Separation Process Principles- 2n - Seader & Henley - Solutions Manual

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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, 128-133 (1996), entitled "Shrinking-Core Leaching Model for Supercritical-Fluid 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 mass-transfer process can be viewed as taking place in two steps, one (internal mass-transfer resistance) by diffusion in the interior of the material and the other (external mass-transfer 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 mass-transfer 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. (3-170), the mass-transfer 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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