The objective of this paper is to present a fundamentals-based, consistent with observation, three-phase relative permeability model to describe flow more accurately in countercurrent movement of gas and liquids situation. While most flooding operations have both gas and liquids flowing in the same direction, in gravity dominated processes such as steam assisted gravity drainage (SAGD) or CO2 storage in water saturated reservoirs, often due to density difference the gases rise above and liquids flow down. This gives rise to a counter-current flow situation. It has been documented by a few researchers including Adebayo et al. (2017) and Prats et al. (2008). At the gas-liquid interface, the shear forces act to oppose movement of gas and liquids resulting in a slowdown in the flow of both. This slow-down or reduced flow is not captured in standard relative permeability curves which are typically generated using co-current flows.

In the current work, the approach adopted by Gupta (2021) for a mechanistic 3-phase flow model is used to develop relative permeability expressions for gravity-incorporated flow. To do this, three-phase core-annular laminar flow expressions are first developed in a single thin tube, then these flow expressions are aggregated for the entire pore volume represented by a bundle of tubes with varying tube sizes mimicking pore-size distribution. An irreducible water saturation, when water is the wetting phase, is also assumed.

The relative permeabilities obtained with counter-current flow considerations are compared with the ones presented in Gupta (2021) for co-current flow to highlight the difference. Additionally, the impact of these modified rel. perms is shown with an example SAGD problem resulting in a slower and more realistic growth of the steam chamber. Similar to the observation of Gupta (2021) this mechanistic model also indicates a natural dependence of rel. perms of the intermediate phase on temperature, which in literature has been a subject of much debate.

The novelty of the work is in development of a three-phase relative permeability model which takes into account gas-liquid countercurrent movement in porous media based on fundamentals of flow in fine capillaries. The significance of the work includes, aside from predicting results more in line with expectations in gravity-dominated processes, an explanation of temperature dependent relative Gupermeabilities of the intermediate phases. Also, unlike Stone-II method, it predicts a more realistic time dependent residual oleic-phase saturation for gravity drainage recovery methods.

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