Dehghan Khalili, Ahmad (University of New South Wales) | Arns, Ji-Youn (University of New South Wales) | Hussain, Furqan (University of New South Wales) | Cinar, Yildiray (University of New South Wales) | Pinczewski, Wolf (University of New South Wales) | Arns, Christoph H. (University of New South Wales)
High-resolution X-ray-computed-tomography (CT) images are increasingly usedto numerically derive petrophysical properties of interest at the porescale--in particular, effective permeability. Current micro-X-ray-CT facilitiestypically offer a resolution of a few microns per voxel, resulting in a fieldof view of approximately 5 mm3 for a 2,0482charge-coupled device. At this scale, the resolution is normally sufficient toresolve pore-space connectivity and calculate transport properties directly.For samples exhibiting heterogeneity above the field of view of such a singlehigh-resolution tomogram with resolved pore space, a second low resolutiontomogram can provide a larger-scale porosity map. This low-resolution X-ray-CTimage provides the correlation structure of porosity at an intermediate scale,for which high-resolution permeability calculations can be carried out, formingthe basis for upscaling methods dealing with correlated heterogeneity. In thisstudy, we characterize spatial heterogeneity by use of overlapping registeredX-ray-CT images derived at different resolutions spanning orders of magnitudein length scales. A 38-mm diameter carbonate core is studied in detail andimaged at low resolution--and at high resolution by taking four 5-mm-diametersubsets, one of which is imaged by use of full-length helical scanning.Fine-scale permeability transforms are derived by use of directporosity/permeability relationships, random sampling of theporosity/permeability scatter plot as a function of porosity, and structuralcorrelations combined with stochastic simulation. A range of these methods isapplied at the coarse scale. We compare various upscaling methods, includingrenormalization theory, with direct solutions by use of a Laplace solver andreport error bounds. Finally, we compare with experimental measurements ofpermeability at both the small-plug and the full-plug scale. We find that bothnumerically and experimentally for the carbonate sample considered, whichdisplays nonconnecting vugs and intrafossil pores, permeability increases withscale. Although numerical and experimental results agree at the larger scale,the digital core-analysis results underestimate experimentally measuredpermeability at the smaller scale. Upscaling techniques that use basicaveraging techniques fail to provide truthful vertical permeability at the finescale because of large permeability contrasts. At this scale, the most accurateupscaling technique uses Darcy's law. At the coarse scale, an accuratepermeability estimate with error bounds is feasible if spatial correlations areconsidered. All upscaling techniques work satisfactorily at this scale. A keypart of the study is the establishment of porosity transforms betweenhigh-resolution and low-resolution images to arrive at a calibrated porositymap to constrain permeability estimates for the whole core.
Cinar, Yildiray (The University of New South Wales) | Arns, Christoph (The University of New South Wales) | Dehghan Khalili, Ahmad (The University of New South Wales) | Yanici, Sefer (The University of New South Wales)
Resistivity measurements play a key role in hydrocarbon in place calculations for oil and gas reservoirs. They are a direct indi-cator 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 sig-nificant 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 for-mation 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 26µm. 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 sam-ple, 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 be-tween 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 proce-dure improves the agreement with the experimental result for the whole core while still underestimating formation factor. Al-lowing 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.
Dehghan Khalili, Ahmad (U Of New South Wales) | Arns, Christoph Hermann (University of New South Wales) | Arns, Jiyoun (U. of New South Wales) | Hussain, Furqan (U. of New South Wales) | Cinar, Yildiray (U. of New South Wales) | Pinczewski, Wolf Val (Australian National University) | Latham, Shane (Saudi Aramco) | Funk, James Joseph
High-resolution Xray-CT images are increasingly used to numerically derive petrophysical properties of interest at the pore scale, in particular effective permeability. Current micro Xray-CT facilities typically offer a resolution of a few microns per voxel resulting in a field of view of about 5 mm3 for a 20482 CCD. At this scale the resolution is normally sufficient to resolve pore space connectivity and transport properties. For samples exhibiting heterogeneity above the field of view of such a single high resolution tomogram with resolved pore space, a second low resolution tomogram can provide a larger scale porosity
map. The problem then reduces to rock-typing the low resolution Xray-CT image, deriving viable porosity-permeability transforms from the high resolution Xray-CT image(s) for all rock types present, and upscaling of the permeability field to derive a plug-scale permeability.
In this study we characterize spatially heterogeneity using overlapping registered Xray-CT images derived at different resolutions spanning orders of magnitude in length scales. A 38mm diameter carbonate core is studied in detail and imaged at low resolution - and at high resolution by taking four 5mm diameter subsets, one of which is imaged using full length helical scanning. Fine-scale permeability transforms are derived using direct porosity-permeability relationships, random sampling of the porosity-permeability scatter-plot as function of porosity, and structural correlations combined with stochastic simulation. A range of these methods are applied at the coarse scale. We compare various upscaling methods including renormalization theory with direct solutions using a Laplace solver and report error bounds.
We find that for the heterogeneous samples permeability typically increases with scale. Conventional methods using basic averaging techniques fail to provide truthful vertical permeability due to large permeability contrasts. The most accurate upscaling technique is employing Darcy's law. A key part of the study is the establishment of porosity transforms between highresolution and low-resolution images to arrive at a calibrated porosity map to constraint permeability estimates for the whole core.