# Rock typing

Calculate pore-throat sizes to group petrophysical data in rock types with python

05-24-2022

Rock typing is the process of splitting the reservoir rock in an specific number of groups according to the petrophysical properties changes, in this example we use core data, porosity and permeability from Volve field. This process is used often in reservoir simulation to group fluid-rock functions, relative permeability and capillary pressure curves.

There are several methods to estimate pore-throat size: Pittman, Winland, Kolodzie and Aguile, most of them fit the pore-throat size from mercury injection capillary pressure experiment at a certain mercury saturation, using linear regression.

In this example, we use Winland correlation to estimate pore-throat size and then, group according this parameter.

$log(R35) = 0.588\ log(k) - 0.588\ log(\phi)- 0.966$

where:

$$R35 = pore \ throat \ radius \ at \ mercury \ saturation \ of \ 35%, \ microns$$

$$k = air-permeability, \ md$$

$$\phi = porosity, \ fraction$$

First, the data is loaded from a CSV file

import pandas as pd

data
       WELL           MD  POROSITY  PERMEABILITY
0    WELL_1  4038.350098     0.201     1973.9240
1    WELL_1  4038.850098     0.203     1158.9270
2    WELL_1  4039.350098     0.207     1935.1169
3    WELL_1  4039.850098     0.206     1003.6810
4    WELL_1  4040.350098     0.190      901.4980
..      ...          ...       ...           ...
401  WELL_2  3918.350098     0.207       31.1830
402  WELL_2  3918.600098     0.198       29.8160
403  WELL_2  3918.850098     0.166        9.8900
404  WELL_2  3919.100098     0.202       31.8940
405  WELL_2  3919.350098     0.150        2.9790

[406 rows x 4 columns]

Using above equation, the PTS (pore-throat size) is estimated

import math
import numpy as np

data["PTS"] = 10**(0.588*np.log10(data.PERMEABILITY) - 0.864*np.log10(data.POROSITY) - 0.996)

data
       WELL           MD  POROSITY  PERMEABILITY        PTS
0    WELL_1  4038.350098     0.201     1973.9240  34.969780
1    WELL_1  4038.850098     0.203     1158.9270  25.350609
2    WELL_1  4039.350098     0.207     1935.1169  33.696552
3    WELL_1  4039.850098     0.206     1003.6810  23.001544
4    WELL_1  4040.350098     0.190      901.4980  23.156673
..      ...          ...       ...           ...        ...
401  WELL_2  3918.350098     0.207       31.1830   2.974578
402  WELL_2  3918.600098     0.198       29.8160   3.010631
403  WELL_2  3918.850098     0.166        9.8900   1.832323
404  WELL_2  3919.100098     0.202       31.8940   3.078629
405  WELL_2  3919.350098     0.150        2.9790   0.987667

[406 rows x 5 columns]

Once we have the PTS parameter, a categorical variable could be created using the following subdivision, using cut() function from Pandas

<0.1 Nano
0.1-0.5 Micro
0.5-2 Meso
2-10 Macro
>10 Mega

data["RT"] = pd.cut(data.PTS, bins = [0,0.1,0.5,2,10,10000000],
labels = ["Nano", "Micro", "Meso", "Macro", "Mega"])
data["RT_n"] = pd.cut(data.PTS, bins = [0,0.1,0.5,2,10,10000000],
labels = [1,2,3,4,5])

data
       WELL           MD  POROSITY  PERMEABILITY        PTS     RT RT_n
0    WELL_1  4038.350098     0.201     1973.9240  34.969780   Mega    5
1    WELL_1  4038.850098     0.203     1158.9270  25.350609   Mega    5
2    WELL_1  4039.350098     0.207     1935.1169  33.696552   Mega    5
3    WELL_1  4039.850098     0.206     1003.6810  23.001544   Mega    5
4    WELL_1  4040.350098     0.190      901.4980  23.156673   Mega    5
..      ...          ...       ...           ...        ...    ...  ...
401  WELL_2  3918.350098     0.207       31.1830   2.974578  Macro    4
402  WELL_2  3918.600098     0.198       29.8160   3.010631  Macro    4
403  WELL_2  3918.850098     0.166        9.8900   1.832323   Meso    3
404  WELL_2  3919.100098     0.202       31.8940   3.078629  Macro    4
405  WELL_2  3919.350098     0.150        2.9790   0.987667   Meso    3

[406 rows x 7 columns]

Now, we can plot porosity vs permeability, mapping by rock types, using matplotlib library


import matplotlib.pyplot as plt

plt.scatter(data.POROSITY,data.PERMEABILITY, c = data.RT_n, alpha=0.8);
plt.xlabel('Porosity');
plt.ylabel('Permeability');
plt.yscale('log');
plt.ylim(0.0001,100000);
plt.show();

### Citation

Vazquez (2022, May 24). Chato Solutions: Rock typing. Retrieved from https://www.chatosolutions.com/posts/2022-05-24-rtpy/
@misc{vazquez2022rock,
}