We present a computational study for the conversion of CH4 and CO2 into value-added chemicals, i.e., the so-called dry reforming of methane, in a dielectric barrier discharge reactor. A zero-dimensional chemical kinetics model is applied to study the plasma chemistry in a 1:1 CH4/CO2 mixture. The calculations are first performed for one microdischarge pulse and its afterglow, to study in detail the chemical pathways of the conversion. Subsequently, long time-scale simulations are carried out, corresponding to real residence times in the plasma, assuming a large number of consecutive microdischarge pulses, to mimic the conditions of the filamentary discharge regime in a dielectric barrier discharge (DBD) reactor. The conversion of CH4 and CO2 as well as the selectivity of the formed products and the energy cost and energy efficiency of the process are calculated and compared to experiments for a range of different powers and gas flows, and reasonable agreement is reached.