Analytical Solution of Gas Flow in Rough‐Walled Microfracture at In Situ Conditions

Abstract

The development of the unconventional gas and CO2 sequestration is moving to deep formations. Because of the small flow pathways in the matrix, the Knudsen number might be high even though the gas is dense. In fact, due to the relatively high pressure at in situ conditions, gas flow in microfractures usually manifests a strong slip and nonideal gas effects. Therefore, understanding the coupling mechanism of these two on gas flow in rough‐walled microfractures is required to accurately model subsurface flow behavior. In this study, pressure‐driven gas flow in rough‐walled microfracture is analyzed in depth. Starting from the local governing equations for gas flow, a local flow model that includes gas slip and nonideal gas effects is derived by solving the Stokes equation with a first‐order slip boundary condition. Focusing at the representative elementary volume scale, the upscaled solutions to gas flow in a fracture with sinusoidal surface are derived to obtain the apparent permeability. The impact of nonideal gas effects, fracture roughness and aperture, and the tangential momentum accommodation coefficient on CH4 and CO2 flow is analyzed. The results show that fracture roughness introduces a high degree of heterogeneity in gas flow. At in situ conditions effects of gas slip, fracture roughness and tangential momentum accommodation coefficient on gas flow are reduced. The ideal gas law is capable of estimating CH4 flow to some extent. However, it fails to estimate CO2 flow in microfractures.

Effective transmissivity for slip flow in a fracture

“…While many studies of flow through rough fractures have adopted no-slip boundary conditions at the solid–fluid interface, this assumption is not always justified in situations of practical interest such as non-wetting fluid flow (Lee, Yo & Lee 2013) or rarefied gas flow (Wang, Tang & Jing 2019). In the slip regime, characterised by a Knudsen number (i.e.…”

Quasi-Continuum Water Flow under Nanoconfined Conditions: Coupling the Effective Viscosity and the Slip Length

“…Nanofluidics, introduced as an analogue to microfluidics, is defined as the study of fluids flowing within a characteristic length scale down to below 100 nm. − Motivations to control fluid flow under such a highly confined condition arise from its tremendous implications in chemical engineering and nanotechnology, including nanofluidic energy conversion, − ultrafiltration and separation, , and next-generation seawater desalination. , The main difference of nanofluidics from macro- and microfluidics lies in the fact that the interactions between a fluid and solid walls cannot be neglected because of a large surface-to-volume ratio. − Surface forces, especially a friction force at a water–solid interface, dominate over volume forces at the nanoscale, leading to various unique transport phenomena. − It is reported that for a flow dimension larger than 1–2 nm, a bulk phase exists and the continuum theory is still valid. − However, the flow properties near a solid surface will be different from that of the bulk phase because of the impact of surface forces. This flow type is usually defined as a quasi-continuum state, indicating a bulk phase flow in the middle of a flow region and a unique boundary flow near a solid surface …”

Characteristics of in situ stress and its influence on coalbed methane development: A case study in the eastern part of the southern Junggar Basin, NW China

“…8 The K values of coal reservoirs are mainly composed of 0.01-5 mD in China, which is lowered by 1-2 magnitudes than overseas, for example, the Powder River Basin in North America (>10 mD) and the Surat Basin in Austria (10-30 mD). 8,9,[19][20][21] The methane adsorbability of coal reservoirs tends to increase with increasing P o and decreasing T em . 8,9,[19][20][21] The methane adsorbability of coal reservoirs tends to increase with increasing P o and decreasing T em .…”

“…10,18 The research showed that in situ stress had obviously affected coal K, and the latter exponentially declined with the increasing of the former. 8,9,[19][20][21] The methane adsorbability of coal reservoirs tends to increase with increasing P o and decreasing T em . 22 By changing the confining pressure of pore fluid, the in situ stress regime can directly control P o and influence the gas-bearing conditions of the coal reservoir.…”