To describe the fracture width is crucial for the flow conductivity evaluation, which influences the exploitation efficiency of unconventional oil and gas resources. Commonly, as the proppants fill in the fracture, the deformation will happen under the closure pressure to resist the fracture width change. Therefore, it is significant to develop the theoretical model to predict the variation. In this work, the mathematical model for the propping behavior of proppants in the fracture under closure pressure is established based on the Hertz contact theory. Compared with the existing models, the developed model considers both the proppant insertion and the elastic compression among the proppants, which is closer to the actual physical process. Furthermore, the experimental cases with different proppant sizes are taken to verify the model, and the good conformity presents its rationality. The parameter sensitivity analysis of this model shows that the fracture width change increases with the increase of the average diameters of proppants () and it declines with the improving of proppant elasticity modulus () and Poisson’s ratio ().

中文翻译：

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基于赫兹接触理论的非常规油藏闭合压力下裂缝宽度变化研究

裂缝宽度的描述是导流能力评价的关键，影响非常规油气资源的开发效率。通常，当支撑剂填充裂缝时，在闭合压力下会发生变形，以抵抗裂缝宽度的变化。因此，建立预测变异的理论模型具有重要意义。在这项工作中，基于赫兹接触理论建立了闭合压力下支撑剂在裂缝中的支撑行为的数学模型。与现有模型相比，所开发的模型同时考虑了支撑剂插入和支撑剂之间的弹性压缩，更接近实际物理过程。此外，采用不同支撑剂粒径的实验案例对模型进行验证，良好的一致性体现了它的合理性。该模型的参数敏感性分析表明，裂缝宽度的变化随着支撑剂平均直径的增加而增加（)且随着支撑剂弹性模量 ( )和泊松比 ( )的提高而下降。