Resistivity measurements play a key role in hydrocarbon in place calculations for oil and gas reservoirs. They are a direct indicator of fluid saturation and connected pore space available in the formation. Carbonate rocks, which host around half of the world's hydrocarbons, exhibit a wide range of porosities with scales spanning from nanometres to centimetres. The often significant amount of microporosity displayed by Carbonate rocks emphasizes the necessity of an adequate characterization of their micro-features and their contribution to hydrocarbon in place. In this paper we examine upscaling methods to probe formation factor of a fully saturated carbonate sample using an X-ray CT based numerical approach and compare to experimental measurements.

Three-dimensional high-resolution X-ray CT enables the numerical calculation of petrophysical properties of interest at the pore scale with resolutions down to a few microns per voxel. For more complex and heterogeneous samples however, a direct calculation of petrophysical properties is not feasible, since the required resolution and a sufficient field of view cannot be obtained simultaneously. Thus an integration of measurements at different scale is required. In this study a carbonate sample of 38mm in diameter is first scanned using the X-ray CT method with a resolution of 26 µm. After accompanying experimental measurements on the full plug, four 5mm plugs were drilled vertically from this sample and X-ray CT images of these plugs acquired at resolutions down to 2.74 µm. We calculate the porosity of the sample (macro- and micro-porosities) using the phase separation methods and then predict the formation factor of the sample at several scales using a Laplace solver. The formation factor is calculated by using a general value of m=2 as cementation factor for intermediate porosity voxels. We compare to experimental measurements of formation factor and porosity both at the small plug and full plug scale and find good agreement.

To assess the degree of uncertainty of the numerical estimate, we probe the extent of heterogeneity by investigating the size of a representative elementary volume (REV) for formation factor. We find that for the considered heterogeneous carbonate sample, formation factor varies considerably over intervals less than a centimetre. Our results show that this variation could be explained by different cementation exponents applied at the micro-voxel scale, with the exemption of one plug, for which the cementation exponent would have to be unreasonably low. These cementation factors are derived by direct comparison between numerical simulation and experiment. We conclude that for one plug an error in experimental measurement might have occurred. The numerical approach presented here therefore aids in quality control. Excluding this plug in the upscaling procedure improves the agreement with the experimental result for the whole core while still underestimating formation factor. Allowing for a constant m=2 in the simulation at the small scale and using directly the resulting relationship between porosity and formation factor in the upscaling process leads to an overestimation of formation factor.

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