Modelling relaxation processes for fluids in porous materials using dynamic mean field theory: application to pore networks

Abstract

We present an application of a recently developed dynamic mean field theory to the study of relaxation dynamics in adsorption and desorption from pore networks. The theory predicts the evolution of density distribution in the system, based on an underlying free energy functional from static mean field theory and the system evolves to equilibrium or metastable equilibrium states consistent with the static theory. The theory makes it possible to follow the evolution of the density distribution with time in response to a change in the bulk pressure or chemical potential. We compare uptake dynamics for a 2D slit pore network with that in a single slit pore. We see more rapid uptake dynamics in the pore network in some cases, due to the greater access of the pore space to the bulk. We also observe that the formation of liquid bridges can slow down the mass transfer in the pore network in certain situations.

Modeling the Influence of Side Stream and Ink Bottle Structures on Adsorption/Desorption Dynamics of Fluids in Long Pores

“…[24][25][26][30][31][32][33][34] The theory provides a mean field approximation to the master equation for the dynamics of a lattice gas 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 …”

“…Our implementation of DMFT follows closely that given in earlier work. − ,− The theory provides a mean field approximation to the master equation for the dynamics of a lattice gas model based on Kawasaki dynamics. The lattice model Hamiltonian has the form ,− where { n i } denotes the configuration of molecules on a lattice via a set of occupation numbers associated with lattice coordinate vectors i .…”

Quasi-Two-Dimensional Phase Transition of Methane Adsorbed in Cylindrical Silica Mesopores

“…Since their introduction nearly 30 years ago, mesoporous silica adsorbents have found applications in many areas related to or exploiting adsorption, such as separations, heterogeneous catalysis, and as pharmaceutical delivery. − Additionally, gas adsorption as a technique for characterizing the pore structure of mesoporous silicas has become practically de rigeur, due to well-proven adsorption kernels for silica based on both molecular simulation and density functional theory, ,− even including an approximation of surface roughness . Studies of silica, especially those based on theory and simulation, have provided excellent insight into the thermodynamic mechanisms of adsorption, including a molecular understanding of the adsorption–desorption hysteresis effect, , in-pore fluid cavitation, , and the details of dynamic adsorption (desorption) processes. − However, while studies of silica adsorbents have been widespread and successful, the adsorbate species is usually an inert characterization gas such as argon or nitrogen; studies with alkanes (whether experiment or simulation) have been done − but are fewer in number. So, while adsorption mechanisms of these light gases in mesoporous silicas is well-understood, an understanding of alkane behavior in shale would benefit from additional study of alkane adsorption in silicas.…”