RadTran (version 1.0)

RnDifAdv.hom: 2D Steady-state radon diffusion & advection in a homogeneous column of sand.

Description

Calls function RnDifAdv.hom for 2D steady diffusion & advection of radon. Gives the radon concentrations and fluxes in a homogeneous column of sand.

Usage

RnDifAdv.hom(lx, ly, nx, ny, e, m, bdc_top,
rn_lam, rn_sol, k_soil, d_bulk, miu, dp, solution, ...)

Arguments

lx

x axis length of the medium column [L].

ly

y axis length (depth) of the medium column [L]. Only positive values are accepted.

nx

Number of grid cells in the x direction.

ny

Number of grid cells in the y direction.

e

Medium porosity [-]. A constant value over the entire column.

m

Medium moisture [-]. A constant value over the entire column.

bdc_top

Fixed value in the upstream boundary in y-direction (bottom of the sand column) for a constant value of radon concentration [(1/T)*(1/L3)].

rn_lam

Radon decay constant [1/T].

rn_sol

Radon solubility in water [-].

k_soil

The gas permeability of the sand [L2].

d_bulk

bulk diffusivity [L2/T].

miu

Air viscosity [M*(1/L*T)].

dp

Fixed value in the upstream boundary in y-direction (bottom of the sand column) for a constant value of disturbance pressure [M*(1/L*1/T2)].

solution

Type of solution to be computed. Only "steady" is avaiable at the moment.

...

...

lx

x axis length of the medium column [L].

ly

y axis length (depth) of the medium column [L]. Only positive values are accepted.

nx

Number of grid cells in the x direction.

ny

Number of grid cells in the y direction.

e

Medium porosity [-]. A constant value over the entire column.

m

Medium moisture [-]. A constant value over the entire column.

bdc_top

Fixed value in the upstream boundary in y-direction (bottom of the sand column) for a constant value of radon concentration [(1/T)*(1/L3)].

rn_lam

Radon decay constant [1/T].

rn_sol

Radon solubility in water [-].

k_soil

The gas permeability of the sand [L2].

d_bulk

bulk diffusivity [L2/T].

miu

Air viscosity [M*(1/L*T)].

dp

Fixed value in the upstream boundary in y-direction (bottom of the sand column) for a constant value of disturbance pressure [M*(1/L*1/T2)].

solution

Type of solution to be computed. Only "steady" is avaiable at the moment.

...

...

Value

A list containing:

x.axis

X axis vector (1:nx) for radon concentrations and fluxes [L].

y.axis.conc

Y axis vector (1:ny) for the radon concentrations output [L].

y.axis.flux

Y axis vector (1:ny+1) for the radon fluxes output [L].

conc

Radon concentrations in the center of each grid cell, a [1:nx,1:ny] matrix [(1/T)*(1/L3)].

flux

Radon fluxes in the interface of each grid cell in the y-direction, a [1:nx,1:ny+1] matrix [1/T2].

Details

To optimize the code: The number of grid cells (nx,ny) will depend on the user's own computer capability. Higher numbers will give a closer approximation to the exact solution. The quantity for ny should be larger than nx, this allows a greater discretization in the y-axis. Boundary conditions: Fixed value for radon concentration and disturbance pressure in the upstream boundary in y-direction (a positive y axis is considered). All the otther boundaries are closed off for transport. Fluxes output: The output of the fluxes indicates the flow direction in correspondence with y-axis. In the case where a negative y-axis is considered, a negative flux value represents upward flow (from bottom to top). If the y-axis considered is positive, then a negative flux value represents downward flow (from top to bottom). The radon fluxes are computed at the interface of each grid cell. Backward finite differences approximation is used for the advection flow.

References

Andersen CE. Radon Transport Modelling: Users guide to RnMod3d. Riso National Laboratory, Roskilde, Denmark, 2000.

Andersen CE, Albarracin D, Csige I, van der Graaf ER, Jiranek M, Rehs B, Svoboda Z, Toro L. ERRICCA radon model intercomparison exercise. Riso-R-1120 (EN), Riso National Laboratory, DK-4000 Roskilde, Denmark (available as a internet publication at www.risoe.dk), 1999.

Soetaert K., Meysman F., 2012. R-package ReacTran: Reactive Transport Modelling in R.

Soetaert K., Meysman F., 2011. Reactive transport in aquatic ecosystems: Rapid model prototyping in the open source software R.

Soetaert K., Meysman F., 2009. Solving partial differential equations, using R package ReacTran.

Examples

#################################################
#####---- Direct input for the function ----#####
#################################################

require(RadTran)

AdvDif=RnDifAdv.hom(lx=1,ly=5,nx=50,ny=100,e=0.3,m=0.0,bdc_top=5000,
rn_lam=2.09838e-6,rn_sol=0.3565,k_soil=1e-11,d_bulk=1e-6,miu=17.5e-6,
dp=-100,solution="steady")