[1] We present a level set method for simulating capillary-controlled displacements with nonzero contact angles in porous media. The main feature of the method is a level set evolution velocity which is different in the pore space and solid phase. This augments the standard level set equation with an extra term such that, at steady state, the contact angle is enforced in the solid phase, whereas capillary and interfacial forces are balanced in the pore space. We employ the method to simulate quasistatic drainage and imbibition processes for different contact angles in several pore geometries, and to compute capillary pressure and fluid/fluid specific interfacial area curves in each case. We validate the method by comparing stable fluid configurations computed in idealized two-dimensional geometries and three-dimensional (3-D) straight tubes with known analytical solutions. Simulations performed in a subset of a 3-D sandstone image show that the developed method accounts for well-known pore-scale mechanisms such as piston-like invasion, Haines jump, interface coalescence, and retraction, swelling of wetting films and snap-off. The contact angle is formed by an intersection of the fluid/fluid interface and the void/solid boundary. Therefore, the solid matrix surrounding the pore space is discretized with at least an equal number of grid points as the size of the numerical stencil used to approximate the level set derivatives.Citation: Jettestuen, E., J. O. Helland, and M. Prodanović, A level set method for simulating capillary-controlled displacements at the pore scale with nonzero contact angles, Water Resour. Res., 49,[4645][4646][4647][4648][4649][4650][4651][4652][4653][4654][4655][4656][4657][4658][4659][4660][4661]

[1] Recently, a considerable effort has been made to determine the precise displacement criteria for three-fluid configurations in pores of angular cross section. These configurations may contain thick conducting fluid layers, such as oil layers residing between gas in the center and water in the corners of the pore. For pores of uniform, but arbitrary, wettability and in the absence of contact angle hysteresis, a precise thermodynamic criterion for the existence of such layers has been established. In this paper we derive similar criteria for layers in pores of nonuniform wettability, where additional and more complicated layer configurations arise. The criteria for formation and removal of layers are consistent with the capillary entry conditions for the accompanying three-phase bulk displacements, which is essential for accurate pore-scale modeling of three-phase flow. We consider the particular case of three-phase gas invasion in a starshaped pore with a specific choice of interfacial tensions and contact angles. For this case all possible fluid configurations arise, but only if the water-wet surface in the pore corners is small.

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.

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