Continuous Injection

The breakthrough curve of a continuous injection can be modeled with with following R script for a river of length $x$, at time $t$ for a dispersion coefficient $D_L$ and with a Peclet number of $Pe$.

| erfc.r

x = seq(0.01,1000,1) #m
t = seq(0.01,1080000,15) #seconds
xs = 240
ts = 10800
c0 = 100 # mg/m³
Pe = 0.1
Lm = 2400 #m 
v = 0.15
DL = Pe*Lm*v
ct = c0*erfc(xs/sqrt(4*DL*t))
cx = c0*erfc(x/sqrt(4*DL*ts))
plot(t,ct)