HYDRAULIC FRACTURING for STRESS MEASUREMENTS
The in situ state of stress in the earth's crust has been widely recognized as a
basic parameter necessary in the engineering design of underground openings.
Quantitative evaluation of horizontal in situ stresses in rock at a specific site
cannot be made since gravitational forces are practically the only one clearly
understood. Therefore, these horizontal stresses require direct measurements in
the field. Presently the most common method of measuring in situ stress from
near-surface to considerable depths is hydraulic fracturing (or hydrofrac).
Typically hydraulic fracturing is conducted in vertical boreholes. A short
segment of the hole is sealed off using an straddle packer. This is followed by the
pressurization of the fracture-free segment of the hole by pumping in water. The pressure
is raised until the rock surrounding the hole fails in tension at a critical pressure.
Following breakdown, the shut-in pressure, the lowest test-interval pressure at which the
hydrofrac closes completely under the action of the stress acting normal to the hydrofrac.
In a vertical test hole the hydrofrac is expected to be vertical and perpendicular to the
minimum horizontal stress.
ELASTIC MODEL
Hubbert and Willis (1957) developed the first realistic model relating the recorded
hydraulic fracturing test variables to the in situ state of stress in rock.
At the borehole wall the tangential stress at the two points aligned perpendicular to the
minimum horizontal stress, Sh, will be the first to meet this criterion as the test-interval
pressure is raised. A hydraulic fracture will thus initiate and extend in the direction of the
maximum horizontal stress, SH.
With these assumptions, Hubbert and Willis (1957) were able to obtain an elastic solution
relating the hydraulic fracturing initiation pressure Pc (also called critical or breakdown
pressure) and the two principal horizontal stresses, Sh and SH.
where T is the tensile strength of the rock.
Adapted from http://www.hydrofrac.com
In their paper, Hubbert and Willis assumed that T is negligible at great depth because of
preexisting fissures traversing the rock and did not incorporate it in the above fracturing
criterion .
Hubbert and Willis suggested that the least horizontal stress is equal to the wellbore
pressure required to extend the hydraulic fracture while holding it open. Kehle (1964)
was more precise about the magnitude of Sh and suggested that it was equal to the shut-in
pressure, Ps, or the minimum pressure needed to keep the fracture open against the
fracture-normal stress (equal to Sh) after pumping has been stopped:
Thus, knowledge of four test variables (Pc, Ps, Po and T) is required to calculate the two
horizontal principal stresses provided the above assumptions hold.
To avoid the need for determining T, one of the most ambiguous rock mechanical
properties (Hudson and Fairhurst, 1969), Bredehoeft et al. (1976) suggested replacing the
breakdown pressure Pc with the fracture reopening (or refrac) pressure, Pr, obtained in
subsequent pressurization cycles. Under the assumption that the hydraulic fracture closes
completely between pressurization cycles and that the state of stress around the borehole
thus returns to its pre-test condition, equation Hubbert and Willis equation reduces to:
Typical Hydrofrac Pressure-Time Record
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POROELASTIC MODEL
One of the simplifying assumptions made in the elast model is that no injected fluid
penetrates into the surrounding rock. This condition may be correct in oil wells lined with
Adapted from http://www.hydrofrac.com
impermeable mud cake, but certainly inaccurate in clean open holes of the type
commonly used for stress measurements. The radial outward flow of the injected fluid
into the rock pores creates an additional stress field around the borehole. Haimson and
Fairhurst (1967) invoked the theory of poroelasticity (Biot, 1941) to incorporate the
effect of the injection fluid permeation on the stress distribution around the borehole, and
obtained the following hydraulic fracturing criterion:
a is the Biot poroelastic parameter (Biot and Willis, 1957), and is defined as a = 1 - Cr/Cb,
where Cr is rock matrix compressibility and Cb is rock bulk compressibility; n is the
Poisson's ratio for the rock.
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FRACTURE MECHANICS MODEL
Conventional elastic and poroelastic criteria assume that the rock subject to hydraulic
fracturing behaves as a continuous medium. However, the presence of natural cracks in
the test interval may violate this simplifying assumption. Abou-Sayed et. al. (1978)
introduced a fracture mechanics approach to the hydraulic fracturing criterion assuming
the existence of arbitrarily oriented cracks in rock. Further assuming that there is always
a symmetrical double crack of length a (typical of the rock type) which extends from the
hole wall in the direction of SH. Rummel and Winter (1983) and Rummel (1987) derived
a fracture mechanics solution that can be used to calculate SH. They suggest that
hydraulic fracturing will occur when the mode I (opening) stress intensity factor K I at the
tip of the crack reaches a critical value (fracture toughness K IC). The peak pressure Pc
recorded on the pressure-time plot is then interpreted as equal to:
where f*, g*, h* are dimensionless stress intensity functions calculated in terms of the
normalized crack length a/r, where r is the radius of the borehole. For comparison with
the classical elastic solution (Hubbert and Willis, 1957) the first term of the equation
f*KIC/Ö r is equivalent to the apparent hydraulic fracturing tensile strength of the rock.
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Adapted from http://www.hydrofrac.com
HTPF
A novel approach to calculating in situ stresses from hydraulic fracturing data has been
proposed by Cornet and Valette (1984). It is the Fracture Pressurization Method,
originally called 'hydraulic tests on preexisting fractures' (HTPF) by Cornet (1986). By
using the general theory of stress in 3-dimensional space, the fracture-normal stress can
be formulated as a nonlinear function of depth and fracture orientation, expressed in the
form of 6 unknown parameters which uniquely define the stress tensor. Unlike the
conventional models, the fracture pressurization method neither invokes the stress-strain
relations nor assumes the idealistic (homogeneous, isotropic, and linear elastic) rock
properties. The only assumptions made where the fracture pressurization criterion is used
are:
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The shut-in pressure is equal to the magnitude of the stress normal to the pressurized
fracture Sn even if it is not oriented along Sh.
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Each non-zero component of the stress tensor varies linearly with depth.
Sv is taken equal to the weight of the overburden and assumed to be a principal
component of the in situ stress tensor.
Under these assumptions, the state of stress at depth D can be represented by the
following tensor (Cornet and Valette, 1984):
where g is the mean weight density of the rock; D is the depth; (S) is symmetric with four
independent components; (A) is the stress tensor at the surface (D=0); and (B) is a tensor
representing the linear variation of the stress components with depth. McGarr (1980) had
Adapted from http://www.hydrofrac.com
shown that the stress linear relationship with depth is a direct result of the equations of
static equilibrium when the horizontal stresses are uniform over large area.
Using the definitions in the above equations A1 and A2 are the principal horizontal
stresses at the surface (D=0). Denoting the direction of A1 with respect to north as l A,
eigenvalues of (B) as B1 and B2, and the direction of the eigenvector corresponding to B1
with respect to A1 as l B. Then each normal (i=j) and shear (i¹ j) stress component Sij
(i,j=x,y) can be related to the six unknown principal components A1,A2,B1,B2,l A and l B
by (Jaeger and Cook, p. 24-26, 1976):
The measured attitude (dip f i, dip direction y i) of the pressurized fracture defines the
unit normal vector (n) of each fracture-normal stress Sn,i across ith fracture, measured by
the respective shut-in pressure Ps,i can be related to each stress component of (S):
By conducting a minimum of six pressurization tests in separate intervals within the same
stress regime, the six unknown parameters (A1, A2, B1, B2, l A and l B) in the fracturenormal stress equation can be determined, using one of several available least squares
techniques. The six parameters completely define three independent components (Sxx,
Syy, Sxy) of horizontal stresses as a function of depth. Thus, the horizontal principal
stresses and their directions are calculated as follows:
Knowledge of the in situ stress in rock mass is required in the design of underground
openings, in the earthquake studies, and in the extraction of oil and gas. The magnitudes
Adapted from http://www.hydrofrac.com
and directions of in situ stresses, obtained by hydraulic fracturing, provide the crucial
design parameters - layout (orientation, depth, and cross-sectional shape) of the opening,
frictional strength of the fault, and orientation of the fracture propagation. The following
are the examples of underground activities requiring the state of in situ stresses.
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Nuclear waste disposal repository design
(YMP, WIPP)
Oil & gas storage design
(SPR)
Compressed Air Energy Storage (CAES) design
(Norton)
Pumped energy storage design
(Bath County, Smith Mt. Lake, Tianhuangping, Snowy Mountains Scheme)
Transportation tunnel design
Earthquake prediction
(Earthquake list, San Andreas, Parkfield)
Man-made earthquake studies
Plate tectonics
(USGS, Earthquakes, platetectonics.com)
Waste injection for environmental restoration
(SPE)
Enhancement of oil / groundwater recovery
(Fracture toughness)
Geothermal energy extraction
(Fenton Hill, Soultz, Deep Heat Mining, Geocrack, Long Valley)
Borehole stability problems
(DEM, Karlsruhe)
Hydraulic fracturing field testing is a two-step procedure. Sequentially, it consists of (a)
pressurization of the selected borehole segment until fracturing occurs, and (b)
delineation of the induced fracture. Typically, a complete test will consist of two trips
downhole to the test interval, each with different equipment assemblies.
The most common tool for fracturing is a straddle packer system; for fracture tracing on
the borehole wall the oldest and still the most reliable is the impression-orienting tool. In
its simplest form the straddle packer system includes two inflatable rubber packer
elements straddled by an interval spacer. The packer elements are used to seal off a
segment of the hole so as to enable its leak-free hydraulic pressurization. The impression
packer-orienting tool assembly comprises of a compass-like (or gyroscopic) device and a
packer element covered with a partially cured thin rubber sleeve for taking an imprint of
the borehole wall when pressurized against it. A common method has been described in
ASTM standard D4645-87 (1989).
Adapted from http://www.hydrofrac.com
Wireline Straddle Packer System (Haimson and Lee, 1984)
Selected References for Hydraulic Fracturing
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ASTM Designation D4645-87, Standard test method for determination of the in-situ
stress in rock using the hydraulic fracturing method, Annual Book of ASTM Standards,
4.08, 851-856 (1989).
Aamodt R. and M. Kuriyagawa, Measurement of Instantaneous Shut-in Pressure in
Crystalline Rock, in Hydraulic Fracturing Stress Measurements, National Academy
Press, Washington, D. C., 28-43 (1983).
Abou-Sayed, A. S., C. E. Brechtel and R. J. Clifton, In Situ Stress Determination by
Hydrofracturing: A Fracture Mechanics Approach, J. Geophys. Res., 83, 2851-2862
(1978).
Ahagen, H., Instruments for Hydrogeological and Geochemical Measurements in Deep
Boreholes, International Symposium on Field Measurements in Geomechanics, Zurich,
1289-1292, (1983).
Baumgartner, J. and F. Rummel, Experience with Hydraulic Fracturing as a Stress
Measuring Technique in Jointed Rock Mass, in Proc. 2nd International Workshop on
Hydraulic Fracturing Stress Measurements, University of Wisconsin-Madison, pp. 168204, (1988).
Adapted from http://www.hydrofrac.com
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Baumgartner, J., F. Rummel, B. C. Haimson, and M. Y. Lee, In Situ Stress
Measurements and Natural Fracture Logging in Drill Hole CY-4, the Troodos ophiolite,
Cyprus, In Cyprus Crustal Study Project, Initial Report, Hole CY-4, Geological Survey of
Canada, paper 88-9, pp. 315-330 (1989).
Biot, M. A, General Theory of Three-dimensional Consolida-tion. J. Appl. Phys. 12, 155164 (1941).
Biot, M. A. and Willis, D.G., The Elastic Coefficients of the Theory of Consolidation, J.
Applied Mechanics, 594, (1957).
Bjarnason, B, C. Ljunggren, and O. Stephansson, New Developments in Hydraulic
Fracturing Stress Measurements at Lulea University of Technology, Int. J. Rock Mech.
Min. Sci. & Geomech. Abstr., 26, 579-586 (1989).
Bradley, W. B., Failure of Inclined Boreholes. J. Energy Res. Tech., Trans. AIME, 102,
232-239 (1979).
Bredehoeft, J., R. Wolff, W. Keys, and E. Shuter, Hydraulic Fracturing to Determine the
Regional In-situ Stress Field, Piceance Basin, Colorado, Geol. Soc. America Bull., 87,
250-258 (1976).
Cheung, L. S. and B. C. Haimson, Laboratory Study of Hydraulic Fracturing Pressure
Data-How Valid Is Their Conventional Interpretation?, Int. J. Rock Mech. Min. SCI &
Geomech. Abstr., 26, 595-604 (1989).
Cheung, L.S., Laboratory Simulated Hydraulic Fracturing Stress Measurements in Intact
and Prefractured Rocks, Ph.D. thesis, University of Wisconsin-Madison (1990).
Clark, J. B., A Hydraulic Process for Increasing the Productivity of Wells, Trans. AIME,
Vol. 186, 1949.
Cornet, F. H. and B. Valette, In Situ Stress Determination from Hydraulic Injection Test
Data, J. Geophys. Res., 89, 11527-11537 (1984).
Cornet F. H., Stress Determination from Hydraulic Tests on Preexisting Fractures- the
H.T.P.F. Method. in Proc. Intl. Symp. Rock Stress and Rock Stress Measurements,
CENTEK Publ., Lulea, pp. 301-311 (1986).
Daneshy, A. A., A Study of Inclined Hydraulic Fractures. Soc. Petr. Engrs. J., 13, 61-68
(1973).
De la Cruz, R. V. and C. B. Raleigh, Absolute Stress Measurements at the Rangely
Anticline, Northwestern Colorado, Int. J. Rock Mech. Min. SCI & Geomech. Abstr., 9,
625-634 (1972).
Dischler, S. A. and K. Kim, Determination of Rock Deformation Modulus during
Hydraulic Fracturing, in Proc. 26th U.S. Symposium on Rock Mechanics, South Dakota
School of Mines and Technology, 363-373, (1985).
Doe, T.W., W.A. Hustrulid, B. Leijon, K. Ingvald and L. Strindell, Determination of the
State of Stress at the Stripa mine, Sweden, in Hydraulic Fracturing Stress Measurements,
National Academy Press, Washington, D. C., pp. 119-129 (1983).
Enever, J. R. and B. A. Wooltorton, Experience with Hydraulic Fracturing as a Means of
Estimating In-Situ Stress in Australian Coal Basin Sediment, in Hydraulic Fracturing
Stress Measurements, National Academy Press, Washington, D. C., pp. 28-43, (1983).
Enever, J. R. and P. N. Chopra, Experience with Hydraulic Fracture Stress Measurements
in Granite, in Proc. International Symposium on Rock Stress and Rock Stress
Measurement, CENTEK Publ., Lulea, pp. 411-420 (1986).
Evans, K., A Laboratory Study of Two Straddle-Packer Systems under Simulated
Hydrofrac Stress-Measurement Conditions, J. Energy Resources Technology, 109, 180190 (1987).
Gronseth J.M. and P. R. Kry, Instantaneous Shut-in Pressure and its Relationship to the
Minimum In-situ Stress, in Hydraulic Fracturing Stress Measurements, National
Academy Press, Washing-ton, D. C., 55-60 (1983).
Adapted from http://www.hydrofrac.com
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Haimson, B. C., Earthquake Related Stresses at Rangely, Colorado, in Proc. 14th US
Rock Mech. Symp., Am. Soc. Civil Engrs, New York, NY, pp. 689-708 (1973).
Haimson, B. C., A Simple Method for Estimating In Situ Stresses at Great Depths, In
Field Testing and Instrumentation of Rock, ASTM STP 554, American Society for
Testing and Materials, pp. 156-182 (1974).
Haimson, B. C., Design of Underground Powerhouses and the Importance of Preexcavation Stress Measurements, in Proc. 16th US Rock Mech. Symp., Am. Soc. Civil
Engrs, New York, NY, 197-204 (1977).
Haimson, B. C., Crustal Stress in the Michigan Basin. J. Geophys. Res. 83, 5857-5863
(1978a).
Haimson, B. C., The Hydrofracturing Stress Measuring Method and Recent Results, Int.
J. Rock Mech. Min. SCI & Geomech. Abstr., 15, 167-178 (1978b).
Haimson, B. C., Field Measurements and Laboratory Tests for the Design of Energy
Storage Caverns, in Proc. 4th ISRM Congress, 2, Balkema, Rotterdam, pp. 195-201
(1979).
Haimson, B. C., Near Surface and Deep Hydrofracturing Stress Measurements in the
Waterloo Quartzite, Int. J. Rock Mech. Min. SCI & Geomech. Abstr., 17, 81-88 (1980).
Haimson, B. C., Stress Measurements at Hanford, Washington for the Design of a
Nuclear Waste Repository Facility, in Proc. 6th Congress of the International Society for
Rock Mechanics, Balkema, Rotterdam, pp. 119-123 (1987).
Haimson, B. C., Current Hydraulic Fracturing Interpretation, How Correctly Does It
Estimate the Maximum Horizontal Crustal Stress?. EOS, Trans. Am. Geophys. U., 69,
1454 (1988).
Haimson, B. C. and T. W. Doe, State of Stress, Permeability, and Fractures in the
Precambrian Granite of Northern Illinois, J. Geophys. Res., 88, 7355-7371 (1983).
Haimson, B. C. and J. N. Edl, Hydraulic Fracturing of Deep Wells, SPE 4061, presented
at the 47th annual fall meeting, AIME, Soc. of Petr. Engr. (1972).
Haimson, B. C. and C. Fairhurst, Initiation and Extension of Hydraulic Fracture in Rocks,
Soc. Petr. Engrs. J., Sept., 310-318 (1967).
Haimson, B. C. and X. Huang, Hydraulic Fracturing Breakdown Pressure and In Situ
Stress at Great Depth. In Rock at Great Depth (Edited by Maury and Fourmaintraux),
Balkema, Rotterdam, pp. 939-946 (1989).
Haimson, B. C. and C. F. Lee, Hydrofracturing Stress Determinations at Darlington,
Ontario. In Proc. 13th Canadian Rock Mech. Symp., Canadian Inst. Min. Met, Toronto,
Ontario, pp. 42-50 (1980).
Haimson, B. C. and M. Y. Lee, Development of a Wireline Hydrofra-cturing Technique
and Its Use at a Site of Induced Seismicity, in Proc. 25th US Rock Mech. Symp., Soc.
Mining Engrs, New York, NY, pp. 194-203 (1984).
Haimson, B. C. and M. Y. Lee, Stress Measurements at the Jordanelle Dam Site, Central
Utah, Using Wireline Hydrofracturing, final report to US Geological Survey, 14-080001-21890 (1985).
Haimson, B. C. and M. Y. Lee, The State of Stress in a Jointed Rhyolite, in Proc. 28th US
Rock Mech. Symp., Rotterdam, Balkema, pp. 231-240 (1987).
Haimson, B. C. and B. Voight, Crustal stress in Iceland. Pageoph, 115, 153-190 (1977).
Haimson, B. C., M.Y. Lee, N. Feknous, and P. de Courval, "Stress Measurements at the
Site of the SM3 Hydroelectric Scheme, Near Sept-Iles, Quebec", Intl. J. Rock Mech. and
Mining Sci., vol.33, 487-497, (1996).
Haimson, B. C., M. Y. Lee, and N. Chandler, Estimating the State of Stress at the
Underground Research Laboratory from Hydraulic Fracturing Tests in Three Holes of
Different Plunges, in Rock Mechanics Tools and Techniques, Eds. M. Aubertin, F.
Hassani and H. Mitri, Balkema Pub., vol. I, 913-919 (1996).
Adapted from http://www.hydrofrac.com
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Healy, J. H. and M. D. Zoback, Hydraulic Fracturing In Situ Stress Measurements to 2.1
km Depth at Cajon Pass, California, Geophys. Res. Lett., 15, 1005-1008 (1988).
Hickman, S. H. and M. D. Zoback, The Interpretation of Hydraulic Fracturing PressureTime Data from In-situ Stress Determination, in Hydraulic Fracturing Stress
Measurements, National Academy Press, Washington, D. C., 44-54 (1983).
Hubbert, M. K. and D. G. Willis, Mechanics of Hydraulic Fracturing, Trans. AIME, 210,
153-166 (1957).
Hudson J. A. and C. Fairhurst, Tensile Strength, Weibull's Theory and a General
Statistical Approach to Rock Failure, in Proc. Southampton 1969 Civil Engineering
Materials Conference, pp. 901-914 (1969).
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Well Fracturing. J. Geophys. Res. 69, 259-273 (1964).
Lee M. Y. and B. C. Haimson, PC-based Data Acquisition and Analysis Software for
Hydraulic Fracturing Stress Measurements, in Field Measurements in Geotechnics, Ed
(Sorum), 455-464 (1991).
Lee M. Y. and B. C. Haimson, Statistical Evaluation of Hydraulic Fracturing Stress
Measurement Parameters, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 26, 447-456
(1989).
Li, F., Q. Zhai, M. D. Zoback, B. C. Haimson, and M. Y. Lee, Stress Measurement in the
Red River Fault Region of Yunnan province, China, EOS, Trans. Am. Geophys. U., 66,
1060 (1985).
Ma, M., Hydraulic Conductivity Evaluation of Potential Underground Sites for Housing
Superconductive Magnet Using Field and Laboratory Methods, M. S. thesis, University
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Adapted from http://www.hydrofrac.com
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Adapted from http://www.hydrofrac.com