1. Data Preparation
2. Creating linear regression model
3. Data visualization
###Recall Karpur Dataset
setwd("/Users/khalilahmed/Desktop/User1/Stage 4/RC/Rstudio files")
kdata<- read.csv("karpur.csv",header=TRUE)
##phi core in karpur.csv file is normal number so in excel conveted to fractin under title (phi.core.)
head(kdata)
dim(kdata)
#use histogram to show diff. ranges and freqs. b/w data
par(mfrow=c(1,3))
hist(kdata$phi.N, xlab ='log porosity', main = '', col = 'red' )
hist(kdata$phi.core., xlab ='core porosity', main = '', col = 'green' )
hist(kdata$k.core, xlab ='core permeability', main = '', col = 'yellow' )
2. Creating linear regression model
##use simple linear regression model foe core porosity as function of log porosity
slr <- lm(phi.core. ~ phi.N, data = kdata)
plot(kdata$phi.N, kdata$phi.core., xlab='log porosity', ylab='core porosity')
coef(slr)
## (Intercept) phi.N
## 0.3096232 -0.1820696
abline(slr, lwd=2, col='red' )
abline(0,1, col='green')
##result alot of out layers far from straight line
summary(slr)
##
## Call:
## lm(formula = phi.core. ~ phi.N, data = kdata)
##
## 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 ***
## 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-16
## simple linear regression model show Root mean square prediction error is low value (0.08462)so there are not relationship
#between (x,y)
#use multiple linear regression model for core porosity as function of log porosity & facies
#to calculate phi core corrected to log scale
# core porosity doesn't need to normlization
phicorelog <- lm(phi.core. ~ phi.N+Facies-1, data = kdata)
summary(phicorelog)
##
## Call:
## lm(formula = phi.core. ~ phi.N + Facies - 1, data = kdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.103530 -0.011573 -0.000206 0.010463 0.102852
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## phi.N 0.013364 0.018060 0.74 0.46
## FaciesF1 0.314805 0.002777 113.37 <2e-16 ***
## FaciesF10 0.207680 0.005072 40.95 <2e-16 ***
## FaciesF2 0.175233 0.009390 18.66 <2e-16 ***
## FaciesF3 0.231939 0.004955 46.81 <2e-16 ***
## FaciesF5 0.272953 0.003914 69.74 <2e-16 ***
## FaciesF7 0.225164 0.008730 25.79 <2e-16 ***
## FaciesF8 0.305884 0.005019 60.94 <2e-16 ***
## FaciesF9 0.264448 0.004825 54.81 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02326 on 810 degrees of freedom
## Multiple R-squared: 0.9928, Adjusted R-squared: 0.9928
## F-statistic: 1.246e+04 on 9 and 810 DF, p-value: < 2.2e-16
#as we look Root mean square prediction error is high value(0.9928)close to 1 so there are linear relationship
#between (x,y)
pphicorelog <- predict(phicorelog, newdata=kdata)
cbind('phi Core'=kdata$phi.core.,'phi log'=kdata$phi.N,phicorelog)
#use multiple linear regression model between porosity of core corrected to log scale(with facies) & core permeability
#to calculate permeability core corrected to log scale
# prediction K without Normalization
outnk <- lm(kdata$k.core ~ pphicorelog+Facies-1, data = kdata)
summary(outnk)
##
## Call:
## lm(formula = kdata$k.core ~ pphicorelog + Facies - 1, data = kdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5613.4 -596.9 -130.3 475.0 10449.1
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## pphicorelog -412352 89814 -4.591 5.11e-06 ***
## FaciesF1 132659 28386 4.673 3.47e-06 ***
## FaciesF10 87869 18968 4.632 4.21e-06 ***
## FaciesF2 73980 16049 4.610 4.69e-06 ***
## FaciesF3 97910 21087 4.643 4.00e-06 ***
## FaciesF5 118916 24729 4.809 1.81e-06 ***
## FaciesF7 95868 20496 4.677 3.40e-06 ***
## FaciesF8 130990 27786 4.714 2.86e-06 ***
## FaciesF9 111324 24050 4.629 4.28e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1546 on 810 degrees of freedom
## Multiple R-squared: 0.7652, Adjusted R-squared: 0.7626
## F-statistic: 293.2 on 9 and 810 DF, p-value: < 2.2e-16
poutnk <- predict(outnk, newdata=kdata)
# normalize core permeability data
nkcore <- log10(kdata$k.core)
par(mfrow=c(1,2))
hist(kdata$k.core, main='', xlab='core permeability' )
hist(nkcore, main='', xlab='normalized core permeability')
kcorelog <- lm( nkcore ~ pphicorelog+Facies-1, data = kdata)
summary(kcorelog)
##
## Call:
## lm(formula = nkcore ~ pphicorelog + Facies - 1, data = kdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.92979 -0.16693 0.02686 0.22160 0.90566
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## pphicorelog -126.548 23.804 -5.316 1.37e-07 ***
## FaciesF1 43.350 7.523 5.762 1.18e-08 ***
## FaciesF10 29.296 5.027 5.827 8.13e-09 ***
## FaciesF2 24.772 4.254 5.824 8.30e-09 ***
## FaciesF3 32.392 5.589 5.796 9.74e-09 ***
## FaciesF5 38.460 6.554 5.868 6.43e-09 ***
## FaciesF7 32.046 5.432 5.899 5.36e-09 ***
## FaciesF8 42.638 7.364 5.790 1.01e-08 ***
## FaciesF9 36.758 6.374 5.767 1.15e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4097 on 810 degrees of freedom
## Multiple R-squared: 0.9833, Adjusted R-squared: 0.9831
## F-statistic: 5289 on 9 and 810 DF, p-value: < 2.2e-16
#Root mean square prediction error is high value(0.9831) so there are linear relationship between (x,y)
pkcorelog <- predict(kcorelog, newdata=kdata)
epkcorelog <- 10^pkcorelog
3. Data visualization
##visualization of data
par(mfrow=c(1,2))
plot(kdata$phi.core.,kdata$depth, xlab='core porosity', ylab='depth', col='blue', xlim = c(0.1570,0.3630),
ylim = c(6083,5667), type ='l')
plot(kdata$phi.N,kdata$depth, xlab='log porosity', ylab='depth', col='red', xlim = c(0.0150,0.4100),
ylim = c(6083,5667), type ='l')
plot(kdata$k.core,kdata$depth, xlab='core permeability', ylab='depth', col='brown', xlim = c( 0.42,15600.00),
ylim = c(6083,5667), type ='l')
plot(pphicorelog,kdata$depth, xlab='corrected porosity', ylab='depth', col='green', xlim = c( 0.1775,0.3203),
ylim = c(6083,5667), type ='l')
plot(epkcorelog,kdata$depth, xlab=' corrected permeability', ylab='depth', col='violet', xlim = c( 130.1,7815.2),
ylim = c(6083,5667), type ='l')
boxplot(depth ~ Facies, data = kdata ,ylim = c(6083,5667))
##show in same graph
par(mfrow=c(1,1))
plot(y=y<-(kdata$depth),ylim = c(6083,5667),
x=x<-(kdata$k.core), type="l",col="red", lwd = 5,
lty=3, pch=17, ylab="Depth,m", xlab="Permeability", xlim=c(0,15600))
par(new = TRUE)
plot(y=y<-(kdata$depth),ylim = c(6083,5667),
x=x<-(poutnk), type="l",col="green",lwd = 4,
lty=1, pch=5, ylab="", xlab="", xlim=c(0,15600))
par(new = TRUE)
plot(y=y<-(kdata$depth),ylim = c(6083,5667),
x=x<-(epkcorelog), type="l",col="darkgreen",lwd = 4,
lty=1, pch=5, ylab="", xlab="", xlim=c(0,15600))
grid()
legend('topright', legend=c("Observed K", "Predicted K", "Predicted Normalize K"),
lty=c(3,1,1),col=c("red", "green", "darkgreen"))
require(xtable)
## Loading required package: xtable
summary(kdata)
## 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
## phi.core. k.core Facies
## Min. :0.1570 Min. : 0.42 Length:819
## 1st Qu.:0.2390 1st Qu.: 657.33 Class :character
## Median :0.2760 Median : 1591.22 Mode :character
## Mean :0.2693 Mean : 2251.91
## 3rd Qu.:0.3070 3rd Qu.: 3046.82
## Max. :0.3630 Max. :15600.00