A Discrete‐Domain Approach to Three‐Phase Hysteresis in Porous Media. Issue 6 (17th June 2021)

• Record Type: Journal Article
• Authors: Helland, Johan Olav; Jettestuen, Espen; Friis, Helmer André
• Is Part Of: Water resources research. Volume 57:Issue 6(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-06-17
• Subjects: three‐phase -- hysteresis -- capillary pressure -- constrained energy minimization -- metastability -- porous media; Hydrology -- Periodicals; 333.91
• DOI: 10.1029/2021WR029560
• Languages: English
• ISSNs: 0043-1397

Abstract

Abstract: We present a discrete‐domain approach to three‐phase displacements and hysteresis in porous media. In this method, constrained energy minimization leads to evolution equations for local saturations that describe a wide range of three‐phase displacements, including pressure‐ and saturation‐controlled displacement with or without preservation of one of the defending phases. Under action of global saturation constraints, irreversible displacements lead to significant fluid redistribution, as well as abrupt fluctuations of both the three‐phase saturation paths and the corresponding capillary pressures. These features are a consequence of Haines jumps with cooperative behavior that occur at pore scale in three‐phase systems. The method is a fast and convenient way to investigate hysteresis behavior of three‐phase displacement in porous media. As free energy is an extensive property, the framework links pore and core scales and provide a means to achieve upscaled three‐phase displacements for higher‐order hysteresis loops, which rarely is obtained in time‐consuming three‐phase measurements or pore‐scale simulations. Plain Language Summary: Knowledge of the way three fluids move through the pore space inside porous rocks is crucial to describe oil recovery and CO2 storage processes in subsurface reservoirs. Because of the complex pore structure, interfaces between fluids do not generally recede (drainage) in the same way as they advance (imbibition), upon reversal of displacement direction. This means that the displacement is irreversible and depends on the history of fluid displacements. This is called hysteresis. At macroscopic scale, hysteresis is often quantified by the difference in capillary pressure‐saturation curves between drainage and imbibition. The extent of hysteresis is a collective effect of many reversible and irreversible displacement events at pore scale. Hysteresis in two‐phase fluid systems has been the subject of many previous studies. Here, we present a method to describe irreversible displacement and hysteresis in three‐phase systems. Based on thermodynamics, we describe hysteresis as irreversible transitions across barriers in an energy landscape exhibiting metastability. Constrained minimization results in saturation evolution equations that collectively describe various irreversible three‐phase displacements and corresponding capillary pressure‐saturation curves. We envision that the approach is a suitable upscaling tool for relating three‐phase hysteresis behavior from pore scale with macroscopic scale. Key Points: Constrained energy minimization in a discrete‐domain model describes three‐phase capillary pressure and hysteresis from pore to core scale Inclusion of saturation constraints leads to a variety of three‐phase displacements with fluid redistribution, pressure, and saturation jumps A fast and flexible method to calculate three‐phase capillary pressure for higher‐order hysteresis loops