More general capillary pressure and relative permeability models from fractal geometry

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.