open_well_response {kitagawa}

Spectral response for an open well

Description

This is the primary function to calculate the response for an open (exposed to air) well.

Usage

open_well_response(omega, T., S., ...)

## Default S3 method:
open_well_response(
  omega,
  T.,
  S.,
  Rs. = (8/12) * (1200/3937),
  rho,
  grav,
  z,
  Hw,
  Ta,
  leak,
  freq.units = c("rad_per_sec", "Hz"),
  model = c("rojstaczer", "liu", "cooper", "hsieh", "wang"),
  as.pressure = TRUE,
  ...
)

Arguments

omega

numeric; frequency, (see freq.units)

T.

numeric; effective aquifer transmissivity [m^2/s]

S.

numeric; well storativity, [unitless]

...

additional arguments

Rs.

numeric; the radius of the open (screened) section

rho

numeric; fluid density (assumed if missing)

grav

numeric; the local gravitational acceleration (assumed if missing)

z

numeric; From Rojstaczer (1988): the depth from the water table (assumed if missing and if needed)

Hw

numeric; height of water column above confined surface (assumed if missing and if needed)

Ta

numeric; thickness of aquifer (assumed if missing and if needed)

leak

numeric; specific leakage K'/b' [1/s]

freq.units

character; setup the units of omega

model

character; use the response model from either Rojstaczer (1988), Liu et al (1989), Cooper et al (1965), Hsieh et al (1987), or Wang et al (2018).

as.pressure

logical; should the response be relative to aquifer pressure? (default is aquifer head)

Details

As opposed to well_response, this calculates the theoretical, complex well response for an unsealed (open) well.

The response depends strongly on the physical properties given. Default values are assumed where reasonable–for instance, the pore-fluid is assumed to be water–but considerable care should be invested in the choice of parameters, especially in the case of starting parameters in an optimization scheme.

The responses returned here are, effectively, the amplification of water levels in a well, relative to the pressure head in the aquifer; or

Z = \frac{z}{h} \equiv \frac{\rho g z}{p}

If as.pressure=TRUE, then the responses are scaled by rho*grav so that they represent water levels relative to aquifer pressure:

Z = \frac{z}{p}

Not all parameters need to be given, but should be. For example, if either rho or grav are not specified, they are taken from constants. Parameters which do not end in . do not need to be specified (they may be excluded); if they are missing, assumptions may be made and warnings will be thrown.

Value

An object with class 'owrsp'

Models

"rojstaczer"

Rojstaczer (1988) is based on measurements of water level and strain from volumetric or areal strainmeters.

"cooper", "hsieh", and "liu"

Cooper et al (1965), Hsieh et al (1987) and Liu et al (1989) are based on measurements of water level and displacements from seismometers or strainmeters; these models are expressed succinctly in Roeloffs (1996).

The sense of the phase shift for the Liu and Rojstaczer models are reversed from their original presentation, in order to account for differences in sign convention.

"wang"

Wang et al (2018) allows for specific leakage – vertical conductivity across a semi-permeable aquitard – but the perfectly confined case (i.e., Hsieh, et al 1987) is recovered when leakage is zero.

Author(s)

A. J. Barbour and J. Kennel

References

See kitagawa-package for references and more background.

See Also

well_response for the sealed-well equivalents, and owrsp-methods for a description of the class 'owrsp' and its methods.

Other WellResponseFunctions: well_response()

Examples

OWR <- open_well_response(1:10,1,1)
plot(OWR)
OWR <- open_well_response(1/(1:200),1,1,Ta=100,Hw=10,model="liu",freq.units="Hz")
plot(OWR)