Calculating The Heterogeneity Index

Heterogeneity Index

refers to a quantitative measure that assesses the degree of heterogeneity or variability in the distribution of geological properties within a subsurface reservoir. This index is utilized to characterize the spatial diversity of key reservoir parameters, such as porosity, permeability, or lithology.

he determination of the Heterogeneity Index involves employing distinct methods: the Dykstra-Parsons method of permeability variation.

1. Dykstra-Parsons Method: The Dykstra-Parsons method entails creating a log-normal probability graph by arranging permeability values in descending order. For each permeability value, the percentage of samples with permeability greater than that value is calculated. To avoid extremes of zero or 100%, the calculated percentage is normalized by n+1, where ‘n’ represents the number of samples. This method provides a comprehensive frequency distribution of permeability, offering insights into the variation across 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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