In recent years, the combination of rod proppants and pulse-fracturing technology has been successfully applied to many reservoirs. It can not only solve the issue of proppant backflow, but also improve the productivity of oil and gas wells. However, fracture conductivity under a sparse distribution of rod proppants is rarely investigated theoretically, and the existing spherical model cannot be used owing to the different shapes of proppants.

Based on the contact mechanisms between cylinders, deformation and embedment models of rod proppants are developed to calculate the fracture width. To solve the problem of sparse distribution, the axial and radial distance coefficients between rod proppants are defined, and a dimensionless permeability model is derived. Finally, a model for fracture conductivity under a rod proppant is developed based on the fracture width and permeability models. The model can predict the fracture conductivity when a rod proppant is used during pulse fracturing.

The results show that in both the radial and axial flow directions, the fracture conductivity under radial proppant spacing is higher than that under axial proppant spacing, and the radial optimal proppant spacing is smaller than that the axial optimal proppant spacing. A critical proppant spacing exists that reverses the fracture conductivity. A larger radial proppant spacing renders it more difficult to obtain an axial optimal proppant spacing. This phenomenon is particularly evident when the closure pressure and proppant size are increased. Increasing the fracture width and improving the radial distribution of the rod proppant can effectively improve the fracture conductivity. The results of this study provide theoretical support for the combined use of rod proppants and pulse fracturing for improving productivity.

近年来，棒状支撑剂与脉冲压裂技术相结合已成功应用于多个油藏。不仅可以解决支撑剂倒流问题，还可以提高油气井的产能。然而，杆状支撑剂稀疏分布下的裂缝导流能力在理论上鲜有研究，并且由于支撑剂的形状不同，现有的球形模型无法使用。

基于圆柱之间的接触机制，建立了杆状支撑剂的变形和嵌入模型，计算裂缝宽度。针对分布稀疏的问题，定义了杆支撑剂的轴向和径向距离系数，并推导了无量纲渗透率模型。最后，基于裂缝宽度和渗透率模型，建立了杆支撑剂下裂缝导流模型。当在脉冲压裂过程中使用棒支撑剂时，该模型可以预测裂缝导流能力。

结果表明，在径向和轴向流动方向上，径向支撑剂间距下的裂缝导流能力高于轴向支撑剂间距，径向最佳支撑剂间距小于轴向最佳支撑剂间距。存在逆转裂缝导流能力的临界支撑剂间距。较大的径向支撑剂间距使得更难以获得轴向最佳支撑剂间距。当闭合压力和支撑剂尺寸增加时，这种现象尤其明显。增加裂缝宽度，改善杆支撑剂的径向分布，可有效提高裂缝导流能力。本研究结果为杆状支撑剂与脉冲压裂联合使用提高产能提供了理论支持。