Some heavy oil production can be established using conventional methods; however, these methods are often somewhat ineffective with low recovery factors of less than 20%. Carbon dioxide (CO2) huff-n-puff or cyclic CO2 injection is one of the Enhanced oil recovery (EOR) methods that can be used in stimulating aging wells to recover some residual oil. The shut-in stage of this method results in a significant delay in the production time, and hence lower oil recovery. For the first time, in this paper, an attempt is made to overcome this issue by a novel approach, employing dual tubing completions. The aim of this is to increase the oil recovery with the production during soak time. Also, a majority of the remaining heavy oil reservoirs are carbonates, hence the research was focused on the same conditions. Numerical simulation is done using dual-tubing conditions in a dual-porosity model with conventional tubing as a base case. Optimization studies are done for injection rate, injection time, soaking time, production time, and huff-n-puff cycles. The results show that the recovery factor can increase significantly, with no discontinuity in production. Preliminary economic studies for the cases also showed a net increase in profit of 7% (1.3 million Dollars for the case chosen). This demonstrates the feasibility of the proposed method which can be implemented into conventional operations, for a more sustainable economy in the era of low oil prices.