Fatty acid methyl esters (biodiesel) were produced by the transesterification of triglycerides with compressed methanol (critical point at 240 degrees C and 81 bar) in the presence of solid acids as heterogeneous catalyst (SAC-13). Addition of a co-solvent, supercritical carbon dioxide (critical point at 31 degrees C and 73 bar), increased the rate of the supercritical alcohols transesterification, making it possible to obtain high biodiesel yields at mild temperature conditions. Experiments were carried out in a fixed bed reactor, and reactions were studied at 150-205 degrees C, mass flow rate 6-24 ml/min at a pressure of 250 bar. The molar ratio of methanol to oil, and catalyst amount were kept constant (9 g). The reaction temperature and space time were investigated to determine the best way for producing biodiesel. The results obtained show that the observed reaction rate is 20 time faster than conventional biodiesel production processes. The temperature of 200 degrees C with a reaction time of 2 min were found to be optimal for the maximum (88%) conversion to methyl ester and the free glycerol content was found below the specification limits. (C) 2011 Elsevier Ltd. All rights reserved.