NOVELTY - Producing fatty acid methyl esters, involves: mixing alcohol with feedstock oil to prepare alcohol/oil mixture; reacting the mixture using first heterogeneous catalyst in acid esterification process to produce glycerin-containing product; separating glycerin from the product to produce biodiesel-containing feedstock and glycerin; separating biodiesel from the feedstock to produce unreacted feedstock and biodiesel; reacting the unreacted feedstock using second heterogeneous catalyst to produce glycerin-biodiesel-methanol mixture; and separating biodiesel and glycerin in separate streams.    USE - For producing fatty acid methyl esters (claimed) such as biodiesel; and also used to convert an input of variable feedstock oils and methanol into refined biodiesel, refined glycerin, and matter organic non-glycerol (MONG) outputs for any suitable application.    ADVANTAGE - The process provides lower equipment costs resulting from the use of non-corrosion resistant materials because the use non-corrosive catalysts do not necessitate it; provides production of product streams requiring significantly less refinement to meet ASTM or EIN specifications, because there are no excess catalysts that need to be treated or impurities (salts) present from the neutralization of catalysts; enable reduction of operating costs related to the use of non-hazardous catalysts which do not require special handling or storage procedures as compared to soluble acids and bases; and the use of low maintenance coalescers which have no moving parts and do not require frequent maintenance schedules.    DETAILED DESCRIPTION - Producing fatty acid methyl esters, involves: mixing an alcohol with a feedstock oil to prepare an alcohol/oil mixture; reacting the alcohol/oil mixture using a first heterogeneous catalyst in an acid esterification process to produce a glycerin-containing product; separating glycerin from the glycerin-containing product using a coalescer to produce a biodiesel-containing feedstock and glycerin; separating biodiesel from the biodiesel-containing feedstock using a coalescer to produce unreacted feedstock and biodiesel; reacting the unreacted feedstock using a second heterogeneous catalyst in a trans-esterification process to produce a glycerin-biodiesel-methanol mixture; and separating biodiesel and glycerin in separate streams from the glycerin-biodiesel-methanol mixture using a coalescer to produce additional glycerin and additional biodiesel.