Radial Multiphase Flow in Stratified Formations: Implications for CO₂ Storage

Despite continuous advancements in numerical simulations of multiphase flow, analytical and semi-analytical solutions remain of significant interest. Earlier efforts related to analytical solutions in heterogeneous porous media primarily focused on linear flow, with limited attention given to radial flow despite its significance in describing fluid movement from wellbores into porous media or vice versa. In this study, we propose a two-step workflow to evaluate the storage capacity and sweep efficiency of incompressible two-phase radial flow in noncommunicating layered media. The first step involves a rigorous mathematical derivation of a general analytical solution for the frontal advance flow problem under viscous-dominated flow conditions. This solution accounts for variability in petrophysical and geometrical properties across different layers. It comprises distinct formulas that describe saturation distribution both before and after the breakthrough of each layer, with the flow rate coupling between layers represented through various combinations of these formulas. In the second step, viscous flow saturation is mapped to its equivalent viscous-gravity flow saturation using a simplified approach outlined in the literature. The workflow is applied to analyze the expected migration of carbon dioxide (CO₂) multiplumes during the injection period in shaly-sand bodies within the Captain sandstone units of the Goldeneye field, North Sea, United Kingdom (UK). The analysis reveals that gravitational forces significantly reduce storage efficiency, from more than 30% in viscous flow to approximately 3% in viscous-gravity flow. These findings are verified through industry standard numerical simulation, confirming the accuracy of the proposed workflow. Unlike linear flow, the distribution of injected CO₂ among flowing layers in radial flow is characterized by a quasistatic trend that stabilizes shortly after the start of injection. The extension of the proposed approach to model the post-injection period is discussed, in addition to the effects of dissolution, vaporization, and salt precipitation.