NOVELTY - Performing a chemical reaction involves substantially continuously inputting chemical reactant(s) into a first end of a reactor through two or more internal reaction chambers; reacting or splitting the chemical reactants in the internal reaction chambers such that the concentration of product(s) in a downstream chamber is greater than that in an upstream chamber; inducing turbulent flow within the internal reaction chambers; heating or cooling the internal reaction chambers with at least one extending heating or cooling element; and removing intermediary or final product from product outlet.    USE - The method is used for performing chemical reaction such as esterification, interesterification, transesterification, hydrolysis, alkoxylation, polyesterification, polyamidation, oxidization, halogenation, nitration, sulfonation, amidation, saponification, dehydrogenation, dehydration, dehydrohalogenation, hydrogenalysis, ozonation, etherification, quaternization, and imidazoline formation. It is used for producing an intermediary or a final product such as methyl ester, triethanolamine ester, biodiesel, soy methyl ester, fatty methyl esters from triglycerides and methanol, fatty acid from methyl esters, fatty acids from triglycerides, phthalic anhydride or dimethyl phthalate and diethylene glycol, amineoxide, dihalide, sulfonic acid, sulfuric acid ester, monoethanolamide, diethanolamides, dimethlyamides of organic acids, alcohols, ethers, quaternized ammonium compounds, or imidazoline (all claimed).    ADVANTAGE - The method exhibits a reaction profile approximating a plug flow or a series of continuous stirred tank reactors, but which exhibits very high heat transfer, high reaction throughput, high reactant conversion rates, the ability to be used in a variety of different chemical reactions, and low operating costs.    DETAILED DESCRIPTION - Performing a chemical reaction involves:    (A) substantially continuously inputting chemical reactant(s) into a first end of a reactor such that the chemical reactant(s) proceeds from the first end of the reactor to a second end of the reactor, sequentially through two or more internal reaction chambers defined by two or more partitions;    (B) reacting or splitting the chemical reactants in the internal reaction chambers such that the concentration of product(s) in a downstream chamber is greater than the concentration of product(s) in an upstream chamber;    (C) inducing turbulent flow within the internal reaction chambers;    (D) heating or cooling the internal reaction chambers with at least one extending heating or cooling element; and    (E) removing an intermediary or a final product from a product outlet proximate to the second end of the reactor.    DESCRIPTION OF DRAWING(S) - The figure is a graph of a hypothetical single batch reaction profile, showing reactant concentration as a function of reaction time.