Carbon integration is a novel concept that targets the recovery and allocation of industrially emitted CO2 streams into CO2-using sinks, with the goal of attaining a CO2 allocation strategy that meets a desired carbon dioxide emission reduction target and an ultimate aim of minimizing the cost of the network while maximizing any revenue. Enhanced oil recovery (EOR) is considered one of the most attractive CO2 sink options. CO2 streams that are delivered and injected into EOR sites are great revenue sources for CO2-supplying entities. Since oil pricing heavily affects the revenue generated via CO2 streams injected into EOR sites, this paper studies the effect of oil price fluctuations onto the design of carbon integration networks. Hence, oil pricing has been selected as the main uncertainty parameter and has been fed into a linearized multiperiod carbon integration model using stochastic data. Since oil prices vary periodically, this model has been formulated over several time periods, in which the oil pricing parameters are allowed to change over time. The proposed model has been optimized using two different approaches: (1) the binomial lattice approach, which primarily utilizes average uncertainties as expected values, and (2) the multiscenario approach.