Universal Capillary Pressure and Relative Permeability Model from Fractal Characterization of Rock

Capillary pressure and relative permeability are important parameters in geothermal reservoir engineering. It is essential to represent capillary pressure curves mathematically in an appropriate way. The Brooks-Corey capillary pressure model has been accepted widely, however it has been found that the Brooks-Corey model cannot represent capillary pressure curves of The Geysers rock samples. In fact, few existing capillary pressure models work for these rock samples. To this end, the porous media were modeled using fractal geometry and a universal capillary pressure model was derived theoretically. It was found that the universal capillary pressure model could be reduced to the frequently-used BrooksCorey capillary pressure model and the Li-Horne imbibition model when the fractal dimension of the porous media takes a limiting value. This also demonstrates that the Brooks-Corey model and the Li-Horne model, which have been considered to be empirical, have a solid theoretical base. The results demonstrated that the new capillary pressure model could represent the capillary pressure curves of The Geysers rock while the Brooks-Corey model cannot. A relative permeability model was also developed from the universal capillary pressure model. Fractal dimension, a parameter associated with the heterogeneity of the rock, determines the shape of relative permeability curves according to the new relative permeability model. The new model can also be reduced to the Brooks-Corey relative permeability model. The relative permeability data of The Geysers rock were calculated using the typical values of the fractal dimension inferred from the mercury intrusion capillary pressure curves. INTRODUCTION Experimental data showed that the capillary pressure curves of rock samples with many fractures (The Geysers rock) were different from those of rock samples without fractures (for example, Berea sandstone). It was found that the Brooks-Corey (1964) capillary pressure model could be used to represent the curves of the rock without fractures but did not work for The Geysers rock samples with many fractures (Li and Horne, 2003). For example, Fig. 1 shows that the capillary pressure curve of Berea sandstone is a straight line on a log-log plot, which implies that the Brooks-Corey capillary pressure model works for Berea sandstone. However the capillary pressure curves of The Geysers rock are not straight lines, which demonstrates that the Brooks-Corey capillary pressure model does not work for The Geysers rock. The capillary pressure curves were measured using a mercury intrusion technique. It would be helpful for reservoir engineers to have a mathematical model to represent such capillary pressure curves appropriately. 0.01 0.1 1 10 10