Generalized radial flow model • hydrorecipes

Generalized radial flow model (Barker, 1988)

This flow model handles flow dimensions between 1 (linear) and 3 (spherical). For the Theis solution a flow dimension of 2 (radial) can be used. In addition, non-integral flow dimensions can also be used. The goal of these functions are to function with large datasets and calibration techniques.

Parameters

time <- 1:2000
flow_rate <- c(runif(1000, 0, 0.003),
               rep(0.0, 1000))

dat <- data.frame(time, flow_rate)

Regularly spaced time series

The following step is designed for regularly spaced times series for both the flow rates and drawdown output times.

# radial (flow_dimension = 2 Theis)
dd_rad <- recipe(time~flow_rate, dat) |>
  step_aquifer_grf(time = time, 
                   flow_rate = flow_rate, 
                   thickness = 1.0,
                   radius = 20, 
                   specific_storage = 1e-5,
                   hydraulic_conductivity = 1e-3,
                   flow_dimension = 2) |> 
  plate()


# linear (flow_dimension = 1)

dd_lin <- recipe(time~flow_rate, dat) |>
  step_aquifer_grf(time = time, 
                   flow_rate = flow_rate, 
                   thickness = 1.0,
                   radius = 20, 
                   specific_storage = 1e-5,
                   hydraulic_conductivity = 1e-3,
                   flow_dimension = 1) |> 
  plate()

# spherical (flow_dimension = 3)
dd_sph <- recipe(time~flow_rate, dat) |>
  step_aquifer_grf(time = time, 
                   flow_rate = flow_rate, 
                   thickness = 1.0,
                   radius = 20, 
                   specific_storage = 1e-5,
                   hydraulic_conductivity = 1e-3,
                   flow_dimension = 3) |> 
  plate()

References

Barker, J.A., 1988. A generalized radial flow model for hydraulic tests in fractured rock. Water Resour. Res. 24, 1796–1804.