applie MLR to model and predict permeability in multiple models
Ali Nayef Assi -BUOG 4stage
2024-11-29
pacman::p_load(rio,psych,ggplot2)
karpur_data <- read.csv("karpur.csv")
data <- read.csv("karpur.csv")
library(Metrics)## Warning: package 'Metrics' was built under R version 4.4.2step1: MLR model to predict Permeability using all well logs without facies
Predicted_Permeabiity_Model_1<- lm(k.core~ .-Facies,data=data)
summary(Predicted_Permeabiity_Model_1 )##
## Call:
## lm(formula = k.core ~ . - Facies, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5549.5 -755.5 -178.1 578.0 11260.8
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 60762.728 16605.360 3.659 0.000269 ***
## depth -7.398 1.446 -5.115 3.92e-07 ***
## caliper -3955.952 1055.105 -3.749 0.000190 ***
## ind.deep -14.183 2.345 -6.048 2.24e-09 ***
## ind.med 17.300 2.509 6.896 1.08e-11 ***
## gamma -77.487 5.475 -14.153 < 2e-16 ***
## phi.N -1784.704 1301.772 -1.371 0.170763
## R.deep -26.007 6.974 -3.729 0.000206 ***
## R.med 63.525 9.841 6.455 1.86e-10 ***
## SP -8.784 3.460 -2.539 0.011313 *
## density.corr -523.060 5358.876 -0.098 0.922269
## density 8011.106 1120.554 7.149 1.96e-12 ***
## phi.core 183.203 23.802 7.697 4.07e-14 ***
## Phi.core.frac. NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1442 on 806 degrees of freedom
## Multiple R-squared: 0.5903, Adjusted R-squared: 0.5842
## F-statistic: 96.77 on 12 and 806 DF, p-value: < 2.2e-16Predicted_Permeabiity_Model_1<- lm(k.core~ .-Facies,data=Karpur) summary(Predicted_Permeabiity_Model_1 )Predicted_permeability_1 <- predict(Predicted_Permeabiity_Model_1, data = data)
library(ggplot2)Predicted_permeability_1 <- predict(Predicted_Permeabiity_Model_1, data = data)
library(ggplot2)
ggplot (data) +
geom_line(aes(x = depth, y = k.core, color = "Measured permeability")) +
geom_line(aes(x = depth, y = Predicted_permeability_1, color = "Predicted permeability")) +
labs(title = "Predicted vs Measured Permeability with Respect to Depth",
x = "Depth",
y = "Permeability",
color = "Legend") +
scale_color_manual(values = c("Measured permeability" = "red",
"Predicted permeability" = "black")) +
theme_minimal()
Stepwise_Model_1<-step(Predicted_Permeabiity_Model_1, direction = "backward")## Start: AIC=11926.91
## k.core ~ (depth + caliper + ind.deep + ind.med + gamma + phi.N +
## R.deep + R.med + SP + density.corr + density + phi.core +
## Facies + Phi.core.frac.) - Facies
##
##
## Step: AIC=11926.91
## k.core ~ depth + caliper + ind.deep + ind.med + gamma + phi.N +
## R.deep + R.med + SP + density.corr + density + phi.core
##
## Df Sum of Sq RSS AIC
## - density.corr 1 19799 1675068713 11925
## - phi.N 1 3906205 1678955118 11927
## <none> 1675048914 11927
## - SP 1 13394190 1688443104 11931
## - R.deep 1 28897686 1703946599 11939
## - caliper 1 29214826 1704263740 11939
## - depth 1 54372650 1729421563 11951
## - ind.deep 1 76022788 1751071701 11961
## - R.med 1 86603706 1761652619 11966
## - ind.med 1 98823752 1773872666 11972
## - density 1 106221406 1781270319 11975
## - phi.core 1 123125117 1798174031 11983
## - gamma 1 416312526 2091361440 12107
##
## Step: AIC=11924.92
## k.core ~ depth + caliper + ind.deep + ind.med + gamma + phi.N +
## R.deep + R.med + SP + density + phi.core
##
## Df Sum of Sq RSS AIC
## <none> 1675068713 11925
## - phi.N 1 4564880 1679633593 11925
## - SP 1 13491079 1688559792 11930
## - R.deep 1 28896144 1703964857 11937
## - caliper 1 29253869 1704322581 11937
## - depth 1 54825159 1729893872 11949
## - ind.deep 1 77573926 1752642639 11960
## - R.med 1 86772220 1761840933 11964
## - ind.med 1 100740701 1775809413 11971
## - density 1 114209586 1789278299 11977
## - phi.core 1 124694278 1799762991 11982
## - gamma 1 417015194 2092083907 12105
summary(Stepwise_Model_1)##
## Call:
## lm(formula = k.core ~ depth + caliper + ind.deep + ind.med +
## gamma + phi.N + R.deep + R.med + SP + density + phi.core,
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5545.3 -753.4 -177.1 576.8 11260.2
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 60910.619 16525.937 3.686 0.000243 ***
## depth -7.409 1.442 -5.139 3.46e-07 ***
## caliper -3957.892 1054.270 -3.754 0.000186 ***
## ind.deep -14.146 2.314 -6.113 1.52e-09 ***
## ind.med 17.263 2.478 6.967 6.74e-12 ***
## gamma -77.461 5.465 -14.174 < 2e-16 ***
## phi.N -1825.771 1231.150 -1.483 0.138470
## R.deep -25.972 6.961 -3.731 0.000204 ***
## R.med 63.466 9.816 6.466 1.75e-10 ***
## SP -8.803 3.453 -2.549 0.010974 *
## density 7980.761 1075.902 7.418 3.02e-13 ***
## phi.core 183.436 23.667 7.751 2.75e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1441 on 807 degrees of freedom
## Multiple R-squared: 0.5903, Adjusted R-squared: 0.5847
## F-statistic: 105.7 on 11 and 807 DF, p-value: < 2.2e-16plot the predicted vs measured permeability with respect to depth.
Predicted_permeability_2 <-predict(Stepwise_Model_1,data=data)
ggplot(data) +
geom_line(aes(x = depth, y = k.core, color = "Measured permeability")) +
geom_line(aes(x = depth, y = Predicted_permeability_2, color = "Predicted permeability")) +
labs(title = "Predicted vs Measured Permeability with Respect to Depth",
x = "Depth",
y = "Permeability",
color = "Legend") +
scale_color_manual(values = c("Measured permeability" = "red",
"Predicted permeability" = "black")) +
theme_minimal()
step3 MLR model to predict Permeability using all well logs ,this time including facies
Predicted_Permeabiity_Model_2<- lm(k.core~ .,data=data)
summary(Predicted_Permeabiity_Model_2 )##
## Call:
## lm(formula = k.core ~ ., data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5585.6 -568.9 49.2 476.5 8928.4
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.783e+04 1.760e+04 -3.853 0.000126 ***
## depth 8.544e+00 1.785e+00 4.786 2.02e-06 ***
## caliper 1.413e+03 1.019e+03 1.387 0.165789
## ind.deep -2.418e-01 2.354e+00 -0.103 0.918220
## ind.med 1.224e+00 2.585e+00 0.473 0.636062
## gamma -4.583e+01 6.010e+00 -7.626 6.88e-14 ***
## phi.N -2.010e+03 1.476e+03 -1.362 0.173540
## R.deep -2.344e+01 6.288e+00 -3.727 0.000207 ***
## R.med 5.643e+01 9.065e+00 6.225 7.76e-10 ***
## SP -7.125e+00 3.145e+00 -2.266 0.023736 *
## density.corr -2.567e+03 4.809e+03 -0.534 0.593602
## density 2.319e+03 1.173e+03 1.976 0.048458 *
## phi.core 1.921e+02 2.282e+01 8.418 < 2e-16 ***
## FaciesF10 8.921e+02 3.590e+02 2.485 0.013157 *
## FaciesF2 9.243e+02 5.818e+02 1.589 0.112514
## FaciesF3 4.393e+02 3.344e+02 1.313 0.189394
## FaciesF5 7.411e+02 3.428e+02 2.162 0.030908 *
## FaciesF7 -4.152e+01 5.742e+02 -0.072 0.942377
## FaciesF8 -1.179e+03 3.927e+02 -3.002 0.002770 **
## FaciesF9 -2.969e+03 4.298e+02 -6.908 1.00e-11 ***
## Phi.core.frac. NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1262 on 799 degrees of freedom
## Multiple R-squared: 0.6889, Adjusted R-squared: 0.6815
## F-statistic: 93.12 on 19 and 799 DF, p-value: < 2.2e-16plot the predicted vs measured permeability with respect to depth.
Predicted_permeability_3 <-predict(Predicted_Permeabiity_Model_2,data=data)
ggplot(data) +
geom_line(aes(x = depth, y = k.core, color = "Measured permeability")) +
geom_line(aes(x = depth, y = Predicted_permeability_3, color = "Predicted permeability")) +
labs(title = "Predicted vs Measured Permeability with Respect to Depth",
x = "Depth",
y = "Permeability",
color = "Legend") +
scale_color_manual(values = c("Measured permeability" = "red",
"Predicted permeability" = "black")) +
theme_minimal()
Step4 Applying step wise elimination to this model.
Stepwise_Model_2<-step(Predicted_Permeabiity_Model_2, direction = "backward")## Start: AIC=11715.43
## k.core ~ depth + caliper + ind.deep + ind.med + gamma + phi.N +
## R.deep + R.med + SP + density.corr + density + phi.core +
## Facies + Phi.core.frac.
##
##
## Step: AIC=11715.43
## k.core ~ depth + caliper + ind.deep + ind.med + gamma + phi.N +
## R.deep + R.med + SP + density.corr + density + phi.core +
## Facies
##
## Df Sum of Sq RSS AIC
## - ind.deep 1 16793 1271937992 11713
## - ind.med 1 356746 1272277945 11714
## - density.corr 1 453661 1272374861 11714
## - phi.N 1 2953609 1274874809 11715
## - caliper 1 3063007 1274984206 11715
## <none> 1271921199 11715
## - density 1 6217927 1278139127 11717
## - SP 1 8171834 1280093033 11719
## - R.deep 1 22117394 1294038593 11728
## - depth 1 36466976 1308388176 11737
## - R.med 1 61690461 1333611660 11752
## - gamma 1 92579723 1364500923 11771
## - phi.core 1 112793101 1384714301 11783
## - Facies 7 403127714 1675048914 11927
##
## Step: AIC=11713.44
## k.core ~ depth + caliper + ind.med + gamma + phi.N + R.deep +
## R.med + SP + density.corr + density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - density.corr 1 437546 1272375538 11712
## - phi.N 1 2938766 1274876758 11713
## - caliper 1 3074396 1275012389 11713
## <none> 1271937992 11713
## - density 1 6228928 1278166920 11715
## - ind.med 1 6905855 1278843848 11716
## - SP 1 8191802 1280129794 11717
## - R.deep 1 22125695 1294063687 11726
## - depth 1 39139470 1311077462 11736
## - R.med 1 61773953 1333711946 11750
## - gamma 1 92865220 1364803212 11769
## - phi.core 1 112960440 1384898432 11781
## - Facies 7 479133709 1751071701 11961
##
## Step: AIC=11711.72
## k.core ~ depth + caliper + ind.med + gamma + phi.N + R.deep +
## R.med + SP + density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - caliper 1 2980713 1275356252 11712
## <none> 1272375538 11712
## - phi.N 1 3279032 1275654571 11712
## - density 1 5792837 1278168375 11713
## - ind.med 1 6813959 1279189497 11714
## - SP 1 8391302 1280766840 11715
## - R.deep 1 22009402 1294384940 11724
## - depth 1 38705776 1311081314 11734
## - R.med 1 61436819 1333812357 11748
## - gamma 1 93974329 1366349868 11768
## - phi.core 1 115336515 1387712053 11781
## - Facies 7 480267100 1752642639 11960
##
## Step: AIC=11711.64
## k.core ~ depth + ind.med + gamma + phi.N + R.deep + R.med + SP +
## density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - phi.N 1 2534906 1277891157 11711
## <none> 1275356252 11712
## - density 1 7270311 1282626562 11714
## - SP 1 8733336 1284089587 11715
## - ind.med 1 12924050 1288280301 11718
## - R.deep 1 22449117 1297805369 11724
## - depth 1 51507476 1326863728 11742
## - R.med 1 60137982 1335494234 11747
## - phi.core 1 112564835 1387921086 11779
## - gamma 1 141535555 1416891807 11796
## - Facies 7 520094756 1795451008 11978
##
## Step: AIC=11711.26
## k.core ~ depth + ind.med + gamma + R.deep + R.med + SP + density +
## phi.core + Facies
##
## Df Sum of Sq RSS AIC
## <none> 1277891157 11711
## - density 1 5155969 1283047127 11713
## - SP 1 8515796 1286406953 11715
## - ind.med 1 10944937 1288836095 11716
## - R.deep 1 23273312 1301164469 11724
## - depth 1 49725248 1327616405 11740
## - R.med 1 59454645 1337345802 11746
## - phi.core 1 110154394 1388045551 11777
## - gamma 1 219059092 1496950249 11839
## - Facies 7 526383446 1804274603 11980summary(Stepwise_Model_2)##
## Call:
## lm(formula = k.core ~ depth + ind.med + gamma + R.deep + R.med +
## SP + density + phi.core + Facies, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5608.3 -567.8 35.9 500.7 8989.7
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.322e+04 6.625e+03 -6.523 1.22e-10 ***
## depth 6.648e+00 1.189e+00 5.590 3.11e-08 ***
## ind.med 1.078e+00 4.111e-01 2.623 0.008894 **
## gamma -5.324e+01 4.537e+00 -11.733 < 2e-16 ***
## R.deep -2.395e+01 6.264e+00 -3.824 0.000141 ***
## R.med 5.515e+01 9.022e+00 6.112 1.53e-09 ***
## SP -7.214e+00 3.118e+00 -2.313 0.020960 *
## density 1.880e+03 1.044e+03 1.800 0.072240 .
## phi.core 1.817e+02 2.184e+01 8.320 3.77e-16 ***
## FaciesF10 8.266e+02 3.533e+02 2.340 0.019553 *
## FaciesF2 7.035e+02 5.567e+02 1.264 0.206697
## FaciesF3 4.100e+02 3.228e+02 1.270 0.204443
## FaciesF5 5.913e+02 3.211e+02 1.841 0.065924 .
## FaciesF7 -3.159e+02 5.402e+02 -0.585 0.558866
## FaciesF8 -1.455e+03 3.122e+02 -4.661 3.69e-06 ***
## FaciesF9 -3.017e+03 3.764e+02 -8.017 3.82e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1262 on 803 degrees of freedom
## Multiple R-squared: 0.6874, Adjusted R-squared: 0.6816
## F-statistic: 117.7 on 15 and 803 DF, p-value: < 2.2e-16plot the predicted vs measured permeability with respect to depth.
Predicted_permeability_4 <-predict(Stepwise_Model_2,data=data)
ggplot(data) +
geom_line(aes(x = depth, y = k.core, color = "Measured permeability")) +
geom_line(aes(x = depth, y = Predicted_permeability_4, color = "Predicted permeability")) +
labs(title = "Predicted vs Measured Permeability with Respect to Depth",
x = "Depth",
y = "Permeability",
color = "Legend") +
scale_color_manual(values = c("Measured permeability" = "red",
"Predicted permeability" = "black")) +
theme_minimal()
Step5 MLR model to predict log10(Permeability) using all well logs including facies.
data$log10_Permeability <-log10(data$k.core)
Predicted_Permeabiity_Model_3<- lm(log10_Permeability~.-k.core,data=data)
summary(Predicted_Permeabiity_Model_3 )##
## Call:
## lm(formula = log10_Permeability ~ . - k.core, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.5804 -0.1138 0.0322 0.1529 0.7384
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.3461877 4.6532000 -0.504 0.61425
## depth 0.0007425 0.0004718 1.574 0.11596
## caliper -0.4605945 0.2693103 -1.710 0.08760 .
## ind.deep -0.0007951 0.0006222 -1.278 0.20168
## ind.med 0.0007137 0.0006833 1.044 0.29659
## gamma -0.0091269 0.0015885 -5.746 1.30e-08 ***
## phi.N -1.7628155 0.3901024 -4.519 7.16e-06 ***
## R.deep -0.0025878 0.0016620 -1.557 0.11987
## R.med 0.0044073 0.0023960 1.839 0.06622 .
## SP -0.0016935 0.0008312 -2.037 0.04194 *
## density.corr 1.4462633 1.2712045 1.138 0.25558
## density 1.6148374 0.3100921 5.208 2.44e-07 ***
## phi.core 0.0948634 0.0060329 15.724 < 2e-16 ***
## FaciesF10 0.0786460 0.0948909 0.829 0.40746
## FaciesF2 -0.0184334 0.1537793 -0.120 0.90462
## FaciesF3 -0.0307548 0.0883957 -0.348 0.72799
## FaciesF5 0.1094193 0.0906034 1.208 0.22753
## FaciesF7 0.2811620 0.1517797 1.852 0.06433 .
## FaciesF8 -0.0976234 0.1038054 -0.940 0.34727
## FaciesF9 -0.3562116 0.1135966 -3.136 0.00178 **
## Phi.core.frac. NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3335 on 799 degrees of freedom
## Multiple R-squared: 0.6806, Adjusted R-squared: 0.673
## F-statistic: 89.6 on 19 and 799 DF, p-value: < 2.2e-16plot the predicted vs measured permeability with respect to depth
Predicted_log10_permeability_5 <-predict(Predicted_Permeabiity_Model_3,data=data)
Predicted_permeability_5<-10^Predicted_log10_permeability_5
ggplot(data) +
geom_line(aes(x = depth, y = k.core, color = "Measured permeability")) +
geom_line(aes(x = depth, y = Predicted_permeability_5, color = "Predicted permeability")) +
labs(title = "Predicted vs Measured Permeability with Respect to Depth",
x = "Depth",
y = "Permeability",
color = "Legend") +
scale_color_manual(values = c("Measured permeability" = "red",
"Predicted permeability" = "black")) +
theme_minimal()
STEP6 Applying step wise elimination to this model.
Stepwise_Model_3<-step(Predicted_Permeabiity_Model_3, direction = "backward")## Start: AIC=-1779.02
## log10_Permeability ~ (depth + caliper + ind.deep + ind.med +
## gamma + phi.N + R.deep + R.med + SP + density.corr + density +
## phi.core + k.core + Facies + Phi.core.frac.) - k.core
##
##
## Step: AIC=-1779.02
## log10_Permeability ~ depth + caliper + ind.deep + ind.med + gamma +
## phi.N + R.deep + R.med + SP + density.corr + density + phi.core +
## Facies
##
## Df Sum of Sq RSS AIC
## - ind.med 1 0.1213 88.981 -1779.9
## - density.corr 1 0.1440 89.004 -1779.7
## - ind.deep 1 0.1816 89.042 -1779.3
## <none> 88.860 -1779.0
## - R.deep 1 0.2696 89.130 -1778.5
## - depth 1 0.2754 89.135 -1778.5
## - caliper 1 0.3253 89.185 -1778.0
## - R.med 1 0.3763 89.236 -1777.6
## - SP 1 0.4617 89.322 -1776.8
## - phi.N 1 2.2710 91.131 -1760.3
## - density 1 3.0160 91.876 -1753.7
## - gamma 1 3.6713 92.531 -1747.9
## - Facies 7 7.0758 95.936 -1730.3
## - phi.core 1 27.4982 116.358 -1560.2
##
## Step: AIC=-1779.9
## log10_Permeability ~ depth + caliper + ind.deep + gamma + phi.N +
## R.deep + R.med + SP + density.corr + density + phi.core +
## Facies
##
## Df Sum of Sq RSS AIC
## - density.corr 1 0.1931 89.174 -1780.1
## <none> 88.981 -1779.9
## - ind.deep 1 0.2179 89.199 -1779.9
## - R.deep 1 0.2447 89.226 -1779.7
## - caliper 1 0.2921 89.273 -1779.2
## - R.med 1 0.3397 89.321 -1778.8
## - SP 1 0.4101 89.391 -1778.1
## - depth 1 0.4622 89.444 -1777.7
## - phi.N 1 2.2035 91.185 -1761.9
## - density 1 3.0113 91.993 -1754.6
## - gamma 1 3.5761 92.557 -1749.6
## - Facies 7 9.1242 98.106 -1714.0
## - phi.core 1 27.4190 116.400 -1561.9
##
## Step: AIC=-1780.12
## log10_Permeability ~ depth + caliper + ind.deep + gamma + phi.N +
## R.deep + R.med + SP + density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - ind.deep 1 0.2180 89.392 -1780.1
## <none> 89.174 -1780.1
## - R.deep 1 0.2526 89.427 -1779.8
## - caliper 1 0.2676 89.442 -1779.7
## - R.med 1 0.3598 89.534 -1778.8
## - SP 1 0.3832 89.558 -1778.6
## - depth 1 0.5404 89.715 -1777.2
## - phi.N 1 2.0726 91.247 -1763.3
## - gamma 1 3.4838 92.658 -1750.7
## - density 1 3.6220 92.796 -1749.5
## - Facies 7 9.3567 98.531 -1712.4
## - phi.core 1 27.2273 116.402 -1563.9
##
## Step: AIC=-1780.12
## log10_Permeability ~ depth + caliper + gamma + phi.N + R.deep +
## R.med + SP + density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## <none> 89.392 -1780.1
## - R.deep 1 0.2869 89.679 -1779.5
## - depth 1 0.3332 89.726 -1779.1
## - SP 1 0.4296 89.822 -1778.2
## - R.med 1 0.5085 89.901 -1777.5
## - caliper 1 0.5746 89.967 -1776.9
## - phi.N 1 2.3337 91.726 -1761.0
## - gamma 1 3.8214 93.214 -1747.8
## - density 1 3.8626 93.255 -1747.5
## - Facies 7 9.2100 98.602 -1713.8
## - phi.core 1 27.0935 116.486 -1565.3summary(Stepwise_Model_3)##
## Call:
## lm(formula = log10_Permeability ~ depth + caliper + gamma + phi.N +
## R.deep + R.med + SP + density + phi.core + Facies, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.58182 -0.12001 0.03437 0.15230 0.70317
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.2671250 3.9316796 -0.322 0.74732
## depth 0.0006562 0.0003796 1.729 0.08420 .
## caliper -0.5608681 0.2470292 -2.270 0.02344 *
## gamma -0.0091497 0.0015626 -5.855 6.94e-09 ***
## phi.N -1.7463527 0.3816550 -4.576 5.50e-06 ***
## R.deep -0.0026554 0.0016551 -1.604 0.10903
## R.med 0.0049837 0.0023334 2.136 0.03300 *
## SP -0.0016140 0.0008221 -1.963 0.04996 *
## density 1.7602255 0.2990153 5.887 5.79e-09 ***
## phi.core 0.0927539 0.0059493 15.591 < 2e-16 ***
## FaciesF10 0.0896953 0.0945929 0.948 0.34330
## FaciesF2 0.0152576 0.1523676 0.100 0.92026
## FaciesF3 -0.0292379 0.0869197 -0.336 0.73667
## FaciesF5 0.1022238 0.0879087 1.163 0.24524
## FaciesF7 0.2794793 0.1462763 1.911 0.05641 .
## FaciesF8 -0.0932936 0.0927473 -1.006 0.31477
## FaciesF9 -0.3877078 0.1030388 -3.763 0.00018 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3339 on 802 degrees of freedom
## Multiple R-squared: 0.6787, Adjusted R-squared: 0.6722
## F-statistic: 105.9 on 16 and 802 DF, p-value: < 2.2e-16Â plot the predicted vs measured permeability with respect to depth.
Predicted_log10_permeability_6 <-predict(Stepwise_Model_3,data=data)
Predicted_permeability_6<-10^Predicted_log10_permeability_6
ggplot(data) +
geom_line(aes(x = depth, y = k.core, color = "Measured permeability")) +
geom_line(aes(x = depth, y = Predicted_permeability_6, color = "Predicted permeability")) +
labs(title = "Predicted vs Measured Permeability with Respect to Depth",
x = "Depth",
y = "Permeability",
color = "Legend") +
scale_color_manual(values = c("Measured permeability" = "red",
"Predicted permeability" = "black")) +
theme_minimal()
STEP7 Random Sub-sampling Cross-Validation applied on MLR of Log10(Permeability) given all well logs with facies (25% testing ,75%training)
library(caTools)## Warning: package 'caTools' was built under R version 4.4.2split=sample.split(data$log10_Permeability,SplitRatio = 0.7)
training_set=subset(data,split==TRUE)
testing_set=subset(data,split==FALSE)Predicted_Permeabiity_Model_4<- lm(log10_Permeability~.-k.core,data=training_set)
summary(Predicted_Permeabiity_Model_4)##
## Call:
## lm(formula = log10_Permeability ~ . - k.core, data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.45736 -0.12617 0.03462 0.14460 0.76050
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.782e+00 5.394e+00 1.443 0.149696
## depth 8.957e-05 5.415e-04 0.165 0.868672
## caliper -1.241e+00 3.127e-01 -3.968 8.21e-05 ***
## ind.deep -7.985e-04 7.251e-04 -1.101 0.271296
## ind.med 8.247e-04 8.010e-04 1.030 0.303638
## gamma -1.085e-02 1.854e-03 -5.855 8.17e-09 ***
## phi.N -1.572e+00 4.437e-01 -3.544 0.000428 ***
## R.deep -2.833e-03 1.855e-03 -1.528 0.127165
## R.med 4.534e-03 2.687e-03 1.687 0.092115 .
## SP -1.148e-03 9.734e-04 -1.179 0.238792
## density.corr 2.003e+00 1.442e+00 1.389 0.165477
## density 1.948e+00 3.624e-01 5.375 1.13e-07 ***
## phi.core 9.056e-02 6.695e-03 13.527 < 2e-16 ***
## FaciesF10 -1.082e-01 1.118e-01 -0.968 0.333322
## FaciesF2 1.188e-01 1.973e-01 0.602 0.547465
## FaciesF3 -3.813e-02 1.013e-01 -0.376 0.706911
## FaciesF5 -2.590e-02 1.063e-01 -0.244 0.807611
## FaciesF7 1.664e-01 2.058e-01 0.809 0.419003
## FaciesF8 -2.166e-01 1.235e-01 -1.754 0.080070 .
## FaciesF9 -4.595e-01 1.329e-01 -3.457 0.000588 ***
## Phi.core.frac. NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3249 on 553 degrees of freedom
## Multiple R-squared: 0.7056, Adjusted R-squared: 0.6955
## F-statistic: 69.77 on 19 and 553 DF, p-value: < 2.2e-16plot the predicted (for testing data) vs measured permeability with respect to depth.
Predicted_log10_permeability_7<-predict(Predicted_Permeabiity_Model_4,newdata=testing_set)
Predicted_permeability_7<-10^Predicted_log10_permeability_7
ggplot(testing_set) +
geom_line(aes(x = depth, y = k.core, color = "Measured permeability")) +
geom_line(aes(x = depth, y = Predicted_permeability_7, color = "Predicted permeability")) +
labs(title = "Predicted vs Measured Permeability with Respect to Depth",
x = "Depth",
y = "Permeability",
color = "Legend") +
scale_color_manual(values = c("Measured permeability" = "red",
"Predicted permeability" = "black")) +
theme_minimal()
STEP8 Applying step wise elimination to this model.
Stepwise_Model_4<-step(Predicted_Permeabiity_Model_4, direction = "backward")## Start: AIC=-1268.88
## log10_Permeability ~ (depth + caliper + ind.deep + ind.med +
## gamma + phi.N + R.deep + R.med + SP + density.corr + density +
## phi.core + k.core + Facies + Phi.core.frac.) - k.core
##
##
## Step: AIC=-1268.88
## log10_Permeability ~ depth + caliper + ind.deep + ind.med + gamma +
## phi.N + R.deep + R.med + SP + density.corr + density + phi.core +
## Facies
##
## Df Sum of Sq RSS AIC
## - depth 1 0.0029 58.363 -1270.8
## - ind.med 1 0.1119 58.472 -1269.8
## - ind.deep 1 0.1280 58.488 -1269.6
## - SP 1 0.1468 58.507 -1269.4
## - density.corr 1 0.2035 58.564 -1268.9
## <none> 58.360 -1268.9
## - R.deep 1 0.2463 58.607 -1268.5
## - R.med 1 0.3004 58.661 -1267.9
## - phi.N 1 1.3253 59.686 -1258.0
## - caliper 1 1.6615 60.022 -1254.8
## - Facies 7 4.1112 62.471 -1243.9
## - density 1 3.0494 61.410 -1241.7
## - gamma 1 3.6182 61.978 -1236.4
## - phi.core 1 19.3112 77.671 -1107.1
##
## Step: AIC=-1270.85
## log10_Permeability ~ caliper + ind.deep + ind.med + gamma + phi.N +
## R.deep + R.med + SP + density.corr + density + phi.core +
## Facies
##
## Df Sum of Sq RSS AIC
## - ind.med 1 0.1383 58.501 -1271.5
## - ind.deep 1 0.1450 58.508 -1271.4
## - SP 1 0.1483 58.511 -1271.4
## <none> 58.363 -1270.8
## - density.corr 1 0.2063 58.569 -1270.8
## - R.deep 1 0.2434 58.607 -1270.5
## - R.med 1 0.2984 58.662 -1269.9
## - phi.N 1 1.3346 59.698 -1259.9
## - density 1 3.1507 61.514 -1242.7
## - caliper 1 3.4211 61.784 -1240.2
## - gamma 1 4.6376 63.001 -1229.0
## - Facies 7 6.4211 64.784 -1225.0
## - phi.core 1 19.3119 77.675 -1109.1
##
## Step: AIC=-1271.49
## log10_Permeability ~ caliper + ind.deep + gamma + phi.N + R.deep +
## R.med + SP + density.corr + density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - ind.deep 1 0.0074 58.509 -1273.4
## - SP 1 0.1066 58.608 -1272.5
## - R.deep 1 0.2016 58.703 -1271.5
## <none> 58.501 -1271.5
## - R.med 1 0.2375 58.739 -1271.2
## - density.corr 1 0.3034 58.805 -1270.5
## - phi.N 1 1.2284 59.730 -1261.6
## - density 1 3.1395 61.641 -1243.5
## - caliper 1 4.0121 62.513 -1235.5
## - gamma 1 4.9744 63.476 -1226.7
## - Facies 7 7.2648 65.766 -1218.4
## - phi.core 1 19.1834 77.685 -1111.0
##
## Step: AIC=-1273.42
## log10_Permeability ~ caliper + gamma + phi.N + R.deep + R.med +
## SP + density.corr + density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - SP 1 0.1113 58.620 -1274.3
## <none> 58.509 -1273.4
## - R.deep 1 0.2176 58.726 -1273.3
## - density.corr 1 0.2978 58.807 -1272.5
## - R.med 1 0.3118 58.821 -1272.4
## - phi.N 1 1.3910 59.900 -1262.0
## - density 1 3.1365 61.645 -1245.5
## - caliper 1 4.0184 62.527 -1237.4
## - gamma 1 5.0041 63.513 -1228.4
## - Facies 7 8.8279 67.337 -1206.9
## - phi.core 1 19.6099 78.119 -1109.8
##
## Step: AIC=-1274.33
## log10_Permeability ~ caliper + gamma + phi.N + R.deep + R.med +
## density.corr + density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - R.deep 1 0.1690 58.789 -1274.7
## <none> 58.620 -1274.3
## - R.med 1 0.2698 58.890 -1273.7
## - density.corr 1 0.2857 58.906 -1273.5
## - phi.N 1 1.3933 60.013 -1262.9
## - density 1 3.1074 61.728 -1246.7
## - caliper 1 4.0241 62.644 -1238.3
## - gamma 1 5.0019 63.622 -1229.4
## - Facies 7 8.9029 67.523 -1207.3
## - phi.core 1 19.6963 78.316 -1110.3
##
## Step: AIC=-1274.68
## log10_Permeability ~ caliper + gamma + phi.N + R.med + density.corr +
## density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - R.med 1 0.1814 58.971 -1274.9
## <none> 58.789 -1274.7
## - density.corr 1 0.2875 59.077 -1273.9
## - phi.N 1 1.5460 60.335 -1261.8
## - density 1 2.9527 61.742 -1248.6
## - caliper 1 3.8655 62.655 -1240.2
## - gamma 1 4.8334 63.623 -1231.4
## - Facies 7 8.9486 67.738 -1207.5
## - phi.core 1 20.0794 78.869 -1108.3
##
## Step: AIC=-1274.91
## log10_Permeability ~ caliper + gamma + phi.N + density.corr +
## density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## <none> 58.971 -1274.9
## - density.corr 1 0.3011 59.272 -1274.0
## - phi.N 1 1.5215 60.492 -1262.3
## - density 1 2.8082 61.779 -1250.3
## - caliper 1 4.2931 63.264 -1236.7
## - gamma 1 5.4168 64.387 -1226.6
## - Facies 7 13.6512 72.622 -1169.6
## - phi.core 1 20.0529 79.024 -1109.2summary(Stepwise_Model_4)##
## Call:
## lm(formula = log10_Permeability ~ caliper + gamma + phi.N + density.corr +
## density + phi.core + Facies, data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.48527 -0.13603 0.02793 0.15362 0.74085
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.642958 2.080891 4.634 4.47e-06 ***
## caliper -1.348508 0.211388 -6.379 3.73e-10 ***
## gamma -0.011219 0.001566 -7.166 2.46e-12 ***
## phi.N -1.564662 0.411997 -3.798 0.000162 ***
## density.corr 2.362730 1.398642 1.689 0.091719 .
## density 1.804200 0.349688 5.159 3.45e-07 ***
## phi.core 0.090485 0.006563 13.787 < 2e-16 ***
## FaciesF10 -0.090593 0.109232 -0.829 0.407257
## FaciesF2 0.131947 0.195731 0.674 0.500510
## FaciesF3 -0.052083 0.098253 -0.530 0.596261
## FaciesF5 -0.019441 0.096065 -0.202 0.839695
## FaciesF7 0.085317 0.189458 0.450 0.652655
## FaciesF8 -0.240516 0.102212 -2.353 0.018962 *
## FaciesF9 -0.509000 0.097061 -5.244 2.23e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3248 on 559 degrees of freedom
## Multiple R-squared: 0.7026, Adjusted R-squared: 0.6957
## F-statistic: 101.6 on 13 and 559 DF, p-value: < 2.2e-16plot the predicted (for testing data) vs measured permeability with respect to depth.
Predicted_log10_permeability_8 <-predict(Stepwise_Model_4,newdata=testing_set)
Predicted_permeability_8<-10^Predicted_log10_permeability_8
ggplot(testing_set) +
geom_line(aes(x = depth, y = k.core, color = "Measured permeability")) +
geom_line(aes(x = depth, y = Predicted_permeability_8, color = "Predicted permeability")) +
labs(title = "Predicted vs Measured Permeability with Respect to Depth",
x = "Depth",
y = "Permeability",
color = "Legend") +
scale_color_manual(values = c("Measured permeability" = "red",
"Predicted permeability" = "black")) +
theme_minimal()