sensing_volume: Calculate volume of fluids in the sensing region of the borehole.

Description

This function calculates the volume of fluid in the screened section, namely Equation 2 in Kitagawa et al (2011).

Usage

sensing_volume(rad_grout, len_grout, rad_screen,
    len_screen)

Arguments

rad_grout

radius of the grouting $[m]$

len_grout

length of the grouting $[m]$

rad_screen

radius of the screened interval $[m]$

len_screen

length of the screened interval $[m]$

Value

scalar, with units of $[m^3]$

Details

Although typical scientific boreholes with water-level sensors are drilled very deeply, pore-fluids are only allowed to flow through a relatively short section, known as the "screened" section. The calculation assumes two pairs of radii and lengths: one for the cemented (grout) section, and another for the screened section.

The volume calculated is $$\pi R_C^2 (L_C - L_S) + \pi R_S^2 L_S$$ where $R$ and $L$ denote radius and length respectively, and subscripts $C$ and $S$ denote the cemented and screened sections respectively.

This calculation assumes the measurement is for a sealed well.

Examples

Run this code

#### dummy example
sensing_volume(1, 1, 1, 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
sensing_volume(Rc, Lc, Rs, Ls) # m**3, ~= 1.8