In this study, steam co-injection with flue gas or N2 was numerically reproduced to determine the best gas composition to be deployed in a Colombian heavy crude oil, using a commercial reservoir simulation software. The oil mixture was characterized via EoS parameters, withtuning average errors of 5%. Injection conditions were evaluated with thermal simulations to analyze the response in oil production, allowing to find a deployment strategy having the highest recovery with the lowest gas injection volume. Results agree with experimental observations regarding the starting times for co-injection and help to narrow the uncertainty range where gas and steam co-injection is asuitable recovery technique in heavy oil reservoirs. The study showed that the incremental oil recovery factor can be enhanced, at least, in 40% when optimizing the deployment of steam and flue gas co-injection for the well studied here