NC0001422_Fig 6-15 One Dimension_20160201

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DATE: JANUARY 2016
FIGURE 6-15
ONE DIMENSIONAL CONVECTIVE-
DISPERSIVE SOLUTE TRANSPORT WITH
SOURCE TERM AND
SORPTION PROPERTIES
FILE PATH: P:\Duke Energy Progress.1026\108. Sutton Ash Basin GW
Assessment Plan\20.EG_CAP\CAP Part 2\Figures\Final
Governing Equation 𝑅𝑅 𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕=𝐷𝐷𝜕𝜕2 𝜕𝜕𝜕𝜕𝑥𝑥2 −𝑣𝑣𝜕𝜕𝜕𝜕𝜕𝜕𝑥𝑥 𝜕𝜕(𝑥𝑥,0)=𝐶𝐶𝑖𝑖 𝜕𝜕(0,𝜕𝜕)=�𝐶𝐶𝑂𝑂0 0 <𝜕𝜕≤𝜕𝜕𝑂𝑂𝜕𝜕>𝜕𝜕𝑂𝑂 𝜕𝜕𝜕𝜕𝜕𝜕𝑥𝑥(∞,𝜕𝜕)=0
𝜕𝜕(𝑥𝑥,𝜕𝜕)=�𝐶𝐶𝑖𝑖+(𝐶𝐶𝑂𝑂−𝐶𝐶𝑖𝑖) 𝐴𝐴(𝑥𝑥,𝜕𝜕) 𝐶𝐶𝑖𝑖+(𝐶𝐶𝑂𝑂−𝐶𝐶𝑖𝑖) 𝐴𝐴(𝑥𝑥,𝜕𝜕)−(𝐶𝐶𝑂𝑂−𝐶𝐶𝑖𝑖) 𝐴𝐴(𝑥𝑥,𝜕𝜕−𝜕𝜕𝑂𝑂) 0 <𝜕𝜕≤𝜕𝜕𝑂𝑂𝜕𝜕>𝜕𝜕𝑂𝑂 }
Where: 𝐴𝐴(𝑥𝑥,𝜕𝜕)=12 𝑒𝑒𝑒𝑒𝑒𝑒𝜕𝜕�𝑅𝑅𝑥𝑥−𝑣𝑣𝜕𝜕2(𝐷𝐷𝑅𝑅𝜕𝜕)12 �+12 exp �𝑣𝑣𝑥𝑥𝐷𝐷�𝑒𝑒𝑒𝑒𝑒𝑒𝜕𝜕�𝑅𝑅𝑥𝑥+𝑣𝑣𝜕𝜕2(𝐷𝐷𝑅𝑅𝜕𝜕)12 �
where:

c(x,t) = concentration at a distance x from the source area and a time t
ci = background concentration
co = source concentration
v = groundwater velocity (v=ki/n)
t = time
to = time when source is terminated
x = distance from source
D = dispersion
R = retardation factor
erfc = complementary error function
exp = exponent