In f0nzie/rNodal: Oil and Gas Well Nodal Analysis for Production Petroleum Engineering

data

# inputs
pres <- 200  # psia
temp <- 180  # deg F
gas.sg <- 0.65
n2 <- 0.1
co2 <- 0.08
h2s <- 0.02

# calculate z factor using Hall-Yarborough method at different depths. show results in dataframe.
# uses data from Guo example

library(ggplot2)
library(dplyr)

load("./data/dpt.rda")    # load Guo base data: depth, pres, temp
source("gascorrs.R")

sgg <- 0.7
nRows <- nrow(dpt)

v = x = vector("list", nRows)

for (i in seq_len(nRows)) {
  depth <- dpt[i, "depth"]
  pres  <- dpt[i, "pres"]
  temp  <- dpt[i, "temp"]

  zlist <- z.hallyarborough(pres, temp, gas.sg) # output is a list
  z <- zlist$z

  v[[i]] <- list(depth = depth,           # concatenate depth, pres with z-factor
              pres = pres, 
              temp = temp,
              z = z)

  x[[i]] <- c(depth = depth,
              pres = pres,
              temp = temp,
              zlist)
}

zfactor <- data.table::rbindlist(v)     # add row to table
zfactorAll <- data.table::rbindlist(x)

zfactorAll

# plot z factor
ggplot(zfactor, aes(pres, z)) + geom_point()

source("zfactor.R")
z <- z.brillbeggs(pres, temp, gas.sg, n2, co2, h2s)
z

# z.hallyarborough
source("zfactor.R")

z.hallyarborough(pres, temp, gas.sg, n2, co2, h2s)

source("zfactor.R")
# inputs
pres <- 5000  # psia
temp <- 180  # deg F
gas.sg <- 0.65
n2 <- 0.1
co2 <- 0.08
h2s <- 0.02

abcd <- z.hallyarborough(pres, temp, gas.sg, n2, co2, h2s)

A = abcd$A
B = abcd$B
C = abcd$C
D = abcd$D
ppr <- abcd$ppr

funcY <- function(y) {
    (y + y^2 + y^3 - y^4) / (1 - y)^3 - A * ppr - B * y^2 + C * y^D
}

curve(funcY, xlim = c(-2, 2), ylab='f(x)', 
      col = 'blue', lty = 2, lwd = 2)
abline(h=0)
abline(v=0)

Y <- uniroot(funcY, c(0, 0.3))
z <- A * ppr / Y$root
z

library(rootSolve)

funcY <- function(y) {
    (y + y^2 + y^3 - y^4) / (1 - y)^3 - A * ppr - B * y^2 + C * y^D
}

curve(funcY(x), -2, 2, main = "uniroot.all")
All <- uniroot.all(funcY, c(0, 10))
points(All, y = rep(0, length(All)), pch = 16, cex = 2)

Y <- min(All)
z <- A * ppr / Y
z

library(rootSolve)

# a well-behaved case...
fun <- function(x) cos(2*x)^3
curve(fun(x), 0, 10, main = "uniroot.all")
All <- uniroot.all(fun, c(0, 10))
points(All, y = rep(0, length(All)), pch = 16, cex = 2)

# inputs
pabs <- pres <- 1000  # psia
tempFar <- temp <- 180  # deg F
gas.sg <- 0.65
n2.frac  <- n2 <- 0
co2.frac <- co2 <- 0
h2s.frac <- h2s <- 0

  pres.pc <- 678 - 50*(gas.sg - 0.5) - 206.7 * n2.frac + 440 * co2.frac + 606.7 * h2s.frac
  temp.pc <- 326 + 315.7 * (gas.sg - 0.5) - 240 * n2.frac - 83.3 * co2.frac + 133.3 * h2s.frac
  pres.pr <- pabs / pres.pc
  temp.pr <- (tempFar + 460) / temp.pc       # worksheet has a bug in the Farenheit add
  temp.r <- 1/ temp.pr  # wrong division in worksheet cell c15

  A <- 0.06125 * temp.r * exp(-1.2 * (1 - temp.r)^2)
  B <- temp.r * (14.76 - 9.76 * temp.r + 4.58 * temp.r^2)
  C <- temp.r * (90.7 - 242.2 * temp.r + 42.4 * temp.r^2)
  D <- 2.18 + 2.82 * temp.r


  funcY <- function(y) {
    # implicit equation
    (y + y^2 + y^3 - y^4) / (1.0 - y)^3 - A * pres.pr - B * y^2 + C * y^D
  }

  All <- uniroot.all(funcY, c(0, 0.9))
  Y <- min(All)
  z <- A * pres.pr / Y
  zfactors <- list(z = z, Y = Y, A = A, B = B, C = C, D = D, pres.pr = pres.pr)
  zfactors

f0nzie/rNodal documentation built on May 6, 2019, 10:14 a.m.