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16/248 PRODUCTION ENHANCEMENT
where The designed acid volume and injection rate should be
adjusted based on the real-time monitoring of pressure
g a ¼ acid specific gravity, water ¼ 1:0 during the treatment.
g m ¼ mineral specific gravity, water ¼ 1:0.
Based on the volumetric model, the required acid volume
per unit thickness of formation can be estimated using the Summary
following equation: This chapter briefly presents chemistry of matrix acidizing
and a guideline to acidizing design for both sandstone and
2
2
V h ¼ pf r wh r ð PVÞ , (16:11) carbonate formations. More in-depth materials can be
bt
w
where (PV) bt is the number of pore volumes of acid found in McLeod (1984), Economides et al. (1994), and
injected at the time of wormhole breakthrough at the end Economides and Nolte (2000).
of the core. Apparently, the volumetric model requires
data from laboratory tests.
References
Example Problem 16.3 A 28 wt% HCl is needed to daccord, g., touboul, e., and lenormand, r. Carbonate
propagate wormholes 3 ft from a 0.328-ft radius wellbore acidizing: toward a quantitative model of the worm-
in a limestone formation (specific gravity 2.71) with a holing phenomenon. SPEPE Feb. 1989:63–68.
porosity of 0.15. The designed injection rate is 0.1 bbl/ da motta, e.p. Matrix Acidizing of Horizontal Wells,
2
min-ft, the diffusion coefficient is 10 9 m =sec, and the
3
density of the 28% HCl is 1:14 g=cm . In linear core Ph.d. Dissertation. Austin: University of Texas at
floods, 1.5 pore volume is needed for wormhole Austin, 1993.
breakthrough at the end of the core. Calculate the acid economides, m.j., hill, a.d., and ehlig-economides, c.
volume requirement using (a) Daccord’s model and (b) the Petroleum Production Systems. Englewood Cliffs, NJ:
volumetric model. Prentice Hall, 1994.
economides, m.j. and nolte, k.g. Reservoir Stimulation,
3rd edition. New York: John Wiley & Sons, 2000.
Solution
fogler, h.s., lund, k., and mccune, c.c. Predicting the
flow and reaction of HCl/HF mixtures in porous
(a) Daccord’s model: sandstone cores. SPEJ Oct. 1976, Trans. AIME,
1976;234:248–260.
y m MW m (1)(100:1) hekim, y., fogler, h.s., and mccune, c.c. The radial
b ¼ C a ¼ (0:28)
y a MW a (2)(36:5) movement of permeability fronts and multiple reaction
¼ 0:3836 lb m CaCO 3 =lb m 28 wt% HCl solution: zones in porous media. SPEJ Feb. 1982:99–107.
(0:15)(0:3836)(1:14) hill, a.d. and galloway, p.j. Laboratory and theoretical
fbg a
N Ac ¼ ¼ ¼ 0:0285 modeling of diverting agent behavior. JPT June
(1 f)g m (1 0:15)(2:71)
3
q h ¼ 0:1 bbl= min -ft ¼ 8:69 10 4 m =sec-m 1984:1157–1163.
hill, a.d., lindsay, d.m., silberberg, i.h., and schechter,
r wh ¼ 0:328 þ 3 ¼ 3:328 ft ¼ 1:01 m
r.s. Theoretical and experimental studies of sandstone
q
r
pfD 2=3 1=3 d f acidizing. SPEJ Feb. 1981;21:30–42.
V h ¼ h wh hoefner, m.l. and fogler, h.s. Pore evolution and channel
bN Ac
4 1=3
9 2=3
p(0:15)(10 ) (8:69 10 ) (1:01) 1:6 formation during flow and reaction in porous media.
¼ AIChE J. Jan. 1988;34:45–54.
5
(1:5 10 )(0:0285) lund, k., fogler, h.s., and mccune, c.c. Acidization I: the
3
¼ 0:107 m =m ¼ 8:6 gal=ft dissolution of dolomite in hydrochloric acid. Chem.
Eng. Sci. 1973;28:691.
(b) Volumetric model:
lund, k., fogler, h.s., mccune, c.c., and ault, j.w.

2
V h ¼ pf r 2 r ð PVÞ Acidization II: the dissolution of calcite in hydro-
wh w bt chloric acid. Chem. Eng. Sci. 1975;30:825.
2
2
¼ p(0:15)(3:328 0:328 )(1:5) mcleod, h.o., jr. Matrix acidizing. JPT 1984;36:2055–
3
¼ 7:75 ft =ft ¼ 58 gal=ft: 2069.
paccaloni, g. and tambini, m. Advances in matrix stimu-
This example shows that the Daccord model gives opti-
lation technology. JPT 1993;45:256–263.
mistic results and the volumetric model gives more realistic
results. paccaloni, g., tambini, m., and galoppini, m. Key factors
The maximum injection rate and pressure for carbon- for enhanced results of matrix stimulation treatment.
ate acidizing can be calculated the same way as that for Presented at the SPE Formation Damage Control
sandstone acidizing. Models of wormhole propagation Symposium held in Bakersfield, California on Febru-
predict that wormhole velocity increases with injection ary 8–9, 1988. SPE Paper 17154.
1
rate to the power of ⁄ 2 to 1. Therefore, the maximum schechter, r.s. Oil Well Stimulation. Englewood Cliffs,
injection rate is preferable. However, this approach may NJ: Prentice Hall, 1992.
require more acid volume. If the acid volume is con- smith, c.f., and hendrickson, a.r. Hydrofluoric acid
strained, a slower injection rate may be preferable. If a
sufficient acid volume is available, the maximum injection stimulation of sandstone reservoirs. JPT Feb. 1965,
rate is recommended for limestone formations. However, Trans. AIME 1965;234:215–222.
a lower injection rate may be preferable for dolomites. taha, r., hill, a.d., and sepehrnoori, k. Sandstone acid-
This allows the temperature of the acid entering the for- izing design with a generalized model. SPEPE Feb.
mation to increase, and thus, the reaction rate increases. 1989:49–55.