Carbon, which is often used as an additive to silicon carbide powder, is thought to facilitate densification during sintering by aiding the removal of the native SiO2 layer, which is present on the starting SiC powder. The mechanism is the reduction of SiO2 to SiC with the formation of primarily CO gas, which diffuses out from the porous compact at a temperature below the normal sintering temperature. It has been found beneficial to hold the compact at an intermediate temperature to allow time for the CO and other gases to diffuse out before the pores close. We investigate this process using a computational model based on codiffusion of multiple gas species, which enables prediction of the gas and condensed phase compositions as a function of time and position in the specimen. The results are used to determine the optimum holding time for complete SiO2 removal as a function of key parameters, such as specimen thickness, particle size, temperature, etc., as well as the necessary amount of C additive. The results of the modeling are consistent with the experimentally observed spatial variation of density and composition in SiC compacts.