Continuous Wavelet Transformation to Quantify small-scale Cycles of Petrophysical Properties; a New Approach Applied in a Potential Disposal Repository of Nuclear Waste, SW Hungary
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Oct 16, 2023
Keywords:
X-ray computed tomography, voxel-porosity, Continuous Wavelet Transform
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Abstract
Continuous Wavelet Transformation (CWT) was applied to study the small-scale repetitive oscillations of porosity distribution patterns in a 5 m silty-claystone core sample of the Boda Claystone Formation. We handled the fluctuations in voxel porosity averages over unequal depth distributions as signals over uneven time intervals. The strength of wavelet analysis lies in the ability to study the fluctuation of a signal in detail, i.e., the wavelet transforms permit automatic localization of the cyclic attributes' sequences both in time (the depth domain) and according to their frequency (the frequency domain). Thereupon, three main frequency branches (cycles) were discerned: small scale (5, 6.67, and 11 cm), intermediate scale (20, 30 cm), and large scale (66.67 cm).
Depending on the CWT coefficients magnitude plot, we were able to detect the developments of porosity oscillation according to the depth variable. Thus, small-scale cycles were seen throughout the core sample., the intermediate-scale cycles were strong in the upper parts of the core sample and dwindled toward greater depths, and the large cycle was predominant in the lower part of the core sample.
The cross-correlation of the wavelet coefficients of porosity and rock-forming components allows a detailed study of the inter-dependence of such parameters as their relationship changes over time. The distinct peaks at zero lag indicates that the measured wavelet coefficient series were contemporaneously correlated; their strong positive correlations suggest that both examined series respond similarly and simultaneously to other exogenous factors. The results emphasize that cyclical porosity fluctuations at all scales would concern three main factors; sediment deposition, diagenetic processes, and structural deformation (i.e., convolute laminations).
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References
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CHAMOLI, A. (2009): Wavelet Analysis of Geophysical Time Series.- Earth Science India, 2/4, 258-275.
CHOWDHURY, A.H. & NOBLE, J.P.A. (1993): Feldspar albitization and feldspar cementation in the Albert formation reservoir sandstones, New Brunswick, Canada.- Mar. Pet. Geol.,10, 394–402. doi: 10.1016/0264-8172(93)90083-5
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DUCHESNE, M. J., MOORE, F., LONG, B.F. & LABRIE, J. (2009): A rapid method for converting medical Computed Tomography scanner topogram attenuation scale to Hounsfield Unit scale and to obtain relative density values.- Engineering Geology, 103, 100 – 105. doi: 10.1016/j.enggeo.2008.06.009
DUTTON, S.P. (2008): Calcite cement in Permian deep-water sandstones, Delaware Basin, west Texas: Origin, distribution, and effect on reservoir properties.- AAPG Bulletin, 92/6, 765–787. doi: 10.1306/01280807107
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FÖLDES, T. (2011): Integrated processing based on CT measurement.- Journal of Geometry and Physics, 1, 23–41.
FÖLDES, T., KISS, B., ÁRGYELÁN, G., BOGNER, P., REPA, I. & HIPS, K. (2004): Application of medical computer tomography measurements in 3D reservoir characterization.- Acta Geologica Hungarica, 47, 63–73.
FOSTER, G. (1996): Wavelets for period analysis of unevenly sampled time series.- The Astronomical Journal, 112, 1709-1729. doi: 10.1086/118137
FRAZER, G., WULDER, M. & NIEMANN, K. (2005): Simulation and quantification of the fine scale spatial pattern and heterogeneity of forest canopy structure: a lacunarity based method designed for analysis of continuous canopy heights.- Forest Ecology and Management, 214, 65–90. doi: 10.1016/j.foreco.2005.03.056
GROSSMAN, A. & MORLET, J. (1985): Decomposition of functions into wavelets of constant shape and related transforms.- In: STREIT, L., (ed.): Mathematics, and physics, lectures on recent results, World Scientific Publishing, Singapore.
GURLEY, K. & KAREEM, A. (1999): Application of wavelet transforms in earthquake, wind, and ocean engineering.- Eng. Struct., 21, 149– 167.
HAAS, J.& PÉRÓ, C.S. (2004): Mesozoic evolution of the Tisza Mega-unit.- International Journal of Earth Sciences 93, 297–313.
HAYATDAVOUDI, A. & GHALAMBOR, A. (1996): Controlling formation damage caused by kaolinite clay minerals: Part I.- In: SPE Formation Damage Control Symposium, Society of Petroleum Engineers, SPE-31118-MS. doi: 10.2118/31118- MS
HEISMANN, B.J., LEPPERT J. & STIERSTORFER, K. (2003): Density and atomic number measurements with spectral x-ray attenuation method.- Journal of Applied Physics, 94, 2073 – 2079. doi: 10.1063/1.1586963
HINAI, A. A., REZAEE, R. & ESTEBAN, L. (2014): Comparisons of Pore Size Distribution: A Case from the Western Australian Gas Shale Formations.- Journal of Unconventional Oil and Gas Resources, 8, 1–13. doi: 10.1016/j.juogr.2014.06.002
HORVÁTH, F. (1993): Towards a mechanical model for the formations of the Pannonian basin.- Tectonophysics, 226, 333–357. doi: 10.1016/0040-1951(93)90126-5
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