Scale Correction of Core Permeability by using Simple Linear Regression
“Ali Abdul Hussein”
“Basra University For Oil and Gas”
“2024-10-21”
Why we need to do Scale Correction of Core Permeability ?
Scale Correction is essential step when we dealing with Reservoir Simulation because the data we get from core samples is in few inches and in Reservoir Simulation we deal with grids that have minimum dimensions(10 X 10 X 10 meters).
So let’s start and upload some Data.
data<-read.csv("C:/Users/Ali/Desktop/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. :15600.00At First , we should find the correlation between phi.core and phi.log
model1 <- lm(phi.core/100 ~ phi.N+Facies-1, data = data)
summary(model1)##
## Call:
## lm(formula = phi.core/100 ~ phi.N + Facies - 1, data = data)
##
## 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-16par(mfrow=c(2,2))
plot(model1, col="red")
Predict the core porosity corrected to the log scale by using phi.core and phi.log
phi.corel<-predict(model1,data)To Compare between core porosity and core porosity corrected to the log scale
#cbind(data$phi.core/100,phi.corel)Construction a relationship between permeability calculated from core and core porosity corrected to the log scale in order to get core premeability corrected to the log scale
model2<-lm(k.core~phi.corel+Facies-1,data=data)
summary(model2)##
## Call:
## lm(formula = k.core ~ phi.corel + Facies - 1, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5613.4 -596.9 -130.3 475.0 10449.1
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## phi.corel -412352 89814 -4.591 5.11e-06 ***
## FaciesF1 132659 28386 4.673 3.47e-06 ***
## FaciesF10 87869 18969 4.632 4.21e-06 ***
## FaciesF2 73980 16049 4.610 4.69e-06 ***
## FaciesF3 97910 21087 4.643 4.00e-06 ***
## FaciesF5 118916 24729 4.809 1.81e-06 ***
## FaciesF7 95868 20496 4.677 3.40e-06 ***
## FaciesF8 130990 27786 4.714 2.86e-06 ***
## FaciesF9 111324 24050 4.629 4.28e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1546 on 810 degrees of freedom
## Multiple R-squared: 0.7652, Adjusted R-squared: 0.7626
## F-statistic: 293.2 on 9 and 810 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(model2, col="red")
Predict and plot the core permeability corrected to the log scale
k.corel<-predict(model2,data)
plot(k.corel, col="red",ylab="K.corel (md)",xlab="Samples (n)")
To Compare between core permeability and core permeability corrected to the log scale
#cbind(data$k.core,k.corel)Combine the new column of corrected permeability to the file
karpur2<-cbind(data,k.corel)
write.csv(karpur2,"karpur2.csv")
head(karpur2)## 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 Facies k.corel
## 1 -0.033 2.205 33.9000 2442.590 F1 589.2371
## 2 -0.067 2.040 33.4131 3006.989 F1 1156.8516
## 3 -0.064 1.888 33.1000 3370.000 F1 1729.9769
## 4 -0.053 1.794 34.9000 2270.000 F1 2192.8857
## 5 -0.054 1.758 35.0644 2530.758 F1 2468.4267
## 6 -0.058 1.759 35.3152 2928.314 F1 2584.1540Now, Data is represent as follow:
#plot histigram
par(mfrow=c(1,2))
hist(phi.corel,col='red',main='')
hist(k.corel,col='gold',main='')
#plot graph
par(mfrow=c(1,5))
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(data$phi.core/100),type="l", col="darkgreen", lwd = 5, pch=17, xlab='phi.core',
ylab='Depth, m', xlim=c(0.14,0.38), cex=1.5, cex.lab=1.5, cex.axis=1.2)
grid()
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(data$ k.core),type="l", col="red", lwd = 5, pch=17, xlab='k.core',
ylab='Depth, m', xlim=c(0.22,15800.00), cex=1.5, cex.lab=1.5, cex.axis=1.2)
grid()
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(data$ phi.N),type="l", col="yellow", lwd = 5, pch=17, xlab='phi.N',
ylab='Depth, m', xlim=c(0.012,0.510), cex=1.5, cex.lab=1.5, cex.axis=1.2)
grid()
plot(y=y<-(data$depth),ylim=rev(range(data$depth)),x=x<-(phi.corel),type="l", col="pink", lwd = 5, pch=17, xlab='phi.corel',
ylab='Depth, m', xlim=c(0.16,0.38), 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.corel),type="l", col="blue", lwd = 5, pch=17, xlab='k.corel',
ylab='Depth, m', xlim=c(10,6400), cex=1.5, cex.lab=1.5, cex.axis=1.2)
grid()