well_response {kitagawa}

Spectral response for a sealed well

Description

This is the primary function to calculate the response for a sealed well.

Usage

well_response(omega, T., S., Vw., Rs., Ku., B., ...)

## Default S3 method:
well_response(
  omega,
  T.,
  S.,
  Vw.,
  Rs.,
  Ku.,
  B.,
  Avs,
  Aw,
  rho,
  Kf,
  grav,
  freq.units = c("rad_per_sec", "Hz"),
  as.pressure = TRUE,
  ...
)

Arguments

omega

frequency, (see freq.units)

T.

effective aquifer transmissivity [m^2/s]

S.

well storativity, [unitless]

Vw.

well volume, [m^3]

Rs.

radius of screened portion, [m]

Ku.

undrained bulk modulus, [Pa]

B.

Skempton's coefficient, [unitless, bounded]

...

additional arguments

Avs

amplification factor for volumetric strain E_{kk,obs}/E_{kk}, []

Aw

amplification factor of well volume change for E_{kk}, []

rho

fluid density [kg/m^3]

Kf

bulk modulus of fluid, [Pa]

grav

local gravitational acceleration [m/s^2]

freq.units

set the units of omega

as.pressure

logical; should the response for water pressure? (default is water height)

Details

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, unless the function is used in an optimization scheme.

Assumed values are:

Avs	1		amplification factor for volumetric strain
Aw	1		amplification factor for water well

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

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

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

Z = \frac{p}{\epsilon}

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, warnings will be thrown.

Value

An object with class 'wrsp'

Author(s)

A. J. Barbour

References

See kitagawa-package for references and more background.

See Also

open_well_response for the open-well equivalents wrsp-methods for a description of the class 'wrsp' and its methods, sensing_volume to easily estimate the volume Vw., and kitagawa-package for references and more background.

Other WellResponseFunctions: open_well_response()

Examples

#### dummy example
well_response(1:10, T.=1, S.=1, Vw.=1, Rs.=1, Ku.=1, B.=1)

#### a more physically realistic calculation:
# Physical params applicable for B084 borehole
# (see: http://pbo.unavco.org/station/overview/B084/ for details)
#
Rc <- 0.0508   # m, radius of water-sensing (2in)
Lc <- 146.9    # m, length of grouted region (482ft)
Rs <- 3*Rc     # m, radius of screened region (6in)
Ls <- 9.14     # m, length of screened region (30ft)
#
# calculate the sensing volume for the given well parameters
Volw <- sensing_volume(Rc, Lc, Rs, Ls) # m**3, ~= 1.8
#
Frqs <- 10**seq.int(from=-4,to=0,by=0.1) # log10-space
head(Rsp <- well_response(omega=Frqs, T.=1e-6, S.=1e-5, 
Vw.=Volw, Rs.=Rs, Ku.=40e9, B.=0.2, freq.units="Hz"))

# Access plot.wrsp:
plot(Rsp)