32
Q3.4 Solution
You will need to derive the formulae (main text Equations 3.21 and 3.22) for the equivalent
bulk horizontal and vertical permeabilities of an alternating layer system, as in the main text
Section 3.6.
For horizontal flow (ie flow parallel to the laminations), the hydraulic gradient between two
vertical sections A and B is the same for both layers (see main text Figure 3.16). The total
flowrate q
T
is the sum of the flowrates through the individual layers. We seek an expression of
the form
q
T
= A
T
.k
H
.i,
where k
H
is the overall (bulk) permeability in the horizontal direction and A
T
is the total area
available for flow. For a unit depth perpendicular to the plane of the paper,
A
T
=d
1
+ d
2
Applying Darcy's law to each layer in turn,
q
1
= d
1
.k
1
.i and q
2
= d
2
.k
2
.i,
hence
q
T
=
q
1
+ q
2
= (d
1
.k
1
+ d
2
.k
2
).i,
and by comparison with the initial expression q
T
= A
T
.k
H
.i, the horizontal permeability is
given by
k
H
=
(d
1
.k
1
+ d
2
.k
2
)/(d
1
+ d
2
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This note was uploaded on 12/28/2011 for the course CHM 4302 taught by Professor Stuartchalk during the Fall '11 term at UNF.
 Fall '11
 StuartChalk
 Analytical Chemistry

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