RelativePermeability

2020-07-08

Rrelperm

Rrelperm generates relative permeability values for two- and/or three-phase mixtures of water and hydrocarbons. It estimates the two-phase relative permeabilities for the water-oil and gas-liquid systems in a tabular format using the modified Brooks-Corey correlation (Brooks & Corey, 1964). It calculates the three-phase relative permeabilities using the modified Stone I, Stone II, and Baker’s linear models (Baker, 1988; Fayers & Matthews, 1984; Stone, 1970).

Relative Permeability Parameters

kr2p_ow() arguments

  • SWCON: connate water saturation, fraction.
  • SWCRIT: critical water saturation, fraction.
  • SOIRW: irreducible oil saturation, fraction.
  • SORW: residual oil saturation, fraction.
  • KRWIRO: water relative permeability at irreducible oil.
  • KROCW: oil relative permeability at connate water.
  • NW: exponent term for calculating krw.
  • NOW: exponent term for calculating krow.
  • NP: number of saturation points in the table, the maximum acceptable value is 501.

kr2p_gl() arguments

  • SWCON: connate water saturation, fraction.
  • SOIRG: irreducible oil saturation, fraction.
  • SORG: residual oil saturation, fraction.
  • SGCON: connate gas saturation, fraction.
  • SGCRIT: critical gas saturation, fraction.
  • KRGCL: gas relative permeability at connate liquid.
  • KROGCG: oil relative permeability at connate gas.
  • NG: exponent term for calculating krg.
  • NOG: exponent term for calculating krog.
  • NP: number of saturation points in the table, the maximum acceptable value is 501.

kr3p_StoneI_So() arguments

  • SWCON: connate water saturation, fraction.
  • SWCRIT: critical water saturation, fraction.
  • SOIRW: irreducible oil saturation, fraction.
  • SORW: residual oil saturation, fraction.
  • SOIRG: irreducible oil saturation, fraction.
  • SORG: residual oil saturation, fraction.
  • SGCON: connate gas saturation, fraction.
  • SGCRIT: critical gas saturation, fraction.
  • KRWIRO: water relative permeability at irreducible oil.
  • KROCW: oil relative permeability at connate water.
  • KRGCL: gas relative permeability at connate liquid.
  • KROGCG: oil relative permeability at connate gas.
  • NW: exponent term for calculating krw.
  • NOW: exponent term for calculating krow.
  • NG: exponent term for calculating krg.
  • NOG: exponent term for calculating krog.
  • NP: number of saturation points in the two-phase relative permeability tables, the maximum acceptable value is 501. The number of data points in the three-phase relative permeability table is (0.5 * NP * (NP + 1)).

kr3p_StoneI_SwSg() arguments

  • SWCON: connate water saturation, fraction.
  • SWCRIT: critical water saturation, fraction.
  • SOIRW: irreducible oil saturation, fraction.
  • SORW: residual oil saturation, fraction.
  • SOIRG: irreducible oil saturation, fraction.
  • SORG: residual oil saturation, fraction.
  • SGCON: connate gas saturation, fraction.
  • SGCRIT: critical gas saturation, fraction.
  • KRWIRO: water relative permeability at irreducible oil.
  • KROCW: oil relative permeability at connate water.
  • KRGCL: gas relative permeability at connate liquid.
  • KROGCG: oil relative permeability at connate gas.
  • NW: exponent term for calculating krw.
  • NOW: exponent term for calculating krow.
  • NG: exponent term for calculating krg.
  • NOG: exponent term for calculating krog.
  • NP: number of saturation points in the two-phase relative permeability tables, the maximum acceptable value is 501. The number of data points in the three-phase relative permeability table is (0.5 * NP * (NP + 1)).

kr3p_StoneII_So() arguments

  • SWCON: connate water saturation, fraction.
  • SWCRIT: critical water saturation, fraction.
  • SOIRW: irreducible oil saturation, fraction.
  • SORW: residual oil saturation, fraction.
  • SOIRG: irreducible oil saturation, fraction.
  • SORG: residual oil saturation, fraction.
  • SGCON: connate gas saturation, fraction.
  • SGCRIT: critical gas saturation, fraction.
  • KRWIRO: water relative permeability at irreducible oil.
  • KROCW: oil relative permeability at connate water.
  • KRGCL: gas relative permeability at connate liquid.
  • KROGCG: oil relative permeability at connate gas.
  • NW: exponent term for calculating krw.
  • NOW: exponent term for calculating krow.
  • NG: exponent term for calculating krg.
  • NOG: exponent term for calculating krog.
  • NP: number of saturation points in the two-phase relative permeability tables, the maximum acceptable value is 501. The number of data points in the three-phase relative permeability table is (0.5 * NP * (NP + 1)).

kr3p_StoneII_SwSg() arguments

  • SWCON: connate water saturation, fraction.
  • SWCRIT: critical water saturation, fraction.
  • SOIRW: irreducible oil saturation, fraction.
  • SORW: residual oil saturation, fraction.
  • SOIRG: irreducible oil saturation, fraction.
  • SORG: residual oil saturation, fraction.
  • SGCON: connate gas saturation, fraction.
  • SGCRIT: critical gas saturation, fraction.
  • KRWIRO: water relative permeability at irreducible oil.
  • KROCW: oil relative permeability at connate water.
  • KRGCL: gas relative permeability at connate liquid.
  • KROGCG: oil relative permeability at connate gas.
  • NW: exponent term for calculating krw.
  • NOW: exponent term for calculating krow.
  • NG: exponent term for calculating krg.
  • NOG: exponent term for calculating krog.
  • NP: number of saturation points in the two-phase relative permeability tables, the maximum acceptable value is 501. The number of data points in the three-phase relative permeability table is (0.5 * NP * (NP + 1)).

kr3p_Baker() arguments

  • SWCON: connate water saturation, fraction.
  • SWCRIT: critical water saturation, fraction.
  • SOIRW: irreducible oil saturation, fraction.
  • SORW: residual oil saturation, fraction.
  • SOIRG: irreducible oil saturation, fraction.
  • SORG: residual oil saturation, fraction.
  • SGCON: connate gas saturation, fraction.
  • SGCRIT: critical gas saturation, fraction.
  • KRWIRO: water relative permeability at irreducible oil.
  • KROCW: oil relative permeability at connate water.
  • KRGCL: gas relative permeability at connate liquid.
  • KROGCG: oil relative permeability at connate gas.
  • NW: exponent term for calculating krw.
  • NOW: exponent term for calculating krow.
  • NG: exponent term for calculating krg.
  • NOG: exponent term for calculating krog.
  • NP: number of saturation points in the two-phase relative permeability tables, the maximum acceptable value is 501. The number of data points in the three-phase relative permeability table is (0.5 * NP * (NP + 1)).

Installation

The Rrelperm can be installed from CRAN with:

install.packages("Rrelperm")

Two-phase Relative Permeability Examples

Example 1:

library(Rrelperm)
library(ggplot2)
library(magrittr)
library(tidyr)

rel_perm_ow <- kr2p_ow(SWCON = 0.13, SWCRIT = 0.13, SOIRW = 0.20, SORW = 0.2,
                       KRWIRO = 0.45, KROCW = 1, NW = 4.25, NOW = 2.5, NP = 101)

rel_perm_ow_df <- as.data.frame(rel_perm_ow)
colnames(rel_perm_ow_df) <- c("Sw", "So", "Krw", "Krow")

head(rel_perm_ow_df, 10)
#>      Sw   So Krw Krow
#> 1  0.00 1.00   0    1
#> 2  0.01 0.99   0    1
#> 3  0.02 0.98   0    1
#> 4  0.03 0.97   0    1
#> 5  0.04 0.96   0    1
#> 6  0.05 0.95   0    1
#> 7  0.06 0.94   0    1
#> 8  0.07 0.93   0    1
#> 9  0.08 0.92   0    1
#> 10 0.09 0.91   0    1

p1 <- rel_perm_ow_df %>% tidyr::pivot_longer(cols = c(Krw, Krow), values_to = "value",
                                             names_to = "Kr") %>%
  ggplot(aes(x = Sw, y = value, col = Kr)) +
  geom_point() +
  labs(title = "water-oil relative permeability", x = "Sw", y = "Kr") +
  theme_bw()

p1

Example 2:

library(Rrelperm)
library(ggplot2)
library(magrittr)

rel_perm_gl <- kr2p_gl(SWCON = 0.13, SOIRG = 0.12, SORG = 0.12, SGCON = 0.05,
                       SGCRIT = 0.05, KRGCL = 0.35, KROGCG = 1, NG = 4.25, NOG = 2.5,
                       NP = 101)

rel_perm_gl_df <- as.data.frame(rel_perm_gl)
colnames(rel_perm_gl_df) <- c("Sg", "Sl", "Krg", "Krog")

head(rel_perm_gl_df)
#>     Sg   Sl Krg Krog
#> 1 0.00 1.00   0    1
#> 2 0.01 0.99   0    1
#> 3 0.02 0.98   0    1
#> 4 0.03 0.97   0    1
#> 5 0.04 0.96   0    1
#> 6 0.05 0.95   0    1

p2 <- rel_perm_gl_df %>% tidyr::pivot_longer(cols = c(Krg, Krog), values_to = "value",
                                             names_to = "Kr") %>%
  ggplot(aes(x = Sg, y = value, col = Kr)) +
  geom_point() +
  labs(title = "gas-liquid relative permeability", x = "Sg", y = "Kr") +
  theme_bw()

p2

Three-phase Relative Permeability Examples

Example 1:

library(Rrelperm)
library(ggplot2)
library(ggtern)
#> Registered S3 methods overwritten by 'ggtern':
#>   method           from   
#>   grid.draw.ggplot ggplot2
#>   plot.ggplot      ggplot2
#>   print.ggplot     ggplot2
#> --
#> Remember to cite, run citation(package = 'ggtern') for further info.
#> --
#> 
#> Attaching package: 'ggtern'
#> The following objects are masked from 'package:ggplot2':
#> 
#>     aes, annotate, ggplot, ggplot_build, ggplot_gtable, ggplotGrob,
#>     ggsave, layer_data, theme_bw, theme_classic, theme_dark,
#>     theme_gray, theme_light, theme_linedraw, theme_minimal, theme_void
library(magrittr)

rel_perm_owg_st_i_swsg <- kr3p_StoneI_SwSg(SWCON = 0.13, SWCRIT = 0.13, SOIRW = 0.20,
                                      SORW = 0.2, SOIRG = 0.1, SORG = 0.1, SGCON = 0,
                                      SGCRIT = 0, KRWIRO = 0.45, KROCW = 1, KRGCL = 0.35,
                                      NW = 4.25, NOW = 2.5, NG = 3, NOG = 2,
                                      NP = 501)

rel_perm_owg_st_i_swsg <- as.data.frame(rel_perm_owg_st_i_swsg)
colnames(rel_perm_owg_st_i_swsg) <- c("Sw", "Sg", "So", "Kro")

head(rel_perm_owg_st_i_swsg, 10)
#>    Sw    Sg    So       Kro
#> 1   0 0.000 1.000 1.0000000
#> 2   0 0.002 0.998 0.9952956
#> 3   0 0.004 0.996 0.9906019
#> 4   0 0.006 0.994 0.9859188
#> 5   0 0.008 0.992 0.9812464
#> 6   0 0.010 0.990 0.9765846
#> 7   0 0.012 0.988 0.9719336
#> 8   0 0.014 0.986 0.9672932
#> 9   0 0.016 0.984 0.9626635
#> 10  0 0.018 0.982 0.9580444

rel_perm_owg_st_i_swsg$Kro_range <- cut(rel_perm_owg_st_i_swsg$Kro, breaks = seq(0,1, by = 0.1),
                                   right = TRUE, include.lowest = FALSE)

rel_perm_owg_st_i_swsg_oil <- rel_perm_owg_st_i_swsg[rel_perm_owg_st_i_swsg$Kro > 0, ]

rel_perm_owg_st_i_swsg_oil <- droplevels(rel_perm_owg_st_i_swsg_oil)

p3 <- ggtern(data = rel_perm_owg_st_i_swsg_oil, aes(x = Sw, y = Sg, z = So, value = Kro)) +
  geom_point(aes(value = Kro, fill = Kro_range, color = Kro_range), size = 1, shape = 22) +
  scale_T_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  scale_L_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  scale_R_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  ggtitle("Three-phase Oil Relative Permeability - STONE I, SWSG") +
  theme_classic()
#> Warning: Ignoring unknown aesthetics: value

p3

Example 2:

library(Rrelperm)
library(ggplot2)
library(ggtern)
library(magrittr)

rel_perm_owg_st_i_so <- kr3p_StoneI_So(SWCON = 0.13, SWCRIT = 0.13, SOIRW = 0.20,
                                      SORW = 0.2, SOIRG = 0.1, SORG = 0.1, SGCON = 0,
                                      SGCRIT = 0, KRWIRO = 0.45, KROCW = 1, KRGCL = 0.35,
                                      NW = 4.25, NOW = 2.5, NG = 3, NOG = 2,
                                      NP = 501)

rel_perm_owg_st_i_so <- as.data.frame(rel_perm_owg_st_i_so)
colnames(rel_perm_owg_st_i_so) <- c("Sw", "Sg", "So", "Kro")

head(rel_perm_owg_st_i_so, 10)
#>    Sw    Sg    So Kro
#> 1   0 0.000 1.000   1
#> 2   0 0.002 0.998   1
#> 3   0 0.004 0.996   1
#> 4   0 0.006 0.994   1
#> 5   0 0.008 0.992   1
#> 6   0 0.010 0.990   1
#> 7   0 0.012 0.988   1
#> 8   0 0.014 0.986   1
#> 9   0 0.016 0.984   1
#> 10  0 0.018 0.982   1

rel_perm_owg_st_i_so$Kro_range <- cut(rel_perm_owg_st_i_so$Kro, breaks = seq(0,1, by = 0.1),
                                   right = TRUE, include.lowest = FALSE)

rel_perm_owg_st_i_so_oil <- rel_perm_owg_st_i_so[rel_perm_owg_st_i_so$Kro > 0, ]

rel_perm_owg_st_i_so_oil <- droplevels(rel_perm_owg_st_i_so_oil)

p4 <- ggtern(data = rel_perm_owg_st_i_so_oil, aes(x = Sw, y = Sg, z = So, value = Kro)) +
  geom_point(aes(value = Kro, fill = Kro_range, color = Kro_range), size = 1, shape = 22) +
  scale_T_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  scale_L_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  scale_R_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  ggtitle("Three-phase Oil Relative Permeability - STONE I, SO") +
  theme_classic()
#> Warning: Ignoring unknown aesthetics: value

p4

Example 3:

library(Rrelperm)
library(ggplot2)
library(ggtern)
library(magrittr)

rel_perm_owg_st_ii_swsg <- kr3p_StoneII_SwSg(SWCON = 0.13, SWCRIT = 0.13, SOIRW = 0.20,
                                      SORW = 0.2, SOIRG = 0.1, SORG = 0.1, SGCON = 0,
                                      SGCRIT = 0, KRWIRO = 0.45, KROCW = 1, KRGCL = 0.35,
                                      NW = 4.25, NOW = 2.5, NG = 3, NOG = 2,
                                      NP = 501)

rel_perm_owg_st_ii_swsg <- as.data.frame(rel_perm_owg_st_ii_swsg)
colnames(rel_perm_owg_st_ii_swsg) <- c("Sw", "Sg", "So", "Kro")

head(rel_perm_owg_st_ii_swsg, 10)
#>    Sw    Sg    So       Kro
#> 1   0 0.000 1.000 1.0000000
#> 2   0 0.002 0.998 0.9948119
#> 3   0 0.004 0.996 0.9896374
#> 4   0 0.006 0.994 0.9844763
#> 5   0 0.008 0.992 0.9793287
#> 6   0 0.010 0.990 0.9741946
#> 7   0 0.012 0.988 0.9690740
#> 8   0 0.014 0.986 0.9639669
#> 9   0 0.016 0.984 0.9588733
#> 10  0 0.018 0.982 0.9537932

rel_perm_owg_st_ii_swsg$Kro_range <- cut(rel_perm_owg_st_ii_swsg$Kro, breaks = seq(0,1, by = 0.1),
                                   right = TRUE, include.lowest = FALSE)

rel_perm_owg_st_ii_swsg_oil <- rel_perm_owg_st_ii_swsg[rel_perm_owg_st_ii_swsg$Kro > 0, ]

rel_perm_owg_st_ii_swsg_oil <- droplevels(rel_perm_owg_st_ii_swsg_oil)

p5 <- ggtern(data = rel_perm_owg_st_ii_swsg_oil, aes(x = Sw, y = Sg, z = So, value = Kro)) +
  geom_point(aes(value = Kro, fill = Kro_range, color = Kro_range), size = 1, shape = 22) +
  scale_T_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  scale_L_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  scale_R_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  ggtitle("Three-phase Oil Relative Permeability - STONE II, SWSG") +
  theme_classic()
#> Warning: Ignoring unknown aesthetics: value

p5

Example 4:

library(Rrelperm)
library(ggplot2)
library(ggtern)
library(magrittr)

rel_perm_owg_st_ii_so <- kr3p_StoneII_So(SWCON = 0.13, SWCRIT = 0.13, SOIRW = 0.20,
                                      SORW = 0.2, SOIRG = 0.1, SORG = 0.1, SGCON = 0,
                                      SGCRIT = 0, KRWIRO = 0.45, KROCW = 1, KRGCL = 0.35,
                                      NW = 4.25, NOW = 2.5, NG = 3, NOG = 2,
                                      NP = 501)

rel_perm_owg_st_ii_so <- as.data.frame(rel_perm_owg_st_ii_so)
colnames(rel_perm_owg_st_ii_so) <- c("Sw", "Sg", "So", "Kro")

head(rel_perm_owg_st_ii_so, 10)
#>    Sw    Sg    So Kro
#> 1   0 0.000 1.000   1
#> 2   0 0.002 0.998   1
#> 3   0 0.004 0.996   1
#> 4   0 0.006 0.994   1
#> 5   0 0.008 0.992   1
#> 6   0 0.010 0.990   1
#> 7   0 0.012 0.988   1
#> 8   0 0.014 0.986   1
#> 9   0 0.016 0.984   1
#> 10  0 0.018 0.982   1

rel_perm_owg_st_ii_so$Kro_range <- cut(rel_perm_owg_st_ii_so$Kro, breaks = seq(0,1, by = 0.1),
                                   right = TRUE, include.lowest = FALSE)

rel_perm_owg_st_ii_so_oil <- rel_perm_owg_st_ii_so[rel_perm_owg_st_ii_so$Kro > 0, ]

rel_perm_owg_st_ii_so_oil <- droplevels(rel_perm_owg_st_ii_so_oil)

p6 <- ggtern(data = rel_perm_owg_st_ii_so_oil, aes(x = Sw, y = Sg, z = So, value = Kro)) +
  geom_point(aes(value = Kro, fill = Kro_range, color = Kro_range), size = 1, shape = 22) +
  scale_T_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  scale_L_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  scale_R_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  ggtitle("Three-phase Oil Relative Permeability - STONE II, SO") +
  theme_classic()
#> Warning: Ignoring unknown aesthetics: value

p6

Example 5:

library(Rrelperm)
library(ggplot2)
library(ggtern)
library(magrittr)

rel_perm_owg_bk <- kr3p_Baker(SWCON = 0.13, SWCRIT = 0.13, SOIRW = 0.20,
                                      SORW = 0.2, SOIRG = 0.1, SORG = 0.1, SGCON = 0,
                                      SGCRIT = 0, KRWIRO = 0.45, KROCW = 1, KRGCL = 0.35,
                                      NW = 4.25, NOW = 2.5, NG = 3, NOG = 2,
                                      NP = 501)

rel_perm_owg_bk <- as.data.frame(rel_perm_owg_bk)
colnames(rel_perm_owg_bk) <- c("Sw", "Sg", "So", "Kro")

head(rel_perm_owg_bk, 10)
#>    Sw    Sg    So       Kro
#> 1   0 0.000 1.000 1.0000000
#> 2   0 0.002 0.998 0.9948119
#> 3   0 0.004 0.996 0.9896374
#> 4   0 0.006 0.994 0.9844763
#> 5   0 0.008 0.992 0.9793287
#> 6   0 0.010 0.990 0.9741946
#> 7   0 0.012 0.988 0.9690740
#> 8   0 0.014 0.986 0.9639669
#> 9   0 0.016 0.984 0.9588733
#> 10  0 0.018 0.982 0.9537932

rel_perm_owg_bk$Kro_range <- cut(rel_perm_owg_bk$Kro, breaks = seq(0,1, by = 0.1),
                                   right = TRUE, include.lowest = FALSE)

rel_perm_owg_bk_oil <- rel_perm_owg_bk[rel_perm_owg_bk$Kro > 0, ]

rel_perm_owg_bk_oil <- droplevels(rel_perm_owg_bk_oil)

p7 <- ggtern(data = rel_perm_owg_bk_oil, aes(x = Sw, y = Sg, z = So)) +
  geom_point(aes(value = Kro, fill = Kro_range, color = Kro_range), size = 1, shape = 22) +
  scale_T_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  scale_L_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  scale_R_continuous(limits = c(0.0,1.0), breaks = seq(0,1,by = 0.05)) +
  ggtitle("Three-phase Oil Relative Permeability - Baker's Linear") +

  theme_classic()
#> Warning: Ignoring unknown aesthetics: value

p7

References

Baker, L. E. (1988). Three-Phase Relative Permeability Correlations. https://doi.org/10.2118/17369-MS

Brooks, R. H., & Corey, A. T. (1964). Hydraulic Properties of Porous Media. Hydrology Papers, (3), 27. Retrieved from https://mountainscholar.org/bitstream/handle/10217/61288/HydrologyPapers_n3.pdf

Fayers, F. J., & Matthews, J. D. (1984). Evaluation of Normalized Stone’s Methods for Estimating Three-Phase Relative Permeabilities. Society of Petroleum Engineers Journal, 24(02), 224–232. https://doi.org/10.2118/11277-PA

Stone, H. L. (1970). Probability Model for Estimating Three-Phase Relative Permeability. Journal of Petroleum Technology, 22(02), 214–218. https://doi.org/10.2118/2116-PA