Deep ocean storage of CO2 captured from, for example, flue gases is being considered as a potential response option to global warming concerns. For storage to be effective, CO2 injected into the deep ocean must remain sequestered from the atmosphere for a long time. However, a fraction of CO2 injected into the deep ocean is expected to eventually evade into the atmosphere. This fraction is expected to depend on the time since injection, the location of injection, and the future atmospheric concentration of CO2. We approximate the evasion of injected CO2 at specific locations using a nonlinear convolution model including explicitly the nonlinear response of CO2 solubility to future CO2 concentration and alkalinity and Green's functions for the transport of CO2 from injection locations to the ocean surface as well as alkalinity response to seafloor CaCO3 dissolution. Green's functions are calculated from the results of a three-dimensional model for ocean carbon cycle for impulses of CO2 either released to the atmosphere or injected a locations deep in the Pacific and Atlantic oceans. CO2 transport in the three-dimensional (3-D) model is governed by offline tracer transport in the ocean interior, exchange of CO2 with the atmosphere, and dissolution of ocean sediments. The convolution model is found to accurately approximate results of the 3-D model in test cases including both deep-ocean injection and sediment dissolution. The convolution model allows comparison of the CO2 evasion delay achieved by deep ocean injection with notional scenarios for CO2 stabilization and the time extent of the fossil fuel era.