In jkennel/aquifer: Well solutions for aquifer tests

knitr::opts_chunk$set(echo = TRUE)
library(aquifer)
library(data.table)
library(plotly)

Solution

Ogata-Banks 1961 solution, Bear's 1972, 1979 solution for 1-D transport with retardation and decay.

Capabilities

Calculation of the Ogata-Banks solution for a grid of times and distances.

D <- 2
v <- 1
C0 <- 1
R <- 1
decay <- 0
x <- seq(1, 120, 2)
t <- seq(0, 80, 10)
ob <- ogata_banks(D, R, decay, v, C0, x, t)

ob <- data.table(ob)
setnames(ob, paste0('time_',t))
ob[, x := seq(1, 120, 2)]

plot_ly(ob, x = ~x, y = ~time_20, type = 'scatter', mode = 'line', 
        name = 20, width = 700, height = 300) %>% 
  add_lines(x = ~x, y = ~time_40, mode = 'line', name = 40) %>%
  add_lines(x = ~x, y = ~time_60, mode = 'line', name = 60) %>%
  add_lines(x = ~x, y = ~time_80, mode = 'line', name = 80) %>%
  layout(xaxis = list(title = "Distance from source"),
         yaxis = list(side = 'left', title = 'Concentration'))

With retardation

D <- 2
v <- 1
C0 <- 1
R <- 2
decay <- 0
x <- seq(1, 120, 2)
t <- seq(0, 80, 10)
ob_r <- ogata_banks(D, R, decay, v, C0, x, t)

ob <- data.table(ob_r)
setnames(ob, paste0('time_',t))
ob[, x := seq(1, 120, 2)]

plot_ly(ob, x = ~x, y = ~time_20, type = 'scatter', mode = 'line', 
        name = 20, width = 700, height = 300) %>% 
  add_lines(x = ~x, y = ~time_40, mode = 'line', name = 40) %>%
  add_lines(x = ~x, y = ~time_60, mode = 'line', name = 60) %>%
  add_lines(x = ~x, y = ~time_80, mode = 'line', name = 80) %>%
  layout(xaxis = list(title = "Distance from source"),
         yaxis = list(side = 'left', title = 'Concentration'))

With retardation and decay

D <- 2
v <- 1
C0 <- 1
R <- 2
decay <- 0.02
x <- seq(1, 120, 2)
t <- seq(0, 80, 10)
ob_rd <- ogata_banks(D, R, decay, v, C0, x, t)

ob <- data.table(ob_rd)
setnames(ob, paste0('time_',t))
ob[, x := seq(1, 120, 2)]

plot_ly(ob, x = ~x, y = ~time_20, type = 'scatter', mode = 'line', 
        name = 20, width = 700, height = 300) %>% 
  add_lines(x = ~x, y = ~time_40, mode = 'line', name = 40) %>%
  add_lines(x = ~x, y = ~time_60, mode = 'line', name = 60) %>%
  add_lines(x = ~x, y = ~time_80, mode = 'line', name = 80) %>%
  layout(xaxis = list(title = "Distance from source"),
         yaxis = list(side = 'left', title = 'Concentration'))

References

Ogata, A. and Banks, R.B., 1961. A solution of the differential equation of longitudinal dispersion in porous media: fluid movement in earth materials. US Government Printing Office.

Bear, J., 1972, Dynamics of fluids in porous media: New York, American Elsevier, 764 p.

Bear, J., 1979, Hydraulics of ground water: New York, McGraw Hill, 569 p.

jkennel/aquifer documentation built on July 31, 2022, 11:33 p.m.