NOVELTY - Increasing the throughput of esterification or transesterification reactions of multiphase immiscible biodiesel reaction constituents, involves: supplying the constituents to a mixing unit; providing methyl ester at temperature and pressure to form single phase solution in mixing unit without the use of a co-solvent to be removed from the constituents so as not to be present in a final biodiesel fuel; passing the solution from the mixing unit to a reactor unit and maintaining the solution at a temperature and pressure to esterify or transesterify at least part of the constituents.    USE - For increasing the throughput of esterification or transesterification reactions of multiphase immiscible biodiesel reaction constituents or reactions of biodiesel fuel production (claimed).    ADVANTAGE - The method increases the throughput of esterification or transesterification reactions of multiphase immiscible biodiesel reaction constituents or reactions of biodiesel fuel production; achieves a steady state reaction with single phase solution created from multiphase constituents without use of co-solvent that can not or should not be present in the final fuel and has to be removed; is completely water-free method; and avoids water and its associated complications. When the reactants in the method are in a single phase solution they can react immediately at a molecular level, providing a much faster, more complete reaction. The constituents are in substantially a single phase rather than an immiscible or multi-phase status significantly increases the reaction speed and throughput of the system. The recirculation allows more contact of constituents with the catalyst surface, enabling a more complete reaction.    DETAILED DESCRIPTION - Increasing the throughput of esterification or transesterification reactions of multiphase immiscible biodiesel reaction constituents, involves: supplying the multiphase immiscible reaction constituents to a mixing unit; providing a methyl ester at temperature and pressure to form single phase solution in the mixing unit without the use of a co-solvent to be removed from the reaction constituents so as not to be present in a final biodiesel fuel; passing the single phase solution from the mixing unit to a reactor unit and maintaining the single phase solution at a temperature and pressure to esterify or transesterify at least part of the reaction constituents.