The data of 3 wells were given. Porosity variation analysis was understood from the correlation coefficient

1. Comparative study of porosity variations-AGeostatistical approach
Name: Vanecha Chirag Nareshbhai
Roll no.: 16BPE137
Course: Geostatistics (PEU501)
Mentor: Dr. Jwngsar Brahma
%Depth %Well 1 %Well2 %Well3
0.00 24.80 45.01 3.50
0.50 22.40 48.69 0.96
1.00 19.80 49.93 1.28
1.50 27.80 45.17 0.89
2.00 25.80 43.77 0.49
2.50 23.00 48.59 0.52
3.00 34.40 39.38 0.80
3.50 29.60 42.26 1.33
4.00 30.80 32.40 1.19
4.50 35.80 33.53 1.18
5.00 40.40 31.74 1.77
5.50 40.00 32.68 1.32
6.00 15.20 32.56 1.69
6.50 17.60 49.98 2.18
7.00 24.20 45.83 2.90
7.50 19.40 4.69 3.30
8.00 35.30 33.95 2.11
8.50 31.40 39.92 2.00
9.00 28.21 32.52 1.99
9.50 34.00 39.02 2.11
10.00 34.40 39.02 1.87
10.50 22.80 43.45 2.29
11.00 26.60 42.58 3.91
11.50 32.40 38.72 3.34
12.00 27.40 42.92 4.34
12.50 25.80 43.89 3.20
13.00 31.40 38.13 3.74
13.50 26.80 42.92 3.04
14.00 24.40 46.13 1.68
14.50 25.60 44.85 2.42
15.00 23.80 44.85 3.33
15.50 21.60 47.41 2.17
16.00 27.60 44.53 3.22
16.50 19.80 48.05 2.70
17.00 27.80 44.21 2.76
17.50 21.20 48.70 2.11
18.00 19.00 49.34 2.34
18.50 28.60 44.21 1.23
19.00 24.80 45.49 2.14
19.50 23.40 46.99 1.59
20.00 17.80 49.66 2.72
20.50 24.60 45.49 1.86
21.00 21.40 48.03 2.32
21.50 24.00 45.49 2.30
22.00 26.00 44.05 2.34
22.50 19.00 49.02 2.95
23.00 24.00 32.34 2.75
23.50 15.60 41.90 2.04
24.00 19.20 47.11 4.63
24.50 17.80 48.70 3.07
25.00 21.20 46.77 3.07
25.50 30.00 49.39 4.10
26.00 23.60 45.01 4.17
26.50 25.20 42.62 5.21
27.00 17.20 50.20 3.25
27.50 20.60 48.03 4.73
28.00 25.00 43.23 5.34
28.50 18.00 56.80 4.55
29.00 25.00 44.20 3.54
29.50 21.40 46.70 3.99

2. Well-1 Well-2 Well-3
Mean 27.3560 29.8269 2.8296
Standard deviation 7.7662 16.0594 1.4947
Increment (l) 1.7366 3.5910 0.3342
N=length 60 60 60
Range=max-min 25.2 52.11 4.85
Figure 1: comparison of p.d.f., c.d.f. and normalized distribution for Well (1), (2) & (3)

3. Figures show correlations between the porosity data of three wells. There is negative correlation between
well (1) & (2) with correlation coefficient rxy -0.4050. When porosity in well (1) increases, at the same time
it reduces in well (2). It indicates if well 1 has porous rock layers, then at the same point well 2 will have
less porous formation. Correlation between well (2) & (3) is positive and correlation coefficient ryz 0.1401.
Porosity in well (3) increases with increase in well (2). But well 3 has comparative less porosity <5% than of
well 2 and low coefficient shows positively poorly correlation more scattered data. Well (3) & (1) has weak
negative correlation with correlation coefficient rzx -0.2530.
Figure 2: Positive/negative correlation for porosity data of Well (1), (2) & (3)

4. Mean Median Max Skewness
Well 1 -0.4582 -0.4415 0.0305 Negatively
Skewed
Well 2 0.1647 0.1437 0.5421 Positively
Skewed
Well 3 -0.2522 -0.2488 0.0991 Negatively
Skewed
Outliers are the reasons for low correlation coefficient. Removing outliers improves correlation coefficient.
Bootstrap resamples the data and finds the value of correlation coefficient every time. Mean of those
correlation coefficients is taken as rfinal and compared with the initial one. And that shows how much
scattered our data are. Final-Initial/initial gives % of scattered data
Well 1: 13.13%
Well 2: 17.55%
Well 3: 0.316%
Figure 3: Histograms for Bootstrap correlations between Well (1), (2) & (3)

5. Table 1: Comparison of expected porosity probability between well (1), (2) & (3)
Porosity range p(well 1) p(well 2) p(well 3)
<5% 0.0012 0.0292 0.8971
5-25% 0.3801 0.3215 0.0735
25-40% 0.5663 0.3536 0
40-60% 0.0516 0.2342 0
Porosity range p(0-10 meters) p(10-20 meters) p(20-30 meters)
<5% 0.0022 0 0
5-25% 0.3679 0.5438 0.7257
25-40% 0.5612 0.4557 0.2703
40-60% 0.0681 0 0
Porosity range p(0-10 meters) p(10-20 meters) p(20-30 meters)
<5% 0.0339 0 0
5-25% 0.3736 0 0.0066
25-40% 0.3647 0.4602 0.3019
40-60% 0.1817 0.5398 0.6757
Porosity range p(0-10 meters) p(10-20 meters) p(20-30 meters)
<5% 0.9772 0.9907 0.9207
5-25% 0.0011 0.0068 0.0793
25-40% 0 0 0
40-60% 0 0 0
Table 2(a): Comparison of expected porosity probability for Well 1 with depth
Table 2(b): Comparison of expected porosity probability for Well 2 with depth
Table 2(c): Comparison of expected porosity probability for Well 3 with depth

6. Table 2(a) shows variations in porosities with depth for well 1. It is clearly seen that there is 56% probability
for porosity range 25-40% which indicates the presence of porous formation may be of sandstone, limestone
with loosely consolidated grains. With increase in depth, there is a trend towards decrease in porosity. For 10-
20 meters, there is 54% probability for the range 5-25% whereas it is 72% probability for 20-30 meters.
Increase in depth increases overburden weight causes reduction in porosity which can be inferred from the
table. This porosity reduction may be due to poorly sorted grains.
Table 2(b) shows variations in porosities with depth for well 2. It seems that porosity is equally distributed for
depth 0-10 meters because there is almost same probability for porosity range 5-25% and 25-40% with 18%
probability for range 40-60%. Rocks with less porosity can act as cap rocks for reservoir rocks of 25-60%
porosity. With depth increases, there is tend towards increase in porosity. It indicates carbonate formation
with channels or with high vuggy porosity due to interaction with acidic solution.
Table 2(c) shows variations in porosities with depth for well 3. Rocks are having very low porosity throughout
the whole depth. Absence of highly porous rocks since there is 0% probability of high porosity. Formation
may comprise thick Igneous formation or metamorphic rocks with fractures or Extremely poorly sorted
sandstone which deposited under turbidity depositional environment.
A petroleum reservoir or oil and gas reservoir is a subsurface pool of hydrocarbons contained in porous or
fractured rock formations. Porosity varies with different rocks. For carbonate it is 5%-25%, 10%-40% for
sandstone & shale, around 2% for Igneous and metamorphic fractured rocks. It is always desirable to have
high porosity for commercially viable hydrocarbons accumulations. Table 1 compares probability of
different porosity ranges for three wells. Porosity reduces with depth in well 1, increases in well 2, and very
low porosity in well 3 which concludes reservoir heterogeneity or the given well data may be of different
reservoir.