Capillary Pressure in Nanopores: Deviation from Young-Laplace Equation

Abstract Recent studies on multi-phase fluids in nanoscale capillaries indicated that the capillary wall-fluid interactions could play a dominant role on the co-existence of the phases, which may change the fundamental properties of the fluids, such as density, viscosity, and interfacial tension. At the extreme of the confinement, these properties become vague. This raises a serious question on the validity of Young-Laplace equation to predict capillary pressure in small capillaries that the unconventional resources commonly exhibit. In this paper, using nonequilibrium molecular dynamics simulation of mercury injection into model nanocapillaries, the nature of multi-phase fluids is investigated in capillaries with sizes below 20nm, and the Young-Laplace equation is re-visited. Higher capillary pressure is predicted for the model nanocapillaries used in the simulations compared to that value obtained using the Young-Laplace equation, in particular, when the capillary diameter is less than 10nm. Good agreement found with the theory in larger size capillary. The capillary pressure increases as the capillary size is decreased and shows a power-law dependence onthe size of the capillary. This dependence yields up to 70% increase in the estimated capillary pressure value for the extreme case of 1nm capillary. Higher tangential local pressures at the nanocapillary entry resulted from the adsorption phase is the cause of the difference. Based on the observations, a modified Young-Laplace equation is proposed for mercury-airfilled pore systems which are commonly used in Mercury Injection Capillary Pressure (MICP) experiments for the pore volume and pore size distribution measurements. At the highest injection pressure of MICP, the minimum captured size is predicted 4.8nm instead of 3.6nm based on the Young-Laplace equation. The increase in the predicted capillary size leads to an increase in total pore volume of the sample. The error in volume is up to 20% for measurements with shale samples. The results are important for the characterization of resource shale formations because the nanopore volume correction influence the hydrocarbon in-place and reserve calculations. The work can be extended to other multi-phase systems, such as oil-water, and water-gas, grouping with other capillary wall material to study the behavior of multi-phase flow in nanocapillaries.