# Shale content methods

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

Rigoberto Chandomí Vázquez
06-05-2021

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).

Linear (Gamma Ray Index) $V_{sh} = I_{GR}$ Based in linear relationship between shale volume and GR response
Larionov  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  $V_{sh}=\frac{0.5I_{GR}}{1.5-I_{GR}}$ Calibration to Gulf coast log
Clavier et al.  $V_{sh}=1.7-(3.38-(I_{GR}+0.7)^2)^{1/2}$ 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)

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)


Files

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

### Citation

Vázquez (2021, June 5). Chato Solutions: Shale content methods. Retrieved from https://www.chatosolutions.com/posts/2021-06-05-firstpost/
@misc{vázquez2021shale,
}