TECHNOLOGY FOCUS - CHEMICAL ENGINEERING - Preferred Apparatus: The reactive distillation column comprises the reactive zone containing the solid acid catalyst, a fatty acid ester inlet above the catalyst, an alcohol inlet below the catalyst, a product outlet at the bottom of the column for separating the produced fatty acid alkyl ester, and an outlet at the top of the column for methanol formed in the reaction and one or more alcohol which is unreacted. The preliminary transesterification reaction of vegetable oil as triglyceride with methanol takes place in a biodiesel production plant and the reactive distillation column is added onto the biodiesel production plant to receive the fatty acid methyl ester product stream.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Compounds: The alkyl alcohol is chosen from ethanol, propanol, isopropanol, butanol, isobutanol, amyl alcohol and iso-amyl alcohol, preferably ethanol. The produced alkyl fatty acid ester(s) is a fatty acid ethyl ester. The mixture of alcohol comprises ethanol and butanol and the reaction with the impure fatty acid methyl ester mixture further produces a fatty acid ethyl ester and a fatty acid butyl ester. The fatty acid methyl ester mixture comprises methyl palmitate, methyl stearate, methyl oleate, methyl linoleate and methyl linolenate. The fatty acid methyl ester mixture further comprises glycerol as impurity. The fatty acid alkyl ester produced is in admixture with the fatty acid methyl ester. The fatty acid alkyl ester is in addition blended with a petroleum diesel fuel (50-95%). A composition comprises a mixture of fatty acid methyl ester and fatty acid alkyl ester of one or more 2-8C alkyl alcohol. The mixture of fatty acid methyl ester comprises ester of palmitic acid, stearic acid, oleic acid, linoleic acid, and linolenic acid from soybean. The composition further contains ester of fermentation or non-fermentation derived organic acid with one or more 1-6C alkyl alcohol and optionally 6C or more ether as oxygenate. The mixture of fatty acid methyl and alkyl ester further comprises ester of dimethyl succinate. The fermentation or non-fermentation derived organic acid ester is derived from an acid chosen from lactic acid, succinic acid and their mixtures. Alternately, the fermentation or non-fermentation derived organic acid ester is derived from an acid chosen from propionic acid, butyric acid, isobutyric acid, dicarboxylic and carboxylic acid, and their mixtures. The ether is chosen from dibutyl ether, methyl tert-butyl ether, tertiary amyl methyl ether, tertiary hexyl methyl ether, ethyl tertiary butyl ether, tertiary amyl ethyl ether, propyl ether, dipropyl ether, dihexyl ether, dioctyl ether and iso-amyl-ether. Oxygenate is ester. Preferred Process: The partially transesterifying process is carried out at temperature of 50-200 degrees C and pressure of 0.5-20 atmosphere in presence of a heterogeneous solid acid catalyst. The fatty acid alkyl ester mixture is continuously produced by countercurrently transesterifying fatty acid methyl ester at temperature of 50-200 degrees C and pressure of 0.5-20 atmosphere with one or more 2-8C alkyl alcohol in presence of solid acid catalyst in a reactive zone in a distillation column to produce a fatty acid alkyl ester mixture, and removing the produced fatty acid alkyl ester mixture at bottom of the column and alcohol from top of the column, where solid catalyst is heterogeneous solid acid catalyst mounted in structured packing elements and supported as a single unit of the structured packing elements. The fatty acid methyl ester is generated from a preliminary transesterification reaction of vegetable oil as triglyceride with methanol. Preferred Property: The produced fatty acid alkyl ester has a cloud point lower in temperature than the methyl fatty acid ester.