Material Balance - Volatile Oil Reservoirs"
In Rmbal: Estimate Original Hydrocarbon in Place and Reservoir Performance

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

`Examples`

`Example 1: Undersaturated Volatile Oil Reservoir` [@Walsh1995]

`Part I: History Match`

library(Rmbal)
library(Rrelperm)
library(pracma)
library(minpack.lm)
library(ggplot2)
library(dplyr)
library(magrittr)

p_pvt <- c(5070, 4998, 4798, 4698, 4658, 4598, 4398, 4198, 3998, 3798, 3598, 3398, 
           3198, 2998, 2798, 2598, 2398, 2198, 1998, 1798, 1598, 1398, 1198, 998, 798, 598)

Bo <- c(2.704, 2.713, 2.740, 2.754, 2.707, 2.631, 2.338, 2.204, 2.093, 1.991, 1.905, 
        1.828, 1.758, 1.686, 1.632, 1.580, 1.534, 1.49, 1.45, 1.413, 1.367, 1.333, 1.305,
        1.272, 1.239, 1.205)  # RB/STB

Rv <- c(343, 343, 343, 343, 116, 111, 106, 94, 84, 74, 66, 60, 54, 49, 44, 39, 36, 
        33, 30, 28, 26, 25, 24.1, 23.9, 24.4, 26.4) / 1e6  # STB/SCF

Rs <- c(2909, 2909, 2909, 2909, 2834, 2711, 2247, 2019, 1828, 1651, 1500, 1364, 1237, 
        1111, 1013, 918, 833, 752, 677, 608, 524, 461, 406, 344, 283, 212)  # SCF/STB

Bg <- c(9.27472e-04, 9.30559e-04, 9.39820e-04, 9.44622e-04, 0.83, 0.835, 0.853, 
        0.874, 0.901, 0.933, 0.97, 1.015, 1.066, 1.125, 1.196, 1.281, 1.38, 1.498, 
        1.642, 1.819, 2.035, 2.315, 2.689, 3.19, 3.911, 5.034) / 1000  # RB/SCF

cw <- 3e-6

Bwi <- 1.05

Bw <- Bwi * exp(cw * (p_pvt[1] - p_pvt))

muo <- c(742, 735, 716, 706, 718, 739, 847, 906, 968, 1028, 1104, 1177, 1242, 1325, 
         1409, 1501, 1598, 1697, 1817, 1940, 2064, 2223, 2438, 2629, 2882, 3193) / 10000

mug <- c(742, 735, 716, 706, 375, 367, 350, 327, 306, 288, 271, 255, 240, 227, 214, 
         203, 193, 184, 175, 168, 161, 155, 150, 146, 142, 138) / 10000

muw <- rep(0.25, length(p_pvt))

liq_vol <- c(1000, 1000, 1000, 1000, 967, 847, 747, 683, 630, 584, 544, 508, 471, 433, 
             402, 368, 336, 305, 271, 239, 209, 177, 146, 117, 89, 63) / 1000

pvt_table <- data.frame(p = p_pvt, Bo = Bo, Rs = Rs, Rv = Rv, Bg = Bg, 
                               Bw = Bw, muo = muo, mug = mug, muw = muw)

p <- c(5070, 4998, 4798, 4698, 4658, 4598, 4398, 4198, 3998, 3798, 3598, 3398, 
           3198, 2998, 2798, 2598, 2398, 2198, 1998, 1798, 1598, 1398, 1198, 998, 798)

We <- rep(0, length.out = length(p))

Np <- c(0, 36, 130, 184, 227, 302, 582, 808, 1022, 1227, 1388, 1528, 1646, 1764, 1861, 
        1947, 2022, 2097, 2151, 2215, 2269, 2323, 2366, 2420, 2463) * 1e6 / 1000

Rp <- c(0, 2909.000, 2909.000, 2909.000, 2894.273, 2887.417, 2847.079, 2928.218, 3072.407, 
        3286.064, 3578.530, 3918.848, 4290.401, 4661.565, 5053.735, 5470.981, 5889.713, 
        6294.230, 6760.576, 7172.009, 7640.811, 8059.836, 8499.155, 8900.413, 9329.679)

Wp <- rep(0, length.out = length(p))

Wi <- rep(0, length.out = length(p))

Gi <- rep(0, length.out = length(p))

wf <- rep(1, length.out = length(p))

mbal_optim_oil_lst <- mbal_optim_param_oil(input_unit = "Field", output_unit = "Field",  
                                          unknown_param = "N", aquifer_model = NULL, 
                                          m = 0, phi = 0.1, swi = 0.2, Np = Np, 
                                          Rp = Rp, Wp = Wp, Gi = Gi, Wi = Wi, We = We, 
                                          pb = 4698, p = p, pvt = pvt_table, cf = 2e-6, 
                                          wf = wf, sorg = 0.15, sorw = 0.0)

time_lst <- mbal_time(c(1:length(p)), "year")

# a number of plots will be automatically generated for quality check

optim_results <- mbal_optim_oil(mbal_optim_oil_lst, time_lst)

glimpse(optim_results)

`Part II: Reservoir Performance`

mbal_results <- mbal_perform_oil(optim_results, time_lst)

mbal_results

`Part III: Reservoir Forecast`

# Step I: generating a set of pseudo relative permeability curves using 
# laboratory 'Kr' values

sg_lab <- c(0.05, 0.152, 0.248, 0.352, 0.448, 0.552, 0.65)

krg_lab <- c(0, 0.05, 0.09, 0.18, 0.3, 0.5, 1)

kro_lab <- c(1, 0.6, 0.35, 0.13, 0.04, 0.01, 0)

swcrit_lab <- 0.2

sgcrit_lab <- 0.05

sorgr_lab <- 0.15

fun_kr <- function(x, swcrit, sgcrit, sorg, sg, krg, kro) {

  kr_est <- Rrelperm::kr2p_gl(SWCON = swcrit, SOIRG = sorg, SORG = sorg, 
                               SGCON = sgcrit, SGCRIT = sgcrit, KRGCL = 1, 
                               KROGCG = 1, NG = x[1], NOG = x[2], NP = 101)

   krg_est_sub <- approx(x = kr_est[,1], y = kr_est[,3], xout = sg, rule = 2)$y

   kro_est_sub <- approx(x = kr_est[,1], y = kr_est[,4], xout = sg, rule = 2)$y

   error <- (krg - krg_est_sub) ^ 2 + (kro - kro_est_sub) ^ 2

   return(error)
}

par <- c(2, 2)

opt_results <- minpack.lm::nls.lm(par = par, fn = fun_kr, swcrit = swcrit_lab, 
                                  sgcrit = sgcrit_lab, sorg = sorgr_lab, sg = sg_lab, 
                                  krg = krg_lab, kro = kro_lab, 
                                  lower = c(0.1,0.1), upper = c(10,10))

sol <- opt_results$par

sol

rel_perm <- as.data.frame(Rrelperm::kr2p_gl(SWCON = swcrit_lab, SOIRG = sorgr_lab, 
                                            SORG = sorgr_lab, SGCON = sgcrit_lab, 
                                            SGCRIT = sgcrit_lab, KRGCL = 1, 
                                            KROGCG = 1, NG = sol[1], NOG = sol[2], 
                                            NP = 101))

colnames(rel_perm) <- c("Sg", "Sl", "Krg", "Krog")

p_forecast <- p

Gi_forecast <- Gi

wf_forecast <- wf

time_lst_forecast <- mbal_time(c(1:length(p_forecast)), "year")

forecast_lst <- mbal_forecast_param_oil(input_unit = "Field", output_unit = "Field",
                                        N = 10179044, m = 0.0, phi = 0.1, swi = 0.2,
                                        Gi = Gi_forecast, pb = 4698, p = p_forecast, 
                                        pvt = pvt_table, cf = 2e-6, wf = wf_forecast, 
                                        sorg = 0.15, rel_perm = rel_perm)

glimpse(forecast_lst)

forecast_results <- mbal_forecast_oil(forecast_lst, time_lst_forecast)

forecast_results

p1 <- forecast_results %>% ggplot(aes(`P (psia)`, SOo, color = "Forecast")) +
  geom_point(size = 3) +
  geom_point(data = mbal_results, aes(`P (psia)`, SOo, color = "Field"))+
  scale_color_manual(name="Data", values=c("Forecast" = "red", "Field" = "black")) +
  ggtitle("Oil Saturation Plot") +
  theme_bw()

p1


p2 <- forecast_results %>% ggplot(aes(`P (psia)`, `GOR (SCF/STB)`, color = "Forecast")) +
  geom_point(size = 3) +
  geom_point(data = mbal_results, aes(`P (psia)`, `GOR (SCF/STB)`, color = "Field")) +
  scale_color_manual(name="Data", values=c("Forecast" = "red", "Field" = "black")) +
  ggtitle("GOR Plot") +
  theme_bw()

p2


p3 <- forecast_results %>% ggplot(aes(`P (psia)`, `RF_oil`, color = "Forecast")) +
  geom_point(size = 3) +
  geom_point(data = mbal_results, aes(`P (psia)`, `RF_oil`, color = "Field")) +
  scale_color_manual(name="Data", values=c("Forecast" = "red", "Field" = "black")) +
  ggtitle("Oil Recovery Plot") +
  theme_bw()

p3


liq_vol_CCE <- data.frame(P = p_pvt, liq_vol = liq_vol)

p4 <- forecast_results %>% ggplot(aes(`P (psia)`, `Liq_volume`, color = "Forecast")) +
  geom_point(size = 3) +
  geom_point(data = liq_vol_CCE, aes(P, `liq_vol`, color = "Lab")) +
  scale_color_manual(name="Data", values=c("Forecast" = "red", "Lab" = "black")) +
  ggtitle("CCE Liquid Volume Plot") +
  theme_bw()

p4


p5 <- forecast_results  %>%
  tidyr::pivot_longer(cols = c("Isd", "Ifwd"), names_to = "Drive Mechanism",
                      values_to = "Fraction", values_drop_na = TRUE) %>%
  ggplot(aes(`P (psia)`, Fraction, fill = `Drive Mechanism`)) +
  geom_area() +
  ggtitle("Energy Plot") +
  theme_bw()

p5

`Example 2: Undersaturated Volatile Oil Reservoir with Water Influx` [@Walsh1994a]

`Part I: History Match`

library(Rmbal)
library(Rrelperm)
library(pracma)
library(ggplot2)
library(dplyr)
library(magrittr)

p_pvt <- c(4998,    4798,   4698, 4658, 4598,   4398,   4198,   3998,   3798,   3598,   3398,   3198,   
           2998,    2798,   2598, 2398, 2198,   1998,   1798,   1598,   1398,   1198,   998, 798, 
           598) # psia

Bo <- c(2.71261,    2.73953,    2.75371, 2.70727,   2.63143,    2.33771,    2.20391,    2.09309,    
        1.99116,    1.90524,    1.82832, 1.75726,   1.68592,    1.63232,    1.58028,    1.53414,    
        1.49008,    1.44996,    1.41304, 1.36658,   1.33283,    1.30465,    1.27171,    1.23937,    
        1.20516) # RB/STB

Rs <- c(2909,   2909,   2909, 2834, 2711,   2247,   2019,   1828,   1651,   1500,   1364,   1237,   
        1111, 1013, 918,    833, 752,   677,    608,    524,    461,    406,    344,    283, 
        212) #SCF/STB

Bg <- c(0.932,  0.942,  0.947, 0.83,    0.835,  0.853,  0.874,  0.901,  0.933,  0.97,
        1.015,  1.066,  1.125, 1.196,   1.281,  1.38,   1.498,  1.642,  1.819,  2.035, 
        2.315,  2.689,  3.19, 3.911,    5.034) / 1000 # RB/SCF

Rv <- c(343,    343,    343, 116,   111,    106,    94, 84, 74, 66, 60, 54, 49, 44, 39, 
        36, 33, 30, 28, 26, 25, 24.1,   23.9,   24.4,   26.4) / 1e6 # STB/SCF

cw <- 3e-6

Bwi <- 1.05

Bw <- Bwi * exp(cw * (p_pvt[1] - p_pvt))

muo <- c(735,   716, 706, 718, 739, 847, 906, 968, 1028, 1104, 1177, 1242, 1325, 
         1409, 1501, 1598, 1697, 1817, 1940, 2064, 2223, 2438, 2629, 2882, 
         3193) / 10000

mug <- c(735,   716, 706, 375, 367, 350, 327, 306, 288, 271, 255, 240, 227, 214, 
         203, 193, 184, 175, 168, 161, 155, 150, 146, 142, 138) / 10000

muw <- rep(0.25, length(p_pvt))

pvt_table <- data.frame(p = p_pvt, Bo = Bo, Rs = Rs, Rv = Rv, Bg = Bg, 
                               Bw = Bw, muo = muo, mug = mug, muw = muw)

p <- c(4998,    4798,   4698, 4658, 4598,   4398,   4198,   3998,   3798,   3598,   3398,   3198,   
      2998, 2798,   2598, 2398, 2198,   1998,   1798,   1598,   1398,   1198,   998, 798, 
      598) # psia

Np <- c(0,  1.05,   1.63,   2.08,   2.88,   5.87,   8.36,   10.64,  12.63,  14.25,  15.65,  16.88,
        17.98,  18.9,   19.71,  20.41,  21.03,  21.59,  22.09,  22.57,  22.98,  23.34,
        23.69,  24.03, 24.38) / 100

Rp <- c(0,  2.909,  2.909, 2.909,   2.87,   2.86,   2.97,   3.18,   3.5,    3.87,   4.27,   4.68,   5.12,
        5.56,   6.02,   6.47,   6.91,   7.36,   7.8,    8.26,   8.68,   9.08,   9.48,   9.86,   
        10.25) * 1000   # SCF/STB

Wp <- rep(0, length.out = length(p))

We <- c(0, 0.0016, 0.0037, 0.005, 0.0067, 0.0149, 0.0261,   0.03096,    0.0559, 0.0742, 
        0.0952, 0.1179, 0.1424, 0.1688, 0.1966, 0.2261, 0.257, 0.2892,  0.3224, 
        0.357, 0.3923, 0.4285,  0.4658, 0.5038, 0.5425)   # RB

Gi <- rep(0, length.out = length(p))

Wi <- rep(0, length.out = length(p))

wf <- rep(1, length.out = length(p))

mbal_optim_oil_lst <- mbal_optim_param_oil(input_unit = "Field", output_unit = "Field",
                                           unknown_param = "N", aquifer_model = NULL,
                                           m = 0, phi = 0.1, swi = 0.2, Np = Np, 
                                           Rp = Rp, Wp = Wp, Gi = Gi, Wi = Wi, 
                                           We = We, pb = 4698, p = p, pvt = pvt_table, 
                                           cf = 2e-6, wf = wf, sorg = 0.15, sorw = 0.15)

time_lst <- mbal_time(c(1:length(p)), "year")

 # a number of plots will be automatically generated for quality check

 optim_results <- mbal_optim_oil(mbal_optim_oil_lst, time_lst)

 glimpse(optim_results)

`Part II: Reservoir Performance`

mbal_results <- mbal_perform_oil(optim_results, time_lst)

mbal_results

reservoir_performance_table <- data.frame(p = p)

reservoir_performance_table$`RF_oil` <- c(0, 1.05, 1.63, 2.08, 2.88, 5.87, 8.36, 
                                          10.64, 12.63, 14.25,  15.65, 16.88, 17.98, 
                                          18.9, 19.71, 20.41, 21.03,    21.59, 22.09,   
                                          22.57, 22.98, 23.34, 23.69, 24.03, 
                                          24.38) / 100

reservoir_performance_table$`Sg` <- c(0,    0,  0,  3.4,    8.6,    26.1,   32.8,   37.7,   41.7,   
                                      44.7, 47.4,   49.7,   52.1,   53.8,   55.4,   57.1,   58.6,
                                      60.1, 61.6,   63.6,   65.1,   66.6,   68.4,   70.3,   
                                      72.5) * 0.8 / 100

reservoir_performance_table$`GOR` <- c(2.91,    2.91,   2.91,   2.83,   2.75,   2.98,   3.49,   4.48,
                                       5.9, 7.62,   9.14,   10.87,  12.96,  15.23,  18.09,
                                       20.54,   22.88,  25.63,  28.03,  31.09,  33.28,  
                                       35.48,   37.12,  37.3,   35.28) * 1000 # SCF/STB

p1 <- mbal_results %>% ggplot(aes(`P (psia)`, SGo, color = "Forecast")) +
  geom_point(size = 3) +
  geom_point(data = reservoir_performance_table, aes(`p`, Sg, color = "Field"))+
  scale_color_manual(name="Data", values=c("Forecast" = "red", "Field" = "black")) +
  ggtitle("Gas Saturation Plot") +
  theme_bw()

p1


p2 <- mbal_results %>% ggplot(aes(`P (psia)`, `GOR (SCF/STB)`, color = "Forecast")) +
  geom_point(size = 3) +
  geom_point(data = reservoir_performance_table, aes(`p`, GOR, color = "Field"))+
  scale_color_manual(name="Data", values=c("Forecast" = "red", "Field" = "black")) +
  ggtitle("GOR Plot") +
  theme_bw()

p2


p3 <- mbal_results %>% ggplot(aes(`P (psia)`, `RF_oil`, color = "Forecast")) +
  geom_point(size = 3) +
  geom_point(data = reservoir_performance_table, aes(`p`, RF_oil, color = "Field"))+
  scale_color_manual(name="Data", values=c("Forecast" = "red", "Field" = "black")) +
  ggtitle("Oil Recovery Plot") +
  theme_bw()

p3


p4 <- mbal_results  %>%
  tidyr::pivot_longer(cols = c("Inwd", "Isd", "Ifwd"), names_to = "Drive Mechanism",
                      values_to = "Fraction", values_drop_na = TRUE) %>%
  ggplot(aes(`P (psia)`, Fraction, fill = `Drive Mechanism`)) +
  geom_area() +
  ggtitle("Energy Plot") +
  theme_bw()

p4

`References`

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Rmbal
Estimate Original Hydrocarbon in Place and Reservoir Performance

Material Balance - Volatile Oil Reservoirs"
In Rmbal: Estimate Original Hydrocarbon in Place and Reservoir Performance

`Examples`

`Example 1: Undersaturated Volatile Oil Reservoir` [@Walsh1995]

`Part I: History Match`

`Part II: Reservoir Performance`

`Part III: Reservoir Forecast`

`Example 2: Undersaturated Volatile Oil Reservoir with Water Influx` [@Walsh1994a]

`Part I: History Match`

`Part II: Reservoir Performance`

`References`

Try the Rmbal package in your browser

R Package Documentation

Browse R Packages

We want your feedback!

Rmbal Estimate Original Hydrocarbon in Place and Reservoir Performance

Material Balance - Volatile Oil Reservoirs" In Rmbal: Estimate Original Hydrocarbon in Place and Reservoir Performance

Examples

Example 1: Undersaturated Volatile Oil Reservoir [@Walsh1995]

Part I: History Match

Part II: Reservoir Performance

Part III: Reservoir Forecast

Example 2: Undersaturated Volatile Oil Reservoir with Water Influx [@Walsh1994a]

Part I: History Match

Part II: Reservoir Performance

References

Try the Rmbal package in your browser

R Package Documentation

Browse R Packages

We want your feedback!

Rmbal
Estimate Original Hydrocarbon in Place and Reservoir Performance

Material Balance - Volatile Oil Reservoirs"
In Rmbal: Estimate Original Hydrocarbon in Place and Reservoir Performance

`Examples`

`Example 1: Undersaturated Volatile Oil Reservoir` [@Walsh1995]

`Part I: History Match`

`Part II: Reservoir Performance`

`Part III: Reservoir Forecast`

`Example 2: Undersaturated Volatile Oil Reservoir with Water Influx` [@Walsh1994a]

`Part I: History Match`

`Part II: Reservoir Performance`

`References`