Investigating Grain Size Influence on the Stress-Dependent Permeability of Porous Rocks Using Particulate Discrete Element Method

ABSTRACT Reservoir in-situ stresses continuously evolve during the reservoir life cycle because of the production of hydrocarbons, injection of water and CO2 for enhanced oil recovery, storage of CO2, and nuclear waste disposal. The induced changes to the stress state deform the reservoir rock, including the pores and fractures in the rock, and hence change the permeability of the rock. Studies demonstrate that grain size significantly affects the mechanical properties and strength of rock, yet little research exists on the effect of grain size on stress-sensitive seepage behavior. In this study, we investigated the effect of grain size on the stress-dependent flow behavior of a porous rock using the three-dimensional discrete element method. We modeled the porous rock geometry using randomly generated rigid spherical grains of given size distribution enclosed in a cuboid. Particle-particle interactions and wall-particle interactions are governed by the Flat-Joint contact model. Rigid boundary walls are used, and a constant strain rate is applied to the boundaries to reach a pre-defined confining stress state. Subsequently, we used the pore scale finite volume method to model the steady-state fluid flow of single-phase fluid at each confining stress state of the model. The permeability-stress relationship data is best described by the exponential model, and the exponent of the exponential model (stress-sensitive coefficient) indicates how rapidly the permeability changes with stress. Our results show that the stress-sensitive coefficient varied very little with the grain size and shows a general decreasing trend with an increase in the mean grain size of the spherical pack. We argue that the effect of other parameters such as pore morphology, micro-cracks, and cementation has a greater influence on the stress-sensitive permeability than the grain size alone. INTRODUCTION The subsurface in-situ stresses exhibit dynamism, which is attributed to the influence of several anthropogenic factors such as reservoir depletion during hydrocarbon extraction, CO2 sequestration, geothermal activities, nuclear waste disposal, and natural causes arising from tectonic movements. Such stress variations significantly impact the physical properties of rocks, particularly their porosity, permeability, and dynamic elastic properties. Given the practical applications associated with these effects, the geoscience community has shown significant interest in this aspect.