Simulation of Three Phase Capillary Pressure Curves Directly in 2D Rock Images

Abstract

Abstract Pore-scale modeling of three-phase capillary pressure in realistic poregeometries could contribute to an increased knowledge of three-phase displacement mechanisms and also provide support to time-consuming and challenging core-scale laboratory measurements. In this work we have developed a semi-analytical model for computing three-phase capillary pressure curves and the corresponding three-phase fluid configurations in uniformly-wet rock image sencountered during tertiary gas invasion. The fluid configurations and favorable entry pressure are determined based on free energy minimization by combining all physically allowed gas-oil, gas-water, and oil-water arc menisciin various ways. The model is shown to reproduce all three-phase displacements and capillary entry pressures that previously have been derived in idealized angular tubes for gas invasion at uniform water-wet conditions. These single-pore displacement mechanisms include (i) gas invasion into pores occupied by oil and water leading to simultaneous displacement of the three fluids, (ii) simultaneous invasion of bulk gas and surrounding oil into water filled pores, and finally (iii) the pure two-phase fluid displacements in which gas invades pores occupied by either water or oil. The proposed novel semi-analytical model is validated against existing analytical solutions developed in a star-shape pore space, and subsequently employed on an SEM image of Bentheim sandstone to simulate three-phase fluid configurations and capillary pressure curves at uniform water-wet conditions and different spreading coefficents. The simulated fluid configurations for the different spreading coefficients show similar oil layer behaviour as previously published experimental three-phase fluid configurations obtained by computed microtomography in Bentheim sandstone. The computed saturation paths indicate that three-phase oil-water capillary pressure is a function of the water saturation only, whereas the three-phase gas-oilcapillary pressure appears to be a function of two saturations. This is explained by the three-phase displacements occurring in the majority of the simulations, in which gas-water interfaces form immediately during gas invasion into oil- and water-saturated pore shapes.