# Arps Type Curves

Generate your own type curve to curve matching

06-19-2021

The type curve matching analysis method is one of different methods to determine the decline parameters: $$b$$, $$q_i$$ and $$D_i$$

Other methods could be trial and error, and curve matching, etc.

Dimensionless time

$t_{Dd} = D_it$

Dimensionless rate, exponential declina

$q_{Dd} = \frac{q}{q_i}=e^{-t_{Dd}}$

hyperbolic decline

$q_{Dd} = (1+bt_{Dd})^{-1/b} \ \text{b is constant,} \ 0<b<1$

harmonic decline

$q_{Dd}= \frac{1}{1+t_{Dd}}$ Using the equation above, we can generate and plot type curve. Define $$t_{Dd}$$ values and $$b$$ value from 0 to 1. With lapply() function we can repeat $$q_{Dd}$$ calculate with every $$b$$ value, the result is a list that we can convert in a single dataframe

With melt() function from reshape2 package we can melt the dataframe in less columns, in this case put all $$q_{Dd}$$ in a single column. Finally plot $$q_{Dd}$$ Vs. $$t_{Dd}$$ and grouping by $$b$$ value

library(ggplot2)
library(reshape2)
library(plotly)

tDd <- c(seq(0.001,100,0.05))
b <- seq(0,1,0.1)
qDd_la <- lapply(b, function(b)
if(b == 0){
exp(-tDd)
}else{
(1+b*tDd)^(-1/b)
}

)

qDd <- data.frame(qDd_la)
colnames(qDd) <- b
qDd\$tDd <- tDd
qDd <- reshape2::melt(qDd,id.vars="tDd")
colnames(qDd) <- c("tDd","b","qDd")

fet_plot <- ggplot() +
#geom_line(data = qDd_tr,aes(tDd_t,qDd_tr,group = reD, col = reD),size = 1) +
geom_line(data = qDd,aes(tDd,qDd,group = b, col = b),size = 1) +
xlab("tDd") +
ylab("qDd") +
scale_y_log10(limits = c(0.001, 10)) +
scale_x_log10(limits = c(0.0001, 100))

fet_plot ggplotly(fet_plot)