Applied Geostatistics in R: 9. K-Means Clustering Analysis for Facies Classification in a Sandstone Formation
Watheq J. Al-Mudhafar, Craft and Hawkins Department of Petroleum Engineering, Louisiana State University
August 29, 2015
In cluster analysis, the k-means algorithm can be used to partition the input data set into k partitions (clusters). The current dataset include core and well log measurements and K-means was used to predict the vertical discrete Facies sequence in a well in sandstone formation.
Install the packages required to implement K-means algorithm with their functions.
require(MASS)## Loading required package: MASSrequire(fpc)## Loading required package: fpcrequire(Rcmdr)## Loading required package: Rcmdr
## Loading required package: splines
## Loading required package: RcmdrMisc
## Loading required package: car
## Loading required package: sandwich
## The Commander GUI is launched only in interactive sessionsrequire(cluster)## Loading required package: clusterlibrary(MASS)
library(Rcmdr)
library(fpc)
library(cluster)Call the dataset and visualize it: -
## depth caliper ind.deep ind.med gamma phi.N R.deep R.med SP
## 1 5667.0 8.685 618.005 569.781 98.823 0.410 1.618 1.755 -56.587
## 2 5667.5 8.686 497.547 419.494 90.640 0.307 2.010 2.384 -61.916
## 3 5668.0 8.686 384.935 300.155 78.087 0.203 2.598 3.332 -55.861
## 4 5668.5 8.686 278.324 205.224 66.232 0.119 3.593 4.873 -41.860
## 5 5669.0 8.686 183.743 131.155 59.807 0.069 5.442 7.625 -34.934
## 6 5669.5 8.686 109.512 75.633 57.109 0.048 9.131 13.222 -39.769
## density.corr density phi.core k.core
## 1 -0.033 2.205 33.9000 2442.590
## 2 -0.067 2.040 33.4131 3006.989
## 3 -0.064 1.888 33.1000 3370.000
## 4 -0.053 1.794 34.9000 2270.000
## 5 -0.054 1.758 35.0644 2530.758
## 6 -0.058 1.759 35.3152 2928.314
Prepare Data by listwise deletion of missing in addition to standardize variables :
## depth caliper ind.deep ind.med gamma phi.N R.deep
## 1 -1.715835 0.5760810 1.3474389 1.2181334 2.3964234 2.570248 -0.6508649
## 2 -1.711672 0.5852006 0.8737459 0.6005397 1.9644806 1.167356 -0.6397151
## 3 -1.707509 0.5852006 0.4309067 0.1101246 1.3018655 -0.249157 -0.6229904
## 4 -1.703345 0.5852006 0.0116661 -0.2799876 0.6760947 -1.393263 -0.5946892
## 5 -1.699182 0.5852006 -0.3602674 -0.5843689 0.3369486 -2.074279 -0.5420973
## 6 -1.695018 0.5852006 -0.6521758 -0.8125326 0.1945336 -2.360306 -0.4371695
## R.med SP density.corr density phi.core k.core
## 1 -0.7059954 -1.5377911 -1.422375 0.8253632 1.526011 0.085294626
## 2 -0.6831533 -1.8577737 -3.427612 -0.4936933 1.419359 0.337753183
## 3 -0.6487268 -1.4941980 -3.250679 -1.7088241 1.350777 0.500130034
## 4 -0.5927655 -0.6535007 -2.601926 -2.4602866 1.745053 0.008094151
## 5 -0.4928268 -0.2376254 -2.660904 -2.7480807 1.781063 0.124732644
## 6 -0.2895722 -0.5279455 -2.896814 -2.7400864 1.835999 0.302561390Determine number of clusters that are derived from the dataset through K-means and Partitioning Around Medoids:
## number of clusters estimated by optimum average silhouette width: 5
## silhouette-optimal number of clusters: 5It was noticeable that the number of facies that can be derived from the given dataset are Five Facies. Now we adopt K-Means Clustering Algorithm to predict the discrete sequence of the five facies distrbution.
## $cluster
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
## 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
## 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2
## 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216
## 2 2 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
## 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 1 1 1
## 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3
## 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324
## 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342
## 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360
## 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2
## 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 3
## 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396
## 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414
## 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2
## 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468
## 2 2 2 2 2 2 2 4 4 4 4 4 4 3 3 3 3 3
## 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486
## 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504
## 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522
## 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540
## 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558
## 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576
## 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594
## 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4
## 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612
## 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
## 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630
## 5 4 4 4 4 4 4 5 5 5 4 4 4 4 4 4 4 4
## 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648
## 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666
## 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684
## 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702
## 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720
## 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738
## 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756
## 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774
## 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792
## 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810
## 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5
## 811 812 813 814 815 816 817 818 819
## 5 5 5 4 4 4 4 4 4
##
## $centers
## depth caliper ind.deep ind.med gamma phi.N
## 1 -1.3159021 0.4681551 -0.88842264 -0.9248661 -0.05383081 -1.8733059
## 2 -0.6354768 1.0052187 0.06306484 0.1651123 1.15778722 0.4849125
## 3 0.1696191 -0.7965027 -0.98085607 -1.0156080 -0.84206089 0.2325962
## 4 1.2027821 -0.5234476 1.20484192 1.1475601 -0.19455217 0.4176434
## 5 1.2265050 -0.5882669 1.75323048 1.7728310 -1.14660486 0.4035138
## R.deep R.med SP density.corr density phi.core
## 1 0.3244141 0.4382221 -0.90978060 -1.57851676 -1.4559977 0.80671775
## 2 -0.5757210 -0.6336317 0.26662821 0.80744088 1.2354105 -1.24781792
## 3 1.1728269 1.2261746 -0.08672092 -0.06107041 -0.4522229 0.63534171
## 4 -0.6450433 -0.7004089 0.29047931 0.19263719 0.1178305 0.06297222
## 5 -0.6573654 -0.7181433 0.63786100 0.20349333 -0.2901632 0.77008611
## k.core
## 1 0.2190921
## 2 -0.6863142
## 3 0.8672108
## 4 -0.5407442
## 5 1.5601515
##
## $totss
## [1] 10634
##
## $withinss
## [1] 474.2580 1293.8665 1185.8267 409.5618 189.2156
##
## $tot.withinss
## [1] 3552.729
##
## $betweenss
## [1] 7081.271Then get cluster means and append cluster assignment with the standerized dataset.
## Group.1 depth caliper ind.deep ind.med gamma
## 1 1 -1.3159021 0.4681551 -0.88842264 -0.9248661 -0.05383081
## 2 2 -0.6354768 1.0052187 0.06306484 0.1651123 1.15778722
## 3 3 0.1696191 -0.7965027 -0.98085607 -1.0156080 -0.84206089
## 4 4 1.2027821 -0.5234476 1.20484192 1.1475601 -0.19455217
## 5 5 1.2265050 -0.5882669 1.75323048 1.7728310 -1.14660486
## phi.N R.deep R.med SP density.corr density
## 1 -1.8733059 0.3244141 0.4382221 -0.90978060 -1.57851676 -1.4559977
## 2 0.4849125 -0.5757210 -0.6336317 0.26662821 0.80744088 1.2354105
## 3 0.2325962 1.1728269 1.2261746 -0.08672092 -0.06107041 -0.4522229
## 4 0.4176434 -0.6450433 -0.7004089 0.29047931 0.19263719 0.1178305
## 5 0.4035138 -0.6573654 -0.7181433 0.63786100 0.20349333 -0.2901632
## phi.core k.core
## 1 0.80671775 0.2190921
## 2 -1.24781792 -0.6863142
## 3 0.63534171 0.8672108
## 4 0.06297222 -0.5407442
## 5 0.77008611 1.5601515## depth caliper ind.deep ind.med gamma phi.N R.deep
## 1 -1.715835 0.5760810 1.3474389 1.2181334 2.3964234 2.570248 -0.6508649
## 2 -1.711672 0.5852006 0.8737459 0.6005397 1.9644806 1.167356 -0.6397151
## 3 -1.707509 0.5852006 0.4309067 0.1101246 1.3018655 -0.249157 -0.6229904
## 4 -1.703345 0.5852006 0.0116661 -0.2799876 0.6760947 -1.393263 -0.5946892
## 5 -1.699182 0.5852006 -0.3602674 -0.5843689 0.3369486 -2.074279 -0.5420973
## 6 -1.695018 0.5852006 -0.6521758 -0.8125326 0.1945336 -2.360306 -0.4371695
## R.med SP density.corr density phi.core k.core
## 1 -0.7059954 -1.5377911 -1.422375 0.8253632 1.526011 0.085294626
## 2 -0.6831533 -1.8577737 -3.427612 -0.4936933 1.419359 0.337753183
## 3 -0.6487268 -1.4941980 -3.250679 -1.7088241 1.350777 0.500130034
## 4 -0.5927655 -0.6535007 -2.601926 -2.4602866 1.745053 0.008094151
## 5 -0.4928268 -0.2376254 -2.660904 -2.7480807 1.781063 0.124732644
## 6 -0.2895722 -0.5279455 -2.896814 -2.7400864 1.835999 0.302561390
## fit.cluster
## 1 2
## 2 1
## 3 1
## 4 1
## 5 1
## 6 1The, plot the optimal five facies:
Visualizing the box plot and distribution of the predicted discrete five Facies.
References
Al-Mudhafar, W. & Bondereko, M. Integrating K-Means Clustering Analysis and General- ized Additive Model for Efficient Reservoir Characterization. Paper presented at the 77th EAGE Conference & Exhibition Incorporating SPE EUROPIC, Madrid, Spain, 1-4 June 2015.
Al-Mudhafar, W. & Zein Al-Abideen, M. Integration Clustering Analysis & Support Vector Machines for Predicting Continuous Electrofacies Posterior Distribution. In Proceedings of Near Surface Geoscience–20th European Meeting of Environmental and Engineering Geophysics, Athens, Greece, 14-18 September 2014.
Karpur, L., L. Lake, and K. Sepehrnoori. (2000). Probability Logs for Facies Classification. In Situ 24(1): 57.