Intermittent proppant injection into hydraulic fractures is a newly-developing technology in well stimulation. It is designed to form voids inside proppant packs which serve as highly conductive channels for oil and gas transport. However, it remains unclear the extent to which this non-homogeneous, pulse-like proppant concentration persists over the extent of the fracture. This paper models proppant transport in a PKN (Perkins–Kern–Nordgren) fracture in which the proppant-laden and proppant-free fluids are pumped intermittently. Simulations are performed to investigate proppant transport and final distribution under the influence of various factors. It can be observed that several parameters such as Young's modulus and fluid injection rate have significant influence on proppant transport, particularly the spatial period and attenuation of the resulting waves of proppant concentration as they move into the growing fracture. In contrast, when fluid viscosity is high, some parameters such as density difference, particle size do not strongly affect spatial period and attenuation of the proppant waves. The simulations show when the proppant is injected intermittently using high viscosity fracturing fluid, proppant concentration inside a hydraulic fracture from wellbore bottom hole to fracture tip is non-uniform and appears like a damped wave. An equation which is similar to damped wave solution is used to describe this proppant concentration characteristic, thus enabling a dimensional analysis to identify the key parameters affecting proppant distribution and specifically the attenuation of the concentration waves. Two characteristic lengths can be associated with attenuation of these proppant waves prior to severe screen-out and settlement– one for cases with leakoff and one for cases without leakoff. After scaling the horizontal coordinate by the appropriate characteristic length, the relationship between concentration amplitude and dimensionless distance for all cases can be depicted in a uniform way.

间歇性支撑剂注入水力压裂是一种新的增产技术。它的设计目的是在支撑剂包装内形成空隙，这些空隙可作为石油和天然气运输的高传导性通道。但是，尚不清楚这种不均匀的脉冲状支撑剂浓度在裂缝范围内持续存在的程度。本文对PKN（珀金斯－肯恩－诺德格伦）裂缝中的支撑剂运移进行了建模，在该裂缝中，间歇地泵入了载有支撑剂和无支撑剂的流体。进行模拟以研究在各种因素影响下的支撑剂运输和最终分布。可以看出，杨氏模量和流体注入速率等几个参数对支撑剂的传输有重要影响，尤其是支撑剂浓度波动进入裂缝中时的空间周期和衰减。相反，当流体粘度高时，某些参数（例如密度差，粒径）不会强烈影响空间周期和支撑剂波的衰减。模拟表明，当使用高粘度压裂液间歇注入支撑剂时，从井眼底孔到裂缝尖端的水力压裂内部的支撑剂浓度是不均匀的，看起来像阻尼波。使用类似于阻尼波解的方程式来描述该支撑剂浓度特性，因此可以进行尺寸分析，以识别影响支撑剂分布的关键参数，特别是影响浓度波衰减的参数。在严重筛除和沉降之前，这些支撑剂波的衰减可能具有两种特征长度-一种用于泄漏的情况，另一种用于不泄漏的情况。在将水平坐标按适当的特征长度缩放后，可以以统一的方式描述所有情况下浓度幅度和无量纲距离之间的关系。