Analysis of Fracture Roughness Control on Permeability Using SfM and Fluid Flow Simulations: Implications for Carbonate Reservoir Characterization

Abstract

Fluid flow through a single fracture is traditionally described by the cubic law, which is derived from the Navier-Stokes equation for the flow of an incompressible fluid between two smooth-parallel plates. Thus, the permeability of a single fracture depends only on the so-called hydraulic aperture which differs from the mechanical aperture (separation between the two fracture wall surfaces). This difference is mainly related to the roughness of the fracture walls, which has been evaluated in previous works by including a friction factor in the permeability equation or directly deriving the hydraulic aperture. However, these methodologies may lack adequate precision to provide valid results. This work presents a complete protocol for fracture surface mapping, roughness evaluation, fracture modeling, fluid flow simulation, and permeability estimation of individual fracture (open or sheared joint/pressure solution seam). The methodology includes laboratory-based high-resolution structure from motion (SfM) photogrammetry of fracture surfaces, power spectral density (PSD) surface evaluation, synthetic fracture modeling, and fluid flow simulation using the Lattice-Boltzmann method. This work evaluates the respective controls on permeability exerted by the fracture displacement (perpendicular and parallel to the fracture walls), surface roughness, and surface pair mismatch. The results may contribute to defining a more accurate equation of hydraulic aperture and permeability of single fractures, which represents a pillar for the modeling and upscaling of the hydraulic properties of a geofluid reservoir.

Comparison of Surface Roughness and Transport Processes of Sawed, Split and Natural Sandstone Fractures

“…The BTCs of the natural fracture, although of similar surface roughness, are significantly smoother. This agrees with previous studies indicating that the influence of surface roughness on channeling decreases with increasing fracture aperture [10][11][12]. In addition, the very high flow velocity and the short duration of the experiment might reduce the differences of the separate flow paths to a degree that they cannot be experimentally resolved.…”

“…In a single fracture, microscopic flow velocity and pore space geometry are determined by the fracture surface morphology and the resulting fracture aperture distribution, respectively [9]. Therefore, the effect of surface roughness on dispersion is primarily through the control of the velocity field, based on the local aperture distribution for narrow fractures, especially if the fracture aperture is smaller than the dispersion length [10][11][12]. The numerical study of [13] shows that surface roughness leads to a higher variability in the velocity field distribution inside a joint compared to smooth plates, causing additional dispersion effects in rough fractures.…”

Experimental Investigation of Grout Nonlinear Flow Behavior through Rough Fractures

“…In which u represents the flow velocity vector; ρ represents the fluid density; µ represents the dynamic viscosity, and P represents the total hydraulic pressure. Nevertheless, the theory of flow through rough rock fractures has not been widely used because of the fracture roughness and nonlinear flow characteristics [30]. The existence of the complex nonlinear partial differential equations and irregular rock fracture geometry makes it very difficult to solve the NS equation through real rough fractures [31,32].…”

Three-Dimensional Separation and Characterization of Fractures in X-Ray Computed Tomographic Images of Rocks

“…The fracture walls also typically have rough and irregular surfaces that strongly affect how natural fluids can flow through or be stored in them. Fluids flow through them on convoluted paths that follow the minimum resistance generated by the local pressure gradients, which strongly depend on the local fracture aperture and roughness (Liu et al, 2016;Luo et al, 2016;Makedonska et al, 2016;Zambrano et al, 2019). Number of fractures, their sizes and geometries also impact generation of space and connections thus the storage and transmissivity of fluids (Long and Witherspoon, 1985;Hyman et al, 2016;Liu et al, 2016;Makedonska et al, 2016;March et al, 2018).…”