Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 14, pp. 49-58. Pergamon Press 1977. Printed in Great Britain

Laboratory Hydraulic Fracturing Experiments in Intact and Pre-fractured Rock M. D. ZOBACK* F. RUMMEL~f R. JUNGI" C. B. RALEIGH*

Laboratory hydraulic fracturing experiments were conducted to inrestigate two factors which could influence the use of the hydrofrac technique for in-situ stress determinations; the possible dependence of the breakdown pres- sure upon the rate of borehole pressurization, and the influence of pre-existing cracks on the orientation of generated fractures. The experiments hare shown that while the rate of borehole pressurization has a marked effect on break- down pressures, the pressure at which hydraulic fractures initiate (and thus tensile strength) is independent of the rate of borehole pressurization when the effect of fluid penetration is negligible. Thus, the experiments indicate that use of breakdown pressures rather than fracture initiation pressures may lead to an erroneous estimate of tectonic stresses. A conceptual model is proposed to explain anomalously high breakdown pressures obserred when fracturing with high viscosity fluids. In this model, initial fracture propagation is presumed to be stable due to large differences between the borehole pres- sure and that within the fracture. In samples which contained pre-existing fractures which were "leaky' to water, we found it possible to generate hydrau- lic fractures oriented parallel to the direction of maximum compression if high viscosity drilling mud was used as the fracturing fluid.

INTRODUCTION

Making routine crustal stress measurements is a for- midable problem addressed by many earth scientists and engineers. In this regard, the technique of deriving in-situ stresses from hydraulic fracturing data has specifically received wide attention because stresses can be measured at large distances from weathered or stress-relieved rock surfaces. Considering the reliability of the stress data derived from such measurements, Raleigh et al. [1] showed for the hydrofrac measure- ments in the Rangely oil field, Colorado [2], that there was excellent correspondence between the stresses measured in-situ and those expected from laboratory derived parameters. Thus, the success of the Rangely experiment seemed to establish the validity of the hyd- rofrac technique as a stress measuring method and has given great impetus to investigators. However, as dis- cussed by Rummel and Jung [3], several factors which may influence hydraulic fracturing experiments remain to be investigated. Furthermore, since hydraulic frac-

* Office of Earthquake Studies, U.S. Geological Survey, 345 Mid- d/efield Rd., Menlo Park, CA 94025, U.S.A.

t" Institut fi~r Geophysik, Ruhr Universit~t Bochum, 4630 Bochum, Gcrman x.

turing has become increasingly important in the fields of oil and gas reservoir stimulation, coal gasification, and geothermal energy extraction, the importance of factors effecting tensile crack development in rock sub- jected to fluid pressures need to be thoroughly studied.

Hydraulic fracturing involves pressurizing a well or borehole until inducing a tensile fracture presumably perpendicular to the least principle compressive stress. From measuring the critical borehole pressure required to induce this fracture (conventionally termed the breakdown pressure) as well as the pressure necessary to merely keep the fracture open (termed the shut-in pressure) one can theoretically determine both the maximum and minimum in-situ stresses, assuming the tensile strength of the rock is known and the rock is isotropic and impermeable to fluid penetration. If Po is the pore pressure in the rock formation investigated, according to the theory of hydraulic fracturing [4, 5], the breakdown associated with the formation of a radial fracture is given by

Pb = T + 3 tTa - trl - Po (1)

where tr t and t H are the greatest and least principal compressive stress and T is the tensile strength of the rock.

50 M.D. Zoback. F. Rummel. R. Jung and ( . B. R:~iciel~

One major problem in applying equation t l} is that prior to fracture the pressurizing fluid may penetrate into the surrounding rock and thus perturb the stress field by increasing the interstitial pore pressure around the borehole. Neglecting this effect would lead to the computation of erroneously high values of the maxi- mum principal stress, even presuming that the correct tensile strength was used. In laboratory experiments to determine the value of tensile strength, this effect would lead to erroneously low values of tensile strength. Haimson [6] addressed this problem and theoretically derived an expression similar to equation (1) when fluid penetration occurs. However, as demonstrated by laboratory hydrofrac experiments in permeable hydro- stone [6, 7] and sandstone [8], use of this relationship did not adequately correct the experimental data.

A second difficulty in in-situ hydrofrac operations and the interpretation of hydrofrac data arises if pre- existing cracks and joints are present in the natural rock formations. Haimson [9] showed that use of a plaster-of-paris liner around a borehole kept fluid out of pre-existing fractures and enabled a correctly oriented hydraulic fracture to be generated in labora- tory specimens. This technique, however, is not amen- able to efficient field operations.

To further investigate these two basic problems--the effect of fluid penetration prior to fracture and the in- fluence of pre-existing cracks on hydrofrac opera- tions--the experiments described below were under- taken.

EFFECT OF F L t I D PENETRATION ON HYDRAt/LIC F R A C f t R I N G

Exper imenta l technique ,

To study the effect of time-dependent fluid pen- etration, laboratory hydraulic fracturing tests were con- ductcd on cylindrical rock specimens under constant triaxial stress conditions, on cubical rock specimens uniaxiallv loaded with a constant stress, and on cubical samples ~ith no external loztd applied.

Hydraulic lructuring x~a~, zlcllic\cd ill the triaxial loaded specimens dength 6 cm, diameter 3 cm) by pres- surizing an axial borcholc (2 3 mm in diameter). The pressurizing fluid was injected into the boreholc through the base-plate of the triaxiat pressure vessel. The specimens xverc pre-loaded by a constant axial stress at of about 4 0 M N m 2. Assuming the rock to be impermeable and the pore pressure to be zero. the tensile strength T of the samples can, in theory, bc simply computed from the breakdown pressure Pb with the expression

T = P ~ - 2~3. (21

The externally stressed cubical samples, 12 cm on a side, were uniaxially loaded with a constant stress, a~. of about 2.5 MNm-e. A borehole (1.05 cm in diameterl perpendicular to the loading axis through the center of the specimen was pressurized over 6.5 cm of its length until a fracture parallel to the loading axis devel-

Fig. 1. Photograph of a loaded cubical specimen of Ruhr sandstone with deformation and acoustic emission transducers attached.

Intact and Pre-fractured Rock 51

oped. In this case the tensilestrength is theoretically given by

T = Pb + al. (3)

Figure 1 shows a loaded cubical specimen instrumented for monitoring borehole pressure, sample deformation, and acoustic emission activity in an attempt to accu- rately determine the borehole pressure at which the hydraulic fractures initiated. LVDTs were externally mounted perpendicular to the plane of the expected fracture. Acoustic emissions were monitored by a piezo- electric transducer mounted to the surface of the speci- men. The acoustic emission system was capable of counting 1000 events per second in the frequency range of 100--200 kHz [10]. The unstressed specimens were similarly instrumented but two orthogonal sets of LVDTs were used.

The fracturing fluid in the triaxial experiments was light lubricating oil. Water, mixed 60:1 with a cor- rosion preventing oil, was used in the tests on the uni- axially loaded cubical spec!mens. High viscosity oil was used in the experiments with the externally unstressed specimens.

Tests were performed on three types of rock. Ruhr sandstone (a fine-grained, massive, weakly-bedded Car- boniferous sandstone from the Ruhr area of Germany) was used in all three types of experimental tests. Weber sandstone (a very well-indurated Permian sandstone from the Rangely boreholes) was only used in the triax- ial tests and a South African gabbro (containing no visible porosity in thin sections) was used in tests where no external load was applied. The permeabilities of both sandstones ranged from about 0.1 to 1.0 mdarcy.

Fluid was injected into the boreholes at either con- stant pressurization rates or constant flow rates. Con- stant pressurization rate was achieved either manually or by using the output of the borehole pressure trans- ducer as control signal for a closed-loop servo system. With this technique we could easily obtain pressuriza- tion rates between 10 -4 and 10 z MNm-2/s. Constant flow rates were achieved using a hydraulic pressure generator in which the piston was moved by servo-con- trolling the displacement rate. Constant flow rates between 10-3 and 1 c m 3 / s w e r e easily obtained.

6 0

~ o

Z :[

4O h i a "

~o O.

~ ~o v

I 0

i 0 - 4

I I l I I I 0

O

o

o o

o • • o o

o

• o

• . 0" * * : . , . 4 o ~ , . / . , p •

o" 3 • I0 M N I m 2 ~

JACKET - ~ , - ~

l l I l I l

iO " z iO o iO z

PRESSURIZATION RATE , (MN/mZ)ISEC

Fig. 2. Breakdown pressure as a function of the rate of borehole pressurization for Weber sandstone. Symbols represent experiments in which the rate of borehole pressurization was either servo-con-

trolled (open circles) or manually controlled (closed circles).

Although the experimental scatter is considerable, the results clearly indicate that the breakdown pressure for both rocks increases with pressurization rate. Consider- ing in detail the results for Weber sandstone (Fig. 2), at medium pressurization rates around 0.1 MNm-Z/s, the breakdown pressures are seen to be fairly constant and indicate a tensile strength of about 9.5 MNm-2 At lower rates of pressurization the breakdown pres- sures are seen to decrease and would lead one to assume a very low value of tensile strength if equation (2) were used. This effect is similar to that reported by Haimson and Fairhurst [7] for permeable hydro- stone, and is consistent with the concept of fluid diffus- ing away from the borehole and increasing the pore pressure in the region surrounding it. At the very high rates of pressurization (above I MNm-Z/s) the break- down pressures increase steeply to almost 60 MNm-z and seem to indicate anomalously high tensile strength values. Only part of this effect can be explained by differential fluid pressures between the pressure trans- ducer and borehole due to fluid friction.

After each test the specimens were cross-sectioned to determine the range of fluid penetration from the borehole into the surrounding rock structure. It was

Results

Hydraulic fracturing under triaxial stress conditions were carried out on 27 specimens of Weber sandstone and 14 specimens of Ruhr sandstone at controlled, constant pressurization rates between 10 -4 and 10-2 MNm-Z/s. The propagation of the induced tensile fractures occurred unstably when the fluid pressure in the borehole reached a critical value. Due to the finite response capability of the pumping system, this un- stable fracture growth was characterized by a sudden drop in fluid pressure. In analogy to field experiments, we call this critical pressure the breakdown pressure, Pb.

Results of the triaxial experiments are shown in Figs. 2 and 3 for Weber and Ruhr sandstone, respectively.

o o

z ~0

uJ t~- o o

o o

3o CL o o o o 01 = tO kfNIm 2 P

~ 2o 03~ 10 MN/m 2 ~

la.l

~m Jocket

I I I I • 10 "2 10 0 10 ~

P R E S S U R I Z A T I O N R A T E , ( M N I m 2 ) I SEC

Fig. 3. Breakdown pressure as a function of the rate of borehole pressurization for Ruhr sandstone tested under the triaxial conditions

shown. All tests were servo-controlled.

52 M. D. Zoback, F. Rummel, R. Jung and C. B. Raleigh

SAMPLE DEFORMATION

~0 " /p~

t = I 0 0 ~

"/p~

Bo

u')

~: IO I - -

4O ~

O i I I I i I I I I I 0 "= 0 2 4 6 8 I0

TIME , SEC

Fig. 4. Measurements made during the pressurization rate controlled experiment with sample R-104. Shown as a function of time are the sample deformation (top), borehole pressure (center), and acoustic

emission activity (bottom).

found that depending on the rate of pressurization, the fluid had penetrated considerably into the rock before a macroscopic tensile fracture occurred. In the case of very slow pressurization the fluid had almost pene- trated to the outer boundary of the specimen.

Controlled pressurization rate experiments were also conducted on externally unstressed cubical samples of Ruhr sandstone and gabbro, using high viscosity oil as pressurization fluid. The experiments were per- formed at either low (0.02 MNm-2/s ) or high rate of pressurization (3.0 MNm-2/s) . Typical of the measure- ments recorded during these experiments are the data for sample R-104 presented in Fig. 4. The rate of pres- surization was 3.0 M N m - 2 / s and the breakdown, Pb, was observed at a pressure of 30.1 MNm-2 . However, both an increase in acoustic emission activity and ano- malous sample deformation perpendicular to the bore- hole axis indicate that fracturing actually initiated before breakdown at a pressure, P~, of 29 MNm-2 .

The results of these experiments are summarized in Table 1. Listed in the table are the pressure at fracture

TABLE 1. PRESSURIZATION RATE CONTROLLED EXPERIMENTS

Pressurization Sample rate P~ Pb Pb - P~

No. (MNm-2/s) (MNm-:)(MNm-2)(MNm -2)

Gabbro

Ruhr SS

G-111 0.02 24.2 26.8 2.6 G-112 0.02 25.0 26.7 1.7 G- 115 0.02 18.8(?) 21.0(?) 2.2 G-113 3.0 25.3 54.3 29.0 G-114 3.0 24.6 50.9 26.3

R-101 0.02 16.1 16.7 0.6 R-102 0.02 18.6 19.2 0.6 R-107 0.02 21.3 22.9 1.3 R-108 0.02 19.0 19.6 0.6

18.8_+2 19.6+2 RoI03 3.0 25.1 29.1 4.0 R-104 3.0 29.0 30.1 2.1 R-105 3.0 28.5 36.1 7.6 R-106 3.0 34.2 40.3 6.1(?)

29.2+2 33.9+5

initiation, Pi, the breakdown pressure, Pb, and the dif- ference between them. It is clear from these experiments that under conditions of controlled pressurization rate the breakdown pressure at the higher pressurization rate is markedly higher than the true tensile strength of the samples. This is most clear for the gabbro samples. Except for sample G - l l 5 (which fractured at an anomalously low pressure), the fracture initiation pressures indicate a rate independent tensile strength (24.8 M N m - 2) approx 2.0 M N m - 2 less than the break- down pressure at 0 .02MNm-2/s , but more than 25.0MNm -2 less than the breakdown pressure at 3 .0MNm-2/s . Similarly, for the Ruhr sandstone samples, the difference between the breakdown and in- itiation pressure at 3 .0MNm-2 / s was considerably greater than at 0.02 MNm-2/s . In related experiments, Jung [111 reports similar results for marble and lime- stone samples as well as sandstone and gabbro. Thus, for four different types of rock the breakdown pressure was found to markedly increase with rate in pressuriza- tion rate controlled experiments.

Results of hydrofrac experiments on 12 uniaxially loaded cubical specimens of Ruhr sandstone tested at controlled constant flow rates are shown in Fig. 5 and

4 0 - -

] . 0 - - ;¢ t~J G:

ILl --J

Z 2 0 W

5) c~o o 0

Fig. 5. Tensile strength as a function of pressurization rate in controlled injection rate experiments with Ruhr sandstone.

po I J lllIIil I i IIil.l m i llil.l I I llltlll I 0 - z I 0 " I 0 I ' I 0 ' I 0 !

PRESSURIZATION RATE , ( M N I m t ) / S E ~ C

Intact and Pre-fractured Rock

TABLE 2. RESULTS OF CONTROLLED INJECTION-RATE EXPERIMENTS

53

Sample No.

Rate of Tensile Flow rate pressurization Pb strength (cm3/s) (MNm='/s) (MNm- 2)(MNm- 2) Comments

R-11 6.6 x 10 -3 0.101 23.3 25.9 R-12 6.6 x 10 -3 0.096 20.0 22.7

R-13 6.6 x 10 -1 17.100 29.1 31.8 R-14 6.6 x 10 -1 16.800 19.6 22.2 R-15 6.6 x 10 -1 16.700 21.0 23.6 R-16 6.6 x 10 -1 15.200 23.7 26.3 R-17 6.6 x 10 -3 0.107 20.6 23.1 R-18 6.6 x 10 -2 1.400 21.0 23.6 R-19 6.6 x 10 -2 1.390 22.7 25.3 R-20 2.64 x 10 -3 6.011 20.2 22.9 R-20 side 2 2.64 x 10 -2 0.282 17.8 20.3

R-II side 2 6.6 x 10 -3 1.260 17.3 23.4 2 4 . 3 + 3

No AE preceding failure AE precedes failure by

2 seconds AE noisy AE noisy AE noisy AE noisy AE precedes failure by 5 s AE precedes failure by ~0.5 s AE precedes failure by ~ 1 s AE precedes failure by ~ 1 s New vertical fracture formed

when old fracture placed perpendicular to load

New vertical fracture formed when old fracture placed perpendicular to load

summarized in Table 2. The flow rates were between 2.64 x 10 -a and 6.6 x 10 -1 cma/s. These correspond to mean pressurization rates between 0.01 and 17.1 MNm-2/s. In Fig. 5 and Table 2, the breakdown pressures, and thus the computed tensile strengths, were clearly found to be rate independent. The tensile strength was 24.3 MNm -2, a rather high value. The significance of the results for the last two samples listed in Table 2 is discussed below.

The onset of acoustic emission activity is believed to be a reliable indication of fracture initiation and, as shown in Table 2, the acoustic emission data indicate that the fracture initiation pressure is essentially equal to the 'breakdown' pressure. In these experiments, then, the breakdown pressure could be used to compute ten- sile strength, and the monitoring of acoustic emissions was actually unnecessary.

Comparison of the results in Tables 1 and 2 illus- trates that for controlled pressurization rates the appar- ent tensile strength at 3.0 MNm-e/s of 29.2 MNm -2 is slightly higher than that indicated by the controlled flow rate experiments (24.3 MNm-2). This is probably due to the difficulty in determining P~ at 3.0 MNm-2/s (due to noisy acoustic emission records) and implies that Pb -- P~ is probably slightly higher than indicated. Second, in the controlled pressurization rate experi- ments, at 0.02 MNm-2/s fluid penetration appears to have lowered the breakdown and fracture initiation pressures. As a result, the apparent tensile strength at 0.02 MNm-2/s appears to be 18.8 MNm -2.

Discussion

Obviously the results of hydraulic fracturing experi- ments conducted under conditions of constant rate of pressurization and constant flow rate are quite differ- ent. In pressurization rate controlled experiments the breakdown pressures [and thus the tensile strength if equation (2) is used] were found to be rate dependent. In flow rate controlled experiments, the breakdown pressure was essentially equal to the fracture initiation pressure and was rate independent. To explain this dis-

crepancy we suggest that anomalously high breakdown pressures at high controlled pressurization rates (seen in Figs. 2 and 3, and Table l) results from a condition of initially stable crack propagation caused by fluid pressure drops occurring in the propagating hydraulic fractures. Thus, when controlling pressurization rate, the pumping system could easily 'keep up' with slight borehole pressure drops resulting from initially stable crack propagation, and presumably breakdown was not observed until a macroscopic fracture developed. Simi- larly, the explanation of the increased difference between the borehole and fracture initiation pressure at higher rates is that fracture propagation is inhibited due to relatively greater hydrodynamic losses in the fracture since the pressure drop would be proportional to the injection rate.

Further support for this explanation of the difference between initiation and breakdown pressure is offered by results of experiments conducted by Jung[ l l ] on marble, limestone, sandstone and gabbro specimens. Jung's experiments on externally unstressed samples were quite similar to those reported here except that a lower viscosity oil was used at the frac fluid. Com- parison of the results show that for both fluids, Pb - Pi at 0.02MNm-2/s was quite low (Table 1), whereas at 3.0 MNm- 2/s Pb -- Pi is about 10 MNm- 2 greater with the more viscous oil. This is consistent with the concept that hydrodynamic losses in the fracture account for the increase in Pb -- P~ with pressurization rate.

Considering the large effect of pressurization rate on P b - P~ for gabbro specimens investigated (Table 1), Jung [11] showed that this effect is more pronounced for rocks with low initial porosity, while there is con- siderably less effect for sedimentary rocks such as sand- stones. A possible explanation of this phenomenon is that in a porous rock the propagating fracture would in part connect pre-existing pores. Thus, a fracture would be effectively 'wider' than a fracture in a non- porous material and the pressure drop, which is highly dependent on the fracture width, would therefore be considerably less.

54 M.D. Zoback, F. Rummel, R. Jung and C. B. Raleigh

In field application, wells are often fractured by pumping fluid at constant flow rates. Thus, at this point the results of these experiments seem to have merely told us to avoid using pressurization rate control systems when determining tensile strength values in laboratory tests. Our experiments with pre-fractured samples, however, suggest that the causes of anoma- lously high breakdown pressures can have important consequences in-situ. Therefore, rather than fully de- velop the hypothesis of initially stable crack propaga- tion at this point, we develop it separately below after presentation of the results with pre-fractured specimens.

As already mentioned, Haimson [6] has derived an equation similar to equation (2) to compensate for the effect of fluid penetration before fracture. In terms of the pressurization rate controlled experiments on un- stressed specimens reported here, his relation reduces to

-- -~-~b ] ~ - f ~ _ v ,]J P,, (4)

where v is Poisson's ratio of the rock (0.15 for Ruhr sandstone), C, the rock matrix compressibility, and Cb the bulk compressibility. For the reasons discussed above, Pi has been substituted for Pb in equation (4) (as the pressure at which the fracture forms) and for most sedimentary rocks (I - C,/Cb) is about 0.85 [12]. Equation (4) predicts a constant 'correction' to compen- sate for the effect of fluid penetration upon tensile strength. However, as mentioned above, the effect of fluid penetration is apparently gradational [7], the greater the fluid penetration, the lower the apparent tensile strength. It is interesting to speculate, nonethe- less, about whether Haimson's relationship might rep- resent an upper limit of the effect of fluid penetration. Considering Ruhr sandstone, equation (4) reduces to T = 1.3 Pi, thus implying that at 0.02 MNm-2/s the tensile strength of the cubical specimens is actually 24.4 MNm- 2 rather than 18.8 MNm- 2. This compares excellently with the tensile strength determined in the controlled flow rate experiments (24.3 MNm-2), and suggests that we have observed the maximum effect fluid penetration can have on this rock. This does not, however, explain the extremely low values of tensile strength in Ruhr sandstone tested under triaxial condi- tions at pressurization rates smaller than 1 MNm-2/s. In this case, the apparent tensile strength of the rock is about 16MNm -2 (using equation (3) for the case of triaxial loading). Thus, it does not seem possible to simply correct for the effect of fluid penetration before fracturing. In the flow rate controlled experiments, it is not known why there was no significant effect of fluid penetration in the single sample at low pressuriza- tion rate (R-20 in Table 2).

PRE-FRACTURED SPECIMENS

As mentioned above, Haimson [9] showed that use of a plaster-of-paris liner around a borehole kept fluid out of pre-existing fractures and enabled a correctly

oriented hydraulic fracture to be generated in labora- tory specimens. Since this technique is not amenable to efficient field operations, we attempted various other techniques. For example, we unsuccessfully attempted to pre-grout samples with an expanding cement and to use an expandable plastic liner around the packer. The plastic liner proved to give inconsistent results; sometimes it worked and a new, theoretically oriented fracture formed, and sometimes an old fracture opened. Due to the relatively large grain size of cement par- ticles, grouting of pre-existing cracks prior to fracturing also proved not to be successful. The technique, how- ever, which gave very encouraging results was to use viscous drilling mud as the fracturing fluid.

Experimental method Used in these experiments were the cubical samples

of Ruhr sandstone pre-fractured under the conditions shown in Fig. 1. It was observed that with a pre-frac- tured specimen under load (turned so that the fracture plane was perpendicular to the applied stress) and with water as the fracturing fluid, the fracture would some- times hold pressure and enable a new fracture to be formed perpendicular to the first (thus explaining the last two entries in Table 2). More often, however, fluid would leak out of the borehole and into the fractures at fairly low pressures, often less than the applied nor- mal stress. This result, of course, is unexpected if one thinks of perfectly planar fractures in an ideal material since the fracture would tend to be closed by a com- pressive stress concentration equal to three times the applied load. However, with real fractures in real rocks, broken and dislodged grains do not allow the fracture to reclose completely and thus leave a relatively per- meable path for fluid flow. This type of fracture, then, was considered ideal for these experiments. While they were barely visible under load, they would leak water at pressures less than the applied stress. If such frac- tures were encounterd in-situ, they would undoubtedly open before the theoretically predicted fracture if water were the fracturing fluid. Thus, before we attempted to use a given pre-fractured sample in these experi- ments, it was tested to meet the requirement of leaking water at a pressure less than the applied normal stress. If necessary, the fractures were slightly extended while under no external load to reach this condition before a test was carried out.

The fracturing fluid used in these experiments was a relatively high viscosity bentonitic drilling mud pre- pared b~, mixing 1:9 with water until a smooth consist- ency was reached. The experiments were performed under conditions of controlled flow rate as in most field experiments. Mud was injected at a rate of 6.6 × 10-~cm3/s (corresponding to an approximate pressurization rate of 1.3 MNm-3/s). As above, acous- tic emissions were monitored to help determine the in- itiation of fracturing.

Results

The most encouraging aspect of these tests was that in every case that a new fracture was formed, it was

A g ~

55

56 M. D. Zoback, F. Rummel, R. Jung and C. B. Raleigh

TABLF 3. PRE-FRACTURED SAMPLES RE-FRACTURED V*'ITH VISCOUS DRILLING MI 1)

Sample No.

Tensile Flow rate Pn Pi Pb - P~ strength

(cmJ:s) [MNm-ZHMNm -2) (MNm -2) {MNm -2) Comments

R-18

R-19

R-12

R-8

R-6

R-4

R-7

R-21 R-22

2.6 x 1 0 - " 33.8 10.5 23.3 18.8 Mud can be seen in both old and new crack

2.6 x lO--' 38.0 12.4 25.6 20.1 New fracture clearly visible

6.6 x 10-2 55.0+ 14.7 40.3+ 19.0 No new macroscopic fracture visible

6.6 x 10-: 41.8 12.5 29.3 20.8 New fracture clearly visible

6.6 x 10 -2 46.6 -5.3? 41.3? l l . 0 ? Although sample totally separated along old fracture, a new, properly oriented fracture was generated

6.6 x 10 -2 38.1 12.7 25.4 20.2 New fracture clearly visible

6.6 x 10 -2 55.0+ ? - - ? No new macroscopic fracture visible

6.6 x 10 -2 50.8 19.9 30.9 20.0 Initially intact specimen 6.6 x 10 -z 48.1 9.3 38.8 17.9 Initially intact specimen

30.5 + 7 20.7 _ 3

parallel to the applied stress. Never did the pre-existing fractures open and propagate in response to the bore- hole pressure when mud was the fracturing fluid. As shown in Fig. 6a, this was even true in sample R-6 which had completely parted along the plane of the pre-existing fracture before we at tempted to generate the new fracture.

As seen in Table 3, the disappointing aspect of these experiments is that even though they were performed under controlled flow rate conditions, the breakdown pressu~-es were anomalous ly high. As illustrated in Fig. 7 (and listed in Table 3) the acoustic emission measure- ments again enabled us to accurately determine that the fracture initiation pressures were considerably less

than the breakdown pressures. In fact, the break- down pressures were so much larger than the fracture initiation pressures that in two specimens we reached the max imum pressure possible with our system ( 5 5 . 0 M N m -2) before breakdown occurred. The fact that the difference between the breakdown and fracture initiation pressures is so inconsistent seems to imply that using the same viscosity fracturing fluid both in the labora tory and in the field may not be a satisfactory technique for compensat ing for anomalous ly high breakdown pressures. It may indeed be necessary to use a relatively sophisticated technique (such as moni- toring acoustic emissions) in-situ to accurately deter- mine the pressure at which hydraulic fractures initiate.

Why is the viscous mud technique so successful in generating correctly oriented fractures? At the very high borehote pressures we reached, the pre-existing frac- tures should certainly have opened. In fact, we did observe trace appearances of mud in the pre-existing fractures (see Table 3 and Fig. 6b). It seems, therefore, that at the injection rates shown, there was a suffi- ciently large pressure drop in the pre-existing fractures for the new fractures to be initiated and propagated. Thus, in the case of sample R-6 (Fig. 6b) a pressure

drop of about 45.0 M N m -2 occurred over about 5 cm. More work of this type is required to determine the

viscosity and rate at which new fractures would cease to form. If progressively less viscous muds had been injected at slower and slower rates, at some point new fractures would not have been generated. However,

40--

3 0

I 0

%

i.u

800

600 --

4 0 0 --

z uJ

t,u

/

2 0 0

0

L I t 1 ~ I I I I ] I l I i ~ 5 0 I 0 0 150

T I M E ( S E C )

Fig. 7. The borehole pressure and number of acoustic emissions second as a function of time for pre-fractured sample (R-191 re-frac-

tured with viscous drilling mud.

Intact and Pre-fractured Rock 57

neither the viscosity of the mud nor the pressurization rate chosen is prohibitive to field operations, while the possible existence of barely visible, leaky fractures seems very likely.

STABLE AND UNSTABLE GROWTH OF HYDRAULIC FRACTURES

Two of the most common assumptions concerning the initiation and propagation of hydraulic fractures are that the breakdown pressure represents the pressure at which hydraulic fractures initiate and that because of the large stress concentration at the tip of a fracture, the borehole pressure need only exceed the stress nor- mal to the fracture in order to keep the fracture open and extend it. We suggest that when using high visco- sity fracturing fluids (such as drilling mud or heavy oil) neither of these assumptions may be true due to fluid pressure drops occurring in the fractures.

For two fractures emanating radially from a circular hole in an infinite medium, Fig. 8 presents the norma- lized stress intensity factor at the crack tips (Kl/p) as a function of the crack length, I. Newman [13] theoreti- cally derived these stress intensity formulae, and the physical dimension (R = 0.5 cm) is similar to that used on controlled flow rate experiments reported above. Two cases are considered, 2 = 0, when fluid pressure is applied only in the borehole, and 2 = 1, when it is applied over the fracture surface as well. We see that when 2 = 1 the stress intensity monotonically increases with crack length. Thus, if fluid pressure is acting along the entire fracture surfaces, the stress intensity grows as the fracture extends and unstable crack growth would naturally result. However, when fluid pressure acts only in the borehole, after an initially unstable growth to 0.3 cm, the stress intensity slowly decreases with crack length. This, of course, represents a case of stable crack growth since continued increases in pressure are required to cause continued crack propa- gation. In actual instances the pressure in the fracture would represent something between these two cases.

z i.o

w

~ 0.5 N

Z

o o

h=O o- - -

I I I 0.5 LO 1.5

CRACK LENGTH ( I ] ,Cg

Fig. 8. Normalized stress intensity factor as a function of crack length for two radial cracks emanat ing from a circular hole in an

infinite medium [12].

In the flow rate controlled experiments with the vis- cous mud, it is reasonable to expect that immediately after initiation of the fractures, there was essentially no fluid pressure in them, thus a condition of stable crack growth. At such time, however, that sufficient pressure built up in the fractures, unstable crack propa- gation occurred corresponding to breakdown as observed on the pressure-time records (we observed, in fact, mud 'ribboning out' of newly formed fractures which reached the edges of .specimens). Similarly, in the pressurization rate controlled experiments, there probably was a period of stable crack growth during which the servo-system could easily keep up with any borehole pressure drop which might have occurred. Only when sufficient fluid pressure built up in the frac- tures to cause unstable propagation, could the servo- system no longer keep up with the pressure drop in the borehole. We believe that it was at this time that breakdown was observed.

SUMMARY AND CONCLUSIONS

We have observed that when the effect of fluid pen- etration before failure is negligible, the pressure at which tensile fracturing initiates is independent of pres- surization rate, whereas the pressure at which break- down occurs is not. This was observed in two types of experiments; when a low-viscosity fracturing fluid

w a s used and the rate of borehole pressurization was servo-controlled, and when viscous drilling mud was injected at a constant rate. Our explanation of the ano- malously high breakdown pressures we observed is that after fracture initiation, the initial growth of the hyd- raulic fractures was stable because of large pressure drops in the narrow fractures. Subsequent increases in pressure caused unstable fracture growth which corre- lates with the pressure at which breakdown was observed.

In pre-fractured samples, when a viscous mud was the fracturing fluid, a correctly oriented hydraulic frac- ture was always generated. This we attribute to the extremely high pressure drops which occurred in the pre-existing fractures.

This study has two direct implications on in-situ hyd- raulic fracturing operations. First, when fracturing with low viscosity fluid in rock with no pre-existing weak- nesses, the breakdown pressure essentially corresponds to the initiation of tensile fracturing and is independent of the rate of borehole pressurization unless the rock is so permeable (and the pressurization rate so slow) that significant fluid penetration occurs. Secondly, using a viscous mud as the fracturing fluid will prob- ably result in a correctly oriented hydraulic fracture even if pre-existing cracks are present but will yield an anomalously high breakdown pressure. The pres- ence of a mud cake may result in a similar behavior even if water is used as the fracturing fluid. Thus, to accurately determine maximum tectonic stresses in practice, it seems necessary to use techniques to deter- mine fracture initiation pressures.

58 M. D. Zoback, F. Rummel, R. Jung and C. B. Raleigh

Acknowledgements--This result summarizes the result of laboratory hydraulic fracturing studies conducted during short periods of tenure of F. Rummel with the OES/USGS Menlo Park and M. Zoback with the lnstitut fiir Geophysik, Ruhr-Universit~t Bochum. Financial support was provided by USGS-Contract No. 14-08-0001-14823 and SBF77 "Felsmechanik', T.P.B8. The authors would like to thank H. J. Alheid and G. Harpeng for experimental assistance and D. Pollard for suggestions which improved the manuscript.

First received 4 June 1976; in revised form 20 September 1976.

REFERENCES

1. Raleigh C. B., Healy J. H. & Bredehoeft J. D. Faulting and crus- tal stress at Rangely, Colorado. In Flow and Fracture of Rocks, Vol. 16, pp. 275-284. American Geophysics Union Monograph (1972).

2. HaimsonB. Earthquake related stresses at Rangely, Colorado. In New Horizons in Rock Mechanics, Proc. 14th Syrup. Rock Mechanics (Edited by Hardy & Stefanko), pp. 689-708. ASCE, New York (1973).

3. Rummel F. & Jung R. Hydraulic fracturing stress measurements near the Hohenzollerngraben-structure, SW Germany. Pageoph. 113. 321-330 0975).

4. Hubbert M. K. & Willis D. G. Mechanics of hydraulic fracturing. Trans. Am. Inst. Min. Engrs 210, 153-168 (1957),

5. Kehle R. O. The determination of tectonic stresses through analy- sis of hydraulic well fracturing, J. Geophys. Res, 69. 259-273 (1964).

6. Haimson B. Hydraulic fracturing in porous and non-porous rock and its potential for determining in-sit,~ stress at depth. Ph.D. thesis, University of Minnesota, Minneapolis. MN (1968).

7. Haimson B. & Fairhurst C. Hydraulic fracturing in porous permeable materials. J. Petrol. Technol. 811 817 (1969).

8. Rummet F. Experimentelle Untersuchungen zum Bruchvorgang in Gesteinen. Berichte des Inst. f. Geophysik, Ruhr-Universitfil Bochum N.4 (1975).

9. Haimson B. Determination of in-situ stresses around under- ground excavations by means of hydraulic fracturing. Final Tech- nical Report to ARPA, Contract H-220080, Monitored by the U.S. Bureau of Mines, Spokane (1974).

10. Alheid H.-J. & Rummel F. Acoustic emissions during frictional sliding along shear planes in rocks. Proc. Co~!I: Acoustic Emission, Philadelphia, Pennsylvania State University Press, in press (1976).

11. Jung R. Bestimmung der Zugfestigheit von Gesteinsproben mit der Methode des Hydraulic Fracturing, Diplomarbeit, Instittit ftir Geophysik der Ruhr Universit[it Bochum (1976).

12. Knutson C. F. & Bohor B. F. Reservoir rock behavior under moderate confining pressure. In 5th Syrup. Rock Mechanics, Uni- versity of Minnesota. Macmillan, New York (1963).

13. Newman J. C. An improved method of collacation for the stress analysis of cracked plates with various shaped boundaries. NASA tech. Note D-6373 (1971).

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