Stanford University, USA.
J Contam Hydrol. 2010 Jan 15;111(1-4):13-24. doi: 10.1016/j.jconhyd.2009.10.005. Epub 2009 Oct 29.
More general capillary pressure and relative permeability models were derived theoretically from fractal modeling of a porous medium. It was found that the new capillary pressure model could be reduced to the frequently-used Brooks-Corey capillary pressure model and the Li-Horne imbibition model when the fractal dimension of a porous medium takes specific values. This also demonstrates that the Brooks-Corey model and the Li-Horne model have a further confirmed theoretical basis. Capillary pressure data measured using mercury intrusion techinque were used to verify the model. The results demonstrated that the new capillary pressure model could represent the capillary pressure curves in those rocks with fracures or with great heterogeneity while the existing models cannot. The new relative permeability models can be reduced to the Brooks-Corey relative permeability model in a specific case. It has been proved theoretically that the relative permeability of each phase in a smooth fracture is only a linear function of its own saturation. Relative permeability data were calculated using the new models and the model results were compared with experimental data measured using a steady-state technique. The comparison demonstrated that the relative permeability models and experimental results were consistent with each other.
从多孔介质的分形建模出发，推导出了更通用的毛管压力和相对渗透率模型。研究发现，当多孔介质的分形维数取特定值时，新的毛管压力模型可以简化为常用的 Brooks-Corey 毛管压力模型和 Li-Horne 吸吮模型。这也证明了 Brooks-Corey 模型和 Li-Horne 模型具有进一步的理论依据。使用压汞技术测量的毛管压力数据验证了模型。结果表明，新的毛管压力模型可以表示具有裂缝或高度非均质性的岩石中的毛管压力曲线，而现有的模型则不能。新的相对渗透率模型在特定情况下可以简化为 Brooks-Corey 相对渗透率模型。理论上证明，在光滑裂缝中每一相的相对渗透率仅是其自身饱和度的线性函数。使用新模型计算了相对渗透率数据，并将模型结果与使用稳态技术测量的实验数据进行了比较。比较表明，相对渗透率模型和实验结果是一致的。
