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16 | 12 | 2019
10.14489/vkit.2019.06.pp.003-009

DOI: 10.14489/vkit.2019.06.pp.003-009

Варфоломеев И. А., Якимчук И. В.
ИЗУЧЕНИЕ ДЕФОРМАЦИЙ В ОБРАЗЦЕ ГОРНОЙ ПОРОДЫ ПО ЕГО МИКРОТОМОГРАФИЧЕСКОМУ ИЗОБРАЖЕНИЮ
(с. 3-9)

Аннотация. Рассмотрена процедура оценки трехмерного поля смещений в образце горной породы при всестороннем сжатии путем получения изображений образца в свободном и сжатом состояниях и последующем поблочном совмещении полученных изображений. Проанализирован случай, когда смещения преимущественно направлены вдоль одной оси, а также случай, близкий к изотропному сжатию. Показаны отличия наблюдаемого поля смещений от модели изотропного сжатия, которые могут быть обусловлены структурной неоднородностью породы. Оценка точности метода проведена с использованием изображений образца в трех различных состояниях: через невязку между полем смещений  и суммой полей смещений .

Ключевые слова:  3D-изображения; совмещение изображений; корреляция цифровых изображений; обработка томографических изображений; деформации пористых сред.

 

Varfolomeev I. A., Yakimchuk I. V.
X-RAY MICROTOMOGRAPHY FOR STUDYING DEFORMATION IN ROCK SAMPLES
(pp. 3-9)

Abstract. We describe a method for estimating 3D-deformation field in a rock sample under confining pressure. The method is based on acquiring micro-computed tomography images of the sample in uncompressed and compressed states. Non-rigid registration of the obtained images is performed in a block-by-block manner. Each pair of blocks is registered independently of each other, using 6-parameter rigid-body approximation. The image registration method is implemented as a simplex optimization of the area-based norm. The initial approximate whole-sample rigid-body transformation is estimated from at least three pairs of points, set by an operator. Next, said transformation parameters are further optimized using area-based registration procedure, similar to those used for individual blocks. We demonstrate the approach on the two distinct samples, both cylindrically shaped with diameter of 8 mm, using confining pressures from 1 up to 40 MPa. Each image consists of ~ 40003 voxels. The first sample represents a proppant-packed fracture model, and demonstrates predominantly axial compression. The second sample is a relatively homogeneous sandstone, and demonstrates near-uniform compression. For the second sample, we focus on the difference between the observed deformation field and the isotropic compression model, the latter being a least squares approximation of the displacements of the individual blocks.We evaluate the precision of our method by imaging the same sample under three distinct confining pressures, and comparing the displacement field between the first and the third states with a sum of two other displacement fields (between first and second states and between second and third states). We conclude that this residual error is below the observed non-uniformity of the deformation field.

Keywords: 3D-images; Image registration; Digital volume correlation; Tomographic image processing; Porous media deformation.

Рус

И. А. Варфоломеев (Московский физико-технический институт (национальный исследовательский университет); Московский научно-исследовательский центр «Шлюмберже», Москва, Россия) E-mail: Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript
И. В. Якимчук (Московский научно-исследовательский центр «Шлюмберже», Москва, Россия)

 

Eng

I. A. Varfolomeev (Moscow Institute of Physics and Technology; Schlumberger Moscow Research Center, Moscow, Russia) E-mail: Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript
I. V. Yakimchuk (Schlumberger Moscow Research Center, Moscow, Russia)

 

Рус

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3. Yakimchuk I. V., Varfolomeev I. A. The Use of X-Ray Micro-CT to Study the Porespace Structure of Dolomite Samples from the Preobrazhensky Reservoir // 3rd EAGE Intern. GeoBaikal Conf. 2014 – Exploration and Field Development in East Siberia. 18 August, 2014. 5 p. doi: 10.3997/2214-4609.20141746
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6. A Digital Volume Correlation Technique for 3-D Deformation Measurements of Soft Gels / J. Huang et al. // Intern. Journal of Applied Mechanics. 2011. V. 3, No. 2. P. 335 – 354. doi: 10.1142/S1758825111001019
7. Smith T. S., Bay B. K., Rashid M. M. Digital Volume Correlation Including Rotational Degrees of Freedom During Minimization // Experimental Mechanics. 2002. V. 42, No. 3. P. 272 – 278.
8. Droske M., Rumpf M. A Variational Approach to Nonrigid Morphological Image Registration // SIAM Journal on Applied Mathematics. 2004. V. 64, No. 2. P. 668 – 687.
9. Toward 4D Mechanical Correlation / F. Hild et al. // Advanced Modeling and Simulation in Engineering Sciences. 2016. V. 3, No. 1. P. 1 – 26 doi: 10.1186/s40323-016-0070-z
10. Computation of Full-Field Displacements in a Scaffold Implant Using Digital Volume Correlation and Finite Element Analysis / K. Mazi et al. // Medical Engineering and Physics. 2013. V. 35, No. 9. P. 1298 – 1312. doi: 10.1016/j.medengphy.2013.02.001
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Eng

1. Kostek S., Schwartz L. M., Johnson D. L. (1992). Fluid Permeability in Porous Media: Comparison of Electrical Estimates with Hydrodynamical Calculations. Physical Review B, Vol. 45, (1), pp. 186-195.
2. Auzerais F. M. et al. (1996). Transport in Sandstone: a Study Based on Three Dimensional Microtomography. Geophysical Research Letters, Vol. 23, (7), pp. 705 – 708. doi: 10.1029/ 96GL00776
3. Yakimchuk I. V., Varfolomeev I. A. (2014). The Use of X-Ray Micro-CT to Study the Porespace Structure of Dolomite Samples from the Preobrazhensky Reservoir. 3rd EAGE International GeoBaikal Conference 2014 – Exploration and Field Development in East Siberia. doi: 10.3997/2214-4609.20141746
4. Horn B. K. (1987). Closed-Form Solution of Absolute Orientation Using unit Quaternions. Journal of the Optical Society of America A, Vol. 4, (4), pp. 629-642.
5. Bay B. K. et al. (1999). Digital Volume Correlation: Three-Dimensional Strain Mapping Using X-Ray Tomography. Experimental Mechanics, Vol. 39, (3), pp. 217-226.
6. Huang J. et al. (2011). A Digital Volume Correlation Technique for 3-D Deformation Measurements of Soft Gels. International Journal of Applied Mechanics, Vol. 3, (2), pp. 335-354. doi: 10.1142/S1758825111001019
7. Smith T. S., Bay B. K., Rashid M. M. (2002). Digital Volume Correlation Including Rotational Degrees of Freedom During Minimization. Experimental Mechanics, Vol. 42, (3), pp. 272-278.
8. Droske M., Rumpf M. (2004). A Variational Approach to Nonrigid Morphological Image Registration. SIAM Journal on Applied Mathematics, Vol. 64, (2), pp. 668-687.
9. Hild F. et al. (2016). Toward 4D Mechanical Correlation. Advanced Modeling and Simulation in Engineering Sciences, Vol. 3, (1), pp. 1-26 doi: 10.1186/s40323-016-0070-z
10. Mazi K. et al. (2013). Computation of Full-Field Displacements in a Scaffold Implant Using Digital Volume Correlation and Finite Element Analysis. Medical Engineering and Physics, Vol. 35, (9), pp. 1298 – 1312. doi: 10.1016/j.medengphy.2013.02.001
11. Walsh S. D. C. et al. (2016). Non-Invasive Measurement of Proppant Pack Deformation. International Journal of Rock Mechanics and Mining Sciences, Vol. 87, pp. 39-47. doi: 10.1016/j.ijrmms.2016.05.005
12. Arshadi M. et al. (2017). The Effect of Deformation on Two-Phase Flow Through Proppant-Packed Fractured Shale Samples: A Micro-Scale Experimental Investigation. Advances in Water Resources, Vol. 105, pp. 108 – 131. doi: 10.1016/j.advwatres.2017.04.0252

Рус

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