Page 150 - Petrophysics 2E

PERMEABILITY-POROSITY RELATIONSHIPS 123

Tortuosity can be estimated from:

Substituting for z into Equation 3.49 yields a general expression for the
Tiab flow unit characterization factor:

(3.51)

The Tiab flow unit characterization factor HT clearly combines all the
petrophysical and geological properties mentioned above by Snyder
and King [29]. Note that HT and FZI are related by the following
equation:
1
HT = - (3.52)
FZI~

The right-hand side of Equation 3.48 is also, of course, HT, i.e.:

OR
HT = - (3.53)
k
where Q,R is given by Equation 3.29. However, HT obtained from
Equation 3.51 reflects microscopic petrophysical properties, whereas HT
calculated using Equation 3.53 reflects the flow unit at the macroscopic
scale. If the petrophysical parameters in Equation 3.51 can be accurately
measured, then a log-log plot of the two HT parameters may be used to
normalize the data. Substituting for HT (Equation 3.51) into Equation 3.48
and solving for permeability gives:

(3.54)

This is the generalized permeability-porosity equation, where the
mean grain diameter dgr and the permeability k are expressed in cm
and cm2, respectively. The porosity term Q, is a fraction.
(d) free fluid index (ffl). The bulk volume water is commonly used to
indicate whether or not a reservoir is at its irreducible water saturation,
hir. It is equal to the product of total porosity and water saturation, S,:

BVW = @Sw (3.55)

Reservoirs with water saturation equal to irreducible or connate water
saturation produce water-free hydrocarbons since water occupies small