Solvation force and adsorption isotherm of a fluid mixture in nanopores of complex geometry based on fundamental measure theory

Abstract

A novel method based on the Fundamental Measure Theory (FMT) is developed to calculate the solvation force and adsorption isotherm of a Lennard-Jones fluid mixture in complex geometries. Fast Fourier Transform and 3D-voxel discretization are used for accurately computing the confined fluid densities in a closed pore of arbitrary geometry. Given the fluid densities, the solvation force distribution at the solid surface can be calculated using a new formulation from either mechanical or thermodynamic approach. Understanding the solvation force behavior, which depends on many factors such as pore geometry, confined density distribution, molecule size, is very important to analyze the pore deformation from a poromechanical point of view. Special attention in the numerical simulations is given to the adsorption problem of CH 4 and CO 2 gas mixture in ellipsoidal pore.

Upscaling Poromechanical Models of Coalbed Methane Reservoir Incorporating the Interplay between Non-Linear Cleat Deformation and Solvation Forces

“…A remarkable consequence of the three-scale approach relies in the construction of the local closure problems for the effective parameters in the incremental laws, whose solution provides the underlying characteristic function profiles. Unlike previous work [14,15,16], the new closure problems show ability to capture the interplay between solvation forces and the corresponding counter force in the cleat system dictated by the non-linear elastic law.…”

“…Our nanoscopic picture consists of a confined mixture of gases distributed in a heterogeneous fashion in nanopores in equilibrium with an outer bulk solution. Unlike bulk fluids, confined gases commonly exhibit anomalous behavior in nanopores [16]. In this setting the solid surfaces of the nanopores interact with the gas molecules through a prescribed Lennard-Jones potential, repulsive and attractive at short and long distances respectively [30].…”

“…For the sake of completeness, we proceed straightforward from our previous Density Functional Theory-based framework constructed in [16]. In such a thermodynamically based context applied to a pore of arbitrary geometry, by postulating proper representation of the grand potential along with fluid-fluid and fluid-solid Lennard-Jones based potentials in the grand canonical ensemble, the derivatives with respect to changes in pore volume furnish the solvation force.…”

“…Consequently, the path B→C is intrinsically linked to matrix swelling. (b) Gas density profiles corresponding to three points for low (A), transition (B) and high (C) bulk pressures [16].…”

“…In such a context, it becomes mandatory to develop an accurate description of the fluid-solid intermolecular interaction with the ability to capture local adsorption in the vicinity of the nanopore walls in conjunction with efficient up-scaling methods to propagate the local information to the macroscopic scale. In a sequence of papers [14,15,16], the authors have combined the Density Functional Theory (DFT) with formal homogenization methods to derive three-scale methods for expansive porous media containing nanopores and natural fractures. More specifically in [15] the authors constructed a new three-scale geomechanical approach for an anomalous mixture of gases in nanopores with spherical geometry coupled with a cleat system of totally open fractures with zero traction on the boundary.…”