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1 多能镨 X 光 CT 数据约束模拟材料微结构表征 Data-constrained modelling (DCM) characterisation of material microstructure with multi-spectrum X-ray CT Sam Yang ( 杨玉双 ) Division of Materials Science & Engineering ( 材料科学与工程研究所 ) CSIRO Commonwealth Scientific and Industrial Research Organisation 澳大利亚联邦科学与工业研究组织 Locked Bag 33, Clayton, Vic 3169, Australia Sam.Yang@csiro.au

Engineering ( 材料科学与工程研究所 ) CSIRO Commonwealth Scientific and Industrial Research Organisation

2 内容数据约束模拟 (data-constrained modelling DCM) 原理简介应用实例软件界面

3 目的 : 更充分有效发挥 X 光断层扫描的潜力 X-ray micro-ct + image segmentation is an excellent technology for sample-non-destructive (SND) 3D characterisation Proceed with caution X-ray CT spatial resolution limit: Sample size 10 3 times pixel size. 5mm sample -> 1μm pixel size In many applications, such as the advanced materials and unconventional reservoir characterisation, it requires a spatial resolution of10 6 (mm-nm) or higher There are fundamental limitations in spatial resolution improvement 提高分辨率 10 倍, 数据量增加 1000 倍通常一组 CT 数据为 10-50GB 保持信噪比不变, 爆光量需增加倍通常样品吸收光能为 mw 级, 温升 C, 扫描时间小时 Mathematical, physical and IT limitations Relies on a unique relationship between compositions and X-ray linear absorption coefficients Such unique relationship may not exist. Such as calcite with fine pores, or fine mixture of multiple material phases 实际应用对微观表征的要求可以超过传统 X 光断层扫描与常规图像分析技术的能力

5mm sample -> 1μm pixel size In many applications, such as the advanced materials and unconventional reservoir characterisation, it requires a spatial resolution of10 6 (mm-nm) or higher There are

4 局部 CT (Region of interest / local X-ray CT) High resolution local CT Standard resolution global CT 3D composition distribution of a coal sample Pseudo-global tomography High resolution local tomography Standard resolution global tomography

composition distribution of a coal sample Pseudo-global

5 几种油气储层 CT 截面 1.8mm 3.6mm 2.8mm 砂岩致密砂岩碳酸盐岩 1.1mm 页岩, 四川盆地页岩, LX 页岩, LX

6 Data-constrained modelling (DCM) of microstructures 微结构数据约束模拟 0 v 1 M (m) vn = 1 m = 0 ( m ) ( l ) M ( m,l ) ( m ) ˆ ( l ) δµ = µ vn µ n 0 n n m =0 m = 0,1,2,, M ; n = 1,2,, N 材料m在体元n中的体分数 (k ) N K M M En = v S m =0 (m) (m) n ( v ] + L [ M Minimize δµn(=l ) 0m+ =Em k =T0n =j = 1 m n l =1 2ζ 1 2 ( m1 ) ( m2 ) n n + n (j k ) v 1 1ms/voxel optimization => 1 week on modern desktop PC. On CSIRO cluster: 50ns. Target: 1ns )I η ( m1, m2 ) k

(m) (m) n ( v ] + L [ M Minimize δµn(=l ) 0m+ =Em k =T0n =j = 1 m n l =1 2ζ 1 2 ( m1 ) ( m2 ) n n + n (j k )

7 Aerospace paint primer case study Compositions Strontium Chromate SrCrO4 Titanium Dioxide TiO2 Polyimide matrix C22H10N2O5 (not displayed) Void (not displayed) XuM - CMSE XuM lab - CMSE X-ray CT with Fe target (6.4keV) DCM X-ray CT with Ti target (4.5keV) DCM predicted microstructure

displayed) Void (not displayed) XuM - CMSE XuM lab - CMSE X-ray CT

8 A carbonate reservoir rock ( 碳酸盐岩 ) SLS Darai carbonate Calcite ( 方解石 ), dolomite ( 白云石 ), pore, X-ray CT sets at 28 & 38 kev pixels, mm, pixel size 1.85 μm 1.8mm Calcite (56.8%) All compositions X-ray CT reconstructed slice. 28keV DCM Dolomite (28.4%) Porosity (14.8%) Void histogram X-ray CT reconstructed slice. 38keV

7mm, pixel size 1.85 μm 1.8mm Calcite (56.

9 Verification with Xe gas K-edge subtraction Xe K-edge: 34.55keV 34keV CT 45keV CT Porosity map by Xe K-edge subtraction Porosity map by DCM

10 Shale rock multi-scale pore microstructure characterization 页岩微孔隙结构多尺度表征 SR-µCT Experimental parameters: Shale sample: Cylinder, D:1.2~1.3 mm Energies:20&30keV SDD:23cm Detector: PCO, pixel size 0.74µm projections:1260/180 Shale sample photo CT experiment at SSRF. 3D alignment & DCM Parts of X-ray µct slices pore=9 %, SiO2=72%, CaCO3=19%

3 mm Energies:20&30keV SDD:23cm Detector: PCO, pixel size 0.

11 Shale rock multi-scale pore microstructure characterization 页岩微孔隙结构多尺度表征 Hypothesis: pores are cylinders inside each cubic pixel. One cubic pixel 0.74μm 0.74μm 0.74μm Effect of sub-pixel pore throat on the upper limit of recoverable reserve can be estimated. 小于 X 光成像分辨率的孔喉对可开采比例的影响是可以估算的 DCM 和定量 Micro-CT 结合可以表征 mm 尺度样品并包括 nm 效应可开采比例上限临界有效孔喉半径 ( 微米 ) Yudan Wang, Sam Y. S. Yang, Keyu Liu, d, Yuqi Ren, Hai Tan, Tiqiao Xiao, CSIRO Data Collection (2013) Sichuan Basin Xujiahe Formation Shale Rock 3D Microstructures

小于 X 光成像分辨率的孔喉对可开采比例的影响是可以估算的 DCM 和定量 Micro-CT 结合可以表征 mm 尺度样品并包括 nm 效应可开采比例上限临界有效孔喉半径 ( 微米 ) Yudan

12 Anthracite coal ( 无烟煤物理结构 ) Derived list of minerals and their overall volume percentages. Minerals name Molecular formula Volume percentage Kaolinite Al 2 O 3 SiO 2 H 2 O 4.32 Illite KAl 2 (AlSi 3 O 10 )(OH) Quartz SiO Pyrite FeS E-03 Titania TiO Chlorite Mg(FeAl) 5 (SiAl) 4 O 10 (OH) Original sample Dolomite CaCO 3 MgCO Plagioclase (NaCa)Al(Al 3 Si)Si Manganese dioxide Organic matrix MnO 2 C 101 H 41 O 4 NS 9.26E (including void volume) Sample: coal(diameter:5mm ±0.2mm) Energies: 14keV 18keV 30keV Exposure time: 5s(14keV) 2.5s(18keV) 3s(30keV) SDD: 12cm CCD: PCO camera, pixel size=3.7μm Projections: 1080/180 The sample after sanded by hand Composition groups void (group A) coal matrix (group B) not displayed Illite, Quartz and Kaolinite (group C) Chlorite and Titania (group D)

0664 Plagioclase (NaCa)Al(Al 3 Si)Si 3 0.0185 Manganese dioxide Organic matrix MnO 2 C 101 H 41 O 4 NS 9.26E-05 93.75 (including void volume) Sample: coal(diameter:5mm ±0.

13 CIPS sandstone Calcite In-situ Precipitation System - CIPS Quartz, calcite, pore, X-ray CT sets at 35 & 45 kev, Porosity 19.5% SEM images X-ray CT reconstructed slice. 35keV DCM. Porosity=19.6% Leaset-square segmentation. Porosity=11.3% DCM Leaset-square segmentation Sam Yang, Keyu Liu, Sherry Mayo, Andrew Tulloh, CIPS sandstone microstructure, CSIRO Data Collection (2012)

6% Leaset-square segmentation. Porosity=11.

14 Aerospace corrosion inhibitor clusters Before and After Corrosion Before Number of Clusters Before After 2,725 3,365 Largest 185,393 21,438 Smallest* 3 3 Mean Standard dev After *clusters smaller than 3 were not considered AFTER CORROSION Breakdown of large (giant) clusters More fragmented, smaller clusters

223 190 Standard dev 724 419 After *clusters smaller than 3 were not considered

15 Data-constrained modelling (DCM) Reconstruct 3D material compositions (phases) explicitly Incorporate multiple sets of (quantitative) X-ray CT data as constraints Incorporate sample-specific domain knowledge about compositions Generate material volume fractions at X-ray CT pixel resolution Sample Data & domain knowledge DCM Multi-energy x-ray CT 3D data sets Attenuation / refraction coefficients (beam energy dependent) Domain knowledge and other measurements

$Generate material volume fractions at X-ray CT pixel resolution Sample Data & domain knowledge DCM Multi-energy$

16 Walk through DCM software main interface

17 Walk through DCM software Define compositions Compositions in a sample are defined by their formulae and densities

18 Walk through DCM software Optimize CT parameters X-ray CT experimental parameters should aim to minimize noise and maximize linear independence for CT data sets

19 Walk through DCM software Import X-ray CT data sets CT data sets need to be spatially aligned (registered), and with known conversion factors to linear absorption coefficients

20 Walk through DCM software Display X-ray CT data sets It would be helpful to confirm the data import operation

21 Walk through DCM software Setup computation method Data constrained non-linear optimisation Y.S. Yang, Lecture Notes in Information Technology 15 (ISBN: , ISSN: , Electronically available at , Information Engineering Research Institute) pp Data constrained linear optimisation Y. S. Yang, K. Y. Liu, S. Mayo, A. Tulloh, B. Clennell, T. Q. Xiao, J. Petroleum Science & Technology 105 (2013) pp doi: Discrete least-square segmentation Y. S. Yang, T. E. Gureyev, A. Tulloh, M. B. Clennell, M. Pervukhina, Measurement Science & Technology 21 (April, 2010) (6pp), doi: / /21/4/047001

22 Walk through DCM software Visualize 3D compositional microstructure

23 Home work additional functionalities Histogram, average, standard deviation, min, max, Generate 3D animations Sample boundary Stereo 3D, grey scale, ISO surface, Clustering, connectivity, property map, Export data and images for further analysis Import data in different format Polychromatic source, filters, estimation of beam hardening, DcmLite download:

24 Acknowledgement

25 Thank You 谢谢 Contact CSIRO Phone enquiries@csiro.au Web

26 背景非常规能源致密汽, 油, 煤层汽页岩 (Shale), 碳酸盐岩 (carbonate / limestone), 致密砂岩 (tight sandstone), 煤 (coal) 储量可能数倍于常规能源储层表征是一个多尺度问题 km mm - nm 常规能源非常规能源地质微观表征微观样品 <mm 难有代表性 - 非常规能源储层微观表征需跨越 6 个以上数量级含油气岩石三维微观结构样品无损表征 Porosity ( 孔隙率 / 孔隙分布 ) reserve ( 储量, 富集程度 ) Pore connectivity ( 孔隙连通性 ) recoverable reserve ( 可开采储量, 可采性 ) Permeability ( 渗透率 ) production rate ( 产出率 ) Mineral phase distribution at fine scale ( 微观尺度岩相分布 ) interfacial effect ( 界面效应 ) Focus: mm/cm

27 数字岩芯 (digital rock) Fine for rocks with pores larger than CT resolution 用于常规能源 OK May not be adequate with multi-scale pores (such as nano to macro) limited by X-ray CT spatial dynamical range 用于非常规能源可能有点问题受限于 X 光断层扫描空间尺度分辨范围 Impractical data size covering length scales 跨越 6 个数量级尺度范围, 数据量可能成为问题 10 9 TB

28 Carbonate porosity critical phenomena Critical Threshold Number% of largest State Porosity% above threshold percolating Connected porosity % If regard a voxel with 20.8% or above pore volume fraction s connected, the sample is percolating. No percolating otherwise Subtle change in structure can affect the pore connectivity significantly (from nonpercolating to percolating). Largest at (above critical) Largest at (below critical)

29 More on coal 煤样煤阶 Proximate (wt%) Ultimate (wt%, daf) A d V daf FC daf C H O * N S 阳泉无烟煤沁水无烟煤西岔沟烟煤小龙潭褐煤煤样 Ash analysis(%) SiO 2 Al 2 O 3 TiO 2 Fe 2 O 3 K 2 O CaO MgO Na 2 O MnO 2 SO 3 P 2 O 5 Other 阳泉沁水西岔沟小龙潭

30 More on coal YQ Coal ( 阳泉 ) QS Coal ( 沁水 ) XCG Coal ( 西岔沟 ) XLT Coal ( 小龙潭 ) void void void void C 102 H 41 O 4 NS C 132 H 50 O 4 N 1.34 S 0.11 C 36 H 26 O 4 N 0.47 S 0.04 C 27 H 21 O 4 N 0.37 S 0.16 Ti MgFe 2.65 Al 1.8 Si 0.8 O 34.3 S 3.3 H 1.6 KAl Si O H Fe 5.63 TiS O 2 Na 3.29 Ca Al 50.4 Si Mg 15.27C O KH Fe 2.62 Mg 1.25 Al 2.25 Si S 2.74 O 4.5 H 2 NaCa 9.01 Al Si Mg 8.01 C O K 2.52 H TiFe Mg 2.56 Al 4.61 Si 2.05 S O H 4.1 KCa Mg Al 17.8 Si O H 16.8 C

31 多尺度多孔介质中的 Darcy 流动体元渗透率为连续变量的随机行走问题 Darcy 流动 ( 扩散 ) 随机行走 Simulated permeability Iso HMean Mean P( ) P( ) Simualted permeability Volume fraction of composition C1 Iso HMean Mean P( ) P( ) P1 = 1 P2 = 100 P1 = 1 P2 = 100

32 具有部分渗透体元的格子波尔兹曼模型 Lattice Boltzmann model with partially percolating voxels on a regular lattice 基本公式 : f α ( x, t ** * + t) = fα ( x, t + t) + (1 Pf ) [ f a ( x, t) fα ** ( x, t + t)] P Percolating volume fraction ( 可渗透体分数 ) f 数值模拟 : 矩形通道中的流速分布 x 10-3 Comparison of analytical solution with MP-LBM results MP-LBM solution Analytical solution 7 x Comparison of different partially bounceback coefficient (PBC) with MP-LBM results PBC=0.1 PBC=0.3 PBC=0.5 PBC=0.7 PBC=0.9 PBC=0.99 P f =1 speed speed P f = location in channel location in channel 二维 P =1 < 1 f 二维 P f 三维, 分层

33 下一步的问题体元孔隙和岩相体分数与渗透率 / 渗透体分数的关系唯像假设尺度自相似性分形 / 重整化群通过钠米 CT 和其它试验手段建立经验关系定量 CT 成像表征精度取决于数据, 数据精度取决于样品, 设备和操作同步加速器机时, 人员图像修正方法软件工具开发分析模型和软件开发 DCM 基本方法和软件已建立扩展, 完善, 开发, 整合从可行到可用通过更多实际问题来指导建立特定问题的流程

34 Summary Unconventional resource research may need some unconventional approachs, such as DCM 非常规能源研究也许需要一些非常规方法, 比如数据约束模拟 DCM + quantitative multi-energy X-ray CT could reveal the rock porosity & effective pore throat distribution below CT resolution nano effect from micro-ct 数据约束模拟 + 定量 X 光多能镨断层扫描在一定程度上可以表征小于扫描分辨率的岩相, 孔隙和有效孔喉分布表征纳米效应不一定需要要纳米分辨率 Probe down to nano length scale may be helped with nano-second level numerical modelling 探讨纳米尺度也许需要纳秒级别模拟计算即将推出 : DCM Pro ( 和 DCM Lite 软件版本

(2015-2016-2)-0004186-04205-1 140242 信号与系统 Ⅰ 学科基础必修课 37 37 1 教 203 17 周 2016 年 06 月 13 日 (08:00-09:35) (2015-2016-2)-0004186-04205-1 141011

(2015-2016-2)-0004186-04205-1 140242 信号与系统 Ⅰ 学科基础必修课 37 37 1 教 203 17 周 2016 年 06 月 13 日 (08:00-09:35) (2015-2016-2)-0004186-04205-1 141011 关于 2015-2016 学年第二学期期末周内考试时间地点安排选课课号班级名称课程名称课程性质合考人数实际人数考试教室考试段考试时间 (2015-2016-2)-0006178-04247-1 130101 测试技术基础学科基础必修课 35 35 1 教 401 17 周