Raquifer

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Raquifer

`Raquifer`

Raquifer estimates the cumulative water influx into hydrocarbon reservoirs using un-steady and pseudo-steady state modeling approaches. It generates a data frame of cumulative water influx over time for edge-drive and bottom-drive aquifers. Van Everdingen and Hurst un-steady state model for the constant terminal pressure solution predicts the cumulative influx for edge-water drive aquifers with radial flow (Van Everdingen & Hurst, 1949). For the bottom-water drive aquifers with linear/radial flow, the Yildiz-Khosravi un-steady state model for the constant terminal pressure solution is used (Yildiz & Khosravi, 2007). Nabor and Barham linear flow model for the constant terminal pressure solution is used for the edge-water and bottom-water drive aquifers modeling(Nabor & Barham, 1964). For the linear and radial pseudo-steady state flow modeling in aquifers, the Fetkovich method is used (Fetkovich, 1971).

Cumulative water influx predictions are generated by three different functions: aquifer_param(), aquifer_time(), and aquifer_predict().

`aquifer_param() arguments`

input_unit: A unit system for parameters, a character string either ‘SI’ or ‘Field’
output_unit: A unit system for properties, a character string either ‘SI’ or ‘Field’
param model: State of flow in the aquifer, a character string either ‘uss’ for the un-steady state flow or ‘pss’ for the pseudo-steady state flow
flow_type: A character string either ‘radial’ or ‘linear’
water_drive: A character string either ‘edge’ or ‘bottom’
phi: Aquifer porosity, a numeric fraction
perm_h: Aquifer horizontal permeability in ‘md’ in both ‘SI’ and ‘Field’ input unit systems. A NULL value must be used for the combination of ‘uss’, ‘linear’, and ‘bottom’ flow
perm_v: Aquifer vertical permeability in ‘md’ in both ‘SI’ and ‘Field’ input unit systems. A NULL value must be used for the combination of ‘uss’, ‘linear’, ‘edge’ flow. A NULL value must be used for the combination of ‘uss’, ‘radial’, ‘edge’ flow. A NULL value must be used for the combination of ‘pss’, ‘radial’, ‘edge’ flow.
h_a: Aquifer` height in ‘m’ or ‘ft’ in ‘SI’ and ‘Field’ input unit systems, respectively.
r_a: Aquifer radius in ‘m’ or ‘ft’ in ‘SI’ and ‘Field’ input unit systems, respectively. A NULL value must be used for the combination of ‘uss’, ‘linear’, ‘edge’ flow. A NULL value must be used for the combination of ‘uss’, ‘linear’, ‘bottom’ flow.
r_R: Reservoir radius in ‘m’ or ‘ft’ in ‘SI’ and ‘Field’ input unit systems, respectively. A NULL value must be used for the combination of ‘uss’, ‘linear’, ‘edge’ flow. A NULL value must be used for the combination of ‘uss’, ‘linear’, ‘bottom’ flow.
w_a: Aquifer width in ‘m’ or ‘ft’ in ‘SI’ and ‘Field’ input unit systems, respectively. A NULL value must be used for the combination of ‘uss’, ‘radial’, ‘edge’ flow. A NULL value must be used for the combination of ‘uss’, ‘radial’, ‘bottom’ flow. A NULL value must be used for the combination of ‘pss’, ‘radial’, ‘edge’ flow.
l_a: Aquifer length in ‘m’ or ‘ft’ in ‘SI’ and ‘Field’ input unit systems, respectively. A NULL value must be used for the combination of ‘uss’, ‘radial’, ‘edge’ flow. A NULL value must be used for the combination of ‘uss’, ‘radial’, ‘bottom’ flow. A NULL value must be used for the combination of ‘pss’, ‘radial’, ‘edge’ flow.
tetha: Fraction of reservoir encircled by the aquifer, reported in “degrees” in both ‘SI’ and ‘Field’ input unit systems. A NULL value must be used for the combination of ‘uss’, ‘radial’, ‘bottom’ flow. A NULL value must be used for the combination of ‘uss’, ‘linear’, ‘edge’ flow. A NULL value must be used for the combination of ‘uss’, ‘linear’, ‘bottom’ flow.
mu_water: Water viscosity in ‘mPa.s’ or ‘cp’ in ‘SI’ and ‘Field’ input unit systems, respectively
c_water: Water compressibility in ‘1/kPa’ or ‘1/psi’ in ‘SI’ and ‘Field’ input unit systems, respectively
c_rock: Rock compressibility in ‘1/kPa’ or ‘1/psi’ in ‘SI’ and ‘Field’ input unit systems, respectively
pressure: A numeric vector of pressure data at the boundary of reservoir/aquifer. Must have the same length as the ‘aquifer_time()’ object

`aquifer_time() arguments`

x: A vector or sequence of times/dates.
unit: A unit system for input vector x.

`aquifer_predict() arguments`

aquifer_lst: A list object of class ‘decline’.
time_lst: A list object of class ‘time’

`Installation`

The Raquifer can be installed from CRAN with:

install.packages("Raquifer")

`Examples`

`Example 1: Un-steady state radial flow, edge-water drive`

library(Raquifer)
library(ggplot2)
library(magrittr)

aqu_time <- aquifer_time(x = c(0,0.368,2.439,4.957,7.732,11.926,18.126,30.044) * 365, unit = "day")

parameters <- aquifer_param(input_unit = "Field", output_unit = "Field", model = "uss", 
                            flow_type = "radial", water_drive = "edge", phi = 0.27, perm_h = 64.2, 
                            h_a = 20, r_a = 5 * 14892, r_R = 14892, tetha = 180,
                            mu_water = 0.485, c_water = 3.88e-6, c_rock = 2e-6, 
                            pressure = c(1640,1600,1400,1200,1000,800,600,400))

aqu_time
#> $t
#> [1]     0.000   134.320   890.235  1809.305  2822.180  4352.990  6615.990
#> [8] 10966.060
#> 
#> $unit
#> [1] "day"
#> 
#> $reference_date
#> [1] "2020-05-12"
#> 
#> attr(,"class")
#> [1] "day"  "time"

parameters
#> $input_unit
#> [1] "Field"
#> 
#> $output_unit
#> [1] "Field"
#> 
#> $model
#> [1] "veh_rad_edge"
#> 
#> $phi
#> [1] 0.27
#> 
#> $perm_h
#> [1] 64.2
#> 
#> $h_a
#> [1] 20
#> 
#> $r_a
#> [1] 74460
#> 
#> $r_R
#> [1] 14892
#> 
#> $tetha
#> [1] 180
#> 
#> $mu_water
#> [1] 0.485
#> 
#> $c_water
#> [1] 3.88e-06
#> 
#> $c_rock
#> [1] 2e-06
#> 
#> $pressure
#> [1] 1640 1600 1400 1200 1000  800  600  400
#> 
#> attr(,"class")
#> [1] "veh_rad_edge" "aquifer"

pred_veh <- aquifer_predict(aquifer_lst = parameters, time_lst = aqu_time)

head(pred_veh)
#>         Date Time (days)  We (MMbbl)
#> 1 2020-05-12       0.000  0.00000000
#> 2 2020-09-23     134.320  0.06185335
#> 3 2022-10-19     890.235  1.27831951
#> 4 2025-04-25    1809.305  4.19222802
#> 5 2028-02-02    2822.180  8.46586625
#> 6 2032-04-11    4352.990 15.65627937

pred_veh %>% ggplot(aes(x = `Time (days)`, y = `We (MMbbl)`)) +
  geom_point(size = 3, color = "blue") +
  theme_bw()

`Example 2: Un-steady state radial flow, bottom-water drive`

library(Raquifer)
library(ggplot2)
library(magrittr)

aqu_time <- aquifer_time(x = c(0,0.368,2.439,4.957,7.732,11.926,18.126,30.044) * 365, unit = "day")

parameters <- aquifer_param(input_unit = "Field", output_unit = "Field", model = "uss", 
                            flow_type = "radial", water_drive = "bottom", phi = 0.27, perm_h = 64.2, 
                            perm_v = 64.2, h_a = 20, r_a = 5 * 14892, r_R = 14892, 
                            mu_water = 0.485, c_water = 3.88e-6, c_rock = 2e-6, 
                            pressure = c(1640,1600,1400,1200,1000,800,600,400))

pred_ykh <- aquifer_predict(aquifer_lst = parameters, time_lst = aqu_time)

head(pred_ykh)
#>         Date Time (days) We (MMbbl)
#> 1 2020-05-12       0.000  0.0000000
#> 2 2020-09-23     134.320  0.1600501
#> 3 2022-10-19     890.235  2.5380986
#> 4 2025-04-25    1809.305  8.0646132
#> 5 2028-02-02    2822.180 16.0265710
#> 6 2032-04-11    4352.990 29.3508862

pred_ykh %>% ggplot(aes(x = `Time (days)`, y = `We (MMbbl)`)) +
  geom_point(size = 3, color = "blue") +
  theme_bw()

`Example 3: Pseudo-steady state radial flow, edge-water drive`

library(Raquifer)
library(ggplot2)
library(magrittr)

aqu_time <- aquifer_time(x = c(0,0.368,2.439,4.957,7.732,11.926,18.126,30.044) * 365, unit = "day")

parameters <- aquifer_param(input_unit = "Field", output_unit = "Field", model = "pss", 
                            flow_type = "radial", water_drive = "edge", phi = 0.27, perm_h = 64.2, 
                            h_a = 20, r_a = 5 * 14892, r_R = 14892, tetha = 180,
                            mu_water = 0.485, c_water = 3.88e-6, c_rock = 2e-6, 
                            pressure = c(1640,1600,1400,1200,1000,800,600,400))

pred_fetk <- aquifer_predict(aquifer_lst = parameters, time_lst = aqu_time)

head(pred_fetk)
#>         Date Time (days)  We (MMbbl)
#> 1 2020-05-12       0.000  0.00000000
#> 2 2020-09-23     134.320  0.02884514
#> 3 2022-10-19     890.235  1.08324703
#> 4 2025-04-25    1809.305  3.94690549
#> 5 2028-02-02    2822.180  8.44348341
#> 6 2032-04-11    4352.990 16.33925334

pred_fetk %>% ggplot(aes(x = `Time (days)`, y = `We (MMbbl)`)) +
  geom_point(size = 3, color = "blue") +
  theme_bw()

`Example 4: Un-steady state linear flow, edge-water drive`

library(Raquifer)
library(ggplot2)
library(magrittr)

aqu_time <- aquifer_time(x = c(0,0.368,2.439,4.957,7.732,11.926,18.126,30.044) * 365, unit = "day")

parameters <- aquifer_param(input_unit = "Field", output_unit = "Field", model = "uss", 
                            flow_type = "linear", water_drive = "edge", phi = 0.27, perm_h = 64.2, 
                            h_a = 20, w_a = 29784, l_a = 161145, mu_water = 0.485, c_water = 3.88e-6, 
                            c_rock = 2e-6, pressure = c(1640,1600,1400,1200,1000,800,600,400))

pred_nb_01 <- aquifer_predict(aquifer_lst = parameters, time_lst = aqu_time)

head(pred_nb_01)
#>         Date Time (days) We (MMbbl)
#> 1 2020-05-12       0.000 0.00000000
#> 2 2020-09-23     134.320 0.03199772
#> 3 2022-10-19     890.235 0.53782163
#> 4 2025-04-25    1809.305 1.63239439
#> 5 2028-02-02    2822.180 3.09768169
#> 6 2032-04-11    4352.990 5.35540873

pred_nb_01 %>% ggplot(aes(x = `Time (days)`, y = `We (MMbbl)`)) +
  geom_point(size = 3, color = "blue") +
  theme_bw()

`Example 5: Un-steady state linear flow, bottom-water drive`

library(Raquifer)
library(ggplot2)
library(magrittr)

aqu_time <- aquifer_time(x = c(0,0.368,2.439,4.957,7.732,11.926,18.126,30.044) * 365, unit = "day")

parameters <- aquifer_param(input_unit = "Field", output_unit = "Field", model = "uss", 
                            flow_type = "linear", water_drive = "bottom", phi = 0.27, perm_v = 64.2, 
                            h_a = 20, w_a = 29784, l_a = 161145, mu_water = 0.485, c_water = 3.88e-6, 
                            c_rock = 2e-6, pressure = c(1640,1600,1400,1200,1000,800,600,400))

pred_nb_02 <- aquifer_predict(aquifer_lst = parameters, time_lst = aqu_time)

head(pred_nb_02)
#>         Date Time (days) We (MMbbl)
#> 1 2020-05-12       0.000  0.0000000
#> 2 2020-09-23     134.320  0.5428142
#> 3 2022-10-19     890.235  3.7996992
#> 4 2025-04-25    1809.305  9.2278409
#> 5 2028-02-02    2822.180 14.6559827
#> 6 2032-04-11    4352.990 20.0841244

pred_nb_02 %>% ggplot(aes(x = `Time (days)`, y = `We (MMbbl)`)) +
  geom_point(size = 3, color = "blue") +
  theme_bw()

`Example 6: Pseudo-steady state linear flow, edge-water drive`

library(Raquifer)
library(ggplot2)
library(magrittr)

aqu_time <- aquifer_time(x = c(0,0.368,2.439,4.957,7.732,11.926,18.126,30.044) * 365, unit = "day")

parameters <- aquifer_param(input_unit = "Field", output_unit = "Field", model = "pss", 
                            flow_type = "linear", water_drive = "edge", phi = 0.27, perm_h = 64.2, 
                            h_a = 20, w_a = 29784, l_a = 161145, mu_water = 0.485, c_water = 3.88e-6, 
                            c_rock = 2e-6, pressure = c(1640,1600,1400,1200,1000,800,600,400))

parameters
#> $input_unit
#> [1] "Field"
#> 
#> $output_unit
#> [1] "Field"
#> 
#> $model
#> [1] "fetk_lin_edge"
#> 
#> $phi
#> [1] 0.27
#> 
#> $perm_h
#> [1] 64.2
#> 
#> $h_a
#> [1] 20
#> 
#> $w_a
#> [1] 29784
#> 
#> $l_a
#> [1] 161145
#> 
#> $mu_water
#> [1] 0.485
#> 
#> $c_water
#> [1] 3.88e-06
#> 
#> $c_rock
#> [1] 2e-06
#> 
#> $pressure
#> [1] 1640 1600 1400 1200 1000  800  600  400
#> 
#> attr(,"class")
#> [1] "fetk_lin_edge" "aquifer"

pred_fetk_02 <- aquifer_predict(aquifer_lst = parameters, time_lst = aqu_time)

head(pred_fetk_02)
#>         Date Time (days)  We (MMbbl)
#> 1 2020-05-12       0.000 0.000000000
#> 2 2020-09-23     134.320 0.004426176
#> 3 2022-10-19     890.235 0.175334148
#> 4 2025-04-25    1809.305 0.668533598
#> 5 2028-02-02    2822.180 1.506005132
#> 6 2032-04-11    4352.990 3.161133684

pred_fetk_02 %>% ggplot(aes(x = `Time (days)`, y = `We (MMbbl)`)) +
  geom_point(size = 3, color = "blue") +
  theme_bw()

`Example 7: Pseudo-steady state linear flow, bottom-water drive`

library(Raquifer)
library(ggplot2)
library(magrittr)

aqu_time <- aquifer_time(x = c(0,0.368,2.439,4.957,7.732,11.926,18.126,30.044) * 365, unit = "day")

parameters <- aquifer_param(input_unit = "Field", output_unit = "Field", model = "pss", 
                            flow_type = "linear", water_drive = "bottom", phi = 0.27, perm_v = 64.2, 
                            h_a = 20, w_a = 29784, l_a = 161145, mu_water = 0.485, c_water = 3.88e-6, 
                            c_rock = 2e-6, pressure = c(1640,1600,1400,1200,1000,800,600,400))

pred_fetk_03 <- aquifer_predict(aquifer_lst = parameters, time_lst = aqu_time)

head(pred_fetk_03)
#>         Date Time (days) We (MMbbl)
#> 1 2020-05-12       0.000  0.0000000
#> 2 2020-09-23     134.320  0.5428142
#> 3 2022-10-19     890.235  3.7996992
#> 4 2025-04-25    1809.305  9.2278409
#> 5 2028-02-02    2822.180 14.6559827
#> 6 2032-04-11    4352.990 20.0841244

pred_fetk_03 %>% ggplot(aes(x = `Time (days)`, y = `We (MMbbl)`)) +
  geom_point(size = 3, color = "blue") +
  theme_bw()

`Example 8: Un-steady state radial flow, edge-water drive`

library(Raquifer)
library(ggplot2)
library(magrittr)

aqu_time <- aquifer_time(x = seq(as.Date("2020/1/1"), by = "year", length.out = 8), unit = "date")

parameters <- aquifer_param(input_unit = "Field", output_unit = "SI", model = "uss", 
                            flow_type = "radial", water_drive = "edge", phi = 0.27, perm_h = 64.2, 
                            h_a = 20, r_a = 5 * 14892, r_R = 14892, tetha = 180,
                            mu_water = 0.485, c_water = 3.88e-6, c_rock = 2e-6, 
                            pressure = c(1640,1600,1400,1200,1000,800,600,400))

aqu_time
#> $t
#> [1]    0  366  731 1096 1461 1827 2192 2557
#> 
#> $unit
#> [1] "date"
#> 
#> $reference_date
#> [1] "2020-01-01"
#> 
#> attr(,"class")
#> [1] "day"  "time"

parameters
#> $input_unit
#> [1] "Field"
#> 
#> $output_unit
#> [1] "SI"
#> 
#> $model
#> [1] "veh_rad_edge"
#> 
#> $phi
#> [1] 0.27
#> 
#> $perm_h
#> [1] 64.2
#> 
#> $h_a
#> [1] 20
#> 
#> $r_a
#> [1] 74460
#> 
#> $r_R
#> [1] 14892
#> 
#> $tetha
#> [1] 180
#> 
#> $mu_water
#> [1] 0.485
#> 
#> $c_water
#> [1] 3.88e-06
#> 
#> $c_rock
#> [1] 2e-06
#> 
#> $pressure
#> [1] 1640 1600 1400 1200 1000  800  600  400
#> 
#> attr(,"class")
#> [1] "veh_rad_edge" "aquifer"

pred_veh <- aquifer_predict(aquifer_lst = parameters, time_lst = aqu_time)

head(pred_veh)
#>         Date Time (days)   We (m3)
#> 1 2020-01-01           0       0.0
#> 2 2021-01-01         366   18021.0
#> 3 2022-01-01         731  135900.7
#> 4 2023-01-01        1096  383984.4
#> 5 2024-01-01        1461  722190.1
#> 6 2025-01-01        1827 1141218.1

pred_veh %>% ggplot(aes(x = `Time (days)`, y = `We (m3)`)) +
  geom_point(size = 3, color = "blue") +
  theme_bw()

`Example 8: Un-steady state radial flow, edge-water drive`

library(Raquifer)
library(ggplot2)
library(magrittr)

aqu_time <- aquifer_time(x = 1:8, unit = "month")

parameters <- aquifer_param(input_unit = "Field", output_unit = "SI", model = "uss", 
                            flow_type = "radial", water_drive = "edge", phi = 0.27, perm_h = 64.2, 
                            h_a = 20, r_a = 5 * 14892, r_R = 14892, tetha = 180,
                            mu_water = 0.485, c_water = 3.88e-6, c_rock = 2e-6, 
                            pressure = c(1640,1600,1400,1200,1000,800,600,400))

aqu_time
#> $t
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $unit
#> [1] "month"
#> 
#> $reference_date
#> [1] "2020-05-12"
#> 
#> attr(,"class")
#> [1] "month" "time"

parameters
#> $input_unit
#> [1] "Field"
#> 
#> $output_unit
#> [1] "SI"
#> 
#> $model
#> [1] "veh_rad_edge"
#> 
#> $phi
#> [1] 0.27
#> 
#> $perm_h
#> [1] 64.2
#> 
#> $h_a
#> [1] 20
#> 
#> $r_a
#> [1] 74460
#> 
#> $r_R
#> [1] 14892
#> 
#> $tetha
#> [1] 180
#> 
#> $mu_water
#> [1] 0.485
#> 
#> $c_water
#> [1] 3.88e-06
#> 
#> $c_rock
#> [1] 2e-06
#> 
#> $pressure
#> [1] 1640 1600 1400 1200 1000  800  600  400
#> 
#> attr(,"class")
#> [1] "veh_rad_edge" "aquifer"

pred_veh <- aquifer_predict(aquifer_lst = parameters, time_lst = aqu_time)

head(pred_veh)
#>         Date Time (months)    We (m3)
#> 1 2020-06-11             1      0.000
#> 2 2020-07-11             2   4236.423
#> 3 2020-08-11             3  31650.466
#> 4 2020-09-10             4  87609.327
#> 5 2020-10-11             5 161084.687
#> 6 2020-11-10             6 249479.619

pred_veh %>% ggplot(aes(x = `Time (months)`, y = `We (m3)`)) +
  geom_point(size = 3, color = "blue") +
  theme_bw()

`References`

Fetkovich, M. J. (1971). A Simplified Approach to Water Influx Calculations-Finite Aquifer Systems. Journal of Petroleum Technology, 23(07), 814–828. https://doi.org/10.2118/2603-PA

Nabor, G. W., & Barham, R. H. (1964). Linear Aquifer Behavior. Journal of Petroleum Technology, 16(05), 561–563. https://doi.org/10.2118/791-PA

Van Everdingen, A. F., & Hurst, W. (1949). The Application of the Laplace Transformation to Flow Problems in Reservoirs. Journal of Petroleum Technology, 1(12), 305–324. https://doi.org/10.2118/949305-G

Yildiz, T., & Khosravi, A. (2007). An Analytical Bottomwaterdrive Aquifer Model for Material-Balance Analysis. SPE Reservoir Evaluation & Engineering, 10(06), 618–628. https://doi.org/10.2118/103283-PA

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.