ABSTRACT

The permeability of rock fractures and its variation with effective stress is of considerable interest in broad energy and environmental applications, such as enhanced oil and gas recovery from hydrocarbon reservoirs, geothermal energy extraction, geological carbon storage, among others. The permeability of a rock fracture is a complex function of various static parameters, including fracture mechanical aperture, roughness, and surface contact area, all of which could be functions of dynamic effective stress acting on the fracture walls. The commonly used cubic law is unfit for most applications as it often overestimates the fracture permeability resulting in unreliable predictions. Several models are proposed in the literature with various levels of complexity, accuracy and general applicability. This work establishes a new comprehensive data-driven model to estimate the hydraulic properties of rock fractures as a function of the fracture static characteristics and dynamic effective stress. A dataset measuring fracture permeability in terms of confining stress, fluid pressure, and other rock parameters is compiled to identify potential correlations. We further verify the proposed model with coupled flow-geomechanics simulations. The results show that the trends observed from the dataset are consistent with the theoretical model. We show that our proposed model is superior to all models that we tested from the literature. The coupled workflow offers an efficient approach to characterize the hydraulic response of rock fractures under effective stress. The proposed model is simple, accurate, and efficient, and therefore can be implemented to capture stress-dependent permeability of fracture networks for field-scale reservoir simulations.

1. INTRODUCTION

Accurate modeling of single and multi-phase fluid flow through fractured porous media requires a fundamental understanding of the stress-dependent hydraulic behaviors of rock fractures (Grant and Bixley, 2011; Nelson, 2001).

The permeability of a rock fracture is a complex function of various static and dynamic parameters, including the fracture mechanical aperture, surface roughness, and fracture contact areas, which are subject to alterations by the stress field acting on the fracture walls. Characterizing the relationship between fracture permeability and effective stress has been extensively investigated in the literature. A review listing 12 empirical and theoretical models, commonly used in the literature, are shown in Table 1. These models, however, exhibit various limitations related to the level of complexity, accuracy, and general applicability. A summary of the major limitations is highlighted in Table 1. For hierarchical fracture systems, a joint-continuum framework has been proposed by Shin and Santamarina (2019). In this study, a new comprehensive model that quantifies the relationship between fracture permeability and effective normal stress is proposed. We first derive a theoretical model based on a modified cubic law, which incorporates the effect of fracture hydraulic aperture, mechanical aperture, roughness, and contact area. To validate the model, we collected a database of experimental data from the literature, reporting fracture permeability in terms of pore pressure, confining stress, and other rock properties such as Young's modulus, Poisson's ratio, and uniaxial compressive strength. The fracture permeability database includes both natural and synthetic fractures with different rock types corresponding to siltstone, sandstone, shale, and carbonate. The subsequent analysis seeks to identify potential correlations in the observed data and to develop a data-driven representative model. We further verify the developed model using coupled flowgeomechanics simulations. Fluid flow in the fracture is described by high-resolution full-physics Navier-Stokes equations (Brush and Thomson, 2003), and the geomechanical deformation is quantified through the elastic contact theory (Brown and Scholz, 1985).

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