Abstract Quantitatively evaluating the gravity effect on spontaneous imbibition in fractured porous media is challenging due to the lack of a suitable model and the complex fracture distribution. In this paper, new analytical solutions for spontaneous imbibition in a single fracture with and without gravity are first derived. Then, assuming a fractal distribution of fractures and with the tortuous plate fracture model, a semianalytical model for spontaneous imbibition of the wetting phase into gas-saturated fractured porous media is derived. Expressions of the wetting phase weight imbibed into fractured porous media with and without gravity are derived. Finally, the effects of gravity on spontaneous imbibition in a single fracture and core-scale fractured porous media are quantitatively evaluated with the inverse Bond number. The research results show that our newly derived analytical solutions attain a better performance in predicting the imbibition height over time in a fracture compared with the Lucas-Washburn model or the Fries and Dreyer model, which has been verified with experimental data from the literature. When N B − 1 is smaller than 3.57, the relative error of the imbibition height in a single fracture η L s will be larger than 10%. In core-scale fractured porous media, the relative error of the total imbibition weight ηM is larger than 10% when N B C − 1 is smaller than 8.8. A method of determining the critical time when the gravity effect should be considered is also proposed.

中文翻译：

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重力对润湿相自吸渗入气体饱和曲折裂缝多孔介质的影响：解析解和诊断图

摘要 由于缺乏合适的模型和复杂的裂缝分布，定量评估重力对裂缝多孔介质中自吸的影响具有挑战性。在本文中，首次推导出了在有重力和无重力的情况下单个裂缝中自吸的新解析解。然后，假设裂缝的分形分布和曲折板裂缝模型，导出润湿相自吸渗入气体饱和裂缝多孔介质的半解析模型。导出了在重力和无重力下渗入裂缝多孔介质的润湿相重量表达式。最后，重力对单个裂缝和岩心尺度裂缝多孔介质中自吸的影响用反键数进行定量评估。研究结果表明，与 Lucas-Washburn 模型或 Fries 和 Dreyer 模型相比，我们新推导出的解析解在预测裂缝中随时间的渗吸高度方面具有更好的性能，这已通过文献中的实验数据进行了验证。当NB - 1 小于3.57 时，单条裂缝渗吸高度的相对误差η L s 将大于10%。在岩心尺度裂缝性多孔介质中，当NBC-1小于8.8时，总渗吸权重ηM的相对误差大于10%。还提出了一种确定应考虑重力效应的临界时间的方法。