Injection of acids into carbonate formations can lead to the formation of macroscopic flow conduits. These so-called wormholes have the potential to dramatically increase effective permeability, leading to an enhanced well injectivity or productivity. The phenomenon has been studied extensively in the context of acid stimulation of oil production wells in carbonates.In recent years the topic has received widespread interest in the context of CO2 storage. However, the experimental and modelling studies conducted so far have been nearly exclusively limited to carbonated brine injection. This is in contrast to ongoing and planned CO2 injection operations, where nearly-pure (dry) supercritical CO2 is injected, which is not an acid, but an acid-forming agent. This leads to a substantially different scenario, since the acid mobility – and hence the dissolution regime – is limited by two-phase flow effects.This paper addresses two-phase flow effects on dissolution patterns. To this extent Reactive Transport Modelling is applied on a fine scale, allowing for an explicit resolution of wormhole formation and direct comparison to experimental results. This is followed by the development of an effective (upscaled) model for modelling wormholing on the field scale. For this purpose, the so-called Global Wormholing Model, that was developed for acid stimulation, is generalised and adapted for application to two-phase CO2-brine systems. The upscaled model is applied to the near-wellbore scale to predict wormhole lengths and their effect on injectivity.The results show that for dry CO2 injection the potential for (or impact of) wormhole formation is negligible. This is different from the case of carbonated brine injection, which leads to significant wormholing potential over extended injection timescales. A Water-Alternating-Gas (WAG) scenario, which is of interest to CO2 Enhanced Oil Recovery (EOR) operations, exhibits only weak signatures of wormhole formation even after a large number of WAG cycles.