Drawdown from a single pumping well

This function estimates the ratio of water level drawdown to pumping rate at an observation well at time `t` after pumping initiates from an individual pumping well. Note that this function does not account for the presence of any aquifer boundaries. See Glover (1954).

get_aquifer_drawdown_ratio(
  df,
  x1 = NULL,
  x2 = NULL,
  y = NULL,
  K = NULL,
  D = NULL,
  V = NULL,
  t = NULL,
  well_diam = NULL
)

Arguments

df

data.frame with columns specifying all parameters

x1

Distance of pumping well to stream

x2

Distance of observation well to stream

y

Distance between pumping and observation well (parallel to stream)

K

Saturated hydraulic conductivity

D

Depth of aquifer

V

Drainable porosity of aquifer

t

Time from pumping onset at which to calculate stream depletion fraction

well_diam

Diameter of the well, inside which drawdown does not increase. Defaults to 0.

Details

Estimate drawdown at observation well due to pumping at another well, either with a nearby stream or without a stream.

Examples

library(units)
y <- set_units(c(1, 5, 10) * 1e3, "ft")
D <- set_units(100, "ft")
K <- set_units(0.001, "ft/sec")
t <- set_units(5, "year")
V <- 0.2 # unitless
aquifer_drawdown_ratio <- get_aquifer_drawdown_ratio(y = y,
                                                     x1 = Inf,
                                                     x2 = Inf,
                                                     K = K,
                                                     D = D,
                                                     V = V,
                                                     t = t)

# Drawdown per cusec pumping:
change_in_waterlevel_per_cusec <- aquifer_drawdown_ratio * set_units(1, "ft^3/sec")
change_in_waterlevel_per_cusec
#> Units: [ft]
#> [1] -4.122375 -1.620171 -0.688698


# Specifying parameters as named data.frame columns
library(tibble) # simplifies specifying data.frames with units objects
df <- tibble(y = y, x1 = Inf, x2 = Inf, K = K, D = D, V = V, t = t)
aquifer_drawdown_ratio <- get_aquifer_drawdown_ratio(df)
aquifer_drawdown_ratio
#> Units: [s/ft^2]
#> [1] -4.122375 -1.620171 -0.688698

# for radius < well_diam/2, drawdown does not increase.
y <- set_units(seq(0.25,2, by = 0.25), "ft")
well_diam <- set_units(2, "ft")
aquifer_drawdown_ratio <- get_aquifer_drawdown_ratio(x1 = Inf, x2 = Inf, y = y,
                                                     K = K, D = D,
                                                     V = V, t = t,
                                                     well_diam = well_diam)
aquifer_drawdown_ratio
#> Units: [s/ft^2]
#> [1] -15.11389 -15.11389 -15.11389 -15.11389 -14.75875 -14.46857 -14.22323
#> [8] -14.01071