Connecting Pressure‐Saturation and Relative Permeability Models to Fracture Properties: The Case of Capillary‐Dominated Flow of Supercritical CO₂ and Brine

Abstract

Fractures are potential pathways for subsurface fluids. In the context of geologic CO2 sequestration, fractures could threaten the security of reservoirs since they are pathways for leakage. However, the constitutive equations describing the pressure‐saturation and relative permeability‐saturation, key inputs for flow modeling and prediction, are poorly understood for two‐phase fracture flow at the field scale where each fracture might be an element of a complex fracture network or dual‐porosity domain. This knowledge is required for the safe storage of CO2 under potentially fractured caprocks. To address this, we numerically simulated two‐phase viscous flow through horizontal heterogeneous fractures across a broad range of roughness and aperture correlation length. The numerical experiments, which solved the modified local cubic law, showed a weak to strong phase interference during the drainage process; that is, supercritical CO2 displaces brine if the imposed pressure + local viscous force > local capillary force. The drainage process ended when no new brine cells can be further invaded by CO2. Afterward, we froze the saturation field for each individual phase and calculated the relative permeability by single‐phase flow modeling. Thousands of simulated pressure‐saturation and relative permeability curves enabled us to estimate and connect the parameters of the Van‐Genuchten model and of the generalized ν‐type model to fracture roughness and aperture correlation length. This empirical connection will be useful for assessing and predicting immiscible two‐phase flow in horizontal rough fractures at the large scale.

Roughness Control on Multiphase Flow in Rock Fractures

“…We perform drainage experiments in fractures with various degrees of roughness using a flow‐visualization system (supporting information Figure S1). Here we quantify the fracture roughness using an index defined as the coefficient of variation of the aperture field λ b = σ b /⟨ b ⟩ (Glass et al, ), where ⟨ b ⟩ and σ b are respectively the mean and the standard deviation of the aperture field (Wang & Cardenas, , ). To investigate the impact of the roughness on multiphase flow, we fabricate two sets of fractures.…”

Effects of Slip Length and Inertia on the Permeability of Fracture with Slippery Boundary Condition

“…Fracture flow is critical for the success of many environmental and engineering applications, including the exploration of oil and gas and geothermal energy [ 1 , 2 ], groundwater contamination remediation [ 3 , 4 , 5 , 6 , 7 ], and geological carbon sequestration [ 8 , 9 , 10 , 11 ]. Essentially, the fluid-borne contaminants travelling along with subsurface fluid flow are normally hard to predict, where non-Fickian transport phenomenon is pervasive [ 3 , 5 ].…”

Two‐Phase Relative Permeability of Rough‐Walled Fractures: A Dynamic Pore‐Scale Modeling of the Effects of Aperture Geometry

“…However, numerous studies have indicated that relative permeabilities are significantly reduced in rough-walled fractures under multi-phase flow conditions, due to the existence of strong phase interferences (Diomampo et al, 2001;Fourar & Bories, 1995;Lian and Cheng et al, 2012;Persoff & Pruess, 1995). In view of this fact, two-phase relative permeabilities in fractures are often described based on the models that are developed for porous media, including the Corey, Brooks-Corey, and van Genuchten models (Diomampo et al, 2001;Fourar & Bories, 1995;Huo & Benson, 2016; L. Wang & Cardenas, 2018). The Corey model describes the relative permeability curves as (Corey et al, 1954):…”

“…Consequently, a new v-type model was proposed (Wang & Cardenas, 2018) with a general power-law form that allowed different power coefficients for the wetting and non-wetting phases:…”

“…For example, Watanabe et al (2015) solved the continuity equation for oil-displacing-water process through granite and limestone fractures under a constant inlet capillary pressure. More recently, Wang and Cardenas (2018) conducted a comprehensive study of the effect of fracture heterogeneity on CO 2 -water primary drainage process using a continuum-scale modeling approach.…”