A new approach to upscaling fracture network models while preserving geostatistical and geomechanical characteristics

Abstract

A new approach to upscaling two-dimensional fracture network models is proposed for preserving geostatistical and geomechanical characteristics of a smaller-scale "source" fracture pattern. First, the scaling properties of an outcrop system are examined in terms of spatial organization, lengths, connectivity, and normal/shear displacements using fractal geometry and power law relations. The fracture pattern is observed to be nonfractal with the fractal dimension D ≈ 2, while its length distribution tends to follow a power law with the exponent 2 < a < 3. To introduce a realistic distribution of fracture aperture and shear displacement, a geomechanical model using the combined finite-discrete element method captures the response of a fractured rock sample with a domain size L = 2 m under in situ stresses. Next, a novel scheme accommodating discrete-time random walks in recursive self-referencing lattices is developed to nucleate and propagate fractures together with their stress-and scale-dependent attributes into larger domains of up to 54 m × 54 m. The advantages of this approach include preserving the nonplanarity of natural cracks, capturing the existence of long fractures, retaining the realism of variable apertures, and respecting the stress dependency of displacement-length correlations. Hydraulic behavior of multiscale growth realizations is modeled by single-phase flow simulation, where distinct permeability scaling trends are observed for different geomechanical scenarios. A transition zone is identified where flow structure shifts from extremely channeled to distributed as the network scale increases. The results of this paper have implications for upscaling network characteristics for reservoir simulation.

Polyaxial stress-dependent permeability of a three-dimensional fractured rock layer

“…To compute larger-scale problems, parallelisation techniques may be employed in the FEMDEM computation (Lukas et al 2014). In addition, the method of upscaling small-scale modelling results with statistical and geomechanical properties preserved (Lei et al 2015b) can also be a possible solution. Extensions of this 3D work also include hydromechanical modelling of a fractured multilayer system, such as the one constructed in Wang et al (2017), where the fluid flow in bedding planes is also stress-dependent and can influence the vertical flow through the layers.…”

“…During the past few decades, the impact of stress on the permeability of fractured sedimentary rocks has been extensively studied based on two-dimensional (2D) fracture network models with the out-of-plane stress (perpendicular to the bedding interface) effect omitted Zhang 1999, 2004;Latham et al 2013;Lei et al 2014Lei et al , 2015b. However, whether the effect of the out-of-plane stress is negligible may need to be examined through three-dimensional (3D) analysis.…”

The impact of different aperture distribution models and critical stress criteria on equivalent permeability in fractured rocks

“…Solving for local stresses requires more robust approaches, such as finite element models [Lei et al, 2014[Lei et al, , 2015Bisdom et al, 2016aBisdom et al, , 2016b. Assuming that the far-field stress equals local stress is a simplification that may overestimate absolute aperture.…”

Influence of Landscape Coverage on Measuring Spatial and Length Properties of Rock Fracture Networks: Insights from Numerical Simulation

“…Actually we can also see from Fig. 5b that the landscape coverage can lead to a curvature at the small scale in the density distribution of fracture lengths, which may be related to the socalled ''truncation effect'' (Pickering et al 1995;Bonnet et al 2001) that is always present in the length distribution plot of outcrop data (Davy 1993;Odling 1997;Odling et al 1999;Bour et al 2002;Davy et al 2010;Le Garzic et al 2011;Bertrand et al 2015;Lei et al 2015;Lei and Wang 2016).…”