Abstract This paper presents a numerical model to study fracture propagation during water-based hydraulic fracturing. To address the computational challenges associated with the numerical model, the proposed approach employs a set of overlapping spheres arranged in a monolayer to construct a porous specimen containing pre-existing cracks. The fluid-filled cracks represent various stages of initiation and propagation of fluid-driven fracture. The high-pressure fluid flow within the fractures is considered under isothermal conditions. Unlike the conventional focus on rock fracture analysis, the presented approach focuses on flow characteristics during fracture growth. The main objective of the presented study is to provide a detailed description of the computational fluid dynamics (CFD) aspects of fracture propagation during hydraulic fracturing to aid in calibration and validation of simplified discrete element method (DEM) models coupled with CFD representing this phenomenon. Experimental validations performed in previous studies support the model's reliability, making it useful in particular for calibration and validation of coupled 2D DEM-CFD models constructed from one layer of spheres. Obtaining experimental data for such cases is practically challenging, and the proposed model addresses the lack of reliable experimental data for hydraulic fracturing. To achieve this, representative specimens are designed, accurate simulations are conducted and precise assessments of the results are performed. Key variables such as density, pressure, velocity, porosity, and permeability were measured to facilitate the validation and calibration of future DEM-CFD studies.

Rezvan Abdi

Marek Krzaczek

Meisam Abdi

Computational Particle Mechanics

一般目标：COMPUTATIONAL PARTICLE MECHANICS (CPM) 是一本季刊，旨在发表涉及粒子和粒子方法的系统的建模和模拟的完整原创文章。目标是加强应用科学研究人员之间的交流，他们在研究中以一种或另一种形式使用“粒子”。具体目标：基于粒子的材料和数值方法已在自然科学和应用科学、工程中得到广泛应用, 生物学。“粒子方法/力学”一词现在对 21 世纪的研究人员来说意味着几个不同的事物，包括： (A) 粒子作为颗粒介质、颗粒流、等离子体、群等中的物理单位。 , (B) 在中尺度、微米和纳米尺度上表示连续材料相的粒子和 (C) 在离散元方法 (DEM)、粒子有限元方法等数值方法中作为连续和不连续的离散单元的粒子(PFEM)、分子动力学 (MD) 和平滑粒子流体动力学 (SPH)，仅举几例。

Computational Particle Mechanics (CPM) is a quarterly journal dedicated to publishing original research articles on systematic modeling and simulation involving particles and particle methods. The aim of the journal is to enhance communication among applied science researchers who utilize 'particles' in their studies in one form or another. Specifically, particle-based materials and numerical methods have found extensive applications in natural sciences, applied sciences, and engineering, including biology. For researchers in the 21st century, the term 'particle methods/mechanics' encompasses several different concepts, including: (A) particles as physical units in granular media, granular flows, plasmas, and clusters; (B) particles representing continuous material phases at mesoscopic, micrometer, and nanometer scales; and (C) particles as continuous and discontinuous discrete units in numerical methods such as Discrete Element Method (DEM), Particle Finite Element Method (PFEM), Molecular Dynamics (MD), and Smoothed Particle Hydrodynamics (SPH), among others.

《Computational Particle Mechanics》是一本季刊，旨在发表关于粒子及其方法的系统建模和模拟的原创研究文章。期刊的目标是促进应用科学研究人员之间的交流，尤其是那些在研究中以某种形式使用“粒子”的研究者。具体而言，基于粒子的材料和数值方法已经在自然科学、应用科学和工程领域得到了广泛应用，包括生物学等多个领域。对于21世纪的研究者而言，“粒子方法/力学”一词涵盖了多个不同的概念，包括： (A) 粒子作为颗粒介质、颗粒流、等离子体和群体等中的物理单位； (B) 在中尺度、微米和纳米尺度上表示连续材料相的粒子； (C) 在离散元方法（DEM）、粒子有限元方法（PFEM）、分子动力学（MD）和光滑粒子流体动力学（SPH）等数值方法中作为连续和不连续的离散单元的粒子。

Category	Quartile
工程技术	3
工程技术, 数学跨学科应用	3
工程技术, 力学	3

Insights into the flow characteristics during hydraulic fracturing

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