Page 473 - Petrophysics
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RADIAL FLOW SYSTEMS 44 1
Equation 7.68 can be written in oilfield units as follows:
kh ]
1 l4l.2qs,pB
4
Pi-@=-[ (7.69)
The right-hand side of this equation corresponds to the amount of fluid
produced, causing the reservoir pressure to drop from pi to p. It can be
demonstrated that this pressure drop is also expressed as:
(7.70)
If Equations 7.69 and 7.70 are combined, one obtains for time t:
(7.71)
where t is in hours, ct is the total compressibility in psi-’ and the permea-
bility is in mD. Craft and Hawkins defined this time as the readjustment
time, tr, or the time required to establish a logarithmic pressure distri-
bution between r, and re 111. For a well in a fully active water drive
reservoir, i.e., f = 1, the constant 0.25 in Equation 7.69 is replaced
by 0.50, and the constant 474.5 in Equation 7.71 is replaced by 949.
Generally, steady-state flow equations should be used only when t, is
small compared to the total producing life of the reservoir. If tr is too large,
as it is often the case in fully active water-drive reservoirs, unsteady-state
flow equations must be used.
Skin Zone
In many cases, it has been found that the permeability in the vicinity
of the wellbore differs from that in the major portion of the reservoir
as shown in Figure 7.7. This zone of altered permeability, ks, and radial
extent, rs, is called the “skin,” and the degree of alteration is expressed in
terms of the skin factor s [23, 241. The permeability of the skin zone can
be reduced (s > 0) as a result of drilling and well completion practices
as discussed in the next chapter.
The average permeability of the formation in the vicinity of the
wellbore also can be higher (s < 0) than that in the major portion
of the reservoir after fracturing or acidizing the well at completion.
Therefore, all the radial flow rate equations in this section, which were
derived on the basis that the permeability of the formation is the same
between r, and re, must be modified to include the effect of skin. This
can be done either by subtracting the additional pressure drop (due to
