Scale Correction of Core Permeability by using Simple Linear Regression
Ali Watheq Shaheed
Reservoir Characterization Class
Basra University For Oil and Gas
2023-1-2
Scale Correction of Core Permeability
Scale Correction is important due to the small Scale of the K.core and the Large Scale of the reservoir (gegascopic)
Data we will use is .
data<-read.csv("D:/karpur.csv",header=T)
head(data)## 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
## 1 -0.033 2.205 33.9000 2442.590 F1
## 2 -0.067 2.040 33.4131 3006.989 F1
## 3 -0.064 1.888 33.1000 3370.000 F1
## 4 -0.053 1.794 34.9000 2270.000 F1
## 5 -0.054 1.758 35.0644 2530.758 F1
## 6 -0.058 1.759 35.3152 2928.314 F1In this step We will draw plot between phi.N and phi.core
plot(data$phi.core/100 ~ data$phi.N)
Now, we find the relationship between phi.N and phi.core
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-16Predict the core porosity corrected to the log scale by using phi.core and phi.log
phi.corel<-predict(model1,data)
#cbind(data$phi.core/100,phi.corel)Construction a relationship between permeability calculated from core and core porosity corrected to the log scale in order to get core premeability corrected to the log scale
model2<-lm(k.core~phi.corel+Facies-1,data=data)
summary(model2)##
## Call:
## lm(formula = k.core ~ phi.corel + Facies - 1, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5613.4 -596.9 -130.3 475.0 10449.1
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## phi.corel -412352 89814 -4.591 5.11e-06 ***
## FaciesF1 132659 28386 4.673 3.47e-06 ***
## FaciesF10 87869 18969 4.632 4.21e-06 ***
## FaciesF2 73980 16049 4.610 4.69e-06 ***
## FaciesF3 97910 21087 4.643 4.00e-06 ***
## FaciesF5 118916 24729 4.809 1.81e-06 ***
## FaciesF7 95868 20496 4.677 3.40e-06 ***
## FaciesF8 130990 27786 4.714 2.86e-06 ***
## FaciesF9 111324 24050 4.629 4.28e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1546 on 810 degrees of freedom
## Multiple R-squared: 0.7652, Adjusted R-squared: 0.7626
## F-statistic: 293.2 on 9 and 810 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(model2)
Predict and plot the core permeability corrected to the log scale
k.corel<-predict(model2,data)
plot(k.corel,ylab="K.corel (md)",xlab="Samples (n)")
#cbind(data$k.core,k.corel)Now, Data is represent as follow:
#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="gold", 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", 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="blue", 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="red", 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()
#plot histigram
par(mfrow=c(2,2))
hist(data$phi.N,col='green',main='',xlab='Phi.N')
hist(data$k.core,col='blue',main='',xlab='k.core')
hist(phi.corel,col='green',main='')
hist(k.corel,col='blue',main='')
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 2584.1540