# Shaly_sand_equations

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```					Shaly sand equations: Laminated shaly sand - forward calculation of resistivity

1  V sh
           
Poupon (1954) equation:                   1                          V
           f m  S w  sh
n

Rt     Rw                  R sh

Input Parameters:
Type into the yellow fields the parameters.
Rw =       0.05       Ohm m
f =        0.2
m=          2
n=         2                               derived parameter:            F=
Rsh =         5        Ohm m

Calculation:

Archie                Poupon
variable                                input:
Sw                Rt                    V-shale               0.05        0.10    0.20
1.00            1.25                               1.30        1.35    1.47
0.95            1.39                               1.44        1.49    1.62
0.90            1.54                               1.60        1.66    1.79
0.85            1.73                               1.79        1.85    1.99
0.80            1.95                               2.01        2.08    2.22
0.75            2.22                               2.29        2.35    2.50
0.70            2.55                               2.62        2.68    2.83
0.65            2.96                               3.02        3.08    3.22
0.60            3.47                               3.53        3.58    3.70
0.55            4.13                               4.17        4.21    4.28
0.50            5.00                               5.00        5.00    5.00
0.45            6.17                               6.10        6.03    5.90
0.40            7.81                               7.60        7.40    7.02
0.35           10.20                               9.70        9.24    8.45
0.30           13.89                              12.76       11.79   10.25
0.25           20.00                              17.39       15.38   12.50
0.20           31.25                              24.75       20.49   15.24
0.15           55.56                              36.90       27.62   18.38
0.10          125.00                              56.82       36.76   21.55
0.05          500.00                              84.03       45.87   24.04
0.01        12500.00                              99.25       49.82   24.96
alculation of resistivity

25

0.40        10000
1.79
1.95                          Vsh
2.13
2.34        1000               0
2.58                           0.05
2.86
3.17                           0.10
3.54                           0.20
100
Rt

3.96
0.40
4.44
5.00
5.64
6.38          10
7.20
8.12
9.09
10.08
11.01           1
11.79            0.01   0.10           1.00
12.32                   Sw
12.49
Shaly sand equations: Estimate of Sw from resistivity and shale content

Equations:
1
        1  V sh       1       1 n                                      (1  Vsh   Rt
Poupon, 1954 S        Rw   
R  R          m 
 f                      Indonesia , 1971
S w  V sh 2          
1  V sh 
w
        t    sh                                                                    R sh

Input: Material parameter
Type into the yellow fields the parameters

Rt =       10.00     Ohm m
Rw =        0.05      Ohm m
R sh =      7.00      Ohm m
F =       0.20
m=        2.00                                derived parameter:                    F=
n=       2.00                                                                     Ro =

Calculation:

Variable Poupon        Indonesia    Simandoux
Vsh           Sw           Sw            Sw                 0.50
0.00         0.354        0.354          0.354
0.45
0.05         0.332        0.346          0.349
0.10         0.311        0.338          0.345              0.40
0.15         0.289        0.329          0.340
0.20         0.267        0.322          0.336              0.35
0.25         0.245        0.314          0.332
0.30
0.30         0.224        0.307          0.328
Sw .

0.35         0.202        0.300          0.324              0.25
0.40         0.179        0.294          0.320
0.45         0.157        0.288          0.316              0.20
0.50         0.134        0.283          0.312              0.15

0.10

0.05

0.00
0.00 0.05 0.10 0.15 0.20
d shale content

2                                               V      
2      
 (1  Vsh               Rt 

1 R         fm                   V
  W  4           sh      sh 
n
Rt                      Simandoux, 1963   SW
Sw    V sh 2                                                      2 f m
    RW   t  R sh      R sh 
               R sh     R0                                                                       

25
1.25

Poupon
Indonesia
Simandoux

0.20 0.25 0.30 0.35 0.40 0.45 0.50
V-shale
V      
2      
fm                   V
  sh      sh 
RW   t  R sh


   R sh 


```
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