© 2015 Elsevier Ltd. Reinjection of CO2 into producing natural gas reservoirs is considered as a promising technology to improve gas recovery, mitigate atmospheric emissions and control climate change. However, natural gas and CO2 are miscible at reservoir conditions and could result in CO2 contamination of produced natural gas. This mixing process and consequently the viability of Enhanced Gas Recovery (EGR) projects can be quantitatively determined by reservoir simulations - such simulations require a description of gas dispersion. Here we conduct fluid transport experiments through carbonate and sandstone rock cores at various reservoir conditions to evaluate the effect of medium heterogeneity on the dispersion between supercritical CO2 and CH4, accounting for erroneous contributions from entrance/exit and gravitational effects. Early breakthrough and long-tailed profiles are observed for one of the carbonate cores (Ketton) which is attributed to the existence of intra-grain micro-pores, which results in a persistent pre-asymptotic transport regime. Thus a revised model (Mobile-Immobile Model) was successfully used for this core to obtain dispersion coefficients characteristic of the eventual asymptotic regime. Both heterogeneous carbonate rocks considered exhibit higher dispersion than that observed in previously-measured homogeneous sandstone cores (Honari et al., 2013). The power law describing the dependency of dispersion coefficient on Péclet number at comparatively high interstitial displacement velocities gave an exponent of 1.2 for sandstones and 1.4 for carbonates, consistent with literature predictions (Bijeljic and Blunt, 2006; Bijeljic et al., 2011) based on pore-scale simulations.