Derivation of Basic Transport Equation (A. Ertürk)

The Advection-Dispersion Equation
We are living in a 3 dimensional space, where the
same rules for the general mass balance and
transport are valid in all dimensions. Therefore
∂C
=
∂t
3
∑
i=
1
⎛
⎜−u
⎝
Equation 31
i
⋅
∂C
∂x
i
+
D
i
⋅
∂
2
∂x
C
2
i
⎞
⎟
⎠
x 1 = x, u 1 = u, D 1 = D x
x 2 = y, u 2 = v, D 2 = D y
x 3 = z, u 3 = w, D 3 = D z
∂C
∂t
= −u
⋅
∂C
∂x
+
D
x
⋅
∂
2
∂x
C
2
− v
⋅
∂C
∂y
+
D
y
⋅
∂
2
∂y
C
2
−
w
⋅
∂C
∂z
+
D
z
⋅
∂
2
∂z
C
2
Equation 32
34