Arps Type Curves

R Reservoir engineering

Generate your own type curve to curve matching

Rigoberto Chandomi Vazquez

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


tDd <- c(seq(0.001,100,0.05))
b <- seq(0,1,0.1)
qDd_la <- lapply(b, function(b) 
  if(b == 0){

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))