多级荷载下煤储层支撑剂嵌入规律与弹塑性嵌入深度模型

Proppant embedment behavior and elastic–plastic embedding depth modeling of coal reservoirs under multi-stage loading

  • 摘要: 为了研究在煤层气开采中支撑剂的弹塑性嵌入规律,利用力学试验系统和高精度位移传感器,设计并开展了多级荷载条件下支撑剂嵌入特性试验。对比分析了每一级加卸载的荷载−位移曲线和支撑剂嵌入特征,根据加卸载过程中的荷载−位移曲线提出了一种测量支撑剂嵌入过程中弹塑性变形值的方法。利用该方法测试了6组不同粒径、不同铺置质量浓度的支撑剂嵌入值,并对支撑剂弹塑性嵌入特征进行分析。基于Hertz弹性接触理论和Von Mises屈服准则,建立了支撑剂弹塑性嵌入深度模型,并通过试验数据对模型进行验证。结果表明:随着荷载的增加,荷载−位移曲线逐渐表现出非线性特征,曲线呈现“疏—密—疏”的特点,压痕的变形由弹性逐渐向塑性转变。随着支撑剂铺置浓度的增大,支撑剂颗粒相互作用导致煤样在受轴向应力的同时也受到颗粒的切向应力,导致接触面处发生剪切破坏。支撑剂的嵌入主要发生在加载初期和高荷载期,嵌入值随着荷载的增加均呈现“增加—稳定—增加”的趋势,对应嵌入过程的3个阶段:由弹性变形主导的接触面局部压溃;由塑性变形主导的接触面塑性区扩展;高荷载下支撑剂完全塑性嵌入。对应着压痕弹性变形、弹塑性变形和完全塑性过程。所构建的模型与试验数据有较好的一致性,平均误差为13.5%,模型能够有效地描述不同荷载下支撑剂嵌入深度。

     

    Abstract: To investigate the elasto-plastic embedment behavior of proppant during coalbed methane (CBM) production, a mechanical testing system equipped with a high-precision displacement sensor was used to design and conduct proppant-embedment tests under multi-stage loading. For each loading/unloading stage, the load–displacement curves and embedment characteristics were comparatively analyzed. Based on the load–displacement response during loading/unloading, a method was proposed to quantify the elastic and plastic components of indentation throughout the embedment process. Using this method, embedment depths were measured for six groups with different proppant sizes and areal placement concentrations, and the associated elasto-plastic features were analyzed. Building on Hertzian elastic contact theory and the von Mises yield criterion, a model for elasto-plastic embedment depth was established and validated against the experimental data. The results show that, with increasing load, the load–displacement response becomes progressively nonlinear; the curve exhibits a “sparse–dense–sparse” pattern, and the indentation response evolves from elastic to plastic. As the proppant placement concentration increases, interparticle interactions introduce tangential stresses in addition to axial stress in the coal specimen, leading to shear failure at the contact interface. Proppant embedment occurs mainly during the initial loading stage and at high load levels, and the embedment depth follows an increase–plateau–increase trend corresponding to three stages: local interfacial crushing dominated by elastic deformation; expansion of the interfacial plastic zone dominated by plastic deformation; and complete plastic embedment under high loads—corresponding to elastic indentation, elastoplastic indentation, and fully plastic indentation, respectively. The proposed model shows good agreement with the experiments, with an average error of 13.5%, and effectively describes embedment depth under varying load levels.

     

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