Calculating the Heterogeneity Index

Heterogeneity Index

The Heterogeneity Index measures the variability of geological properties within a reservoir, focusing on factors like porosity and permeability. It employs methods such as the Dykstra-Parsons method, which analyzes permeability distributions using a log-normal probability graph and normalizes data to avoid extreme values. This index helps characterize spatial diversity in reservoir parameters.

#importing data and sorting the permeability values in a descending order.
data <- read.csv("karpur.csv")
data = data[order(data$k.core, decreasing=TRUE), ]
head(data)

#Calculating Number of Samples >= k
sample = c(1: length(data$k.core))

# Calculating % >= k
k_percent = (sample / length(data$k.core) ) * 100

plotting samples with permeability

plot(k_percent, data$k.core, log =  'y',
     xlab = "Portion of total samples having larger or equal K",
     ylab = "Permeability (md)",
     pch = 19, cex = 0.4, col = "yellow4")

Machine learning ( linear regression model )

model = lm(log(data$k.core) ~ k_percent)
summary(model)

Call:
lm(formula = log(data$k.core) ~ 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

plot(k_percent, log(data$k.core),
     xlab = "Portion of Total Samples Having Larger or Equal K", 
     ylab = "Permeability (md)",
     pch = 19, cex = 0.4, col = "blue4")
abline(model, col = 'red4', lwd = 2)

Calculating the Heterogeneity Index

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

        1 
0.2035464 

HI = 0.2035464 ; The reservoir has moderate heterogenetiy.