In f0nzie/zFactor: Calculate the Compressibility Factor 'z' for Hydrocarbon Gases

knitr::opts_chunk$set(echo=T, comment=NA, error=T, warning=F, message = F, fig.align = 'center')

Example 1. Fatoorechi paper

Find z given the data below:

Temperature = 366.5 K = 200 F
Pressure = 13.7895 MPa = 2000 psia
Gas specific gravity = 0.7 
yN2 = 0.05 
yCO2 = 0.05 
yH2S = 0.02

We convert to oilfield units (Farenheit and psia).

library(rNodal)

# Example 1 in Fantoorechi paper

print(z.hallyarborough(pres.a = 2000, temp.f = 200, gas.sg = 0.7,
                       n2.frac = 0.05, co2.frac = 0.05, h2s.frac = 0.02))

If we compare the value obtained with the value in the paper, $z(NR) = 0.8362$.

Let's use the internal function z.hallyarboroughL to check all the calculated values to obtain z.

# use the internal function z.hallyarboroughL
print(rNodal:::z.hallyarboroughL(pres.a = 2000, temp.f = 200, gas.sg = 0.7,
                       n2.frac = 0.05, co2.frac = 0.05, h2s.frac = 0.02))

Using the equation for impurities in gas:

knitr::include_graphics("./images/eq_10_11-HY_FARA.jpg")

# applying equation 11
gas.sg <- 0.7
n2.frac = 0.05
co2.frac = 0.05
h2s.frac = 0.02

temp.pc <- 326 + 315.7 * (gas.sg - 0.5) - 240 * n2.frac -
              83.3 * co2.frac + 133.3 * h2s.frac
print(temp.pc)
# 375.641 R = 208.6894 K

Which gives us 208.7 Kelvin,

# from Fatorechi paper:
# Table 1, Example 1 solution
pres.pc.M <- 4.7697  # Mpa

# All temperatures in Kelvin
temp.K    <- 366.5   # sample temperature, Kelvin
temp.pc.K <- 208.6   # pseudo-critical temperature, Kelvin
temp.r <-  temp.pc.K / temp.K  # reduced temperature, adimensional
print(temp.r)

This value is different of what is shown in the solution of example 1 in the paper.

knitr::include_graphics("./images/solution_1_HY_FARA.jpg")

# To double check the calculation, we run it in Farenheit (Rankine), not Kelvin.
# All temperatures in Rankine now
temp.F <- 200
temp.R <- temp.F + 460
temp.r <- temp.pc / temp.R
print(temp.r)

Note. Definitely, something is not right: 0.569153 not equal to 0.617678.

Performing the reverse process: calculating the sampling temperature from the reduced temperature.

# calculating the sampling temperature from the reduced temperature.
# from the solution in Example 1, Fatoorechi
temp.pc.K <- 208.6 # Kelvin
temp.r    <- 0.617678
temp.K <-  temp.pc.K / temp.r
print(temp.K)

Note: 337.7164 Kelvin is not equal either to 366.5 K given in the example.

Example 2 from Fatoorechi paper

Given the second set of data, calculate Z.

Temperature = 355.4 K = 180 F
Pressure = 34.4747 MPa = 5000 psi
Gas specific gravity = 0.65 
yN2 = 0.1 
yCO2 = 0.08 
yH2S = 0.02

We convert the Kelvin to Farenheit.

library(rNodal)

# Example 2 in Fantoorechi paper

print(z.hallyarborough(pres.a = 5000, temp.f = 180, gas.sg = 0.65,
                       n2.frac = 0.1, co2.frac = 0.08, h2s.frac = 0.02))

From the paper, $z = 1.0002$.

Example 3 from Fatoorechi paper

Temperature = 310.9 K = 100 F
Pressure = 6.8947 MPa = 1000 psi
Gas specific gravity =  ?
Tpc = 237.2 K  = -32.71 F = 427.29 R
Ppc = 4.4815 MPa = 650 psia

In this example the sepecific gravity of the gas is not provided.

print(rNodal:::z.hallyarboroughL(pres.a = 1000, temp.f = 100, gas.sg = 0.82)$z)
# z = 0.760227
# from paper, z = 0.7557

From the paper, $z = 0.7557$. The difference is very small.

Modifying the `rNodal` script to accept multiple parameters

We do this in order to enter not only sampling pressure and temperature but also be able to provide pseudo-critical and pseudo-reduced pressures and temperatures as well.

source("HY.R")      # modified script saved as HY.R

# supplying gas.sg
with_gas.sg <- c(method = "use_gas.sg", 
                 z.hallyarboroughL(pres.a = 1000, temp.f = 100, gas.sg = 0.82))
# z = 0.760227
# pres.pc = 662
# temp.pc = 427.024

# no gas.sg provided
with_pseudo_crit <- c(method = "use_pseudo_critical", 
                      z.hallyarboroughL(pres.a = 1000, temp.f = 100,  
                                        pres.pc = 662, temp.pc = 427))

# no gas.sg provided
with_pseudo_red <- c(method = "use_pseudo_reduced", 
                     z.hallyarboroughL(pres.a = 1000, temp.f = 100,  
                                       pres.pr = 1.51, temp.pr = 1.31))

only_pseudo_red <- c(method = "only_pseudo_reduced", 
                     z.hallyarboroughL(pres.pr = 1.51, temp.pr = 1.31))

# put the results in a dataframe
df <- data.frame(stringsAsFactors = FALSE)
df <- rbind(df, with_gas.sg, with_pseudo_crit, with_pseudo_red, only_pseudo_red)
df