NOVELTY - Esterifying (201) free fatty acids in biodiesel feedstock (203), with methanol, comprises: (a) passing feedstock through guard bed column reactor; (b) contacting biodiesel feedstock comprising free fatty acids with methanol and solid heterogeneous catalyst; (c) separating (210) water and methanol from esterification product; (d) contacting esterification product with methanol and esterification catalyst; (e) optionally repeating step (d) for at least one time, to provide esterification product comprising biodiesel; and (f) separating water and methanol from subsequent esterification product.    USE - The method is useful for esterifying free fatty acids in biodiesel feedstock, with methanol, to produce a reaction product comprising biodiesel, water, triglycerides, unreacted methanol, unreacted free fatty acids (all claimed), and/or glycerin.    ADVANTAGE - The method: is carried out in a continuous fashion; provides separation of the methanol from at least one esterification reaction product which is purified to a purity of at least 99.9 wt.%, and is employed in a subsequent esterification or transesterification; employs a second stage reactor or a third stage reactor in step (d) that provides the conversion of free fatty acids and methanol to biodiesel and water, with a conversion of at least 90 wt.% (all claimed), preferably greater than or equal to 99.8 wt.%; is carried out in the absence of a toxic mineral acid (e.g. phosphoric acid, sulfuric acid, hydrochloric acid and/or citric acid), thus achieving high conversions of the feedstock; reuses the methanol e.g. by distillation, in a safe and renewable manner, which lowers the overall operating cost, lowers the carbon footprint, and avoids the time and costs associated with any reagent disposal; does not include the generation of toxic waste, that would otherwise be disposed of, e.g. in a land-fill; utilizes a relatively wide-variety of inexpensive and low-grade feedstock e.g. brown grease, trap grease and high free fatty acid based grease used cooking oil and animal fats, such as tallow, pork fat, poultry fat, lard and choice white grease; employs relatively low energy consumption; produces little or no soap, thus any subsequent glycerin separation becomes relatively easier (in the absence of soaps and salts); and can effectively convert any feedstock, even at very high free fatty acids content.    DETAILED DESCRIPTION - Esterifying (201) free fatty acids in a biodiesel feedstock (203), with methanol, comprises: (a) passing a biodiesel feedstock through a guard bed column reactor comprising an ion exchange resin, so that after passing through the guard bed column reactor, the phosphorus level of the biodiesel feedstock is below 10 ppm, and the sulfur level of the biodiesel feed-stock is below 10 ppm; (b) contacting the biodiesel feedstock comprising free fatty acids, with methanol, and a solid heterogeneous catalyst, where the contacting is carried out under conditions suitable to provide an esterification reaction product comprising biodiesel, methanol, water and free fatty acids; (c) separating (210) water and methanol from the esterification reaction product, so that the esterification reaction product comprises less than 1.5 wt.% water; (d) contacting the esterification reaction product with methanol and a solid heterogeneous esterification catalyst, where the contacting is carried out under conditions suitable to provide a subsequent esterification reaction product comprising biodiesel, methanol, water and optionally free fatty acids; (e) optionally repeating step (d) for at least one time, to provide an esterification reaction product comprising biodiesel; and (f) separating water and methanol from the subsequent esterification reaction product, so that the esterification reaction product comprises less than 1 wt.% water.    DESCRIPTION OF DRAWING(S) - The figure shows a process flow diagram for the esterification of free fatty acids.    Esterifying free fatty acids (201)    Biodiesel feedstock (203)    Reaction products comprising water, methanol, biodiesel, triglycerides and free fatty acid (209)    Separating water and methanol (210)    Reaction product comprising biodiesel, triglycerides and free fatty acids (213)