Rock types used in our experiments.
1. Introduction
Hydraulic tensile strength is a crucial value for planning reservoir stimulation and stress measurements. It is used in the classical breakdown pressure (
For hydraulic fracturing laboratory experiments (MiniFrac – MF) under isostatic confining pressure
The coefficient
Thus, when poroelasticity is excluded in the experiments by taking dry samples and sealing off the central borehole by an impermeable membrane (like a polymer tube), one would expect that c equals two and
However, experiments with jacketed boreholes (sleeve MiniFrac – SMF) yield remarkable high values for
1.1. Theory of hydraulic and sleeve fracturing on hollow cylinders
Fracture mechanics deal with stress concentrations around fractures and the definition of propagation criteria for fractures. The theory is essentially based on the works of Griffith [5] and Irwin [6], which led to the introduction of the stress intensity factor K.
Mode I stress intensity factors
The direction of propagation is the x-axis and the stresses are applied perpendicular to the fracture. As can be seen from equation (4),
Two fractures of length
As an analytical solution for
Solving
MF-equation (Equation 13) with full injection pressure in the fracture yields unstable fracture propagation at constant injection pressures as soon as microcracks start to propagate. On the other hand, the SMF-equations (Equation 14) show a minimum. Thus, after a fracture reaches the crack length corresponding to the minimum critical injection pressure, stable fracture propagation (i.e. to propagate the fracture, the injection pressure has to be increased) could be expected.
To calculate the coefficient
2. Sample preparation and rock testing
The core specimens are drilled either with 40 mm or 62 mm water cooled diamond core drills. Core end planes are cut with a water flushed diamond saw blade and ground coplanar to a maximum deviation of ± 0.02 mm. The length and diameter ratio is chosen between 1.5:1 and 2.25:1. After sample preparation core specimens were dried for two days at a temperature of 105°C. For calculations of porosity
|
|
|
|
marble | Triassic Upper |
Carrara Italy |
coarse monocrystalline polygonal fabric |
limestone | Jurassic upper Malm | Treuchtlingen South Germany |
micritic limestone with abundant fossils and stylolites |
sandstone | Carboniferous Mississippian |
Dortmund/Hagen West Germany |
fine-grained arcose |
andesite D | Permian Rotliegend |
Doenstedt N German Basin |
porphyric fine-grained partly altered and pre-fractured |
rhyolite | Permian Rotliegend |
Flechtingen N German Basin |
porphyric fine-grained partly pre-fractured and sealed joints |
andesite R | Permian Rotliegend |
Thuringian Forest Rotkopf |
porphyric coarse-grained and pre-fractured |
2.1. Stress field and injection
Figure 3 shows schematically the components of the MF and SMF experimental set-up. The stress field is induced by a hydraulic ram (capacity 4500 kN) through a servo controlled MTS Test Star II system with a Hoek triaxial cell which is pressurized using a hand pump to achieve simultaneous pressure increase of confining pressure and axial load. In all tests axial stress is set to be 2.5 MPa higher than
2.2. Acoustic emission monitoring
Acoustic Emission (AE) signals are acquired with an AMSY5 Acoustic Emission Measurement System (Vallen Systeme GmbH, Germany) equipped with 5 Sensors of type VS150-M. The VS150-M Sensors operate over a frequency range of 100-450 kHz with a resonance frequency at 150 kHz. Due to machine noise in the range below 100 kHz incoming signals are filtered by a digital bandpass-filter that passes a frequency range of 95-850 kHz. AE data are sampled with a sampling rate of 10 MHz. The sensors are fixed using hot-melt adhesive to ensure best coupling characteristics. Pencil-break tests (Hsu-Nielsen source [12]) and sensor pulsing runs (active acoustic emission by one sensor) are used to test the actual sensor coupling on the sample.
3. Results
3.1. Petrophysical and mechanical parameters
An overview of the rock properties is given in Table 2. A wide range of low porosity/permeability rocks with
|
|
|
|
|||||
marble | 2.71 ±0.002 |
0.40 ±0.08 |
1E-19 | 5.67 ±0.06 |
1.57 ±0.11 (N=3) |
29/22 | 36.0 ±1.0 |
6.4 ± 1.5 |
limestone | 2.56 ±0.008 |
5.64 ±0.04 |
1E-18 | 5.59 ±0.05 |
1.19 ±0.14 (N=8) |
27/53 | 32.2 ±1.6 |
8.2 ± 2.2 |
sandstone | 2.57 ±0.006 |
4.39 ±0.06 |
8E-18 | 4.61 ±0.13 |
1.54 ±0.13 (N=4) |
36/50 | 29.4 ±1.6 |
13.2 ± 2.1 |
rhyolite | 2.63 ±0.015 |
1.02 ±0.12 |
9E-19 | 5.39 ±0.34 |
2.16 ±0.10 (N=4) |
20…36/55 | 30.2 ±1.9 |
15.8 ± 3.2 |
andesite D | 2.72 ±0.023 |
0.51 ±0.09 |
6E-19 | 5.26 ±0.28 |
1.90 ±0.08 (N=2) |
20…41/50 | 28.7 ±3.1 |
14.6 ± 4.5 |
andesite R | 2.60 ±0.013 |
1.70 ±0.08 |
4E-20 | 4.35 ±0.27 |
1.63 ±0.24 (N=4) |
31/46 | 21.3 ±0.9 |
11.4 ± 2.8 |
3.2. MF and SMF experiments
A schematic example of typical experiment data for MF and SMF tests is shown in Figure 4. Acoustic emission recordings are used to identify fracture processes in the test specimens. AE counts (threshold crossings per time interval – corresponding to AE activity) can directly be linked to localized fracture propagation [4]. The pressure at which the AE count rate raises rapidly is defined as
In MF experiments, there is almost no AE activity prior to failure. Failure occurs in a very short time span just before sample breakdown (which occurs at maximum injection pressure
Noteworthy is the discrepancy between the MF and SMF initial fracture propagation pressures PAE at zero confining pressure. This result would imply different hydraulic tensile strength values for the same rock type when using equation (2). Furthermore there is a significant difference between the values of coefficient
|
|
||||||
|
|
|
|
|
|||
marble | 4 mm | 8 | 7.7 | 1.03 | 6 | 31.7 | 6.97 |
6 mm | 8 | 9.4 | 0.96 | 4 | 19.6 | 8.54 | |
limestone | 4 mm | 9 | 10.3 | 1.00 | 6 | 26.7 | 6.06 |
6 mm | 8 | 8.2 | 1.01 | 7 | 29.1 | 5.79 | |
sandstone | 4 mm | 8 | 18.2 | 1.13 | 5 | 41.7 | 6.29 |
6 mm | 8 | 18.5 | 1.14 | 4 | 40.5 | 7.26 | |
rhyolite | 4 mm | 11 | 18.2 | 0.89 | 4 | 51.6 | 6.04 |
6 mm | 8 | 16.0 | 0.85 | 5 | 50.9 | 5.88 | |
andesite D | 4 mm | 9 | 16.1 | 1.00 | 3 | 64.2 | 4.17 |
6 mm | 6 | 10.9 | 0.87 | 4 | 48.1 | 4.83 | |
andesite R | 4 mm | 10 | 10.0 | 1.17 | 4 | 47.4 | 6.26 |
6 mm | 6 | 8.2 | 1.17 | 5 | 29.7 | 7.44 | |
∑ 93 | - | Ø 1.02 | ∑ 57 | - | Ø 6.33 |
4. Conclusion
With SMF tests, stable fracture propagation was achieved over a wide range of injection pressure. Fracture initiation can be confidently linked to the AE count rates. This can be concluded from experiments that were interrupted after
Due to high data scatter, the theoretical scale effect (critical injection pressure
The simple fracture mechanics model is able to explain the higher
We excluded poroelastic effects in our analysis due to the use of initially dry rocks with low permeabilities.
Appendix
Superposition of stress intensity factors for two radial cracks of length
Note: In equations 10 and 12 the borehole was excluded from the integration of stresses (cf. equation 4). The critical fracture propagation pressure at a given fracture length
Acknowledgments
The authors wish to thank the German Federal Ministry for the Environment, Nature Conservation and Nuclear Safety for financing our project (FKZ 0325279B). Many core specimens were prepared and analyzed by our student staff: T. Hoferichter, J. Braun, S. Hönig, K. Bartmann and A. Kraft. A great praise to the precision mechanics workshop guys for the construction of the fine working pressure intensifier system. We appreciate fruitful discussions with geomecon GmbH, Potsdam.
References
- 1.
Hubbert M, Willis D. Mechanics of hydraulic fracturing. Petroleum Transactions. 1957;210:153–68. - 2.
Rummel F. Fracture Mechanics Approach to Hydraulic Fracturing Stress Measurements. In: Atkinson BK, editor. Fracture mechanics of rock. Academic Press geology series. London [.u.a.]: Academic Pr; 1987. p. 217–39. - 3.
Winter R. Bruchmechanische Gesteinsuntersuchungen mit dem Bezug zu hydraulischen Frac-Versuchen in Tiefbohrungen. Berichte des Instituts für Geophysik der Ruhr-Universität Bochum: Reihe A. Bochum; 1983. - 4.
Ito T, Hayashi K. Physical background to the breakdown pressure in hydraulic fracturing tectonic stress measurements. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts. 1991;28:285–93. - 5.
Griffith AA. The Phenomena of Rupture and Flow in Solids. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character. 1921;221:163–98. - 6.
Irwin GR. Analysis of stresses and strains near the end of a crack traversing a plate. Journal of Applied Mechanics. 1957;24:361–64. - 7.
Sih GC. Handbook of stress-intensity factors: Stress-intensity factor solutions and formulars for reference. Bethlehem, Pa: Lehigh Univ., Inst. of Fracture and Solid Mechanics; 1973. - 8.
Tada H, Paris PC, Irwin GR. The stress analysis of cracks handbook. 3rd ed. New York: ASME Press; 2000.Ulusaihutsen - 9.
Ulusay R, Hudson JA, editors. The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974-2006. 2007th ed. Ankara: Commission on Testing Methods, International Society of Rock Mechanics; 2007. - 10.
Mutschler T. Neufassung der Empfehlung Nr. 1 des Arbeitskreises “Versuchstechnik Fels” der Deutschen Gesellschaft für Geotechnik e. V.: Einaxiale Druckversuche an zylindrischen Gesteinsprüfkörpern. Bautechnik. 2004;81:825–34. - 11.
Selvadurai APS, Jenner L. Radial Flow Permeability Testing of an Argillaceous Limestone. Ground Water. 2013;51:100–07. - 12.
ASTM E976. Standard guide for determining the reproducibility of acoustic emsission sensor response. American Society for Testing and Materials. 1994;386-391.