rock typing

ISE-5013 Statistical Analysis for System Design

Graduate Project

Rock Typing based on Petrophysical Properties

Submitted by: Karan Bathla

OU ID: 113072138

ISE – 5013: Statistical Analysis For System Design

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Abstract

Shale is a type of sedimentary rock and is most abundant in earth’s crust. It was formed due to deposition of silt and organic debris on sea bottoms millions of years ago. Due to geothermal effects, it cooked and transformed into oil. It has drastically changed the oil and gas production in United States of America contributing 33 trillion cubic feet of natural gas (source: Energy Information Administration). However since shale is composed of mud, silt, quartz, calcite and other minerals, it is very important to classify the properties that have a greater impact on production for estimation of reservoir. The experiments were performed at the Integrated Core Characterization Center at University of Oklahoma to know the most important petrophysical properties at various depths of the same shale rock. By knowing these properties, we can analyze and identify the properties that have most variation and use them to do clustering to perform rock typing. In this paper, principal component statistical analysis will be performed using XLSTAT on shale composition primarily mineralogy, mainly clays, carbonates and feldspar, porosity and total organic carbon to study the parameters that have maximum variation in them. Further, k-means will be performed using XLSTAT on essential parameters identified by PCA to classify the rock and cluster them. Principal Component Analysis: Saville and Wood in their book Statistical Methods: A Geometric Approach wrote the following definition for Principal Component Analysis: Definition: Given n points in , principal components analysis consists of choosing a dimension and then finding the affine space of dimension k with the property that the squared distance of the points to their orthogonal projection onto the space is minimized. Principal Components are sum of independent linear components and arrange the data set according to variability and helps to understand the internal structure of our data set. They are used to identify the patterns and reduce the dimensions of the dataset (reduce the dispersion) with minimum loss of information. The number of components extracted in PCA equals the number of observed variables. If the data set has n variables then there will be n principal components:

• The first component will have the largest variance and will be linear combination of original variables

• The subsequent components are unrelated with previous defined components and will consist of linear combination of variables with greatest variance

Since, it is a truncated transformation, we will be able to focus on the essential data sets and perform a detail analysis on them. It is an important step for pattern recognition. Eigen Value and Eigen Vector: We can get an estimate of the variance in the data by calculating eigenvalue. The principal component is therefore the eigenvector, which has the highest eigenvalue. The number of eigenvector is equal to the dimensions of the system. Dimension reduction using eigenvalue The Principal Component Analysis is used to reduce the dimensions of the data set. For example, there is 3 dimension data that is represented in the figure below. It is plotted along x-axis, y-axis, and z-axis. Since the data has a common z value and variance in that direction is 0, the value of eigenvalue along


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that direction will be zero as shown in figure 2. Hence, we can represent the data in two dimensions now since there is no information that can be extracted in z-axis.

Figure 1: 3 Dimensional data set represented alond x-axis, y-axis and z-axis

Figure 2: Calculation of eigenvector for the data set represented in Fig 1

Source: Dallas, George. Access on 11/25/2014, “Principal Component Analysis 4 Dummies: Eigenvectors, Eigenvalues and Dimension Reduction.” Web blog post, access on 11/25/2014.

Weblink:https://georgemdallas.wordpress.com/2013/10/30/principal-component-analysis-4-dummies-eigenvectors-eigenvalues-and-dimension-reduction/

Petroleum Engineering Definitions Some Petroleum Engineering terms that have used in this paper have been defined below: Porosity – is the ratio of pore space and bulk volume TOC - Total Organic Content is composed of kerogen (hydrocarbon forming material) and hydrocarbons (found in pore space) Mineralogy: shales can be found in quartz a) clastics (quartz or clay rich) b) carbonates (carbon rich). However shales are composed of both clastics minerals and carbonates and FTIR (Fourier Transform Infrared Spectroscopy) is done to obtain the specific mineralogy. The data used is from 168 core samples of Barnett shale at various depths from the lab Integrated Core Characterization tabulated in the Appendix to perform Principal Component Analysis on the petrophysical properties: Porosity, Total Organic Carbon, Quartz, Carbonates, Illite + Chlorite and mixed clays to identify the most varying properties that can be for rock typing. The data was scaled


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before performing the PCA by subtracting the mean and dividing by standard deviation. Table 1 indicates the various petrophysical properties and their correlation with each other. The matrix contains the statistical parameters such as minimum, maximum, mean of the scaled properties. We try to capture the variation in the eigenvalue of the 6 principal components. We can capture 58% variation if we consider only the first principal component and 87.4% by considering three principal components and 100% if we take all 6 principal components corresponding to 6 petrophysical properties. Table 2 summarizes the variation captured by every principal component and their cumulative variance.

Table 1: Various petrophysical properties along with their statistical parameters

Table 2: Principal Component Analysis using eigenvalue Eigenvalues: F1 F2 F3 F4 F5 F6 Eigenvalue 3.496 1.161 0.592 0.491 0.219 0.040 Variability (%) 58.269 19.352 9.869 8.187 3.656 0.667 Cumulative % 58.269 77.621 87.490 95.677 99.333 100.000

Figure 3: The independent (blue) and cumulative variance captured by each component (red line) Table 3 gives the correlation between the different parameters and tells us how they are related. The data has been normalized before calculating the co-variance matrix. From the table we can observe that porosity, quartz, TOC and mineralogy are inversely proportional to carbonates. However, they are proportional to each other. Similarly the interrelation between other properties can be observed.

0

20

40

60

80

100

0 0.5 1

1.5 2

2.5 3

3.5 4

F1 F2 F3 F4 F5 F6 Cumulative variability (%

)

Eigenvalue

axis

Screen plot

Variable Obs. Minimum Maximum Mean Std deviation

Scaled porosity 168 -2.506 2.787 0.000 1.000 Scaled TOC 168 -2.212 2.268 0.000 1.000

Scaled quartz 168 -1.985 2.257 0.000 1.000 Scaled carbonates 168 -0.913 2.796 0.000 1.000

Scaled illite + chlorite

168 -2.591 2.610 0.000 1.000

Scaled mixed clays 168 -1.336 2.264 0.000 1.000


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Table 3: Correlation between 6 different shale composition parameters.

Table 4 represents the contribution of each petrophysical property to the 3 principal components that captures almost 85% variability. Therefore it is observed that most significant parameters that contribute maximum to the variability are Total Organic Carbon, Carbonates, and Illite + Chlorite. Also, the porosity has very less contribution in variability of the matrix and remains almost constant. Therefore we identify the 3 petrophysical properties Total Organic Carbon, Carbonates and Illite + Chlorite to perform the k-means clustering in order to perform rock typing.

Table 4 : Correlation between various shale composition parameters with principal components.

*Values in bold correspond for each variable to the factor for which the squared cosine is the largest k-means The second step would be to do k-means clustering on the orthogonal data set obtained after based on Lloyd’s algorithm. The algorithm is based on minimizing the sum of squares within the clusters to identify the similar clusters required for classification of rocks.

Covariance matrix (Covariance (n-1)):

Variables Scaled porosity

Scaled TOC

Scaled quartz

Scaled carbonates


Scaled Mixed Clays

Scaled porosity 1 0.309 0.572 -0.551 0.236 0.223 Scaled TOC 0.309 1 0.579 -0.796 0.564 0.507 Scaled quartz 0.572 0.579 1 -0.685 0.153 0.182 Scaled carbonates -0.551 -0.796 -0.685 1 -0.744 -0.615 Scaled illite + chlorite

0.236 0.564 0.153 -0.744 1 0.522

Scaled mixed clays

0.223 0.507 0.182 -0.615 0.522 1

Contribution of the variables (%):

F1 F2 F3 Scaled porosity 10.584 26.691 48.632 Scaled TOC 20.539 0.535 27.877 Scaled quartz 13.900 31.838 12.518 Scaled carbonates 27.250 0.027 0.140 Scaled illite + chlorite 14.928 21.498 2.413 Scaled mixed clays 12.799 19.411 8.421 Squared cosines of the variables:

F1 F2 F3 Scaled porosity 0.370 0.310 0.288 Scaled TOC 0.718 0.006 0.165 Scaled quartz 0.486 0.370 0.074 Scaled carbonates 0.953 0.000 0.001 Scaled illite + chlorite 0.522 0.250 0.014 Scaled mixed clays 0.447 0.225 0.050


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Algorithm: We define k centroids for k clusters. For clustering, we place k centroids very far from each other and arrange the data on minimum distance from the centroid. After this, we identify k new centroids (close to the mean of the data points assigned to it) and try to group the same data set according to the nearest new centroid which is the mean of the data points assigned to it. We repeat this step until a convergence is obtained and there is no movement of data point from one cluster to another. This algorithm is based on minimizing the following distance:

!! = New centroid after every iteration

!! = Data point

Steps for k-means clustering:

1. Plot all the points in the space. These points represent initial group centroids. 2. Assign the data points with respect to the closest centroid according to equation 1. 3. After arranging all the data points, reassign the centroids based on the mean of data points present in the cluster. 4. Repeat Steps 2 and 3 until the data points converge towards common centroid and centroids don’t change. 5. The result of above process clusters the data in specific groups.

Figure 4: Representation of k-means clustering algorithm As we can see that k-means clustering is sensitive to the initial centroids selected, it is sometimes not able to produce the most optimal configuration. Therefore it is an iterative process and is applied multiple times on the data set in order to reduce the error. We can identify any number of data points in any specific number of numbers. PCA points in the direction of maximum variance. Since TOC, Carbonates and Illite +Chlorite have highest variation, they are used for clustering for k-means. XL-STAT was used for performing the k-means and upto 6 classes were used to captured so as to observe the within class variance. 500 iterations were performed to make the results more precise. The summary statistics is given below in the table 5.

1


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Table 5: Summary statistics for k-means for 3 petrophysical properties. Variable Observation Minimum Maximum Mean Std. deviation

Scaled TOC 168 -‐2.212 2.268 0.000 1.000 Scaled carbonates

168 -‐0.913 2.796 0.000 1.000


168 -‐2.591 2.610 0.000 1.000

From the table 6, we can observe that class 1 has maximum within-class variance and we can cluster the data by noting the 3 classes as the change (figure 5) in between-class variance (red line) is almost 0 after 3 classes. Also, there is not a significant change in within–class variance after 3 classes. Therefore we will cluster or differentiate the data into 3 classes.

Table 6: Evolution of variance within classes and between classes Variance\Classes 1 2 3 4 5 6 Within-‐class 3.000 1.124 0.855 0.661 0.584 0.477 Between-‐classes 0.000 1.876 2.145 2.339 2.416 2.523 Total 3.000 3.000 3.000 3.000 3.000 3.000

Figure 5: The between-class variance (red line) and within-class variance (blue line) plotter versus

number of classes. Results: By performing the k-means clustering, we have obtained the following results. Table 8 gives the scaled and the true value of centroid for every petrophysical property in each of the three clusters. Table 9 gives the mean value of every petrophysical property for the 3 clusters.

Table 8: Class Centroids and their true values Class Scaled

TOC Scaled

carbonates Scaled illite + chlorite

Within-‐class

variance

True TOC

True Carbonates

True Illite+Chlorite

1 -‐0.19 -‐0.369 0.382 0.904 3.43637 12.7953 28.9343 2 -‐1.411 1.717 -‐1.38 0.9 1.42739 61.83870 278.597 3 0.978 -‐0.57 0.37 0.779 5.35814 8.0697 28.8283

0

0.5

1

1.5

2

2.5

3

3.5

1 2 3 4 5 6

Within-‐class variance

Number of classes


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Table 9:Class central value and their true values

Class Scaled TOC Scaled carbonates


True TOC True Carbonates

True Illite+Chlorite

1 (6444.5)

-‐0.151 -‐0.394 0.593 3.50053974 12.20761685 30.79640611

2 (6474.5)

-‐1.403 1.941 -‐1.231 1.44055736 67.10510541 14.69934199

3 (6756.4)

0.754 -‐0.628 0.299 4.98958450 6.706112641 28.20181353

Table 10 gives the final clustering of the cores on the basis of these petrophysical properties.

Table 10: Final clustering of the wells done by k-means using PCA on TOC, Illite + Chlorite, and Carbonates

Class 1 2 3 Objects 67 36 65 Within-‐class variance 0.904 0.900 0.779 Minimum distance to centroid 0.216 0.269 0.242 Average distance to centroid 0.835 0.851 0.786 Maximum distance to centroid 2.276 1.620 1.882 6432.5 6438.5 6450.5 6434.5 6456.5 6454.5 6436.5 6458.5 6519.4 6440.6 6463.2 6522.3 6442.5 6464.5 6524.2 6444.5 6466.5 6527.7 6446.5 6468.5 6531.7 6448.4 6470.5 6534 6452.5 6472.7 6535.8 6460.5 6474.5 6542.1 6491 6476.5 6544.1 6493 6478.2 6548.3 6495.2 6480.2 6558.8 6496.8 6482.2 6570.3 6503.6 6484.2 6572 6505.6 6487 6573.8 6507.4 6489 6575.65 6515 6498.6 6578.8 6517.3 6501.2 6580.9 6526.1 6509.5 6585.3 6529.2 6511.2 6589 6538 6513.6 6600 6543 6520.8 6601.4 6546.2 6540 6617 6550.6 6554.6 6619 6552.5 6561.8 6627.5 6556.8 6565.35 6629.3


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6560.6 6583.1 6631.1 6563.6 6591.4 6635.2 6567 6604 6637.1 6568 6633.3 6643.9 6587 6700 6645.9 6593 6722.6 6647.8 6594.6 6745.9 6650 6596.05 6752.6 6652 6598.1 6794 6654 6606 6657.7 6608.7 6660 6611 6662 6613.2 6665.6 6615.1 6669.7 6621 6671.7 6623.2 6673.8 6639.8 6675.6 6641.7 6678.7 6667.6 6680 6669.1 6682 6686 6684 6690 6688 6704.2 6691.9 6708 6693.9 6719 6696 6731 6702.1 6734 6706 6736.1 6709.9 6742.1 6712.1 6750.2 6714 6754.5 6716.3 6760.15 6724.4 6765 6727 6769.1 6729 6771.8 6738.1 6773.9 6744.1 6775.1 6756.4 6780.6 6762.3 6782.2 6784.3 Conclusions: PCA can be used to identify the most varying components and helps in reducing the dimensions of data set for appropriate analysis of k-means. We were successfully able to classify the rocks by using PCA and k-means. We can conclude from the PCA that TOC, Carbonates and Illite+Chlorite are the principal components that capture maximum variability. k-means can cluster the data in any number of classes, however the variance within-class reduces as we increase the number of clusters. The data has been


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clustered into 3 groups to obtain the maximum variation. Most of the rocks (67) belong to class 1 and have mean TOC= 3.5, mean carbonates=12.2 and mean illite +chlorite= 30.7 and least number of rocks (36) belong to cluster 2 and have mean TOC = 1.44, mean carbonates=67.105 and mean illite +chlorite= 14.699. Class 1 has maximum within-class variance and Class 3 has least within-class variance. Acknowledgement The support was this work was provided by Professor Charles Nicholson, University of Oklahoma. Appreciation is extended to Integrated Core Characterization Center, Department of Petroleum Engineering, The University of Oklahoma for providing parameter information about the petrophysical properties for various cores. References Hotelling, H. 1933. Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24, 417-441, and 498-520. Mendelhall, W. & Sincich, T. 2007. Statictics for Engineering and the Sciences, fifth edition. Published by Pearson Prentice Hall Inc., New Jersey. ISBN 0-13-187706-2.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. Prentice Hall, 2007.

Brier, E., Clavier, C., Olivier, F.: Correlation Power Analysis with a Leakage Model. In: CHES. Volume 3156 of LNCS., Springer (2004) 16–29 Cambridge, MA, USA.

Batina, L., Gierlichs, B., Lemke-Rust, K.: Differential Cluster Analysis. In Clavier, C., Gaj, K.,eds.: Cryptographic Hardware and Embedded Systems – CHES 2009. Volume 5747 of Lecture Notes in Computer Science., Lausanne, Switzerland, Springer-Verlag (2009) 112–127

Kumar, V., C.H. Sondergeld, and C.S. Rai. 2012. Nano to macro mechanical characterization of shale. SPE 159804 Presented in SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 8-10 October 2012.DOI 10.2118/159804-MS Appendix The sample data for which rock typing was performed. Depth Corrected

porosity TOC Quartz Carbonates Illite + Chlorite

6432.5 6.67 4.15 38.6 4.7 29.1 14.7 6434.5 6.07 4.25 48.6 14.1 25.4 3.9 6436.5 4.91 3.4 41 8.4 27.7 12.4 6438.5 6 0.39 4.6 75.5 6.9 0 6440.6 5.63 3.9 37 4.9 30.2 8.9 6442.5 5.85 3.95 40.6 6.5 26.5 7.7 6444.5 0.88 3.5 29.3 12.2 30.8 14.9 6446.5 6.14 4.12 43.1 16.4 23.8 4.4 6448.4 5.27 3.61 33.7 27.8 27.6 1 6450.5 6.02 5.92 54.8 3.3 18.6 9.8 6452.5 4.46 3.15 50 13.3 21.9 0 6454.5 5.27 4.68 42.1 18.2 16 11.4 6456.5 4.42 2.49 27.3 42.7 17.9 1.5 6458.5 5.55 1.7 35.6 32.5 13.6 6.4 6460.5 5.09 3.49 40.9 6.7 27.4 12.9


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6463.2 2.52 2.5 20.4 48.8 21.2 0 6464.5 2.7 1.51 3.7 68.9 14.4 2.1 6466.5 2.77 1.7 11.1 54.7 21.5 0 6468.5 2.09 0.83 6.8 73.6 11.5 0 6470.5 1.96 1.14 10.6 62.3 19.6 0 6472.7 2.13 1.29 10.3 63.5 19 0 6474.5 2.74 1.44 8.4 67.1 14.7 0 6476.5 2.03 0.49 1.8 75.3 11.3 0 6478.2 2.16 0.64 0 87.2 7.8 0 6480.2 2.65 0.8 4.3 79.9 10.7 0 6482.2 2.34 0.92 6.4 73.5 9.5 2.3 6484.2 1.79 0.53 0 76.2 16.4 0 6487 2.61 1.09 12.7 67.5 12.2 0 6489 4.46 1.12 11.3 58.5 15.6 3.1 6491 6.38 2.84 3.9 7.1 42.4 26.1 6493 3.39 2.23 18.1 27.5 31.3 13.2 6495.2 6.39 2.87 5 7.4 44.1 25.4 6496.8 5.38 2.17 4.4 21 39 19.3 6498.6 3.34 1.67 14.4 47.1 19.5 7.9 6501.2 2.73 1.07 2.3 65.4 13.9 0 6503.6 5.22 2.34 10.4 25.6 28.1 20.2 6505.6 4.83 2.44 9.8 20.3 32.5 21.3 6507.4 3.66 2.69 7.2 21.1 34.7 19.7 6509.5 1.82 1.11 6.3 76.2 12.1 0 6511.2 1.49 0.97 6.7 75.7 10.2 0 6513.6 3.19 1.67 14.2 56.2 16.8 4.9 6515 4.13 3.46 30.3 10.2 30.8 17.7 6517.3 3.82 3.23 20 33.6 23.2 0 6519.4 4.59 4.72 36.7 15.3 21.3 17.5 6520.8 3.72 2.57 29.4 37.5 13.1 3.2 6522.3 5.57 4.78 30.6 5.4 32.8 17.7 6524.2 5.3 5.58 43.8 9.7 23 15.6 6526.1 4.14 3.2 39.4 19.7 19.3 12.2 6527.7 5.11 6.01 34.8 6.3 26.4 20.8 6529.2 3.86 3.46 37.8 18.4 26.8 2.4 6531.7 4.8 4.68 38.7 8.6 28.9 15.7 6534 4.38 5.2 29 7.2 24.2 27.1 6535.8 4.46 4.87 25.3 11.9 29.9 15.5 6538 4.14 4.36 29.1 15.4 28.7 9.8 6540 1.47 1.24 14.4 33.4 20 14.2 6542.1 5.88 5.15 39.5 6.4 24.8 8.2 6543 7.11 3.91 59.4 6.5 14.2 0.1 6544.1 6.86 4.42 54.7 6 13.9 9.6 6546.2 6.17 3.59 51.2 7.7 21.3 5.9 6548.3 6.31 4.69 44.8 5.9 26.3 14.2 6550.6 4.64 3.96 35.7 10.2 30.2 2.9 6552.5 5.19 2.9 42.8 4.1 30.6 6.3 6554.6 2.99 2 25.4 40.2 13.8 0


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6556.8 6.15 3.86 43.7 4.3 29.6 5.4 6558.8 5.81 5.02 41.8 4.9 32.9 6.8 6560.6 5.28 3.9 37.5 5.3 28.5 20 6561.8 1.8 0.8 12.1 67.7 8.6 0 6563.6 4.51 3.35 20.9 30.6 24.1 8.6 6565.35 2.59 1.3 8.5 73.9 13.6 0 6567 5.18 3.72 41.9 2.3 30.2 10.8 6568 6.06 3.95 38.7 5.3 23.3 22.5 6570.3 5.89 4.53 47 3.3 30.7 8.7 6572 5.76 4.36 44.2 2.2 26.8 19.9 6573.8 4.99 4.66 31.2 25.2 23.9 3.7 6575.65 5.72 5.18 44.1 4.7 30.8 4.2 6578.8 5.12 5.76 37.4 6.2 26.8 12.6 6580.9 5.75 5.09 41.7 8.8 30.4 5 6583.1 4.75 2.97 36.2 35.8 8.2 7.4 6585.3 1.41 4.91 25.5 8.2 26.7 15.9 6587 4.48 3.89 23.6 15.3 20.3 0 6589 5.22 4.69 33.7 5.5 29.6 11.7 6591.4 4.4 2.64 23.2 41.2 15.5 8.8 6593 5.34 4 33 9.1 27.7 4.1 6594.6 5.54 3.71 40.9 10 22.2 14.9 6596.05 7.02 3.38 38 7.9 16.9 0 6598.1 6.71 4.11 51.4 6.1 28.2 9.4 6600 5.91 5.3 50.3 6 21.2 8.7 6601.4 6.08 4.5 59.2 12.7 17.4 0 6604 4.1 1.79 9.3 56.7 14.2 8.9 6606 4.74 3.79 26 3.1 35.6 21.8 6608.7 6 4.06 43.8 4 26 16.9 6611 3.4 3.66 38.6 4.7 25.3 21 6613.2 5.1 2.82 9.7 7.3 34 0 6615.1 4.39 3.72 37 7.9 26.6 15.4 6617 4.8 4.61 35 4.5 26.7 23 6619 3.54 5.35 34.5 23.7 18.8 0 6621 3.22 4.27 34.1 2.8 27.6 8.3 6623.2 4.98 4 26.5 5 29.2 24.9 6627.5 4.06 6.23 30.4 4.5 22.1 24 6629.3 4.4 4.64 34 4.8 31.6 20.1 6631.1 3.97 5.41 33.6 6.5 26.5 23 6633.3 3.17 1.98 19.1 62.7 7.7 0 6635.2 4.63 4.62 35.7 5.5 23.1 25.5 6637.1 4.73 5.55 39.5 4.8 23.6 19.3 6639.8 4.23 3.43 36.1 8.6 26.8 14.9 6641.7 8.05 3.48 26.5 4.9 22.5 30.4 6643.9 4.64 4.85 23.7 2.3 35.1 14.2 6645.9 5.04 4.94 28.5 4.1 35.4 21 6647.8 4.47 4.99 28.2 5 36.2 20.3 6650 4.61 5.09 28.1 3.7 39.1 18.6 6652 4.01 4.92 33.2 5.2 40 8.7


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6654 3.77 4.42 33.2 5.1 33.1 19.4 6657.7 3.38 6.76 31.1 5.4 26.2 26.5 6660 3.01 5.86 32.6 6.9 23.7 28.6 6662 3.58 5.49 30.8 17.5 30.8 12.1 6665.6 3.99 6.81 46.3 8.4 26.4 10.8 6667.6 5.43 3.67 37.8 15.8 20.5 21.1 6669.1 4.38 3.9 24.5 20 24.3 22.2 6669.7 2.05 6.77 20.1 5.1 32.9 27.5 6671.7 4.82 5.83 40.4 5.8 29.8 15.9 6673.8 4.13 6.69 42.1 7.1 32 9.6 6675.6 4.51 5.86 32.1 5.7 31.1 23.9 6678.7 3.96 7.48 29.7 4.5 35.9 23.3 6680 3.42 7.21 26.7 6.3 30.6 25.8 6682 3.77 5.71 37.9 5.4 26.4 22.5 6684 4.48 4.72 34.8 4.5 30.5 18.9 6686 4.81 3.72 37.8 3.8 35.5 19.3 6688 3.26 5.01 42.3 13.2 31.2 3.5 6690 3.41 4.18 36.3 5.6 26.8 25.3 6691.9 4.85 4.98 43.2 7.5 20.7 19 6693.9 3.92 5.1 28.4 3.7 35.3 21.7 6696 3.59 5.79 28.1 7.8 34.5 13.9 6700 1.41 0.72 5.2 81.6 2.7 3.4 6702.1 3.57 6.31 23.1 4.1 30 24.3 6704.2 3.32 3.55 16.8 6.7 38.9 7.7 6706 3.45 6.94 29.6 0 31.1 9.6 6708 5.23 3.8 20.8 1.7 43.9 18.4 6709.9 4.61 5.11 17.7 13 34.9 12.6 6712.1 4.61 5.07 19.1 2.9 37.9 23.7 6714 3.74 6.73 17.3 5.1 36.5 15.8 6716.3 3.75 5.39 32.6 15.5 26.8 12.1 6719 4.75 3.59 15.2 2.1 48.6 18.9 6722.6 3.54 2.73 10.9 55.1 18.1 9.1 6724.4 3.9 4.88 31.7 6 30.8 20.7 6727 4.2 5.49 12.8 5.5 38 0 6729 3.4 4.78 10.8 27.4 27.4 6.2 6731 3.66 2.67 10.8 42.1 23.3 13.1 6734 4.25 3.09 20 13.9 40 10.1 6736.1 3.51 4.38 18.2 12.4 37.7 6.5 6738.1 3.34 6.75 12.8 4.2 43.6 2.2 6742.1 4.08 3.94 19.5 4 43.9 17.7 6744.1 2.54 4.86 17.6 28.8 36.7 8.3 6745.9 1.35 1.7 6.4 72 11.6 0 6750.2 2.99 3.95 30 30.5 26.3 6.4 6752.6 2.81 1.75 8.7 53 13.1 5.6 6754.5 5.41 2.83 33.4 3.9 25.7 16.3 6756.4 6.37 4.99 43.4 6.7 28.2 7.3 6760.15 3.84 3.42 39.3 31.3 19.8 1.6 6762.3 4.65 4.56 50 18.5 19.6 4.8


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6765 4.39 2.78 21.6 35.9 22.4 10 6769.1 3.46 2.91 29.3 19.2 28.9 13.5 6771.8 3.86 1.53 43.1 8.9 28.7 9.8 6773.9 3.77 2.06 26.7 20.8 30.2 11.5 6775.1 4.6 3.52 31 5.8 34.3 11.8 6780.6 4.16 2.47 16 13.9 30.4 19 6782.2 2.49 2.32 24.8 26.1 27 12.6 6784.3 2.99 3.66 20.2 17 29.3 12.4 6794 6.28 0.11 0 87.2 5.4 0

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