Dense gas flow simulations in ultra-tight confinement

Abstract

Modelling dense gas flows inside channels with sections comparable to the diameter of gas molecules is essential in porous media applications, such as in non-conventional shale reservoir management and nanofluidic separation membranes. In this paper, we perform the first verification study of the Enskog equation by using particle simulation methods based on the same hard-sphere collisions dynamics. Our in-house Event-Driven Molecular Dynamics (EDMD) code and a pseudo-hard-sphere Molecular Dynamics (PHS-MD) solver are used to study force-driven Poiseuille flows, in the limit of high gas densities and high confinements. Our results showed (a) very good agreement between EDMD, PHS-MD, and Enskog solutions across density, velocity, and temperature profiles for all the simulation conditions, and (b) numerical evidence that deviations exist in the normalized mass flow rate versus Knudsen number curve compared to the standard curve without confinement. While we observe slight deviations in the Enskog density and velocity profiles from the MD when the reduced density is greater than 0.2, this limit is well above practical engineering applications, such as in shale gas. The key advantages of promoting the Enskog equation for upscaling flows in porous media lie in its ability to capture the non-equilibrium physics of tightly confined fluids, while being computationally more efficient than fundamental simulation approaches, such as molecular dynamics and derivative solvers.

Knudsen minimum disappearance in molecular-confined flows

“…Despite the availability of computational procedures to describe the flow of confined fluids, the fundamental understanding of many phenomena occurring under tight confinement is still lacking. A notable example is that, for simple fluids, the Poiseuille mass flow rate (MFR) is found to monotonically increase in channels of molecular dimensions when the fluid density decreases, by using numerical solutions of the Enskog equation (Wu et al 2016) and event-driven molecular dynamics (EDMD) simulations (Sheng et al 2020). This behaviour is in sharp contrast with the long-standing recognition of flow mechanics in microchannels, which instead exhibits a non-monotonic variation of the MFR and the formation of a stationary point referred to as the 'Knudsen minimum' (Pollard & Present 1948;Cercignani & Sernagiotto 1966;Tatsios, Stefanov & Valougeorgis 2015), as long as the channel is sufficiently long and does not contain any bends (Ho et al 2020).…”

“…2016) and event-driven molecular dynamics (EDMD) simulations (Sheng et al. 2020). This behaviour is in sharp contrast with the long-standing recognition of flow mechanics in microchannels, which instead exhibits a non-monotonic variation of the MFR and the formation of a stationary point referred to as the ‘Knudsen minimum’ (Pollard & Present 1948; Cercignani & Sernagiotto 1966; Tatsios, Stefanov & Valougeorgis 2015), as long as the channel is sufficiently long and does not contain any bends (Ho et al.…”

Molecular kinetic modelling of nanoscale slip flow using a continuum approach

“…As discussed above, the non-monotonicity of the slip length dependency on density reflects the competition between the fluid-solid and fluid molecular interactions, which can be characterised by the friction coefficient and the viscosity, respectively. This slip length minimum is interestingly analogous to the Knudsen minimum (Sheng et al 2020).…”

A weighted particle scheme for Enskog-Vlasov equation to simulate spherical nano-droplets/bubbles

“…The systematic study of the droplet/bubble growth rates is an additional novelty worth being stressed. Note that the proposed numerical scheme has a broad interest not limited to studies on nucleation, as the Enskog theory is increasingly used for many applications, including shale gas exploitation [41,42] and fluidized beds [43] to cite a few, and paves the way to the simulation of three-dimensional dense and/or liquid-vapour flows.…”