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HYDRAULIC FRACTURING 17/265
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cleary, m.p., coyle, r.s., teng, e.y., cipolla, c.l., 162 lb=ft . The pore–pressure gradient in the sand-
stone is 0.36 psi/ft. Assuming a tectonic stress of
meehan, d.n., massaras, l.v., and wright, t.b.
Major new developments in hydraulic fracturing, with 1,000 psi and a tensile strength of the sandstone of
documented reductions in job costs and increases in 800 psi, predict the breakdown pressure for the sand-
stone.
normalized production. Presented at the 69th Annual 17.2 A carbonate at a depth of 12,000 ft has a Poison’s
Technical Conference and Exhibition of the Society of ratio of 0.3 and a poro-elastic constant of 0.75. The
Petroleum Engineers, held in New Orleans, Louisiana, average density of the overburden formation is
3
25–28 September 1994. SPE 28565. 178 lb=ft . The pore–pressure gradient in the sand-
clifton, r.j. and abou-sayed, a.s. On the computation of stone is 0.35 psi/ft. Assuming a tectonic stress of
the three-dimensional geometry of hydraulic fractures. 2,000 psi and a tensile strength of the sandstone of
Presented at the SPE/DOE Low Perm. Gas Res. Sympo- 1,500 psi, predict the breakdown pressure for the
sium, held in Denver, Colorado, May 1979. SPE 7943. sandstone.
17.3 A gas reservoir has a permeability of 5 md. A vertical
economides, m.j., hill, a.d., and ehlig-economides, c. well of 0.328-ft radius draws the reservoir from the
Petroleum Production Systems, Upper Saddle River, center of an area of 320 acres. If the well is hydraul-
New Jersey, Prentice Hall PTR, 1994. ically fractured to create a 2,000-ft long, 0.15-in. wide
economides, m.j. and nolte, k.g. Reservoir Stimulation, fracture of 200,000-md permeability around the cen-
3rd edition. New York: John Wiley & Sons, 2000. ter of the drainage area, what would be the fold of
geertsma, j. and de klerk, f. A rapid method of predict- increase in well productivity?
ing width and extent of hydraulic induced fractures. 17.4 A reservoir has a permeability of 100 md. A vertical
J. Petroleum Technol. Dec. 1969;21:1571–1581. well of 0.328-ft radius draws the reservoir from the
center of an area of 160 acres. If the well is hydraul-
guo, b. and schechter, d.s. A simple and rigorous IPR
ically fractured to create a 2,800-ft long, 0.12-in. wide
equation for vertical and horizontal wells intersecting
fracture of 250,000-md permeability around the cen-
long fractures. J. Can. Petroleum Technol. July 1999.
ter of the drainage area, what would be the fold of
khristianovich, s.a. and zheltov, y.p. Formation of
increase in well productivity?
vertical fractures by means of highly viscous liquid. 17.5 For the following situation, estimate the minimum
In: Proceedings of the SPE Fourth World Petroleum required compressive strength of 20/40 proppant. If
Congress held in Rome, Section II. 1955, pp. 579–586. high-strength proppant is used, estimate the perme-
lee, w.j. and holditch, s.a. Fracture evaluation with ability of the proppant pack:
pressure transient testing in low-permeability gas res-
ervoirs. J. Petroleum Technol. September 1981. Formation depth: 12,000 ft 3
meyer, b.r., cooper, g.d., and nelson, s.g. Real-time 3-D Overburden density: 165 lb m =ft
Poison’s ratio:
0.25
hydraulic fracturing simulation: theory and field case Biot constant: 0.72
studies. Presented at the 65th Annual Technical Con- Reservoir pressure: 6,800 psi
ference and Exhibition of the Society of Petroleum Production drawdown: 3,000 psi
Engineers, held in New Orleans, Louisiana, 23–26 Sep-
tember 1990. Paper SPE 20658. 17.6 For the Problem 17.5, predict the maximum expected
surface injection pressure using the following addi-
meyer, b.r. and jacot, r.h. Implementation of fracture
tional data:
calibration equations for pressure dependent leakoff.
Presented at the 2000 SPE/AAPG Western Regional
Specific gravity of fracturing fluid: 1.1
Meeting, held in Long Beach, California, 19–23 June Viscosity of fracturing fluid: 10 cp
2000. Paper SPE 62545. Tubing inner diameter: 3.0 in.
nolte, k.g. and smith, m.b. Interpretation of fracturing Fluid injection rate: 20 bpm
pressures. J. Petroleum Technol. September 1981.
nordgren, r.p. Propagation of vertical hydraulic fracture. 17.7 The following data are given for a hydraulic fractur-
ing treatment design:
SPEJ Aug. 1972:306–314.
perkins, t.k. and kern, l.r. Width of Hydraulic Fracture. Pay zone thickness: 50 ft
J. Petroleum Technol. Sept. 1961:937–949. Young’s modulus of rock: 4 10 psi
6
sneddon, i.n. and elliott, a.a. The opening of a griffith Poison’s ratio: 0.25
crack under internal pressure. Quart. Appl. Math. Fluid viscosity: 1.25 cp
1946;IV:262. Leakoff coefficient: 0:003 ft= min 1=2
valko, p., oligney, r.e., economides, m.j. High permeability Proppant density: 185 lb=ft 3
Proppant porosity: 0.4
fracturing of gas wells. Gas TIPS. October 1997;3:31–40.
Fracture half length: 1,200 ft
wright, c.a., weijers, l., germani, g.a., maclvor, k.h., Fracture height: 70 ft
wilson, m.k., and whitman, b.a. Fracture treatment
Fluid injection rate: 35 bpm
design and evaluation in the Pakenham field: a real- Final proppant concentration: 5 ppg
data approach. Presented at the SPE Annual Technical
Conference and Exhibition, held in Denver, Colorado, Assuming KGD fracture, estimate
6–9 October 1996. Paper SPE 36471.
a. Fluid volume requirement
b. Proppant mixing schedule
Problems c. Proppant weight requirement
d. Propped fracture width
17.1 A sandstone at a depth of 8,000 ft has a Poison’s
ratio of 0.275 and a poro-elastic constant of 0.70. 17.8 Predict the productivity index of the fractured well
The average density of the overburden formation is described in Problem 17.7.