Heterogeneity Quantification by Dykstra-Parson

1-Dykstra-Parson Coefficient

Let’s load the data

data = read.csv('karpur.csv')
head(data)

Sorting permeability values in a descending order and finding samples >= k portions

data = data[order(data$k.core, decreasing=TRUE), ]
K = data$k.core

#Calculating Number of Samples >= k
sample = c(1: length(K))

# Calculating % >= k
k_percent = (sample * 100) / length(K)

Straight line can be shown

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")

A linear model is fitted to the data.

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 = 'red', lwd = 2)

Calculating the Heterogeneity Index

new_data = data.frame(k_percent  = c(50, 84.1))
predicted_values = predict(model, new_data)
heterogenity_index = (predicted_values[1] - predicted_values[2]) / predicted_values[1]
heterogenity_index

        1 
0.2035464