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decreases as a result. Enlargement of pores also results in the reduction of the
surface/volume ratio. These two effects are opposite in significance.
The following assumptions are made in evaluating a matrix acid treatment (Craft
et al., 1962, p.
538):
(1)
the pores are of uniform size, (2) the formation is
homogeneous,
(3)
the acid penetration is uniform and radial,
(4)
uniform decline in
reaction rate with decreasing acid concentration, and
(5)
uniform decrease in the
weight of formation dissolved per increment of distance penetrated until the acid is
completely spent. The volume of acid injected is equal to the pore volume invaded
(see Craft et al., 1962, p.
538):
qit
=
T@h(
r,’
-
r:’)
(5-15)
where
qi
=
acid injection rate, bbl/min,
t
=
spending time of acid, sec,
r,
=
radial
distance of penetration until acid is spent,
ft,
@
=
fractional porosity,
r,
=
wellbore
radius,
ft,
h
=
formation thickness,
ft.
In order to acheve greater penetration during matrix acidizing, it is necessary to
decrease the reaction rate (increase the spending time) and/or increase the rate of
injection. Solving for
r,:
r,
=
[
(0.0936
qit/T@h)
+
r:]1’2
(5-16)
The spending time for several different acids is presented in Table 5-VII. Hendrick-
son et al. (1960) found that for most acids the spending time is less than 15 sec,
because of large specific surface area of reservoir rocks. Table 5-VIII shows various
required injection rates computed by Hendrickson et al. (1960) for a carbonate
formation. Craft et al. (1962, p.
540)
pointed out that inasmuch as spending time is
affected by many variables, it should be determined by laboratory tests for each
particular formation to be treated. In tight formations, acidizing at pressures lower
than fracturing pressures will result in an increase in permeability only in the
vicinity of the wellbore. Consequently, matrix acidizing is applicable for overcoming
formation damage only.
The most important variable, which must be determined prior to acidizing, is the
volume of acid to be used in a particular stimulation job. In most cases, however,
the optimum volume of acid required cannot be determined accurately. This is
critical because insufficient volumes of acid may cause damage to a sandstone
formation, for example. In the case of excessive volumes of acid, cementing
materials in the sandstones can be dissolved, resulting in damage through the
collapse of pore structure and thus, incurring additional costs. Acid volumes
required for optimum treatment are determined by the following variables:
(1)
porosity, (2) specific surface area of rock,
(3)
chemical composition of the forma-
tion,
(4)
thickness of the formation interval to be treated,
(5)
mineralogy and the
minerals distribution within the rock, (6) rock strength,
(7)
extent and type of
wellbore damage,
(8)
acid type, (9) acid strength,
(10)
treatment rate, (11) pressure,
and (12) formation temperature. Direct laboratory tests must be made to determine