water, S = 0.00575(3)/1 = 0.0173, and the Kremser plot gives approximately 1.7%
extracted, again independent of the number of stages above 3. For carbon dioxide, an absorption
factor is used, where A = L/KV = 1/[34.5(3)] = 0.00966. From the Kremser plot, approximately
1% of the carbon dioxide is transferred to the raffinate. These values are very close to the
following values computed from the above material balance:
% extraction of ethanol = 0.0140/0.0417 x 100% = 33.6%
% extraction of water = 0.0161/0.9583 x 100% = 1.68%
% loss of carbon dioxide to raffinate = 0.0287/3.0 x 100% = 0.957% Exercise 11.26
Subject: Development of a mathematical model for the supercritical extraction of a solute from
particles of natural material. An example is the extraction of caffeine from coffee beans by
supercritical CO2.
Given: Rate of extraction is independent of the flow rate of CO2 past the particles, but
dependent on the particle size.
Find: A mathematical model for the rate of extraction. The parameter in the model that must
be determined by experiment.
Analysis: In the extraction of a solute from a natural material by a fluid solvent, the following
mechanism may be considered. It is discussed in several places in the literature, including an
article by Goto, Roy, and Hirose in The Journal of Supercritical Fluids, 9, 128133 (1996),
entitled "ShrinkingCore Leaching Model for SupercriticalFluid Extraction". The particle of
natural material is soaked in the solvent so that the solvent penetrates into the particle, usually
causing it to swell. The material may be thought of as a porous or cellular matrix that fixes or
traps the solute in the matrix. However, in the presence of the solvent, the solute is released and
can diffuse from the interior of the material to the surface of the particle, and from there into the
bulk of the solvent. Thus, the solute masstransfer process can be viewed as taking place in two
steps, one (internal masstransfer resistance) by diffusion in the interior of the material and the
other (external masstransfer resistance) by convection in the exterior solvent surrounding the
material. Assuming that the solvent flows past the particles so as to sweep away the solute as it
leaves the surface of the particles, it can be assumed that the external masstransfer resistance is
negligible because the rate of extraction is given as independent of the solvent flow rate past the
particle. This is so because it is recalled from Chapter 3 that for forced convection past a
spherical particle, Eq. (3170), the masstransfer coefficient is proportional to the fluid mass
velocity or velocity past the particle to the 0.6 exponent and inversely proportional to the particle
diameter to the 0.4 exponent. Since there is no effect of velocity, all of the mass transfer
resistance resides in the in...
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 Spring '11
 Levicky
 The Land

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