The Effect of Displacement History on Three-Phase Capillary Pressure and Relative Permeability Derived from Triangular Pore Cross Sections with Contact-Angle Hysteresis

Abstract

Abstract We present a model of mixed-wet triangular tubes that calculates three-phase capillary pressure and relative permeability curves. Several fluid configurations may occur in triangular pore cross-sections, and capillary displacements may either occur as piston-like displacements of the fluids occupied in the bulk, or as piston-like displacements of the fluids in layers. To our knowledge, this latter type of displacement has not been analyzed before in mixed-wet pores. Using minimization of Helmholtz free energy, we derive accurate three-phase capillary entry pressures for such layer displacements, accounting for contact-angle hysteresis. Numerical examples are presented to illustrate how the entry pressures for the different possible displacements relate to each other during gas and water invasion into pores with a specific fluid configuration. It turns out that the entry pressures for related displacements are consistent. This implies that pores occupied by the same fluid in the bulk portion must have the same fluid configuration for a constant value of capillary pressure. With this model we calculate three-phase capillary pressure and relative permeability, and explore how the saturation-dependencies of these quantities change according to saturation-reversal points. We simulate the sequence of processes primary drainage, imbibition and gas invasion, for different maximum capillary pressures Powmax er primary drainage. In the simulation results presented here, we find that the oil and gas relative permeability, and their saturation-dependencies, are sensitive to variations of Powmax, While the water relative permeability is less sensitive. Such effects are absent in cylindrical tubes. This is caused by the capillary entry pressures, which are strongly affected by hinging interfaces in the corners of angular pores when contact-angle hysteresis is assumed. Thus the choice of pore geometry is important if hysteretic capillary pressure and relative permeability relationships are simulated using network models. With respect to these findings, relative permeability and capillary pressure correlations should be formulated with parameters that strongly depend on saturation-reversal points such that different saturation-dependencies can be accounted for in subsequent invasion processes.