The objective of this work was to establish fixed bed sorption enhanced reactors (SER) and simulated moving bed reactors (SMBR) for the production of high purity biodiesel (fatty acid methyl ester, FAME) using esterification reactions between fatty acids (FA) in used oils and methanol. This study has demonstrated that these processes have tremendous potential in terms of overcoming the low conversion and separation difficulties that are faced in conventional biodiesel production processes. Additionally, the SMBR process operating conditions call be optimized to produce FAME at it desired purity in a continuous mode. The novelty of this work lays in the development of generic and comprehensive dynamic simulation and systematic parametric analysis frameworks. These were used to deduce the following operating conditions for achieving more than 90% conversion of FA and 80% purity of FAME, from an SMBR process: switching time of 900 s, length of 0.25 m, and feed, raffinate, and eluent flow rate ratios of 0.41, 0.49, and 0.75, for a given velocity of 2.4 x 10(-4) m/s in the reaction zone.