Abstract In this paper, a resolved CFD-DEM method based on the immersed boundary method is proposed to simulate the proppant transport process, which is a multi-phase problem with strong fluid-particle coupling mechanisms in the oil and gas industry. A multi-sphere model is integrated into this method to describe complex particle shapes, in which Lagrangian points uniformly distributed on the particle surface are efficiently utilized for solving particle-particle interactions. This approach is validated by several benchmarks, including single-sphere and two-sphere settling tests. A modified driving pressure gradient is also adopted to satisfy bulk velocity constraints for simulating particle settling problems in periodic channels. Transport and settling behaviors of hundreds of sphere and cylinder proppant particles in periodic narrow channels with different widths are investigated, and settling laws and apparent viscosity models for proppant clouds with different shapes are then extracted from the simulation results. Benefiting from the features of multi-sphere modeling, this approach is demonstrated to be both robust and efficient for simulating fluid-particle coupling flow with complex particle shapes.

中文翻译：

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水力裂缝中支撑剂输运的直接数值模拟与浸入边界法和多球体建模

摘要 本文提出了一种基于浸入边界法的求解CFD-DEM方法来模拟支撑剂输运过程，这是石油和天然气工业中具有强流体颗粒耦合机制的多相问题。该方法集成了多球模型来描述复杂的颗粒形状，其中均匀分布在颗粒表面的拉格朗日点被有效地用于解决颗粒-颗粒相互作用。该方法已通过多个基准测试的验证，包括单球和双球沉降测试。还采用改进的驱动压力梯度来满足体积速度约束，以模拟周期性通道中的颗粒沉降问题。研究了数百个球体和圆柱体支撑剂颗粒在不同宽度的周期性窄通道中的输运和沉降行为，从模拟结果中提取了不同形状支撑剂云的沉降规律和表观粘度模型。受益于多球体建模的特点，这种方法被证明在模拟具有复杂颗粒形状的流体-颗粒耦合流方面既稳健又高效。