TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The acid catalyst is a titanate catalyst. The Lewis acid catalyst is maintained at a concentration of 0.1-1%.    TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Components: The first reaction chamber comprises the glycerol at a molar concentration of at least 0.75 glycerol to 1 mole of the fatty acid. The first reaction chamber comprises a fractionating column. The first reaction chamber comprises a continuous stirred tank reactor. The temperature of the intermediate reaction chamber is the same or higher than the selected temperature of the first reaction chamber and the selected pressure of the intermediate reaction chamber is the same or lower than the pressure of the first reaction chamber. The second reaction chamber comprises: second alcohol at a concentration of 50-100% molar excess of the fatty acid ester; and a continuous plug flow reactor.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: The method further comprises: separating glycerol from the mixture product of step (d) through phase separation; returning the separated glycerol phase to the first reaction chamber; removing water from the collected raw material of step (a); contacting a trace base with raw material of step (a), thus any strong acids in the raw material are neutralized; feeding the water in a gas phase into a catalytic oxidizer, thus any acrolein in the water in a gas phase is oxidized; (e) evaporating an excess of the second alcohol from the product of step (d) to form a recovered second alcohol product and a first purified product; (f) distilling out fatty acid methyl esters and glycerol from first purified product to form a distillate and an undistilled product; phase separating the distillate into a glycerol layer and a biodiesel product layer; mixing the undistilled product with an oil and acidic solution and performing a phase separation to extract free fatty acids in an organic phase product; and feeding the organic phase product as a reactant in the first reaction chamber. The selected pressure and temperature are at reflux conditions of the glycerol. The selected pressure is 10-30 torr. The selected temperature is 150-200 degrees C. The water is removed by heating the collected raw material of step (a). The step (b) comprises feeding the mixture product in the first reaction chamber to an intermediate reaction chamber at a selected pressure and temperature. The esterification method further comprises: removing the mixture product from first reaction chamber; and recycling a portion of glycerol in the mixture product. Preferred Components: The raw material is trap grease or yellow grease. The mixture product of step (b) comprises a fatty acid monoglyceride or diglyceride. The mixture product of step (d) comprises a fatty acid monoester of a volatile alcohol such as methanol or ethanol. The fatty acid monoester comprises methanol or ethanol. The reaction by-product of step (d) comprises glycerol. The second alcohol comprises methanol or ethanol.