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.
Laminar fluid flow in concentric annular ducts of non-conventional cross-section applying GBI method
