Conduct MLR to model and predict permeability in multiple scenarios
Lubaba Hakeem 29.11.2024
data<-read.csv("C:/Users/HP/Desktop/Rdata/Karpur.csv",header=T)
summary(data)## depth caliper ind.deep ind.med
## Min. :5667 Min. :8.487 Min. : 6.532 Min. : 9.386
## 1st Qu.:5769 1st Qu.:8.556 1st Qu.: 28.799 1st Qu.: 27.892
## Median :5872 Median :8.588 Median :217.849 Median :254.383
## Mean :5873 Mean :8.622 Mean :275.357 Mean :273.357
## 3rd Qu.:5977 3rd Qu.:8.686 3rd Qu.:566.793 3rd Qu.:544.232
## Max. :6083 Max. :8.886 Max. :769.484 Max. :746.028
## gamma phi.N R.deep R.med
## Min. : 16.74 Min. :0.0150 Min. : 1.300 Min. : 1.340
## 1st Qu.: 40.89 1st Qu.:0.2030 1st Qu.: 1.764 1st Qu.: 1.837
## Median : 51.37 Median :0.2450 Median : 4.590 Median : 3.931
## Mean : 53.42 Mean :0.2213 Mean : 24.501 Mean : 21.196
## 3rd Qu.: 62.37 3rd Qu.:0.2640 3rd Qu.: 34.724 3rd Qu.: 35.853
## Max. :112.40 Max. :0.4100 Max. :153.085 Max. :106.542
## SP density.corr density phi.core
## Min. :-73.95 Min. :-0.067000 Min. :1.758 Min. :15.70
## 1st Qu.:-42.01 1st Qu.:-0.016000 1st Qu.:2.023 1st Qu.:23.90
## Median :-32.25 Median :-0.007000 Median :2.099 Median :27.60
## Mean :-30.98 Mean :-0.008883 Mean :2.102 Mean :26.93
## 3rd Qu.:-19.48 3rd Qu.: 0.002000 3rd Qu.:2.181 3rd Qu.:30.70
## Max. : 25.13 Max. : 0.089000 Max. :2.387 Max. :36.30
## k.core Facies
## Min. : 0.42 Length:819
## 1st Qu.: 657.33 Class :character
## Median : 1591.22 Mode :character
## Mean : 2251.91
## 3rd Qu.: 3046.82
## Max. :15600.00model1 <- lm(data$phi.core/100 ~ data$phi.N)
summary(model1)##
## Call:
## lm(formula = data$phi.core/100 ~ data$phi.N)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.135237 -0.030779 0.009432 0.033563 0.104025
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.30962 0.00485 63.846 <2e-16 ***
## data$phi.N -0.18207 0.02080 -8.753 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04368 on 817 degrees of freedom
## Multiple R-squared: 0.08573, Adjusted R-squared: 0.08462
## F-statistic: 76.61 on 1 and 817 DF, p-value: < 2.2e-16plot(data$phi.N,data$phi.core,xlab="phi.log",ylab="phi.core",axes = F)
axis(2,col = "blue",col.axis="black")
axis(1,col = "blue",col.axis="red")
abline(model1, lwd=3, col='green')
par(mfrow=c(1,1))
hist(data$k.core, main='Histogram of Permeability', xlab='Permeability, md', col='darkblue')
model1<-lm(k.core~.-1 ,data=data)
par(mfrow=c(2,2))
plot (model1)
phi.corel <- predict(model1,data)
#cbind(karpur$phi.core/100,phi.corel)model2<-lm(k.core~phi.corel+Facies-1,data=data)
summary(model2)##
## Call:
## lm(formula = k.core ~ phi.corel + Facies - 1, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5585.6 -568.9 49.2 476.5 8928.4
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## phi.corel 1.000e+00 4.690e-02 21.32 <2e-16 ***
## FaciesF1 -2.353e-11 1.617e+02 0.00 1
## FaciesF10 4.619e-11 1.026e+02 0.00 1
## FaciesF2 2.128e-11 4.433e+02 0.00 1
## FaciesF3 1.105e-10 1.766e+02 0.00 1
## FaciesF5 2.318e-11 2.795e+02 0.00 1
## FaciesF7 -2.737e-11 4.261e+02 0.00 1
## FaciesF8 -6.261e-11 1.851e+02 0.00 1
## FaciesF9 -1.092e-11 1.046e+02 0.00 1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1253 on 810 degrees of freedom
## Multiple R-squared: 0.8457, Adjusted R-squared: 0.844
## F-statistic: 493.2 on 9 and 810 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(model2)
m1.red <- lm(k.core ~ depth+gamma+R.deep+R.med+SP+density+phi.core+Facies-1, data = data)
summary(m1.red)##
## Call:
## lm(formula = k.core ~ depth + gamma + R.deep + R.med + SP + density +
## phi.core + Facies - 1, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5461.7 -545.5 37.0 505.0 9072.8
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## depth 8.088 1.059 7.639 6.23e-14 ***
## gamma -51.915 4.526 -11.471 < 2e-16 ***
## R.deep -22.467 6.261 -3.588 0.000353 ***
## R.med 48.859 8.730 5.597 2.99e-08 ***
## SP -6.490 3.118 -2.082 0.037671 *
## density 2013.607 1047.054 1.923 0.054818 .
## phi.core 188.002 21.791 8.628 < 2e-16 ***
## FaciesF1 -51703.918 5802.150 -8.911 < 2e-16 ***
## FaciesF10 -50893.923 5917.391 -8.601 < 2e-16 ***
## FaciesF2 -51009.565 5854.625 -8.713 < 2e-16 ***
## FaciesF3 -51322.213 5871.731 -8.741 < 2e-16 ***
## FaciesF5 -51174.044 6008.663 -8.517 < 2e-16 ***
## FaciesF7 -52302.690 5971.976 -8.758 < 2e-16 ***
## FaciesF8 -53362.629 6033.789 -8.844 < 2e-16 ***
## FaciesF9 -54796.231 6100.716 -8.982 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1266 on 804 degrees of freedom
## Multiple R-squared: 0.8436, Adjusted R-squared: 0.8407
## F-statistic: 289.1 on 15 and 804 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(m1.red)
k.core.pred1 <- predict(m1.red,data)#cbind(data$k.core ,k.core.pred1 )par(mfrow=c(1,3))
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(data$k.core),type="l", col="darkred", lwd = 5, pch=17, xlab='Measured',
ylab='Depth,m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2)
grid()
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(k.core.pred1),type="l", col="green", lwd = 5, pch=17, xlab='Predicted',
ylab='Depth, m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2,)
grid()
# Matching the two curves for ease of comparison
par(mfrow=c(1,1))
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(data$k.core),type="l", col="darkred", lwd = 5, xlab='Permeability',
ylab='Depth,m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2)
grid()
par(new = TRUE)
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(k.core.pred1),type="l", col="blue", lwd = 5, xlab='',
ylab='Depth,m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2, main='R-sq=8436')
grid()
legend('topright', legend=c("Observed", "Predicted"), lty=c(1,1), col=c("darkred", "blue"))
AdjR.sq1 <- 1-sum((k.core.pred1 - data$k.core))/sum((data$k.core-mean(data$k.core))^2)
AdjR.sq1## [1] 1mspe.model1 <- sqrt(sum((k.core.pred1 - data$k.core)^2)/nrow(data))
mspe.model1## [1] 1254.46par(mfrow=c(1,1))
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(data$k.core),type="p", col="darkred", lwd = 5, pch=16, xlab='Permeability',
ylab='Depth, m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2)
grid()
par(new = TRUE)
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(k.core.pred1),type="p", col="green", lwd = 5, pch=15, xlab='',
ylab='Depth, m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2, main='AdjR.sq1=0.6847 & RMSE=1254')
grid()
legend('topright', legend=c("Observed", "Predicted"), pch=c(16,15), col=c("darkred", "green"))
hist(log10(data$k.core) ,main='Histogram of log Permeability', xlab='log Permeability, md', col='darkred')
m2<-lm(log10(k.core) ~ .-1,data=data)
summary(m2)##
## Call:
## lm(formula = log10(k.core) ~ . - 1, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.5804 -0.1138 0.0322 0.1529 0.7384
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## depth 0.0007425 0.0004718 1.574 0.1160
## caliper -0.4605945 0.2693103 -1.710 0.0876 .
## ind.deep -0.0007951 0.0006222 -1.278 0.2017
## ind.med 0.0007137 0.0006833 1.044 0.2966
## 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 0.1199
## R.med 0.0044073 0.0023960 1.839 0.0662 .
## SP -0.0016935 0.0008312 -2.037 0.0419 *
## density.corr 1.4462633 1.2712045 1.138 0.2556
## density 1.6148374 0.3100921 5.208 2.44e-07 ***
## phi.core 0.0948634 0.0060329 15.724 < 2e-16 ***
## FaciesF1 -2.3461877 4.6532000 -0.504 0.6143
## FaciesF10 -2.2675417 4.6652182 -0.486 0.6271
## FaciesF2 -2.3646211 4.6544047 -0.508 0.6116
## FaciesF3 -2.3769425 4.6697172 -0.509 0.6109
## FaciesF5 -2.2367684 4.6697432 -0.479 0.6321
## FaciesF7 -2.0650257 4.6623059 -0.443 0.6579
## FaciesF8 -2.4438111 4.6776859 -0.522 0.6015
## FaciesF9 -2.7023993 4.7023453 -0.575 0.5657
## ---
## 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: 0.9891, Adjusted R-squared: 0.9888
## F-statistic: 3613 on 20 and 799 DF, p-value: < 2.2e-16# Plot the model (m2)
par(mfrow=c(2,2))
plot(m2)
m2.red <- lm(log10(k.core) ~ caliper+gamma+phi.N+SP+density+phi.core+Facies-1,data=data)
summary(m2.red)##
## Call:
## lm(formula = log10(k.core) ~ caliper + gamma + phi.N + SP + density +
## phi.core + Facies - 1, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.60108 -0.11891 0.03253 0.15792 0.70925
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## caliper -0.840136 0.182354 -4.607 4.74e-06 ***
## gamma -0.010369 0.001337 -7.754 2.68e-14 ***
## phi.N -1.596764 0.359392 -4.443 1.01e-05 ***
## SP -0.001585 0.000793 -1.998 0.04600 *
## density 1.762145 0.287056 6.139 1.31e-09 ***
## phi.core 0.093920 0.005931 15.835 < 2e-16 ***
## FaciesF1 4.981486 1.783281 2.793 0.00534 **
## FaciesF10 5.101106 1.793029 2.845 0.00455 **
## FaciesF2 4.995149 1.796855 2.780 0.00556 **
## FaciesF3 4.967152 1.799799 2.760 0.00591 **
## FaciesF5 5.158638 1.760353 2.930 0.00348 **
## FaciesF7 5.272425 1.759300 2.997 0.00281 **
## FaciesF8 4.952389 1.753512 2.824 0.00486 **
## FaciesF9 4.687264 1.762588 2.659 0.00799 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3346 on 805 degrees of freedom
## Multiple R-squared: 0.9889, Adjusted R-squared: 0.9887
## F-statistic: 5128 on 14 and 805 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(m2.red)
k.core.pred2 <- predict(m2.red,data)k.core.pred2 <- 10^(k.core.pred2) # this back transformation to log # cbind(data$k.core ,k.core.pred2 )par(mfrow=c(1,3))plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(data$k.core),type="l", col="darkred", lwd = 5, xlab='Measured',
ylab='Depth,m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2)
grid()
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(k.core.pred2),type="l", col="yellow", lwd = 5, xlab='Predicted',
ylab='Depth, m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2,)
grid()
# Matching the two curves for ease of comparison
par(mfrow=c(1,1)) plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(data$k.core),type="l", col="green", lwd = 5, xlab='Permeability',
ylab='Depth,m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2)
grid()
par(new = TRUE)
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(k.core.pred2),type="l", col="yellow", lwd = 5, xlab='',
ylab='Depth,m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2, main='R-sq=8436')
grid()
legend('topright', legend=c("Observed", "Predicted"), lty=c(1,1), col=c("green", "yellow"))
AdjR.sq2 <- 1-sum((k.core.pred2 - data$k.core)^2)/sum((data$k.core-mean(data$k.core))^2)
AdjR.sq2## [1] 0.6366977mspe.model2 <- sqrt(sum((k.core.pred2 - data$k.core)^2)/nrow(data))
mspe.model2## [1] 1346.681par(mfrow=c(1,1))
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(data$k.core),type="p", col="darkred", lwd = 5, pch=16, xlab='Permeability',
ylab='Depth, m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2)
grid()
par(new = TRUE)
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(k.core.pred2),type="p", col="green", lwd = 5, pch=17, xlab='',
ylab='Depth, m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2, main='AdjR.sq1=0.6367 & RMSE=1346')
grid()
legend('topright', legend=c("Observed", "Predicted"), pch=c(16,17), col=c("darkred", "green"))