Capillary pressure, hysteresis and residual saturation in porous media

We present a new numerical model for macro-scale two-phase flow in porous media which is based on a physically consistent theory of multi-phase flow. The standard approach for modeling the flow of two fluid phases in a porous medium consists of a continuity equation for each phase, an extended form of Darcy’s law as well as constitutive relationships for relative permeability and capillary pressure. This approach is known to have a number of important shortcomings and, in particular, it does not account for the presence and role of fluid–fluid interfaces. An alternative is to use an extended model which is founded on thermodynamic principles and is physically consistent. In addition to the standard equations, the model uses a balance equation for specific interfacial area. The constitutive relationship for capillary pressure involves not only saturation, but also specific interfacial area. We show how parameters can be obtained for the alternative model using experimental data from a new kind of flow cell and present results of a numerical modeling study.

Download Full-text

Lattice-Boltzmann simulations of the capillary pressure–saturation–interfacial area relationship for porous media

Advances in Water Resources ◽

10.1016/j.advwatres.2009.08.009 ◽

2009 ◽

Vol 32 (11) ◽

pp. 1632-1640 ◽

Cited By ~ 132

Author(s):

Mark L. Porter ◽

Marcel G. Schaap ◽

Dorthe Wildenschild

Keyword(s):

Porous Media ◽

Capillary Pressure ◽

Lattice Boltzmann ◽

Interfacial Area ◽

Lattice Boltzmann Simulations

Download Full-text

Study on the effect of pore-scale heterogeneity and flow rate during repetitive two-phase fluid flow in microfluidic porous media

Petroleum Geoscience ◽

10.1144/petgeo2020-062 ◽

2021 ◽

pp. petgeo2020-062

Author(s):

Jingtao Zhang ◽

Haipeng Zhang ◽

Donghee Lee ◽

Sangjin Ryu ◽

Seunghee Kim

Keyword(s):

Porous Media ◽

Fluid Flow ◽

Flow Rate ◽

Sweep Efficiency ◽

Residual Saturation ◽

Flow Rates ◽

Content Type ◽

Lower Flow ◽

Supplementary Material ◽

Lower Flow Rate

Various energy recovery, storage, conversion, and environmental operations may involve repetitive fluid injection and, thus, cyclic drainage-imbibition processes. We conducted an experimental study for which polydimethylsiloxane (PDMS)-based micromodels were fabricated with three different levels of pore-space heterogeneity (coefficient of variation, where COV = 0, 0.25, and 0.5) to represent consolidated and/or partially consolidated sandstones. A total of ten injection-withdrawal cycles were applied to each micromodel at two different flow rates (0.01 and 0.1 mL/min). The experimental results were analyzed in terms of flow morphology, sweep efficiency, residual saturation, the connection of fluids, and the pressure gradient. The pattern of the invasion and displacement of nonwetting fluid converged more readily in the homogeneous model (COV = 0) as the repetitive drainage-imbibition process continued. The overall sweep efficiency converged between 0.4 and 0.6 at all tested flow rates, regardless of different flow rates and COV in this study. In contrast, the effective sweep efficiency was observed to increase with higher COV at the lower flow rate, while that trend became the opposite at the higher flow rate. Similarly, the residual saturation of the nonwetting fluid was largest at COV = 0 for the lower flow rate, but it was the opposite for the higher flow rate case. However, the Minkowski functionals for the boundary length and connectedness of the nonwetting fluid remained quite constant during repetitive fluid flow. Implications of the study results for porous media-compressed air energy storage (PM-CAES) are discussed as a complementary analysis at the end of this manuscript.Supplementary material: Figures S1 and S2 https://doi.org/10.6084/m9.figshare.c.5276814.Thematic collection: This article is part of the Energy Geoscience Series collection available at: https://www.lyellcollection.org/cc/energy-geoscience-series

Download Full-text

Foam Flow in Different Pore Systems—Part 2: The Roles of Pore Attributes on the Limiting Capillary Pressure, Trapping Coefficient, and Relative Permeability of Foamed Gas

SPE Journal ◽

10.2118/205523-pa ◽

2021 ◽

pp. 1-23

Author(s):

Abdulrauf Rasheed Adebayo

Keyword(s):

Porous Media ◽

Capillary Pressure ◽

Relative Permeability ◽

Average Pore Size ◽

Volume Ratio ◽

Graphical Analysis ◽

Pore Characteristics ◽

Average Pore ◽

Rock Samples ◽

Foam Properties

Summary The limiting capillary pressure of foam (Pc*) and foam trapping in porous media are pore-scale foam properties that affect foam transport in porous media. They are strongly influenced by the characteristics of rock pores and throats. Because of experimental limitations, these foam properties are difficult to measure at core scale. As a result, our understanding of their relationship with different pore characteristics is limited. In this paper, novel coreflood and graphical analysis techniques were used to measure Pc* and the foam-trapping coefficient (FTC) at core scale. FTC is a new parameter synonymous to Land’s (1968) trapping coefficient, which describes foam-trapping behavior across an entire range of saturation as opposed to a single endpoint trapped saturation. The scalability of these two foam properties with permeability and other pore characteristics [average pore size (PS), average throat size (TS), average aspect ratio (AR), coordination number (CN), surface area/volume ratio, and reservoir-quality index (RQI)] were also investigated. Pore characteristics of 12 different rock samples were measured from 3D pore-network models generated from high-resolution X-raycomputed-microtomography images. The heterogeneity of the rock samples were quantified by the Dykstra-Parsons index (Dysktra and Parsons 1950), while the RQI and J-function methods were used to classify them according to their storage and flow properties. Each of the measured pore characteristics and their combination [combined pore character (CPC)] were then correlated with Pc* and FTC to understand their respective roles. Furthermore, the data points obtained from the graphical analysis of the coreflood data provided the required input data for a mechanistic foam model for relative permeability of foamed gas (Kovscek and Radke 1994). The estimated relative permeability of foamed gas was then used to study foam mobility in the different pore geometries. The overall results showed the following: P c * has strong negative correlations with all pore characteristics except AR, which has a weak positive correlation. P c * has the strongest correlation with RQI, CPC, and permeability; a moderate correlation with CN and TS; and a very weak correlation with PS. Foam trapping has positive correlations with all pore characteristics except AR, which has a negative correlation. Low AR appears to be responsible for significant trapping of foam in high-permeabilityrocks. Low AR favors more foam trapping, while high AR favors trapping of oil and gas during water imbibition in water-wetrocks. Foam trapping appears to have the dominant control on foam mobility.

Download Full-text