Determination of Heterogeneity Index(HI) First by Dykstra-Parsons Coefficient (Vk)
shahad ali kadhim/Basra University For Oil and Gas/4th stage
Supervised by PhD Watheq J. Al-Mudhafar
2022-12-23
Dykstra-parsons Coefficient (Vk)
This method used Log-Normal distribution of permeability to define the Coefficient of permeability Variation, Vk.
Let’s upload some Real Data to work on it.
data<-read.csv("C:/Users/Lenovo/Desktop/shahed1/karpur.csv",header=T)
summary(data)## depth caliper ind.deep ind.med
## Min. :5667 Min. :8.487 Min. : 6.532 Min. : 9.386
## 1st Qu.:5769 1st Qu.:8.556 1st Qu.: 28.799 1st Qu.: 27.892
## Median :5872 Median :8.588 Median :217.849 Median :254.383
## Mean :5873 Mean :8.622 Mean :275.357 Mean :273.357
## 3rd Qu.:5977 3rd Qu.:8.686 3rd Qu.:566.793 3rd Qu.:544.232
## Max. :6083 Max. :8.886 Max. :769.484 Max. :746.028
## gamma phi.N R.deep R.med
## Min. : 16.74 Min. :0.0150 Min. : 1.300 Min. : 1.340
## 1st Qu.: 40.89 1st Qu.:0.2030 1st Qu.: 1.764 1st Qu.: 1.837
## Median : 51.37 Median :0.2450 Median : 4.590 Median : 3.931
## Mean : 53.42 Mean :0.2213 Mean : 24.501 Mean : 21.196
## 3rd Qu.: 62.37 3rd Qu.:0.2640 3rd Qu.: 34.724 3rd Qu.: 35.853
## Max. :112.40 Max. :0.4100 Max. :153.085 Max. :106.542
## SP density.corr density phi.core
## Min. :-73.95 Min. :-0.067000 Min. :1.758 Min. :15.70
## 1st Qu.:-42.01 1st Qu.:-0.016000 1st Qu.:2.023 1st Qu.:23.90
## Median :-32.25 Median :-0.007000 Median :2.099 Median :27.60
## Mean :-30.98 Mean :-0.008883 Mean :2.102 Mean :26.93
## 3rd Qu.:-19.48 3rd Qu.: 0.002000 3rd Qu.:2.181 3rd Qu.:30.70
## Max. : 25.13 Max. : 0.089000 Max. :2.387 Max. :36.30
## k.core Facies
## Min. : 0.42 Length:819
## 1st Qu.: 657.33 Class :character
## Median : 1591.22 Mode :character
## Mean : 2251.91
## 3rd Qu.: 3046.82
## Max. :15600.00head(data)## depth caliper ind.deep ind.med gamma phi.N R.deep R.med SP
## 1 5667.0 8.685 618.005 569.781 98.823 0.410 1.618 1.755 -56.587
## 2 5667.5 8.686 497.547 419.494 90.640 0.307 2.010 2.384 -61.916
## 3 5668.0 8.686 384.935 300.155 78.087 0.203 2.598 3.332 -55.861
## 4 5668.5 8.686 278.324 205.224 66.232 0.119 3.593 4.873 -41.860
## 5 5669.0 8.686 183.743 131.155 59.807 0.069 5.442 7.625 -34.934
## 6 5669.5 8.686 109.512 75.633 57.109 0.048 9.131 13.222 -39.769
## density.corr density phi.core k.core Facies
## 1 -0.033 2.205 33.9000 2442.590 F1
## 2 -0.067 2.040 33.4131 3006.989 F1
## 3 -0.064 1.888 33.1000 3370.000 F1
## 4 -0.053 1.794 34.9000 2270.000 F1
## 5 -0.054 1.758 35.0644 2530.758 F1
## 6 -0.058 1.759 35.3152 2928.314 F1Here we will find the distrirbutin of K (md),but first we should find the Frequency for each K and we will work on 100 samples to simplifed the resultant.
K_md<-kf$k.core
Vk<-tab1(K_md , sort.group = "decreasing", cum.percent = FALSE)
summary(Vk)## Length Class Mode
## first.line 1 -none- character
## output.table 1616 -none- numericThen after finding the Frequency we will find the Cumlative Frequency Distirpution for X-values then after that ploting K (md) with Cumlative Frequency Distirpution.
Cumlative_Frequency_Distirpution## # A tibble: 807 × 4
## k.core Frequency Num.samples cumulative_frequency
## <dbl> <dbl> <dbl> <dbl>
## 1 14225. 1 1 0.122
## 2 13545. 1 2 0.244
## 3 13034. 1 3 0.367
## 4 11842. 1 4 0.489
## 5 11117. 1 5 0.611
## 6 10860 1 6 0.733
## 7 10650. 1 7 0.856
## 8 10540 1 8 0.978
## 9 9898. 1 9 1.10
## 10 9533. 1 10 1.22
## # … with 797 more rowsNow we are Ready to plot our Graph
df = read_xlsx("C:/Users/Lenovo/Desktop/shahed1/shahed_al.xlsx")
model1 <- lm( df$k.core~ df$cumulative_frequency)
plot(df$cumulative_frequency,df$k.core,xlab="Cumlative Frequency Distirpution", ylab="K (md)")
abline(model1, lwd=4, col='Pink', untf=FALSE)
Now by using this relationship,
Vk= (K50-k84.1)/K50
we will be able to quantify Heterogeneity Index (HI)
Vk= (1591.2185-392.78)/1591.2185
Vk= 0.7531577
Therefore from this Value, we know that this reservoir is Extremely Heterogeneous.