Physical properties of rock fractures are influenced by stress and geometric factors. The ability to describe the structure of fractures is of significance to subsurface engineering. Owing to the relative roughness of rock surfaces, the distribution of fracture openings fundamentally controls both the conductivity and elastic responses of the medium. Implicitly, the stress-dependent fracture aperture height distribution links flow properties to elasticity. A comprehensive understanding on the connections among fracture aperture distribution, stress conditions and flow-elastic properties thus forms an applicable basis for medium characterization. We propose a method to characterize fracture apertures with their stress-dependent flow-elastic relations. The dependencies of various flow and elastic properties in single rough fracture hosting rock, on aperture distribution and normal stress levels are first investigated. Statistical roughness parameters, which capture the spatial correlation and overall height variation of first-contact fracture apertures are adopted for the description. Apertures in rough fracture are numerically generated and their flow and elastic properties under static compressions are simulated. We examine the permeability and resistivity as indicators for flow properties, and elastic wave velocities for elastic properties, respectively. The geometric sensitivity of the respective stress-dependent flow, elastic properties, as well as their joint relations are then extracted. From that we obtain insights on the differentiating power of fracture roughness parameters from these relations. Subsequently, we present a workflow for characterizing fracture apertures with permeability and velocities and illustrated the application with a case study. Measurements are made on an artificial single-fractured granite core and simulation results on various synthetic apertures under the same modelling framework are incorporated. By pursuing for consistent permeability-velocity relations against stress, we invert for a potential range of roughness parameters for the target fracture. Results obtained are in close agreement with actual measured statistics.

1. Introduction

From hydrocarbon production, geothermal energy extraction, ground water flow, carbon sequestration to nuclear waste disposal, characterization of fractured medium plays a critical role in design and risk assessment of subsurface engineering activities. Alongside with lithological factors, the physical properties of fractured rocks are controlled by their internal geometries. For single fractures, the implicit linkages between fracture flow and elastic responses via their aperture distribution has been conceptualized (Pyrak-Nolte and Morris, 2000). For instance, the connected fracture apertures provide percolation passage for fluid transports. Responses of which are dictated by the size and spatial variability of apertures (Li et al., 2008; Ma et al., 2019). The rock asperities in contact and stressfree surfaces controls the static and dynamic stiffness of the fractured rocks (Swan, 1983; Choi et al., 2014). These properties evolve distinctively under stressing on fracture for different aperture distributions. A thorough understanding on aperture and stress dependency of fracture flow characteristics and elasticity properties enables the prediction of fracture properties from geometric characteristics and stress conditions. With that, inter-property interpretations (Brown and Fang, 2012; Ma et al., 2018; Al-Dughaimi et al., 2020) as well as formulation of inverse problems (Ma et al., 2020a) could be enabled. It eventually provides an opportunity for integrating the flow and the seismic data for the purpose of field scale fracture characterization (Kang et al., 2016).

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