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The rate of carbon dioxide (CO2) dissolution in saline aquifers is the least well‐constrained of the secondary trapping mechanisms enhancing the long‐term security of geological carbon storage. CO2 injected into a heterogeneous saline reservoir will preferentially travel along high permeability layers increasing the CO2‐water interfacial area which increases dissolution rates. We provide a conservative, first‐principles analysis of the quantity of CO2 dissolved and the rate at which free‐phase CO2 propagates in layered reservoirs. At early times, advection dominates the propagation of CO2. This transitions to diffusion dominated propagation as the interfacial area increases and diffusive loss slows propagation. As surrounding water‐filled layers become CO2 saturated, propagation becomes advection dominated. For reservoirs with finely bedded strata, ∼10% of the injected CO2 can dissolve in a year. The maximum fraction of CO2 that dissolves is determined by the volumetric ratio of water in low permeability layers and CO2 in high permeability layers. Plain Language Summary: To limit global warming to 2°C, it is likely that large amounts of carbon dioxide (CO2) will need to be stored underground. A significant fraction of the total possible storage space for CO2 is in salt water reservoirs, kilometers beneath the surface. It is important that once the CO2 has been injected underground, it is securely trapped, otherwise, there is a risk that it could leak back to the surface. After the CO2 is injected into these reservoirs, it can dissolve in the surrounding water, greatly reducing the risk of leakage, although complete dissolution of all the injected CO2 may take millions of years. However, preferential flow of CO2 along more permeable layers in geological formations creates a complex front between the water and CO2 which increases the surface area available for dissolution. This study calculates the minimum amount of injected CO2 that can dissolve in such a reservoir and how far it travels. Using injection of CO2 for enhanced oil recovery at the Salt Creek Field in Wyoming as an example, we find that in one year around 10% of the total injected CO2 can dissolve into the surrounding water by this process and become trapped. Key Points: Injection of carbon dioxide into finely bedded reservoirs leads to enhanced contact area with water and hence enhanced dissolution ratesPropagation rates of free‐phase carbon dioxide transition from advection to diffusion dominated as the contact area with water increasesFor injection into the Salt Creek reservoir, Wyoming, nearly 10% of the injected carbon dioxide is predicted to dissolve in one year [ABSTRACT FROM AUTHOR]