NOVELTY - Reactor (10) comprises: many tubes (12), where at least one of the tubes is at least partially disposed within a lumen of another one of the tubes; many fluidly coupled chambers (14) defined, at least in part, by the tubes; at least one inlet (16) fluidly coupled to a first chamber of the chambers for receiving reactants; and at least one outlet (18) fluidly coupled to a second chamber of the chambers for receiving products generated during a reaction within the chambers. The reactor is configured to generate a generally helical flow pattern through at least one of the chambers.    USE - The reactor is useful for transesterification of oils (claimed) such as vegetable, lipid, animal, trapped grease, or recycled cooking oil into biodiesel.    ADVANTAGE - The reactor: generates a helical flow pattern that increases the residence time of the reactants in the chambers and also increases the interaction of the catalyst with the reactants, thus facilitating the transesterification reaction; has compact design, modularity and flexibility to adjust for different throughputs (e.g. chambers may be added or eliminated by adding or eliminating tube stacks and/or by replacing the tubes with longer or shorter tubes while using the same end caps); minimizes pumping loss; and increases throughput and yield.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for transesterification of oil, comprises: introducing oil and methanol into a first chamber and subsequently into a second chamber, where the first chamber is defined, at least in part, by a first lumen of a first tube, and the second chamber is defined, at least in part, by a second lumen of a second tube, and the first tube is at least partially disposed within the second lumen; generating a generally helical turbulent flow pattern through at least one of the first and the second chambers in the presence of a catalyst to facilitate the transesterification of the oil into glycerol and at least one of fatty acid methyl ester and fatty acid ethyl ester; and removing the glycerol and at least one of fatty acid methyl ester and fatty acid ethyl ester from the second chamber.    DESCRIPTION OF DRAWING(S) - The figure shows a side perspective view of the multichamber tubular reactor.    Reactor (10)    Tubes (12)    Chambers (14)    Inlet (16)    Outlet (18)