longitudinal dispersion in nonuniform isotropic porous media

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max1mum error). The breakthrough curve for the exit concentration from
a finite medium has a maximum error of about 4% relative to the other
solutions when X = 80. The solution for a semi-infinite medium with a
flux boundary condition is approximated to within 2% for X = 8.0
(Figure B.3) by the solution for an infinite medium.
For high Peclet flows (Pe > 1.0), we can write for the dispersion
coefficient 1n a uniform medium
DL > vd/2
Using this in the expression for X we find,
X < 2x/d
which says that X is less than two times the number of grain diameters
downstream. Thus, for Pe > 1.0, equation (B.6) approximates equation
(B.12) within 2% maximum error for X = 8.0, which is less than 16 grain
diameters downstream. This is probably well within the accuracy
requirements for most situations. By 48 grain diameters downstream,
equations (B.6), (B.ll), and (B.12) have less than 1% maximum error.
For low Pee let number flows (Pe < 1.0), DL tends to a constant, which
means X + 0 as v + 0 for a given x. Under these conditions, the
different solutions according to the different boundary conditions may
remain distinct far enough downstream to be significant.