Permeability Upscaling for Carbonates From the Pore Scale by Use of Multiscale X-Ray-CT Images
- Ahmad Dehghan Khalili (University of New South Wales) | Ji-Youn Arns (University of New South Wales) | Furqan Hussain (University of New South Wales) | Yildiray Cinar (University of New South Wales) | Wolf Pinczewski (University of New South Wales) | Christoph H. Arns (University of New South Wales)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- October 2013
- Document Type
- Journal Paper
- 353 - 368
- 2013. Society of Petroleum Engineers
- 5.6.2 Core Analysis, 4.3.4 Scale, 1.6.9 Coring, Fishing, 5.5.2 Core Analysis, 5.6.1 Open hole/cased hole log analysis
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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.
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