Properti Reservoir Model Nugget (C0) Sill (C0+C) RSS

(a) Porositas

(Min)

Linear 0.005989 0.005989 1.405 x 10-5 Spherical 0.000010 0.006100 1.145 x 10-5 Exponential 0.000420 0.006120 1.153 x 10-5 Gaussian 0.000820 0.006110 1.143 x 10-5

(b) Saturasi Air (Min)

Linear 0.001555 0.020769 1.761 x 10-4 Spherical 0.000010 0.017720 1.161 x 10-4 Exponential 0.000010 0.027220 1.471 x 10-4 Gaussian 0.001010 0.018520 9.821 x 10-5

(c) Porositas x Saturasi Air (Min)

Linear -0.000001 -3.661 x 10-7 4.091 x 10-5 Spherical -0.000001 -0.001762 3.740 x 10-5 Exponential -0.000001 -0.002862 3.757 x 10-5 Gaussian -0.000010 -0.006040 3.548 x 10-5

0.000E+00

1.880E-03

3.761E-03

5.641E-03

7.521E-03

0.00 2255.14 4510.27 6765.41

Sem

ivariance

Separation Distance (h)

Por_Min: Isotropic Variogram

Gaussian model (Co = 0.00082; Co + C = 0.00611; Ao = 310.00; r2 = 0.187; RSS = 1.143E-05)

0.0000

0.0052

0.0103

0.0155

0.0206

0.00 2255.14 4510.27 6765.41

Sem

ivariance

Separation Distance (h)

Sw _Min: Isotropic Variogram

Gaussian model (Co = 0.00101; Co + C = 0.01852; Ao = 3060.00; r2 = 0.852; RSS = 9.821E-05)

-3.328E-03

-1.746E-03

-1.649E-04

1.417E-03

2.998E-03

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Por_Min x Sw _Min: Isotropic Cross Variogram

Gaussian model (Co = -0.00001; Co + C = -0.00604; Ao = 13910.00; r2 = 0.209; RSS = 3.548E-05)

Variogram isotropi

(a) Model Gaussian (b) Model Gaussian

(c) Model Gaussian

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (2a) Porositas Minimum

Variogram anisotropi Properti

Reservoir Model Nugget (C0) Sill (C0+C) RSS

(a) Porositas

(Min)

Linear 0.005900 0.017644 2.326 x 10-4 Spherical 0.005900 0.017644 2.326 x 10-4 Exponential 0.005900 0.017644 2.326 x 10-4 Gaussian 0.006000 0.017744 2.325 x 10-4

(b) Saturasi Air (Min)

Linear 0.002400 0.044914 3.964 x 10-3 Spherical 0.001900 0.043014 3.926 x 10-3 Exponential 0.000400 0.041514 3.815 x 10-3 Gaussian 0.005400 0.046514 4.294 x 10-3

(c) Porositas x Saturasi Air

(Min)

Linear -0.000010 -0.009820 4.334 x 10-4 Spherical -0.000010 -0.009820 4.352 x 10-4 Exponential -0.000010 -0.009820 4.316 x 10-4 Gaussian -0.000100 -0.029420 4.198 x 10-4

0.0000

0.0029

0.0058

0.0087

0.0116

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Por_Min: Anisotropic Variogram (0º)

Gaussian model (Co = 0.00600; Co + C = 0.01774; AMajor = 751300.00; AMinor = 751300.00; r2 = 0.119; RSS = 2.325E-04)

0.0000

0.0103

0.0205

0.0308

0.0410

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Sw _Min: Anisotropic Variogram (0º)

Exponential model (Co = 0.00040; Co + C = 0.04151; AMajor = 13710.00; AMinor = 6810.00; r2 = 0.376; RSS = 3.815E-03)

-9.800E-03

-5.790E-03

-1.779E-03

2.231E-03

6.242E-03

0.00 2255.14 4510.27 6765.41Se

miva

rianc

e

Separation Distance (h)

Por_Min x Sw _Min: Anisotropic Cross Variogram (0º)

Gaussian model (Co = -0.00010; Co + C = -0.02942; AMajor = 70790.00; AMinor = 19620.00; r2 = 0.178; RSS = 4.198E-04)

(a) Model Gaussian (b) Model Eksponential

(c) Model Gaussian 22

Well Name

Koord. X Koord.Y Data

Aktual Estimasi Isotropi

Estimasi Anisotropi

AU-16 230662.8 9399394 0.078538 0.107 0.060 AUA-5 227441.9 9410011 0 0.136 0.176 AUB-5 226485.2 9408922 0.246595 0.024 0.047 AUC-5 227984 9408461 0.056055 0.053 0.077 AUD-5 229513.4 9408031 0.071253 0.000 0.006 AUE-5 226521.9 9407448 0.245034 0.073 0.043 AUF-5 228048.5 9406977 0.005828 0.192 0.119 AUG-5 229543.8 9406584 0.117598 0.210 0.198 AUK-3 229107.8 9401041.29 0.0055 0.065 0.065 AZZ-1 226990.1 9411303 0.133 0.233 0.230

-0.06

0.02

0.11

0.19

0.28

-0.06 0.05 0.17 0.28

Actu

al Po

r_M

in

Estimated Por_Min

Regression coeff icient = 0.679 (SE = 0.083 , r2 =0.568,y intercept = 0.03, SE Prediction = 0.053, n = 53)

-0.07

0.03

0.13

0.23

0.34

-0.07 0.06 0.20 0.34

Actu

al Po

r_M

in

Estimated Por_Min

Regression coeff icient = 0.630 (SE = 0.088 , r2 =0.499,y intercept = 0.04, SE Prediction = 0.057, n = 53)

0

0,05

0,1

0,15

0,2

0,25

0,3

Data Aktual

Estimasi Isotropi

Estimasi Anisotropi

Cross-Variogram Isotropi Cross-Variogram Anisotropi

R2 =56.8% R2 =49.9%

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (2a) Porositas Minimum

23

Variogram isotropi Properti

Reservoir Model Nugget (C0) Sill (C0+C) RSS

(a) Porositas (Mean)

Linear 0.000743 0.005036 8.965 x 10-6 Spherical 0.000720 0.007550 9.148 x 10-6 Exponential 0.000640 0.014890 9.394 x 10-6 Gaussian 0.001260 0.006530 7.704 x 10-6

(b) Saturasi Air (Mean)

Linear 0.006782 0.039250 3.847 x 10-4 Spherical 0.001900 0.034300 2.454 x 10-4 Exponential 0.001500 0.045400 3.065 x 10-4 Gaussian 0.006480 0.035360 2.286 x 10-4

(c) Porositas x Saturasi Air

(Mean)

Linear -0.000010 -0.000001 5.056 x 10-4 Spherical -0.000010 -0.009420 5.220 x 10-5 Exponential -0.000010 -0.023720 5.341 x 10-5 Gaussian -0.000300 -0.009500 4.589 x 10-5

0.000E+00

1.726E-03

3.452E-03

5.177E-03

6.903E-03

0.00 2255.14 4510.27 6765.41

Sem

ivariance

Separation Distance (h)

Isotropic Variogram

Gaussian model (Co = 0.00126; Co + C = 0.00653; Ao = 5690.00; r2 = 0.769; RSS = 7.704E-06)

0.0000

0.0104

0.0208

0.0311

0.0415

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Isotropic Variogram

Gaussian model (Co = 0.00648; Co + C = 0.03536; Ao = 3120.00; r2 = 0.871; RSS = 2.286E-04)

-0.0134

-0.0100

-0.0067

-0.0033

0.0000

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

x : Isotropic Cross Variogram

Gaussian model (Co = -0.00030; Co + C = -0.00950; Ao = 4050.00; r2 = 0.736; RSS = 4.589E-05)

(a) Model Gaussian (b) Model Gaussian

(c) Model Gaussian

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (2b) Porositas Mean

Variogram anisotropi Properti

Reservoir Model Nugget (C0) Sill (C0+C) RSS

Porositas (Mean)

Linear 0.000400 0.013983 1.805 x 10-4 Spherical 0.000300 0.012983 1.816 x 10-4 Exponential 0.000500 0.016183 1.841 x 10-4 Gaussian 0.001200 0.013883 1.805 x 10-4

Saturasi Air (Mean)

Linear 0.008300 0.078779 7.471 x 10-3 Spherical 0.007700 0.074679 7.418 x 10-3 Exponential 0.005500 0.072479 7.267 x 10-3 Gaussian 0.013300 0.080279 8.169 x 10-3

Porositas x Saturasi Air

(Mean)

Linear -0.000100 -0.094567 6.742 x 10-4 Spherical -0.000100 -0.065667 6.741 x 10-4 Exponential -0.000100 -0.094467 6.727 x 10-4 Gaussian -0.002000 -0.217867 7.454 x 10-4

0.0000

0.0031

0.0063

0.0094

0.0126

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Anisotropic Variogram (0º)

Gaussian model (Co = 0.00120; Co + C = 0.01388; AMajor = 9183.00; AMinor = 9183.00; r2 = 0.541; RSS = 1.722E-04)

0.0000

0.0167

0.0334

0.0502

0.0669

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Anisotropic Variogram (0º)

Exponential model (Co = 0.00550; Co + C = 0.07248; AMajor = 14560.00; AMinor = 7000.00; r2 = 0.384; RSS = 7.267E-03)

-0.0197

-0.0146

-0.0095

-0.0044

0.0007

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

x : Anisotropic Cross Variogram (0º)

Exponential model (Co = -0.00010; Co + C = -0.09447; AMajor = 74020.00; AMinor = 52740.00; r2 = 0.452; RSS = 6.727E-04)

(a) Model Gaussian (b) Model Exponential

(c) Model Exponential 24

Well Name

Koord. X Koord.Y Data

Aktual Estimasi Isotropi

Estimasi Anisotropi

ZU-16 230662.8 9399394 0.259356 0.270 0.180 ZUA-5 227441.9 9410011 0.288877 0.293 0.297 ZUB-5 226485.2 9408922 0.351903 0.280 0.280 ZUC-5 227984 9408461 0.226796 0.310 0.300 ZUD-5 229513.4 9408031 0.242863 0.246 0.266 ZUE-5 226521.9 9407448 0.314740 0.290 0.284 ZUF-5 228048.5 9406977 0.275069 0.301 0.300 ZUG-5 229543.8 9406584 0.262654 0.339 0.321 ZUK-3 229107.8 9401041.29 0.208200 0.202 0.190 ZZZ-1 226990.1 9411303 0.321367 0.320 0.320

0.14

0.20

0.26

0.32

0.38

0.14 0.22 0.30 0.38

Actu

al

Estimated

Regression coeff icient = 1.230 (SE = 0.070 , r2 =0.859,y intercept = -0.07, SE Prediction = 0.020, n = 53)

0.14

0.20

0.26

0.32

0.38

0.14 0.22 0.30 0.38

Actu

al

Estimated

Regression coeff icient = 1.196 (SE = 0.057 , r2 =0.897,y intercept = -0.05, SE Prediction = 0.017, n = 53)

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

Data Aktual

Estimasi Isotropi

Estimasi Anisotropi

Cross-Variogram Isotropi Cross-Variogram Anisotropi

R2 =89.7% R2 =85.9%

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (2b) Porositas Mean

25

Properti Reservoir Model Nugget

(C0) Sill (C0+C) RSS

(a) Porositas

(Max)

Linear 0.000461 0.005067 1.087 x 10-5 Spherical 0.000330 0.005660 1.090 x 10-5 Exponential 0.000260 0.011880 1.120 x 10-5 Gaussian 0.000860 0.005560 9.177 x 10-6

(b) Saturasi Air (Max)

Linear 0.049691 0.069128 8.398 x 10-4 Spherical 0.019900 0.062900 4.859 x 10-4 Exponential 0.000100 0.063300 4.517 x 10-4 Gaussian 0.028500 0.063000 4.780 x 10-4

(c) Porositas x Saturasi Air

(Max)

Linear -0.000010 -0.000001 1.189 x 10-4 Spherical -0.000010 -0.008990 2.898 x 10-5 Exponential -0.000010 -0.014740 3.015 x 10-5 Gaussian -0.000010 -0.011210 2.158 x 10-5

0.000E+00

1.701E-03

3.403E-03

5.104E-03

6.805E-03

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Isotropic Variogram

Gaussian model (Co = 0.00086; Co + C = 0.00556; Ao = 4580.00; r2 = 0.764; RSS = 9.177E-06)

0.0000

0.0186

0.0371

0.0557

0.0743

0.00 2255.14 4510.27 6765.41

Sem

ivariance

Separation Distance (h)

Isotropic Variogram

Exponential model (Co = 0.00010; Co + C = 0.06330; Ao = 460.00; r2 = 0.666; RSS = 4.517E-04)

-70.188E-04

-50.145E-04

-30.103E-04

-10.061E-04

99.808E-05

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

x : Isotropic Cross Variogram

Gaussian model (Co = -0.00001; Co + C = -0.01121; Ao = 8570.00; r2 = 0.649; RSS = 2.158E-05)

(a) Model Gaussian (b) Model Exponential

(c) Model Gaussian

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (2c) Porositas Maximum

Variogram isotropi

Variogram anisotropi Properti

Reservoir Model Nugget (C0) Sill (C0+C) RSS

(a) Porositas

(Max)

Linear 0.000200 0.014450 3.020 x 10-4 Spherical 0.000200 0.014450 3.019 x 10-4 Exponential 0.000100 0.013750 3.046 x 10-4 Gaussian 0.001000 0.014650 3.023 x 10-4

(b) Saturasi Air (Max)

Linear 0.030000 0.192400 0.0409 Spherical 0.028000 0.190400 0.0420 Exponential 0.024000 0.186400 0.0423 Gaussian 0.048000 0.210400 0.0376

(c) Porositas x Saturasi Air

(Max)

Linear -0.000100 -0.082200 2.930 x 10-3 Spherical -0.000100 -0.053100 2.931 x 10-3 Exponential -0.000100 -0.082100 2.938 x 10-3 Gaussian -0.003000 -0.260700 3.169 x 10-3

0.0000

0.0034

0.0068

0.0102

0.0136

0.00 2255.14 4510.27 6765.41

Sem

ivaria

nce

Separation Distance (h)

Anisotropic Variogram (0º)

Spherical model (Co = 0.00020; Co + C = 0.01445; AMajor = 24370.00; AMinor = 24370.00; r2 = 0.534; RSS = 3.019E-04)

0.000

0.040

0.081

0.121

0.161

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Anisotropic Variogram (0º)

Gaussian model (Co = 0.04800; Co + C = 0.21040; AMajor = 12770.00; AMinor = 12770.00; r2 = 0.173; RSS = 0.0376)

-0.0467

-0.0339

-0.0211

-0.0083

0.0046

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

x : Anisotropic Cross Variogram (0º)

Linear model (Co = -0.00010; Co + C = -0.08220; AMajor = 74650.00; AMinor = 74650.00; r2 = 0.225; RSS = 2.930E-03)

(a) Model Spherical (b) Model Gaussian

(c) Model Linear 26

Well Name

Koord. X Koord.Y Data

Aktual Estimasi Isotropi

Estimasi Anisotropi

ZU-16 230662.8 9399394 0.367488 0.390 0.330 ZUA-5 227441.9 9410011 0.379958 0.340 0.390 ZUB-5 226485.2 9408922 0.403155 0.340 0.380 ZUC-5 227984 9408461 0.364601 0.399 0.409 ZUD-5 229513.4 9408031 0.322108 0.450 0.420 ZUE-5 226521.9 9407448 0.374384 0.348 0.390 ZUF-5 228048.5 9406977 0.427058 0.390 0.400 ZUG-5 229543.8 9406584 0.407871 0.420 0.400 ZUK-3 229107.8 9401041.29 0.388924 0.370 0.305 ZZZ-1 226990.1 9411303 0.417000 0.357 0.380

0.24

0.30

0.35

0.41

0.46

0.24 0.31 0.39 0.46

Actu

al

Estimated

Regression coeff icient = 1.215 (SE = 0.029 , r2 =0.971,y intercept = -0.08, SE Prediction = 0.009, n = 53)

0.24

0.30

0.35

0.41

0.46

0.24 0.31 0.39 0.46

Actu

al

Estimated

Regression coeff icient = 1.126 (SE = 0.129 , r2 =0.601,y intercept = -0.05, SE Prediction = 0.034, n = 53)

0 0,05

0,1 0,15

0,2 0,25

0,3 0,35

0,4 0,45

0,5

Data Aktual

Estimasi Isotropi

Estimasi Anisotropi

R2 =60.1% R2 =97.1%

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (2c) Porositas Maximum

Cross-Variogram Isotropi Cross-Variogram Anisotropi

27

Properti Reservoir Model Nugget (C0) Sill (C0+C) RSS

(a) Porositas

(Max)

Linear Linear 0.001555 0.020769 Spherical Spherical 0.000010 0.017720 Exponential Exponential 0.000010 0.026020 Gaussian Gaussian 0.001050 0.018600

(b) Saturasi Air (Max)

Linear 0.005989 0.005989 1.405 x 10-5 Spherical 0.000010 0.006100 1.145 x 10-5 Exponential 0.000010 0.006120 1.151 x 10-5 Gaussian 0.000010 0.006110 1.143 x 10-5

(c) Porositas x Saturasi Air

(Max)

Linear -0.000001 -3.661 x 10-7 4.091 x 10-5 Spherical -0.000001 -0.001762 3.740 x 10-5 Exponential -0.000001 -0.002862 3.757 x 10-5 Gaussian -0.000010 -0.006040 3.548 x 10-5

0.0000

0.0052

0.0103

0.0155

0.0206

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Isotropic Variogram

Gaussian model (Co = 0.00105; Co + C = 0.01860; Ao = 3080.00; r2 = 0.852; RSS = 9.825E-05)

0.000E+00

1.880E-03

3.761E-03

5.641E-03

7.521E-03

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Isotropic Variogram

Gaussian model (Co = 0.00001; Co + C = 0.00611; Ao = 290.00; r2 = 0.187; RSS = 1.143E-05)

-3.328E-03

-1.746E-03

-1.649E-04

1.417E-03

2.998E-03

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

x : Isotropic Cross Variogram

Gaussian model (Co = -0.00001; Co + C = -0.00604; Ao = 13910.00; r2 = 0.209; RSS = 3.548E-05)

(a) Model Gaussian (b) Model Gaussian

(c) Model Gaussian

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (3a) Saturasi Air Minimum

Variogram isotropi

Variogram anisotropi Properti

Reservoir Model Nugget (C0) Sill (C0+C) RSS

Porositas (Min)

Linear 0.002400 0.044914 3.964 x 10-3 Spherical 0.001900 0.043014 3.926 x 10-3 Exponential 0.000400 0.041514 3.815 x 10-3 Gaussian 0.005400 0.046514 4.294 x 10-3

Saturasi Air (Min)

Linear 0.005900 0.017644 2.326 x 10-4 Spherical 0.005900 0.017644 2.326 x 10-4 Exponential 0.005900 0.017644 2.326 x 10-4 Gaussian 0.006000 0.017744 2.325 x 10-4

Porositas x Saturasi Air

(Min)

Linear -0.000010 -0.009820 4.334 x 10-4 Spherical -0.000010 -0.009820 4.352 x 10-4 Exponential -0.000010 -0.009820 4.316 x 10-4 Gaussian -0.000100 -0.029420 4.198 x 10-4

0.0000

0.0103

0.0205

0.0308

0.0410

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Anisotropic Variogram (0º)

Exponential model (Co = 0.00040; Co + C = 0.04151; AMajor = 13710.00; AMinor = 6810.00; r2 = 0.376; RSS = 3.815E-03)

0.0000

0.0029

0.0058

0.0087

0.0116

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Anisotropic Variogram (0º)

Gaussian model (Co = 0.00600; Co + C = 0.01774; AMajor = 751300.00; AMinor = 751300.00; r2 = 0.119; RSS = 2.325E-04)

-9.800E-03

-5.790E-03

-1.779E-03

2.231E-03

6.242E-03

0.00 2255.14 4510.27 6765.41Se

miv

aria

nce

Separation Distance (h)

x : Anisotropic Cross Variogram (0º)

Gaussian model (Co = -0.00010; Co + C = -0.02942; AMajor = 70790.00; AMinor = 19620.00; r2 = 0.178; RSS = 4.198E-04)

(a) Model Exponential (b) Model Gaussian

(c) Model Gaussian 28

Well Name

Koord. X Koord.Y Data Aktual

Estimasi Isotropi

Estimasi Anisotropi

ZU-16 230662.8 9399394 0.3818 0.302 0.197 ZUA-5 227441.9 9410011 0.1326 0.191 0.256 ZUB-5 226485.2 9408922 0.263517 0.033 0.102 ZUC-5 227984 9408461 0.1 0.241 0.293 ZUD-5 229513.4 9408031 0.2976 0.029 0.090 ZUE-5 226521.9 9407448 0.1 0.131 0.281 ZUF-5 228048.5 9406977 0.1981 0.000 0.164 ZUG-5 229543.8 9406584 0.247 0.404 0.387 ZUK-3 229107.8 9401041.29 0.1981 0.253 0.084 ZZZ-1 226990.1 9411303 0.2964 0.380 0.441

0.00

0.17

0.35

0.53

0.71

0.00 0.23 0.47 0.71

Actu

al

Estimated

Regression coeff icient = 1.045 (SE = 0.032 , r2 =0.953,y intercept = -0.01, SE Prediction = 0.026, n = 53)

-0.11

0.14

0.39

0.63

0.88

-0.11 0.22 0.55 0.88

Actu

al

Estimated

Regression coeff icient = 0.246 (SE = 0.079 , r2 =0.160,y intercept = 0.14, SE Prediction = 0.110, n = 53)

0 0,05

0,1 0,15

0,2 0,25

0,3 0,35

0,4 0,45

0,5

Data Aktual

Estimasi Isotropi

Estimasi Anisotropi

R2 =16.0% R2 =95.3%

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (3a) Saturasi Air Minimum

Cross-Variogram Isotropi Cross-Variogram Anisotropi

29

Properti Reservoir Model Nugget (C0) Sill (C0+C) RSS

(a) Saturasi Air (Mean)

Linear 0.006782 0.039250 3.847 x 10-4 Spherical 0.001900 0.034300 2.454 x 10-4 Exponential 0.001800 0.047400 3.067 x 10-4 Gaussian 0.006520 0.035540 2.287 x 10-4

(b) Porositas (Mean)

Linear 0.000743 0.005036 8.965 x 10-6 Spherical 0.000720 0.007550 9.148 x 10-6 Exponential 0.000640 0.014890 9.394 x 10-6 Gaussian 0.001260 0.006530 7.704 x 10-6

(c) Saturasi Air x

Porositas (Mean)

Linear -0.000010 -0.000001 5.056 x 10-4 Spherical -0.000010 -0.009020 5.236 x 10-5 Exponential -0.000010 -0.023720 5.341 x 10-5 Gaussian -0.000350 -0.009300 4.584 x 10-5

0.0000

0.0104

0.0208

0.0311

0.0415

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Isotropic Variogram

Gaussian model (Co = 0.00652; Co + C = 0.03554; Ao = 3140.00; r2 = 0.871; RSS = 2.287E-04)

0.000E+00

1.726E-03

3.452E-03

5.177E-03

6.903E-03

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Isotropic Variogram

Gaussian model (Co = 0.00126; Co + C = 0.00653; Ao = 5690.00; r2 = 0.769; RSS = 7.704E-06)

-0.0134

-0.0100

-0.0067

-0.0033

0.0000

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

x : Isotropic Cross Variogram

Gaussian model (Co = -0.00035; Co + C = -0.00930; Ao = 3980.00; r2 = 0.736; RSS = 4.584E-05)

(a) Model Gaussian (b) Model Gaussian

(c) Model Gaussian

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (3b) Saturasi Air Mean

Variogram isotropi

Variogram isotropi Properti

Reservoir Model Nugget (C0) Sill (C0+C) RSS

(a) Saturasi Air (Mean)

Linear 0.008300 0.078779 7.471 x 10-3 Spherical 0.007700 0.074679 7.418 x 10-3 Exponential 0.005500 0.072479 7.267 x 10-3 Gaussian 0.013300 0.080279 8.169 x 10-3

(b) Porositas (Mean)

Linear 0.000400 0.013983 1.805 x 10-4 Spherical 0.000300 0.012983 1.816 x 10-4 Exponential 0.000500 0.016183 1.841 x 10-4 Gaussian 0.001200 0.0138883 1.722 x 10-4

(c) Saturasi Air x

Porositas (Mean)

Linear -0.000100 -0.094567 6.742 x 10-4 Spherical -0.000100 -0.065967 6.741 x 10-4 Exponential -0.000100 -0.094467 6.727 x 10-4 Gaussian -0.002000 -0.217867 7.454 x 10-4

0.0000

0.0103

0.0205

0.0308

0.0410

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Anisotropic Variogram (0º)

Exponential model (Co = 0.00040; Co + C = 0.04151; AMajor = 13710.00; AMinor = 6810.00; r2 = 0.376; RSS = 3.815E-03)

0.0000

0.0029

0.0058

0.0087

0.0116

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Anisotropic Variogram (0º)

Gaussian model (Co = 0.00600; Co + C = 0.01774; AMajor = 751300.00; AMinor = 751300.00; r2 = 0.119; RSS = 2.325E-04)

-9.800E-03

-5.790E-03

-1.779E-03

2.231E-03

6.242E-03

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

x : Anisotropic Cross Variogram (0º)

Gaussian model (Co = -0.00010; Co + C = -0.02942; AMajor = 70790.00; AMinor = 19620.00; r2 = 0.178; RSS = 4.198E-04)

(a) Model Exponential (b) Model Gaussian

(c) Model Exponential 30

Well Name

Koord. X Koord.Y Data

Aktual Estimasi Isotropi

Estimasi Anisotropi

AU-16 230662.8 9399394 0.584312 0.000 0.473 AUA-5 227441.9 9410011 0.29159 0.000 0.199 AUB-5 226485.2 9408922 0.3669 0.400 0.323 AUC-5 227984 9408461 0.514379 0.100 0.309 AUD-5 229513.4 9408031 0.50847 0.400 0.417 AUE-5 226521.9 9407448 0.490939 0.000 0.334 AUF-5 228048.5 9406977 0.439418 0.300 0.314 AUG-5 229543.8 9406584 0.442798 0.000 0.358 AUK-3 229107.8 9401041.29 0.327507 0.400 0.432 AZZ-1 226990.1 9411303 0.39099 0.400 0.274

-17.26

-12.19

-7.11

-2.03

3.04

-17.26 -10.49 -3.73 3.04

Act

ual

Estimated

Regression coeff icient = 0.009 (SE = 0.008 , r2 =0.026,y intercept = 0.37, SE Prediction = 0.149, n = 53)

0.16

0.31

0.46

0.60

0.75

0.16 0.36 0.55 0.75

Actu

al

Estimated

Regression coeff icient = 1.187 (SE = 0.044 , r2 =0.934,y intercept = -0.07, SE Prediction = 0.039, n = 53)

0 0,05

0,1 0,15

0,2 0,25

0,3 0,35

0,4 0,45

0,5

Data Aktual

Estimasi Isotropi

Estimasi Anisotropi

R2 =96.4% R2 =2.6%

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (3b) Saturasi Air Mean

Cross-Variogram Isotropi Cross-Variogram Anisotropi

31

Properti Reservoir Model Nugget (C0) Sill (C0+C) RSS

(a) Saturasi Air (Mean)

Linear 0.049691 0.069128 8.398 x 10-4 Spherical 0.019900 0.062900 4.859 x 10-4 Exponential 0.010800 0.063800 4.292 x 10-4 Gaussian 0.028500 0.063000 4.780 x 10-4

(b) Porositas (Mean)

Linear 0.000461 0.005067 1.087 x 10-5 Spherical 0.000330 0.005660 1.090 x 10-5 Exponential 0.000260 0.011880 1.120 x 10-5 Gaussian 0.000870 0.005520 9.181 x 10-6

(c) Saturasi Air x

Porositas (Mean)

Linear -0.000010 -0.000001 1.189 x 10-4 Spherical -0.000010 -0.008990 2.898 x 10-5 Exponential -0.000010 -0.014740 3.015 x 10-5 Gaussian -0.000010 -0.011290 2.158 x 10-5

0.0000

0.0186

0.0371

0.0557

0.0743

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Isotropic Variogram

Exponential model (Co = 0.01080; Co + C = 0.06380; Ao = 580.00; r2 = 0.682; RSS = 4.292E-04)

0.000E+00

1.701E-03

3.403E-03

5.104E-03

6.805E-03

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Isotropic Variogram

Gaussian model (Co = 0.00087; Co + C = 0.00552; Ao = 4550.00; r2 = 0.764; RSS = 9.181E-06)

-70.188E-04

-50.145E-04

-30.103E-04

-10.061E-04

99.808E-05

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

x : Isotropic Cross Variogram

Gaussian model (Co = -0.00001; Co + C = -0.01129; Ao = 8610.00; r2 = 0.649; RSS = 2.158E-05)

(a) Model Exponential (b) Model Gaussian

(c) Model Gaussian

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (3c) Saturasi Air Maksimum

Variogram isotropi

Variogram anisotropi Properti

Reservoir Model Nugget (C0) Sill (C0+C) RSS

(a) Saturasi Air (Mean)

Linear 0.030000 0.192400 0.0409 Spherical 0.028000 0.190400 0.0420 Exponential 0.024000 0.186400 0.0423 Gaussian 0.048000 0.210400 0.0376

(b) Porositas (Mean)

Linear 0.000200 0.014450 3.020 x 10-4 Spherical 0.000200 0.014450 3.019 x 10-4 Exponential 0.000100 0.013750 3.046 x 10-4 Gaussian 0.001000 0.014650 3.023 x 10-4

(c) Saturasi Air x

Porositas (Mean)

Linear -0.000100 -0.082200 2.930 x 10-3 Spherical -0.000100 -0.053100 2.931 x 10-3 Exponential -0.000100 -0.082100 2.938 x 10-3 Gaussian -0.003000 -0.260700 3.169 x 10-3

0.000

0.040

0.081

0.121

0.161

0.00 2255.14 4510.27 6765.41

Sem

ivar

ianc

e

Separation Distance (h)

Anisotropic Variogram (0º)

Gaussian model (Co = 0.04800; Co + C = 0.21040; AMajor = 12770.00; AMinor = 12770.00; r2 = 0.173; RSS = 0.0376)

0.0000

0.0034

0.0068

0.0102

0.0136

0.00 2255.14 4510.27 6765.41

Sem

ivaria

nce

Separation Distance (h)

Anisotropic Variogram (0º)

Spherical model (Co = 0.00020; Co + C = 0.01445; AMajor = 24370.00; AMinor = 24370.00; r2 = 0.534; RSS = 3.019E-04)

-0.0467

-0.0339

-0.0211

-0.0083

0.0046

0.00 2255.14 4510.27 6765.41

Semi

varia

nce

Separation Distance (h)

x : Anisotropic Cross Variogram (0º)

Linear model (Co = -0.00010; Co + C = -0.08220; AMajor = 74650.00; AMinor = 74650.00; r2 = 0.225; RSS = 2.930E-03)

(a) Model Gaussian (b) Model Spherical

(c) Model Linear 32

Well Name

Koord. X Koord.Y Data

Aktual Estimasi Isotropi

Estimasi Anisotropi

AU-16 230662.8 9399394 1 0.000 0.830 AUA-5 227441.9 9410011 1 0.000 0.610 AUB-5 226485.2 9408922 0.49608 0.000 0.620 AUC-5 227984 9408461 1 0.000 0.740 AUD-5 229513.4 9408031 1 1.000 0.920 AUE-5 226521.9 9407448 0.8186 1.000 0.640 AUF-5 228048.5 9406977 1 1.000 0.740 AUG-5 229543.8 9406584 0.9137 0.000 0.830 AUK-3 229107.8 9401041.29 0.7271 0.000 0.850 AZZ-1 226990.1 9411303 0.5637 1.000 0.560

-8.30

-5.74

-3.18

-0.61

1.95

-8.30 -4.89 -1.47 1.95

Act

ual

Estimated

Regression coeff icient = -0.004 (SE = 0.024 , r2 =0.000,y intercept = 0.76, SE Prediction = 0.244, n = 53)

0.28

0.46

0.64

0.82

1.00

0.28 0.52 0.76 1.00

Actu

al

Estimated

Regression coeff icient = 1.170 (SE = 0.247 , r2 =0.306,y intercept = -0.13, SE Prediction = 0.203, n = 53)

0

0,2

0,4

0,6

0,8

1

1,2

ZU-1

6

ZUA-

5

ZUB-

5

ZUC-

5

ZUD-

5

ZUE-

5

ZUF-

5

ZUG

-5

ZUK-

3

ZZZ-

1

Data Aktual

Estimasi Isotropi

Estimasi Anisotropi

R2 =30.6% R2 =0%

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (3c) Saturasi Air Maksimum

Cross-Variogram Isotropi Cross-Variogram Anisotropi

33

No Metode Variate Covariate R2

Isotropi Anisotropi

1 Cokriging Porositas (minimum)

Saturasi Air (minimum)

56,8% 49,9%

2 Cokriging Porositas (mean) Satuasi Air (mean) 89,9% 89,7%

3 Cokriging Porositas (maksimum)

Saturasi Air (maksimum)

97,1% 60,1%

4 Cokriging Saturasi Air (minimum)

Porositas (minimum) 96,3% 16%

5 Cokriging Satuasi Air (mean) Porositas (mean) 2,6% 93,4%

6 Cokriging Saturasi Air (maksimum)

Porositas (maksimum)

0% 30,6%

7 Ordinary Kriging Thickness - 2,1% 0,6%

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : Perbandingan Variogram

34

Titik X Y Estimasi POINT-1 229518 9409644.5 29.2 POINT-2 230621 9408394.6 27.7 POINT-3 229797 9407425.6 31.2 POINT-4 229065 9407946.4 32.3 POINT-5 226924 9410311.3 35.1 POINT-6 226863 9409730 31.6 POINT-7 228087 9410700 35.2 POINT-8 227736 9409426.8 32.6 POINT-9 229057 9406553.2 32.6 POINT-10 229457 9405922.7 26.5

0,00

16,00

32,00

48,00

64,00

0,00 21,33 42,67 64,00

Actua

l

Estimated

Regression coeff icient = 0,679 (SE = 0,363 , r2 =0,054,y intercept = 9,38, SE Prediction = 11,254, n = 63)

39,237,535,834,032,330,628,927,225,423,722,020,318,616,815,113,4

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (a) Thickness

35

Titik X Y Estimasi POINT-1 229518 9409644.5 0.086 POINT-2 230621 9408394.6 0.131 POINT-3 229797 9407425.6 0.113 POINT-4 229065 9407946.4 0.000 POINT-5 226924 9410311.3 0.210 POINT-6 226863 9409730 0.146 POINT-7 228087 9410700 0.014 POINT-8 227736 9409426.8 0.062 POINT-9 229057 9406553.2 0.258

POINT-10 229457 9405922.7 0.227

-0,04

0,04

0,13

0,21

0,29

-0,04 0,07 0,18 0,29

Actua

l

Estimated

Regression coeff icient = 0,861 (SE = 0,111 , r2 =0,497,y intercept = 0,02, SE Prediction = 0,058, n = 63)

0,3800,3490,3170,2860,2550,2230,1920,1610,1290,0980,0670,0350,004-0,027-0,059-0,090

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (2a) Porositas Minimum

36

Titik X Y Estimasi POINT-1 229518 9409644.5 0.270 POINT-2 230621 9408394.6 0.310 POINT-3 229797 9407425.6 0.270 POINT-4 229065 9407946.4 0.250 POINT-5 226924 9410311.3 0.310 POINT-6 226863 9409730 0.295 POINT-7 228087 9410700 0.285 POINT-8 227736 9409426.8 0.279 POINT-9 229057 9406553.2 0.340

POINT-10 229457 9405922.7 0.314

0,14

0,20

0,26

0,32

0,38

0,14 0,22 0,30 0,38

Actu

al

Estimated

Regression coeff icient = 1,367 (SE = 0,095 , r2 =0,772,y intercept = -0,10, SE Prediction = 0,025, n = 63)

0,3500,3390,3270,3160,3050,2930,2820,2710,2590,2480,2370,2250,2140,2030,1910,180

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (2b) Porositas Mean

37

Titik X Y Estimasi POINT-1 229518 9409644.5 0.440 POINT-2 230621 9408394.6 0.440 POINT-3 229797 9407425.6 0.410 POINT-4 229065 9407946.4 0.400 POINT-5 226924 9410311.3 0.372 POINT-6 226863 9409730 0.380 POINT-7 228087 9410700 0.380 POINT-8 227736 9409426.8 0.384 POINT-9 229057 9406553.2 0.431 POINT-10 229457 9405922.7 0.413

0,24

0,30

0,35

0,41

0,46

0,24 0,31 0,39 0,46

Actua

l

Estimated

Regression coeff icient = 1,599 (SE = 0,127 , r2 =0,723,y intercept = -0,24, SE Prediction = 0,027, n = 63)

0,4500,4410,4310,4220,4130,4030,3940,3850,3750,3660,3570,3470,3380,3290,3190,310

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (2c) Porositas Maksimum

38

Titik X Y Estimasi POINT-1 229518 9409644.5 0.193 POINT-2 230621 9408394.6 0.244 POINT-3 229797 9407425.6 0.144 POINT-4 229065 9407946.4 0.074 POINT-5 226924 9410311.3 0.264 POINT-6 226863 9409730 0.179 POINT-7 228087 9410700 0.071 POINT-8 227736 9409426.8 0.072 POINT-9 229057 9406553.2 0.467 POINT-10 229457 9405922.7 0.426

-0,09

0,11

0,31

0,51

0,71

-0,09 0,18 0,44 0,71

Actua

l

Estimated

Regression coeff icient = 0,317 (SE = 0,088 , r2 =0,176,y intercept = 0,13, SE Prediction = 0,105, n = 63)

0,6200,5710,5230,4740,4250,3770,3280,2790,2310,1820,1330,0850,036-0,013-0,061-0,110

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (3a) Saturasi Air Minimum

39

Titik X Y Estimasi POINT-1 229518 9409644.5 0.380 POINT-2 230621 9408394.6 0.428 POINT-3 229797 9407425.6 0.410 POINT-4 229065 9407946.4 0.454 POINT-5 226924 9410311.3 0.269 POINT-6 226863 9409730 0.251 POINT-7 228087 9410700 0.315 POINT-8 227736 9409426.8 0.284 POINT-9 229057 9406553.2 0.497 POINT-10 229457 9405922.7 0.436

0,16

0,31

0,46

0,60

0,75

0,16 0,36 0,55 0,75

Actu

al

Estimated

Regression coeff icient = 1,278 (SE = 0,062 , r2 =0,875,y intercept = -0,11, SE Prediction = 0,051, n = 63)

0,6700,6400,6100,5800,5500,5200,4900,4600,4300,4000,3700,3400,3100,2800,2500,220

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (3b) Saturasi Air Mean

40

Titik X Y Estimasi POINT-1 229518 9409644.5 0.940 POINT-2 230621 9408394.6 1.000 POINT-3 229797 9407425.6 0.980 POINT-4 229065 9407946.4 0.890 POINT-5 226924 9410311.3 0.600 POINT-6 226863 9409730 0.630 POINT-7 228087 9410700 0.690 POINT-8 227736 9409426.8 0.720 POINT-9 229057 9406553.2 0.770

POINT-10 229457 9405922.7 0.830

0,28

0,46

0,64

0,82

1,00

0,28 0,52 0,76 1,00

Actua

l

Estimated

Regression coeff icient = 1,147 (SE = 0,230 , r2 =0,290,y intercept = -0,11, SE Prediction = 0,200, n = 63)

1,041,000,970,930,900,860,830,790,760,720,690,650,620,580,550,51

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : (3c) Saturasi Air Maksimum

41

Titik Estimasi Thickness Porositas Saturasi Air Minimum Mean Maksimum Minimum Mean Maksimum

POINT-1 29.20 0.086 0.270 0.440 0.193 0.380 0.940 POINT-2 27.20 0.131 0.310 0.440 0.244 0.428 1.000 POINT-3 31.20 0.113 0.270 0.410 0.144 0.410 0.980 POINT-4 32.30 0.000 0.250 0.400 0.074 0.454 0.890 POINT-5 35.10 0.210 0.310 0.342 0.264 0.269 0.600 POINT-6 31.60 0.146 0.295 0.380 0.179 0.251 0.630 POINT-7 35.20 0.014 0.285 0.380 0.071 0.315 0.690 POINT-8 32.60 0.062 0.279 0.384 0.072 0.284 0.720 POINT-9 32.60 0.258 0.340 0.431 0.467 0.497 0.770

POINT-10 26.50 0.227 0.314 0.413 0.426 0.436 0.830

0,000

0,200

0,400

0,600

0,800

1,000

1,200

1 2 3 4 5 6 7 8 9 10

Axis

Titl

e

Saturasi Air

Minimum

Mean

Maksimum 0,000 0,050 0,100 0,150 0,200 0,250 0,300 0,350 0,400 0,450 0,500

1 2 3 4 5 6 7 8 9 10

Axis

Titl

e

Porositas

Minimum

Mean

Maksimum

Batas Atas

Batas Bawah

Batas Atas

Batas Bawah

Karakteristik Data

Analisis Vriogram Interpolasi

Analisis & Pembahasan : Summary

42

Kesimpulan & Saran

Kesimpulan & Saran Kesimpulan Saran

1. Zona-1 merupakan area yang bagus dan besar kemungkinan terdapat akumulasi minyak atau gas (Nilai porositas > 25% dengan angka permeabilitas > 50mD yang termasuk dalam kategori “istimewa” )

4. Estimasinilai Thickness memberikan hasil lebih baik menggunakan ordinary kiging dengan variogram isotropi bervariasi antara range 13.4 sampai 39.2 feet dengan R2 sebesar5.4%.

2. Estimasi porositas memberikan hasil yang baik untuk Interpolasi cokriging baik pada data porositas minimum, mean maupun maksimum dengan variogram dan cross-variogram isotropi serta covariate saturasi air dengan R2 hasil cross-validasi cukup tinggi.

3. Estimasi nilai saturasi air memberikan hasil yang baik untuk interpolasi cokriging menggunakan variogram dan cross-variogram isotropi pada kategori data saturasi air minimum, dan anisotropi pada data saturasi air mean serta maksimum dengan covariate porositas.

43

Kesimpulan

44

Saran

Kesimpulan & Saran

Dapat mengaplisikan metode kriging lain

pada variabel thickness atau mencari

variabel tambahan yang dapat

mendukung thickness sehingga hasil analisis

mampu meningkatkan nilai keakuratan.

Menggunakan alternative metode Cokriging Bayesian

untuk menginterpolasikan

nilai variabel pemrmeabilitas yang terbatas data pada

lapangan “Z”

Menggunakan model variogram teoretis lain

yang dapat menggambarkan

varians data secara spasial seakurat

mungkin

1

bibliography Alfiana, A.N. 2010. Metode Ordinary Kriging pada Geostatistika [Skripsi]. Yogyakarta: Fakultas Matematika dan

Ilmu Pengetahuan Alam. Universitas Negeri Yogyakarta Cressie, N. A. C. 1993. Statistics for Spatial Data Revised Edition. United States of America : John Wiley & Sons,

Inc. Darwish, Kh. M. dan Ali, M.M. 2010. Mapping Soil Salinity Using Collocated Cokriging in Baharya Oasis, Egypt.

Cairo : National research Centre (NRC) Delfiner, P. C. P. (1999). Geostatistics Modeling Spatial Uncertainty. New York: JohnWiley and Sons, Inc. Diggle P.J dan Ribeiro P.J. 2007. Model-Based Geostatistics. New York: Springer Dubrule, O. 2003. Geostatistics for Seismic Data Integration in Earth Models. Tulsa: Europeam Association of

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Interpolasi Nilai Property Reservoir Di Lapangan “Z Perairan Laut Jawa

Dengan Metode Ordinary Kriging dan Cokriging

Seminar Hasil Tugas Akhir (Rabu, 16 Juli 2014)

Oleh : Nur Anisyah (1310100012) Pembimbing : Prof. Drs. Nur Iriawan, MIKom., Ph.D.