heterogeneity index

dataset=read.csv("karpur.csv")
head(dataset)
dataset=dataset[order(dataset$k.core,decreasing = TRUE),]
k=dataset$k.core
sample=c(1:length(k))
k_percent=(sample*100)/length(k)
xlab="portion of total samples having larger or equal k"
ylab="permeability(md)"
plot(k_percent,k,log = 'y',xlab = xlab,ylab = ylab,pch=10,cex=0.5,col="#001C49")

log_k=log(k)
model=lm(log_k~k_percent)
plot(k_percent,log_k,xlab = xlab,ylab = ylab,pch=10,cex=0.5,col="#001c49")
abline(model,col='green',lwd=2)

summary(model)
## 
## Call:
## lm(formula = log_k ~ k_percent)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.8697 -0.2047  0.1235  0.3150  0.4280 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  9.2584172  0.0377994  244.94   <2e-16 ***
## k_percent   -0.0425617  0.0006541  -65.07   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5404 on 817 degrees of freedom
## Multiple R-squared:  0.8382, Adjusted R-squared:  0.838 
## F-statistic:  4234 on 1 and 817 DF,  p-value: < 2.2e-16
new_data=data.frame(k_percent=c(50,84.1))
predicted_values=predict(model,new_data)
heterogeneity_index=(predicted_values[1]-predicted_values[2])/predicted_values[1]
heterogeneity_index
##         1 
## 0.2035464

lorentz method

data=read.csv("karpur.csv")
#thickness calculation
thickness=c(0.5)
for (i in 2:819) {
h=data$depth[i]-data$depth[i-1]
thickness=append(thickness,h)
}
  
data=data[order(data$k.core,decreasing = TRUE),]
kh=thickness*data$k.core
ph=thickness*data$phi.core
cum_sum_kh=cumsum(kh)
cum_sum_ph=cumsum(ph)
frac_tot_vol=(cum_sum_ph/100)/max(cum_sum_ph/100)
frac_tot_flow=cum_sum_kh/max(cum_sum_kh)
plot(frac_tot_vol,frac_tot_flow,pch=10,cex=0.2,col='#001c49',text(0.4,0.8,"D"))
text(0,0,"A",pos=2)
text(1,1,"B",pos=1)
text(0,1,"C",pos=2)
abline(0,1,col='green',lwd=2)

require("DescTools")
## Loading required package: DescTools
library(DescTools)

area=AUC(frac_tot_vol,frac_tot_flow,method="trapezoid")

\[ Lorenz\ Coefficient=\frac{area\ADBA}{area\ABCA} \]

Lcoff=(area-0.5)/0.5
Lcoff
## [1] 0.4524741