Calculating The Heterogeneity Index

Heterogeneity Index describes a numerical evaluation of the level of differences or diversity in the spread of geological characteristics within an underground reservoir. This index is used to describe the spatial variety of important reservoir characteristics like porosity, permeability, and lithology.

The Dykstra-Parsons Method involves arranging permeability values in descending order to create a log-normal probability graph. The percentage of samples with permeability higher than each value is computed. In order to prevent 0% or 100% extremes, the percentage calculated is adjusted by adding 1 to ‘n’, which represents the sample size. This approach gives a thorough distribution of permeability frequencies, providing understanding of the variability within the reservoir.

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

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)

# plot best strighat line between sorted 
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 = 'red', lwd = 2)

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

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