TECHNOLOGY FOCUS - CHEMICAL ENGINEERING - Preferred Method: Fresh alcohol (7) and catalyst are added to pressurized reaction tank. Triglyceride (95% or more) in pre-reaction mixture is converted by applying cavitational energy and agitating in pressurized reaction tank. The intermediate biodiesel reaction mixture is introduced into a separation vessel (25) to remove portion of glycerol. At least one component of pre-reaction mixture is heated at 60-150 degrees C. The biodiesel reaction mixture is introduced into pressurized reaction tank at 30-65 degrees C. The pre-reaction mixture is subjected to cavitation by passing the pre-reaction mixture through at least one cavitation apparatus (20) chosen from a flow-through constriction orifice, an ultrasonic transducer, a homogenizer, a rotor-stator mixer or colloid mill. The biodiesel reaction product is further introduced into a separation vessel (35) to produce a purified biodiesel reaction product (11). The reaction mixture (4) is agitated in pressurized reaction tank to form biodiesel reaction product comprising fatty acid alkyl ester and glycerol, and then portion of glycerol is removed from the reaction mixture (4). The biodiesel reaction product is further agitated in a secondary pressurized reaction tank to form a secondary biodiesel reaction product. Fresh alcohol and catalyst are added to secondary pressurized reaction tank. The secondary biodiesel reaction product is introduced into separation vessel to remove glycerol from secondary biodiesel reaction product. Preferred Product: The purified biodiesel reaction product has a cold soak filtration time of less than 150 seconds, preferably less than 90 seconds determined by ASTM D6217. The purified biodiesel reaction product has less than 10 ppm of phosphorus or phosphorus compound. The triglyceride feedstock of pre-reaction mixture contains more than 150 ppm of phosphorus or phosphorus compound. The phosphorus compound is phosphorus steryl glucoside. The secondary biodiesel reaction product has cold soak filtration time of less than 150 seconds determined by ASTM D6217, and less than 10 ppm of phosphorus or phosphorus compound.