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Shale rocks are abundant in nanopores that range in size from 1 to 20 nanometers. Within these small pores, the pore surfaces can significantly influence all fluid molecules within the confined space. This strong pore-fluid interaction and its competition with fluid-fluid interactions could lead to a heterogeneous distribution of fluid molecules in the pore spaces, which results in modified phase behavior. A fundamental example is the capillary condensation phenomenon occurring in a slit-like nanopore (Fig.1a), which has been studied by numerous studies. Figure.1 Illustration of the (a) slit-like nanopore and the (b) semi-closed nanopore model. The pore diameters are d and that could shrink to d’, the adsorbing layers are of the width H, the depth of semi-closed nanopore is w. As we know, capillary condensation in a planar slit can be explained as a simple finite-size shift of the bulk liquid-gas phase transition, controlled by a geometric parameter d (the width of the slit. The basic mechanism of capillary condensation in slits of different pore sizes is the same, but the degree of geometric constraints caused by changes in pore size leads to quantitative differences in capillary condensation behavior at different pore sizes. Specifically, as the pore size shrinks from d to d’, the confinement effect of the pore wall on the fluid strengthens, confined fluid is more likely to condensation at same pressure and temperatures (Fig.1a). On the mean-field level, the gas-liquid phase transition can be determined by constructing adsorption isotherms, calculating the capillary condensation pressure and other parameters of the fluid under different conditions. However, the pore structure in shale formation could be more complex and irregular. It means that the translation symmetry of pore may be broken not only across (among x-direction) but also along the confining walls (among z-direction), which may change the phenomenon of capillary condensation much more subtle. Taking a semi-closed pore with finite depth w was an example (Fig.1b), the asymmetric effective forces acting from both ends of the pore on the liquid surface may smooth and shift the phase transition process, leading to a change from a first-order to a second-order phase transition. Researchers have proven that in a semi-finite slit, as the pressure (or chemical potential) increases, a single meniscus first forms at the sealed end, and then it gradually expands outward. This process is continuous, without sudden phase transitions, and therefore appears as a second-order phase transition. Therefore, studying only the phase behavior of fluids in parallel slit pores that maintain translational symmetry is not comprehensive.
In this paper, the phase behavior of hydrocarbon in nanopores formed of undulated pore walls is presented. Firstly, we present a purely macroscopic theory based on geometric arguments. This allows us to understand two possible capillary condensation mechanism in nano spaces. Then, the molecular simulation is conducted to capture the micro-structural evolution of confined hydrocarbon to determine the effect of adsorbed layers which the purely macroscopic theory neglects. The phase diagram also is drawled to illustrated the importance of geometric shape of nanopore.
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