During the volume fracturing process, part of the proppant enters the natural micro-fractures with the working fluid. Due to the complexity of the micro-fracture morphology and structure, the conventional fracture model cannot accurately describe the state of the proppant in the tortuous micro-fractures. In this study, carrying out the rock mechanics experiment to obtain the mechanical parameters, the finite element method was used to establish the physical and mechanical models of micro-fractures to analyze the mechanics of proppant rock matrix under different tortuosity conditions, and to clarify the propping mechanism of proppant in tortuous micro-fractures. Studies have shown that tortuosity has a significant impact on the residual width of fractures, and the degree of closure between propped and unpropped areas is quite different; Young's modulus significantly affects the deformation characteristics of tortuous micro-fractures; stress concentration mainly occurs at the corners of the fractures and effective areas with smaller fracture widths.

1. Introduction

Hydraulic fracturing is currently the main oil and gas stimulation measure. Micro-fractures are widespread in various reservoirs, and their capacity of storage and seepage for oil and gas cannot be ignored. Under the process of hydraulic fracturing, micro-fractures will be activated and communicate branch fractures. Micro-fractures then become part of the fracture network. After the proppant enters the micro-fractures with the working fluid, it becomes an important oil and gas flow channel. Therefore, it is a great significance to study the proppant propped mechanism in tortuous micro-fractures.

The surface morphology of micro-fractures has an important influence on the state of proppants in the fractures. Rose and Bruce (1949) put forward the concept of tortuosity in the evaluation of rock capillary characteristics. That is the ratio of actual flow distances to the apparent flow distance. Then extended and applied to fracture description. Belem et al. (2000) used two methods to calculate the tortuosity of the fracture. One is based on the line scanning of profile, and the other is the rough fracture surface area. Qu et al. (2016) used a three-dimensional profiler to obtain the tensile fracture surface morphology of shale outcrop, and used its two-dimensional morphology to calculate characteristic parameters such as tortuosity, inclination and roughness. At last they conducted permeability research. Hooker et al. (2018) used Scanning electron microscope to test natural micro-fractures in sandstone and found that under low strain conditions, the distribution of micro-fractures is random, while under high strain conditions, the fractures are usually clustered. And clearly pointed out that the shear micro-fractures follow the Mohr-Coulomb failure criterion. Qi et al. (2018) used software to process and segment the rock CT scan images, and quantitatively describe the micro-fractures inside the core, including parameters such as fracture size, direction, and extension length. Research shows that the geometric characteristics of fractures are similar on large and small scales. Scholars mainly use experiments or observation methods to describe and characterize the morphology of micro-fractures, but it is not easy to obtain the morphological characteristics due to the influence of closure stress to micro-fractures. Therefore, it is necessary to study the deformation of tortuous micro-fractures under closure stress and clarify its propping principle.

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