Physically Based Capillary Pressure Correlation for Mixed-Wet Reservoirs From a Bundle-of-Tubes Model

Abstract

Summary It is shown that the main characteristics of mixed-wet capillary pressure curves with hysteretic scanning loops can be reproduced by a bundle-of-triangular-tubes model. Accurate expressions for the entry pressures are employed, truly accounting for the mixed wettability and the diverse fluid configurations that arise from contact angle hysteresis and pore shape. The simulated curves are compared with published correlations that have been suggested by inspection of laboratory data from core plug experiments. Introduction Knowledge of the functional relationship between capillary pressure and saturation is required in numerical models to solve the equations for fluid flow in the reservoir. In practice, this relationship is formulated as a capillary pressure correlation with several parameters that usually are to be determined from experimental data. Generally, it is not evident how these parameters should be adjusted to account for variations in physical properties such as wettability, pore shape, pore-size distribution, and the underlying pore-scale processes. Therefore, a more physically based correlation, accounting for observable properties, would improve the reliability of the correlation and extend its applicability range. Analytical correlations may be derived assuming a bundle-of-tubes representation of the pore network. Following this approach for a model of cylindrical tubes, Huang et al. (1997) derived a capillary pressure correlation for primary drainage and the hysteresis bounding loop, accounting for variations in wettability. Princen (1992) computed numerically the relationship between capillary pressure and saturation for primary drainage and imbibition for a bundle of tubes with curved triangular cross sections of uniform wettability. He made no attempt, however, to develop any correlation.

Dynamic Capillary Pressure Curves From Pore-Scale Modeling in Mixed-Wet-Rock Images

“…In addition to predicting fundamental flow parameters (e.g., capillary pressure and relative permeability) (Kovscek et al, 1993;Øren et al, 1998;van Dijke & Sorbie, 2002a;Silin & Patzek, 2006;Helland & Skjaeveland, 2006a;Mousavi et al, 2013), pore scale modeling is also capable of investigating the effects of micro-scale phenomena on the macro-scale behaviors, and thus it provides a physically-based approach to upscale multiphase flow in porous media from micro-scale to macroscale (Middleton et al, 2012;Mehmani et al, 2012;Al-Dhahli et al, 2013;Porta et al, 2013).…”

“…Layers of oil surrounded by identical fluid (water) have a sandwiched shape and can exist at negative capillary pressure during forced imbibition in mixed-wet pore spaces (Kovscek et al, 1993;Blunt, 1997b;Piri & Blunt, 2004;Helland & Skjaeveland, 2006a; as shown in Figure 2.3(a). However, this sandwiched shape layer type can also occur in pore necks during primary drainage process , in which water is the layer fluid surrounded by oil, see Layers surrounded by different fluids are formed by intermediate-wet…”

“…This criterion is consistent with the MS-P capillary entry pressures for other types of piston-like invasions. The thermodynamical-based criterion was implemented both into a capillary bundle model (Helland & Skjaeveland, 2006a) and porenetwork modeling (Ryazanov et al, 2009;Al-Dhahli et al, 2013) …”

“…Literature Review of the corner and the radius of the inscribed circles and the pore-size frequency can be given by a truncated two-parameter Weibull distribution (Diaz et al, 1987;Hui & Blunt, 2000;Helland & Skjaeveland, 2006a;Wang & Dong, 2011).…”

“…teresis is modeled by introducing a hinging interface with pinned contact lines (see Figure 2.2) that separates the remaining corner water and center oil and thus allowing the contact angle to change at this position in order to maintain capillary equilibrium (Ma et al, 1996;Valvatne et al, 2005;Helland & Skjaeveland, 2006a;van Dijke & Sorbie, 2003b;van Dijke et al, 2007). The interface does not move until the hinging contact angle reaches the advancing contact angle.…”