EXAMPLE 4.9 Soybeans are the predominant oilseed crop in the world, followed by cottonseed, peanuts, and sunflower seed. While soybeans are not generally consumed directly by humans; they can be processed to produce valuable products. Large-scale production of soybeans in the United States began after World War II, increasing in recent years to more than 140 billion pounds per year. Most of the soy- beans are processed to obtain soy oil and vitamins like niacin and lecithin for human consumption, and a defatted meal for livestock feed. Compared to other vegetable oils, soy oil is more economical, more stable, and healthier. Typically, 100 pounds of soybeans yields 18 pounds of soy oil and 79 pounds of defatted meal. To recover oil, soybeans are first cleaned, cracked to loosen the seeds from the hulls, dehulled, and dried to 10-11% moisture. They are then leached with a hexane solution to remove the oil. However, before leaching, the soybeans are flaked to reduce the time required for mass transfer of the oil out of the bean and into hexane. Fol- lowing leaching, the hexane in the overflow is separated from the soy oil and recovered for recycle by evaporation, while the under- flow is treated to remove residual hexane and toasted with high-temperature air to produce defatted meal. Modern soybean- extraction plants crush up to 3.000 tons of soybeans per day. This example is concerned with just the leaching step. Oil is to be leached from 200000 kg/h of soybean flakes, con- taining 19% by weight oil, in a single stage by 100,000 kg/h of a hexane solvent. Experimental data indicate that the oil content of the flakes will be reduced to 0.5 wt%. For the type of equipment to be used, the expected contents of the underflows is as follows: B, Mass fraction of 0.68 0.67 0.65 0.62 0.58 0.53 solids in underflow Mass ratio of 0.0 0.2 0.4 0.6 0.8 1.0 solute in underflow liquid, XB Calculate by both a graphical and an analytical method, the com- positions and flow rates of the underflow and overflow, assuming an ideal leaching stage. What percentage of the oil in the feed is recovered in the overflow