Analytical modeling of flow regimes during cyclic CO₂ injection in hydraulically fractured tight reservoirs for enhanced oil recovery

This paper presents several analytical models for the pressure distribution in hydraulically fractured reservoirs depleted by horizontal wells with the aid of cyclic CO₂ injection. The objective is to eliminate uncertainties in predicting reservoir performance after the enhancement by CO₂ injection and develop accurate tools for designing CO₂ injection projects. This paper's primary purpose is to present novel analytical models for flow regimes and validate them. The proposed models are unique because they are derived without using an approximated approach, they consider multiphase flow and can be utilized for injection applications. Although CO₂-injection has been a favorable enhanced oil recovery (EOR) approach in the petroleum industry, some studies reported its negative impact due to the premature decline in production. Additionally, few researchers have linked the cyclic injection with the flow response inside the formation. This paper presents three flow regimes (hydraulic fracture regime, bilinear flow regime, and formation linear-flow regime) that develop during production and injection in unconventional reservoirs. The analytical solutions that encompass the non-approximated trilinear pressure transient model for hydraulically fractured reservoirs are developed. The models are solved by one of the state-of-the-art computational tools. The solutions are used to characterize the analytical models for the three aforementioned flow regimes. Then, the numerical solution is designed to validate the analytical models. The results show a good agreement between analytical and numerical solutions. The hydraulic fracture linear flow regime and bilinear flow regime occur at the early and intermediate well production stage. These flow regimes indicate the end of the CO₂ injection into the fractures and the stimulated reservoir volume, respectively. Thus, knowing the period for the CO₂ injection and the hydraulic fracture characteristics will facilitate the optimization of the CO₂ injection process in tight formations depleted by multiple hydraulic fractures.