TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The feedstock comprises at least one of impurity, unsaponifiable material, monoglyceride, diglyceride, triglyceride, and free fatty acid; 0-100 wt.% free fatty acids. The fatty acid alkyl ester stream and second stream contains at least one of impurity, unsaponifiable material, glycerin, monoglyceride, diglyceride, triglyceride, free fatty acids, and fatty acid alkyl ester. The second stream is an overhead fraction comprising primarily alcohol. The overhead fraction comprises primarily alcohol. Preferred Method: In the process (A), and method (M3), the purifying step is accomplished by one of reduced pressure distillation and reactive distillation; is accomplished using at least one of distillation vessels and distillation columns; is conducted at 180 to -280 degrees C at pressure of less than 2 psia. In the process (B), the separation is accomplished by evaporation or distillation; is accomplished by one of reduced pressure distillation and reactive distillation; or is accomplished using at least one of distillation vessels and distillation columns. In the method (M2), the purification step ii) occurs at the same time as the purification step iii); the purification step ii) occurs in the same vessel as the purification step iii); the purification step ii) occurs before the purification step iii); the purification step ii) occurs after the purification step iii). EXAMPLE - Rendered yellow grease with a free fatty acid concentration of 20 wt.% and 2 wt.% moisture, impurities and unsaponifiables (MIU) was fed to continuous stirred tank glycerolysis reactors at 100 pounds per minute (lbs/minute). The grease was filtered and titrated intermittently as it was fed to the glycerolysis reactor. Glycerin was added at a rate of 13 lbs/minute. The temperature of the grease and glycerin mixture was raised to 210 degrees C as it was fed into the first of the glycerolysis continuous stirred tank reactors. In the reactor, the pressure was reduced to 2 psia and the temperature was maintained at 210 degrees C. The vessel was fitted with a high intensity agitator to keep the immiscible liquids in contact. Water vapor produced by the reaction was removed through vents in the reactor headspace. The residence time in each of the glycerolysis reactors was 2.5 hours. The conversion of fatty acids to glycerides in the first vessel was 85%. The fatty acid concentration leaving the second reactor was maintained at 0.5 wt./wt.%. The product from the glycerolysis reactors was cooled to 50 degrees C and fed continuously to the transesterification reactors in which a solution of potassium hydroxide in methanol was added. The potassium hydroxide was added at a rate of 1.1 lbs/minute and mixed with 22 lbs/minute of methanol. The transesterification took place in two continuous stirred tank reactors in series, each with a two-hour residence time. The transesterified product was then fed to a phase separation tank where the majority of the fatty acid methyl esters, a small amount of unreacted glycerides and a small concentration of the unreacted methanol floated to the top. The glycerin, the majority of the unreacted methanol, some fatty acid methyl esters, potassium hydroxide and soaps sank to the bottom. The bottom, or heavy phase was sent to an acidification reactor where the potassium hydroxide catalyst added in the transesterification step was reacted with 1.96 lbs/minute phosphoric acid. The soaps converted to free fatty acids and the potassium hydroxide was neutralized. The product of this acidification was monobasic potassium phosphate, which was not soluble in this system. The monobasic potassium phosphate precipitate was filtered out and the filtrate was fed to a second phase separation tank where the fatty acid methyl esters and free fatty acids present in the filtrate floated to the top and the glycerin and methanol sank to the bottom. The top, or light, phase was mixed with the light phase from the first phase separation tank and fed to the fatty acid methyl ester fractionation column. The pH of the heavy phase was adjusted back to 7.5 with potassium hydroxide and fed to the glycerin fractionation column. The glycerin fractionation column recovered 10 lbs/minute of methanol and 18 lbs/minute of glycerin. The glycerin produced was more than 95% pure with non-detectable concentrations of salts and methanol. This glycerin stream was split into two streams: 13 lbs/minute was recycled back to the glycerin feed tank for the glycerolysis reaction and 5 lbs/minute was pumped through the decolorization column and collected for market. The two light phase streams were fed to the fatty acid methyl ester fractionation column where 2 lbs/minute of methanol was recovered and 92 lbs/minute of fatty acid methyl esters meeting ASTM D 6751-02 (Standard Specification for Biodiesel Fuel (B100) Blend Stock for Distillate Fuels) were produced.