Fundamentals-Based Alternative Addresses Issue With Three-Phase Permeability Model

Abstract

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 205883, “Issue With Stone II Three-Phase Permeability Model and a Novel Robust Fundamentals-Based Alternative to It,” by Subodh Gupta, SPE, Heretech Energy. The paper has not been peer reviewed. _ The objective of this paper is to present a fundamentals-based, three-phase flow model consistent with observation that avoids the pitfalls of conventional models. Though the use of the Stone II model is very popular for three-phase flow across the industry, one issue in the context of gravity drainage is how it appears counterintuitively to limit the flow of oil when water is present near its irreducible saturation. The novelty of the work presented in the complete paper is in the development of a model based on fundamentals of flow in fine channels that better explains observed results in the context of flow in porous media. Problem Definition Residual oil saturation (So) from retrieved cores from oil-drained chambers of steam-assisted gravity drainage (SAGD) reservoirs invariably shows values as low as 1 or 2%, whereas reservoir simulations using Stone II-based relative permeabilities (an industrywide favorite) predict significantly higher numbers (14–18%). In previous work, the author and others, in an attempt to remedy the situation, extended the oil-phase relative permeability in the presence of the water phase (krow) and oil-phase relative permeability in the presence of the gas phase (krog) curves all the way to water and gas saturation values less than unity; however, they discovered that, in the presence of water saturation (Sw) near the irreducible water saturation (Swi), the use of the Stone II formula for oil relative permeability still resulted in high residual So. Correct estimation of residual oil-phase saturation is even more important for solvent/steam mixed thermal recovery processes such as solvent-aided processes, where a small amount of solvent is added with steam in SAGD, and significantly more important for solvent-dominated processes, where a small amount of steam or heat is added with a large amount of solvent. A large amount of residual oleic-phase saturation and associated pessimistic solvent-recovery prediction will lead to erroneous economic assessment of these processes. The discrepancy in residual So, as the author and coauthors discovered in previous work, stems from a peculiarity of the Stone II formulation given by Equation 1 of the complete paper. To model this 1D problem numerically, a program developed by the author for his PhD thesis for modeling of moving front reservoir processes with dynamic gridding was modified and run with constant fluid properties for hexane and water at constant pressure and temperature. It also incorporated the three-phase relative permeabilities given by Equation 1 and Table 1 of the complete paper. The results are shown in Fig. 1.