Page 188 - Petroleum Geology

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Because the acceleration due to gravity is a constant in this context, the
energy of the water is indicated for practical purposes by its total head, h:
this is the algebraic sum of the elevation head z relative to an arbitrary datum
(measured negative downwards) and the pressure head, p/pg (Fig. 8-10). Note
most carefully that the pressure head is measured from the point at which
the pressure is measured, and the elevation head from an arbitrary datum,
commonly sea level. All heads have the dimension of Zength.
Intrinsic permeability, h, with the dimensions of an area, is a material con-
stant that is a function of porosity, the tortuosity of the flow paths through
the pores, and the harmonic mean diameter of the grains. Tortuosity can be
approximated by a porosity term, and the combined expansion is:
k = CfXd2/(1 -f)* (8.8)
where x varies from about 3.5 for unconsolidated sands to about 5 for well-
consolidated sands. The dimensionless coefficient C is not a true constant be-
cause it takes some undeterminable properties of the material into account.
Before proceeding, we must pause to note that eq. 8.7 is commonly and
erroneously written:

4 = (k/V)AP/l.
That this is an incomplete expression of Darcy’s law is evident from the fact
that when the fluid is at rest, q = 0, and this implies that Ap = 0. This is only
true on a horizontal plane in the water-saturated porous. material, so that
the equation is only valid for horizontal flow. It is on the basis of this equa-

P
Fig. 8-10. The total head, h, is the algebraic sum of the pressure head, p/pg, and the eleva-
tion head, z.