Determination of Capillary Pressure Function from Resistivity Data

Abstract

A model has been derived theoretically to correlate capillary pressure and resistivity index based on the fractal scaling theory. The model is simple and predicts a power law relationship between capillary pressure and resistivity index (P c = p e · I β ) in a specific range of low water saturation. To verify the model, gas-water capillary pressure and resistivity were measured simultaneously at a room temperature in 14 core samples from two formations in an oil reservoir. The permeability of the core samples ranged from 0.028 to over 3000 md. The porosity ranged from less than 8% to over 30%. Capillary pressure curves were measured using a semi-permeable porous-plate technique. The model was tested against the experimental data obtained in this study. The results demonstrated that the model could match the experimental data in a specific range of low water saturation. The experimental results also support the fractal scaling theory in a low water saturation range. The new model developed in this study may be deployed to determine capillary pressure from resistivity data both in laboratories and reservoirs, especially in the case in which permeability is low or it is difficult to measure capillary pressure.

Interrelationship between Resistivity Index, Capillary Pressure and Relative Permeability

“…Note that the gas slippage is greater in core samples with low permeabilities than in those with high permeabilities. Li and Williams (2006) verified, to some extent, the relationship between capillary pressure and resistivity index (Eq. 8) using the experimental data of gas-water capillary pressure and resistivity measured simultaneously.…”

“…The second approach to determining capillary pressure is the application of the model developed by Li and Williams (2006):…”

“…Longeron et al (1989) did not attempt to correlate the two parameters. Li and Williams (2006) developed a correlation between resistivity and capillary pressure theoretically. The model was derived according to the fractal modeling of porous media.…”

A New Method for Calculating Two-Phase Relative Permeability from Resistivity Data in Porous Media

“…However, such models have been few. Li and Williams (2006) developed a correlation between resistivity and capillary pressure theoretically; but relative permeability was not considered. Pirson et al (1964) proposed a model to calculate relative permeability from resistivity data; the model reported by Pirson et al (1964) was empirical.…”

Fractal Prediction Model of Spontaneous Imbibition Rate

“…Some researchers (Tyler and Wheatcraft 1990;Li 2009) derived the empirical Brooks-Corey capillary pressure model theoretically from fractal modeling of a porous medium. Recently Li and Williams (2006) and Li (2007Li ( , 2011 developed interrelationship between resistivity index, capillary pressure, and relative permeability using fractal geometry. These studies showed the fractal feature of pore (including fractures) size distribution in different porous media and the capability of fractal geometry as well as its applications in many industries.…”