Exercise 5.1 Sensitivity on Vsh Calculation Ref. Sanni, M. (2019) Petroleum Engineering. Principles, Calculatios, and Workflows

Gamma Ray logs can be used for determining the shale content in a formation using differents relationship between Vsh and GR. Data.

Vsh Calculation Methods (Sanni, 2019).

Method | Formula | Formulation and comments |
---|---|---|

Linear (Gamma Ray Index) | \[V_{sh} = I_{GR}\] | Based in linear relationship between shale volume and GR response |

Larionov [1969] for tertiary (unconsolidated) rock | \[V_{sh} = 0.083(2^{3.7I{GR}}-1)\] | Based on empirical correlation. Linear relationship overestimates \(V_{sh}\) for tertiary (unconsolidated) rocks. |

Larionov (1969) for pre-tertiary (older and consolidated) rock | \[V_{sh} = 0.33(2^{2I{GR}}-1)\] | Based on empirical correlation. Linear relationship overestimates \(V_{sh}\) pre-tertiary (consolidate) rocks |

Stieber [1970] | \[V_{sh}=\frac{0.5I_{GR}}{1.5-I_{GR}}\] | Calibration to Gulf coast log |

Clavier et al. [1971] | \[V_{sh}=1.7-(3.38-(I_{GR}+0.7)^2)^{1/2}\] | Compromise between Larionov Tertiary and old rock model |

\(I_{GR}\) is called the gamma ray index and it is defined as: \[I_{GR} = \frac{GR_{Zone}-GR_{Clean}}{GR_{Shale}-GR_{Clean}}\]

First, read the log data and plot the GR log

```
library(ggplot2)
library(dplyr)
library(DT)
library(plotly)
log_data <- read.csv("Ex_5.1_log.csv")
datatable(log_data)
```

```
fig <- ggplot(log_data) + geom_line(aes(MD,GR), color = "green", size = 1.25) +
coord_flip() + ylab("GR (GAPI)") + xlab("MD (ft)") +
scale_x_continuous(trans = "reverse") +
scale_y_continuous(position = "right") + ylim(0, 150)
fig
```

According GR plot we can define as \(GR_{Shale} = 111.86\) and \(GR_{Clean} = 58.12\)

```
fig <- fig + geom_hline(yintercept = 58.12, linetype="dotted",
color = "blue", size=1.5) +
geom_hline(yintercept = 111.86, linetype="dotted",
color = "blue", size=1.5)
fig
```

Now, we can calculate Gamma Ray Index and Shale content (\(V_{sh}\)) using the equations above.

```
Vsh <- log_data %>%
mutate(IGR = (GR-58.12)/(111.86-58.12),
IGR = ifelse(IGR>1, 1, IGR),
IGR = ifelse(IGR<0, 0, IGR),
Vsh_Linear = IGR,
Vsh_LarionovUn = 0.083*(2^(3.7*IGR)-1),
Vsh_LarionovC = 0.33*(2^(2*IGR)-1),
Vsh_Stieber = (0.5*IGR)/(1.5-IGR),
Vsh_Clavier = 1.7-(3.38-(IGR+0.7)^2)^0.5) %>%
select(MD, IGR, Vsh_Linear, Vsh_LarionovUn, Vsh_LarionovC, Vsh_Stieber, Vsh_Clavier)
datatable(Vsh)
```

```
plot_Vsh <- ggplot(Vsh) + geom_line(aes(MD,Vsh_Linear, colour = "Linear"), size = 1.25) +
geom_line(aes(MD,Vsh_LarionovUn, colour = "Larinov (Tertiary)"), linetype = "dashed", size = 1.25) +
geom_line(aes(MD,Vsh_LarionovC, colour="Larinov (Pre-Tertiary)"), linetype = "dotted", size = 1.25) +
geom_line(aes(MD,Vsh_Stieber, colour = "Steiber"), linetype = "longdash", size = 1.25) +
geom_line(aes(MD,Vsh_Clavier, colour = "Clavier"), linetype = "dotdash", size = 1.25) +
coord_flip() + ylab("Vsh") +
scale_x_continuous(trans = "reverse") +
theme(text = element_text(size=14), legend.position="right") +
scale_color_manual(name = "Vsh methods", breaks = c("Linear", "Larinov (Tertiary)",
"Larinov (Pre-Tertiary)",
"Steiber","Clavier"),
values = c("black", "red" , "green4", "blue","brown"))
plot_Vsh
```

```
#ggplotly(plot_Vsh)
```

References Sanni, M. (2019) Petroleum Engineering. Principles, Calculatios, and Workflows

For attribution, please cite this work as

Vázquez (2021, June 5). Chato Solutions: Shale content methods. Retrieved from https://www.chatosolutions.com/posts/2021-06-05-firstpost/

BibTeX citation

@misc{vázquez2021shale, author = {Vázquez, Rigoberto Chandomí}, title = {Chato Solutions: Shale content methods}, url = {https://www.chatosolutions.com/posts/2021-06-05-firstpost/}, year = {2021} }