Determination of Capillary Pressure Function from Resistivity Data
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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.
Keywordscapillary pressure resistivity well logging mathematical model fractal scaling
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