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
- 3 in the last 30 days
- 915 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
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.
|File Size||1 MB||Number of Pages||16|
Arns, C.H. and Adler, P.M. 2013. "A Fast Laplace Solver Approach toPore-Scale Permeability." preprint.
Arns, J.Y., Arns, C.H., Sheppard, A.P. et al. 2003. Relative PermeabilityFrom Tomographic Images; Effect of Correlated Heterogeneity. J. Petrol. Sci.& Eng. 39 (3-4): 247-259.
Arns, H., Averdunk, H., Bauget, F. et al. 2004. Digital Core Laboratory:Reservoir Core Analysis From 3D Images. Paper presented at Gulf Rocks 2004, the6th North America Rock Mechanics Symposium (NARMS). Houston, Texas, 5-9June.
Bachu, S. and Cuthiell, D. 1990. Effects of Core-Scale Heterogeneity onSteady-State and Transient Fluid-Flow in Porous-Media--Numerical-Analysis.Water Resour. Res. 26 (5): 863-874.
Bauget, F., Arns, C.H., Saadatfar, M. et al. 2005. What Is theCharacteristic Length Scale for Permeability? Direct Analysis FromMicrotomographic Data. Paper presented at the SPE Annual Technical Conferenceand Exhibition, Dallas, Texas, 9-12 October. http://dx.doi.org/10.2118/95950-MS.
Baur, P. 1997. Lognormal Distribution of Water Permeability and OrganicSolute Mobility In Plant Cuticles. Plant Cell and Environment 20 (2): 167-177.
Baveye, P., Rogasik, H., Wendroth, O. et al. 2002. Effect of Sampling Volumeon the Measurement of Soil Physical Properties: Simulation With X-RayTomography Data. Measurement Sci. & Technol. 13 (5):775-784.
Bear, J. 1972. Dynamics of Fluids in Porous Media, New York:Elsevier.
Caers, J. 2005. Petroleum Geostatistics, Richardson, Texas: Societyof Petroleum Engineers.
Cardwell, W.T. and Parsons, R.L. 1945. Average Permeabilities ofHeterogeneous Oil Sands. Trans. of the AIME 160 (1):34-42.
Clauser, C. 1992. Permeability of Crystalline Rocks. Eos Trans. AGU 73 (21): 233-240.
Dagan, G. 1986. Statistical Theory of Groundwater Flow and Transport: Poreto Laboratory, Laboratory to Formation, and Formation to Regional Scale.Water Resour. Res. 22 (9S): 120S-134S.
Desbarats, A.J. (1992. Spatial Averaging of Hydraulic Conductivity inThree-Dimensional Heterogeneous Porous Media. Math. Geol. 24 (3): 249-267.
Desbarats, A.J. and Dimitrakopoulos, R. 1990. Geostatistical Modeling ofTransmissibility for 2D Reservoir Studies. SPE Form Eval 5(4): 437-443. http://dx.doi.org/10.2118/19355-PA.
Deutsch, C. 1989. Calculating Effective Absolute Permeability inSandstone/Shale Sequences. SPE Form Eval 4 (3): 343-348. http://dx.doi.org/10.2118/17264-PA.
Deutsch, C.V. and Journel, A.G. 1997. GSLIB: Geostatistical SoftwareLibrary and User's Guide, Oxford University Press.
Durlofsky, L.J. 2005. Upscaling and Gridding of Fine-Scale Geological Modelsfor Flow Simulation. Paper presented at the 8th International Forum onReservoir Simulation Iles Borromees, Stresa, Italy, 20-24 June.
Ehrenberg, S.N. 2007. Whole Core Versus Plugs: Scale Dependence of Porosityand Permeability Measurements in Platform Carbonates. AAPG Bull. 91 (6): 835-846.
Farmer, C.L. 2002. Upscaling: A Review. International J. for NumericalMethods in Fluids 40 (1-2): 63-78.
Gautier, Y. and Noetinger, B. 1997. Preferential Flow-Paths Detection forHeterogeneous Reservoirs Using a New Renormalization Technique. Transport inPorous Media 26 (1): 1-23.
Ghous, A., Senden, T.J., Sok, R.M. et al. 2007. 3D Characterization ofMicroporosity in Carbonate Cores. Paper presented at the SPWLA Middle EastRegional Symposium, Abu Dhabi, UAE, 15-19 April.
Gómez-Hernández, J.J. and Wen, X.-H. 1998. To Be or Not To BeMulti-Gaussian? A Reflection on Stochastic Hydrogeology. Advances in WaterResour. 21 (1): 47-61.
Gomez-Hernandez, J.J. and Gorelick, S.M. 1990. Effective Groundwater ModelParameter Values--Influence of Spatial Variability of Hydraulic Conductivity,Leakage, and Recharge--Reply. Water Resour. Res. 26 (8):1847-1848.
Green, C.P. and Paterson, L. 2007. Analytical Three-DimensionalRenormalization for Calculating Effective Permeabilities. Transport inPorous Media 68 (2): 237-248.
Haldorsen, H.H. 1986. Simulator Parameter Assignment and the Problem ofScale in Reservoir Engineering, 293-340, ed. L.W. Lake and H.B. Carroll Jr.,London: Academic Press.
Hastings, J.J. and Muggeridge, A.H. 2001. Upscaling Uncertain PermeabilityUsing Small Cell Renormalization. Math. Geol. 33 (4):491-505.
Honarpour, M.M., Djabbarah, N.F., and Sampath, K. 2005. Whole-CoreAnalysis—Experience and Challenges. SPE Res Eval & Eng 8 (6): 460-469. http://dx.doi.org/10.2118/81575-PA.
Journel, A.G., Deutsch, C., and Desbarats, A.J. 1986. Power Averaging forBlock Effective Permeability. Paper presented at the SPE California RegionalMeeting, Oakland, California, 2-4 April. http://dx.doi.org/10.2118/15128-MS.
Karim, M.R. and Krabbenhoft, K. 2010. New Renormalization Schemes forConductivity Upscaling in Heterogeneous Media. Transport in Porous Media 85 (3): 677-690.
Khan, S.A., Land, S., and Dawson, A.G. 2004. Method of UpscalingPermeability for Unstructured Grids. USA Patent US 6826520 B1.
King, P.R. 1989. The Use of Renormalization for Calculating EffectivePermeability. Transport in Porous Media 4 (1): 37-58.
King, P.R., Muggeridge, A.H., and Price, W.G. 1993. RenormalizationCalculations of Immiscible Flow. Transport in Porous Media 12(3): 237-260.
Knackstedt, M.A., Sok, R.M., Sheppard, A.P. et al. 2008. Probing PoreSystems in Carbonates: Correlations to Petrophysical Properties. Paperpresented at the 49th Annual Logging Symposium, Austin, Texas, 25-28 May.
Krige, D.G. 1994. A Statistical Approach to Some Basic Mine ValuationProblems on the Witwatersrand. J. South African Institute of Mining andMetallurgy 94 (3): 95-111.
Latham, S.J., Varslot, T., and Sheppard, A.P. 2008. Image Registration:Enhancing and Calibrating X-Ray Micro-CT Imaging. In Proceedings ofInternational Symposium of the Society of Core Analysts, ed. New York:Society of Core Analysts (SCA), p. 12.
Ling, K. 2012. Correlation Between Rock Permeability and FormationResistivity Factor-A Rigorous and Theoretical Derivation. Paper presented atthe SPE Middle East Unconventional Gas Conference and Exhibition, Abu Dhabi,UAE, 23-25 January. http://dx.doi.org/10.2118/152724-MS.
Lunati, I., Bernard, D., Giudici, M. et al. 2001.A Numerical ComparisonBetween Two Upscaling Techniques: Non-Local Inverse Based Scaling andSimplified Renormalization. Advances in Water Resour. 24(8): 913-929.
Mohamed, S.S.E.D., Dernaika, M., Hosani, I.A. et al. 2010. Whole Core VersusPlugs: Integrating Log and Core Data to Decrease Uncertainty in PetrophysicalInterpretation and STOIP Calculations. Paper presented at the Abu DhabiInternational Petroleum Exhibition and Conference, Abu Dhabi, UAE, 1-4November. http://dx.doi.org/10.2118/137679-MS.
Neuman, S.P. 1994. Generalized Scaling of Permeabilities—Validation andEffect of Support Scale. Geophys. Res. Lett. 21 (5):349-352.
Noetinger, B. 1994. The Effective Permeability of a HeterogeneousPorous-Medium. Transport in Porous Media 15 (2):99-127.
Paterson, L., Painter, S., Zhang, X. et al. 1996. Simulating ResidualSaturation and Relative Permeability in Heterogeneous Formations. Paperpresented at the SPE Annual Technical Conference and Exhibition, Denver,Colorado, 6-9 October. http://dx.doi.org/10.2118/36523-MS.
Prince, C.M. 2007. Petrophysics, Image Analysis, and Sample Size. PaperSCA2007-54 presented at the International Symposium of the Society of CoreAnalysts, Calgary, Canada, 10-12 September.
Renard, P. and deMarsily, G. 1997. Calculating Equivalent Permeability: AReview. Adv. in Water Resour. 20 (5-6): 253-278.
Sakellariou, A., Senden, T.J., Sawkins, T.J. et al. 2004. An X-RayTomography Facility for Quantitative Prediction of Mechanical and TransportProperties in Geological, Biological, and Synthetic Systems. Developments inX-Ray Tomography Iv 5535: 473-484.
Shabro, V., Torres-Verdin, C., Javadpour, F. et al. 2012. Finite-DifferenceApproximation for Fluid-Flow Simulation and Calculation of Permeability inPorous Media. Transport in Porous Media 94 (3):775-793.
Sheppard, A.P., Sok, R.M., and Averdunk, H. 2004. Techniques for ImageEnhancement and Segmentation of Tomographic Images of Porous Materials.Physica a-Statistical Mechanics and Its Applications 339(1-2): 145-151.
Sok, R.M., Varslot, T., Ghous, A. et al. 2010. Pore-Scale Characterizationof Carbonates at Multiple Scales: Integration of Micro-CT, BSEM, and FIBSEM.Petrophysics 51 (6): 379-387.
Vakili-Ghahani, S.A. and Jansen, J.D. 2010. Control-Relevant Upscaling.SPE J. 15 (2): 471-479. http://dx.doi.org/10.2118/113647-PA.
VandenBygaart, A.J. and Protz, R. 1999. The Representative Elementary Area(REA) in Studies of Quantitative Soil Micromorphology. Geoderma 89 (3-4): 333-346.
Varslot, T., Kingston, A., Myers, G. et al. 2011. High-Resolution HelicalCone-Beam Micro-CT With Theoretically-Exact Reconstruction From ExperimentalData. Medical Physics 38 (10): 5459-5476.
Wackernagel, H. 2003. Multivariate Geostatistics: An Introduction WithApplications, Springer-Verlag.
Wen, X.H. and Gomez-Hernandez, J.J. 1996. Upscaling HydraulicConductivities in Heterogeneous Media: An Overview. J. Hydrology 183 (1-2): R9-R32.
Worthington, P.F. 2004. The Effect of Scale on the Petrophysical Estimationof Intergranular Permeability. Petrophysics 45 (1).