kitagawa (version 1.1-1)

well_response: Calculate the pressure/strain response spectrum for given formation properties

Description

This is the primary function which calculates the theoretical, complex well response, namely Equation 17 in Kitagawa et al (2011). The results, however, are expressed as amplitude and phase.

Usage

well_response(omega, T., S., Vw., Rs., Ku., B., Avs. = 1,
    Aw. = 1, rho. = 1000, Kf. = 2.2e+09, grav. = 9.81,
    freq.units = NULL)
  ## S3 method for class 'default':
well_response(omega, T., S., Vw., Rs.,
    Ku., B., Avs. = 1, Aw. = 1, rho. = 1000, Kf. = 2.2e+09,
    grav. = 9.81, freq.units = NULL)

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, $[unitless, bounded]$

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 what the units of frequency (omega) are: "rad_per_sec" (default, NULL), or "Hz"

Value

• Matrix with three columns: radial frequency, amplitude, and phase [$\omega$), $A_\alpha (\omega)$, $\Phi_\alpha (\omega)$] where the units of $\omega$ will be radians per second, $A_\alpha (\omega)$ in meters per strain, and $\Phi_\alpha (\omega)$ in radians.

Details

The response depends strongly on the physical properties given. Default values are assumed where resonable, mostly that the pore-fluid is water, but considerable care should be invested in the choice of parameters, unless the function is used in an optimization scheme.

Assumed values are: [object Object],[object Object],[object Object],[object Object],[object Object]

Note that Skempton's coefficient, B., is bounded inclusively within $[0,1]$; an error is thrown if it's not.

References

Kitagawa, Y., S. Itaba, N. Matsumoto, and N. Koisumi (2011), Frequency characteristics of the response of water pressure in a closed well to volumetric strain in the high-frequency domain, J. Geophys. Res., 116, B08301, doi:10.1029/2010JB007794.

http://www.agu.org/pubs/crossref/2011/2010JB007794.shtml

See Also

sensing_volume, kitplot

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"))
#
kitplot(Rsp)