TECHNOLOGY FOCUS - MECHANICAL ENGINEERING - Preferred Components: The apparatus comprises a single reactor, consolidator and separator, two processors, consolidators and separators or multiple processors, consolidators and separators arranged serially or alternate. The processor is a modular processor comprising interchangeable tubes which can be assembled in different configurations to provide variable path length flow paths for the reactants to follow when passing through the processor to provide sufficient residence time within the processor to enable the reactants to react with each other in the transesterification reaction to form the converted reaction product. The consolidator is a hydrocyclone or coalescing hydrocyclone. The separator is a sedimentation separator optionally provided with a diffuser.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Materials: The converted reaction product includes a triglyceride or other similar long chain hydrocarbon. The by-product is glycerin, glycerin-containing material, or glycerol, glyceritol, glycyl alcohol or derivatives or precursors. The contaminants include soap, saponifiables, particulate material, residues, unreacted materials, catalysts, or alcohols. The converted reaction product is the main product of the transesterification reaction and includes alkyl esters, preferably a fatty acid alkyl ester, e.g. methyl or ethyl fatty acid ester. The converted reaction product may also be bio-diesel or its precursor or derivative. The raw material is waste material, virgin material, unused material, refined material, recovered material, recycled material, blended material, vegetable and/or animal-derived product including oils, fats and greases derived from vegetable and/or animals including vegetable oil, e.g. sunflower oil, rapeseed oil, palm oil, cotton, corn, tallow, canola, coconut, or soya.Preferred Process: The converted reaction product or upgraded product is water-washed and acid-washed to remove unwanted material to provide a bio-diesel or bio-diesel component.Preferred Reaction: The transesterification reaction is an alkali-catalyzed reaction, an acid-catalyzed reaction or an alkali and acid-catalyzed reaction.Preferred Composition: The raw material to be transesterified contains up to 20% fatty acid.