The accuracy of predicting fracture conductivity is very important in hydraulic fracturing. However, most models pay more attention to the solution of fracture conductivity value, without considering the distribution of the fracture conductivity. It is also important to couple the proppant embedment depth and fracture conductivity, especially for the coal bed and shale formations with strong plasticity. In this paper, analytical models were derived to compute fracture conductivity considering the proppant transport and embedment. The proppant transport model is coupled with the fracture propagation model, which describes the distribution of fracture conductivity. The calculation of proppant embedment depth considering the rock plasticity is derived from the underground stress equilibrium, which provides a calculation basis of the propped fracture width. The proppant-pack permeability is calculated based on the Carman-Kozeny formula. Finally, fracture conductivity is defined as the product of fracture width and permeability. Based on the comparison with the previously established models, the proposed model is employed for sensitivity studies of parameters influencing the fracture conductivity. The effects of closure pressure, proppant size, rock plasticity, fluid viscosity, proppant concentration, and proppant carrying liquid volume on fracture conductivity are analyzed. Analysis results contribute to a better understanding of the effects of related factors on fracture conductivity. The new and more accurate model for calculating the fracture conductivity considering proppant transport and embedment is of great significance for fracturing design and helps to achieve high fracture conductivity and high oil and gas production in conventional and unconventional reservoirs.

预测裂缝导流能力的准确性在水力压裂中非常重要。然而，大多数模型更关注裂缝导流能力值的求解，没有考虑裂缝导流能力的分布。支撑剂嵌入深度和裂缝导流能力的耦合也很重要，特别是对于可塑性强的煤层和页岩地层。在本文中，推导出了分析模型来计算考虑支撑剂输送和嵌入的裂缝导流能力。支撑剂输运模型与裂缝扩展模型相结合，裂缝扩展模型描述了裂缝导流能力的分布。考虑岩石塑性的支撑剂埋设深度计算由地下应力平衡推导，为支撑裂缝宽度的计算提供了依据。支撑剂充填渗透率是根据 Carman-Kozeny 公式计算的。最后，裂缝导流能力被定义为裂缝宽度和渗透率的乘积。基于与先前建立的模型的比较，所提出的模型用于影响裂缝导流能力的参数的敏感性研究。分析了闭合压力、支撑剂尺寸、岩石塑性、流体粘度、支撑剂浓度和支撑剂携带液体体积对裂缝导流能力的影响。分析结果有助于更好地了解相关因素对裂缝导流能力的影响。