Article

Geosciences JournalVol. 5, No. 3, p. 263�271, September 2001

orea

A laboratory study of hydraulic fracturing breakdown pressure in table-rock sandstone

Nondestructive Research Lab. of Cultural Property, Kongju National University, Chungnam 314-701, K

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Insun Song

Mancheol Suh

Kyoung Sik WonBezalel Haimson

(e-mail: [email protected])Nondestructive Research Lab. of Cultural Property, Kongju National University, Chungnam 314-701, Korea (e-mail: [email protected])Geotech Consultant Co. Ltd., Kyunggi 435-826, Korea (e-mail: [email protected])Geological Engineering Program, University of Wisconsin-Madison, WI 53706, USA(e-mail: [email protected])

ABSTRACT: We carried out hydraulic fracturing tests in hollowcylinders of Tablerock sandstone subjected to vertical (σσσσv), con-fining (σσσσh) and pore (Po) pressures. Borehole fluid was injected ata constant flow rate until a peak pressure was reached, and ver-tical fracture was observed. Based on the analysis of pressure-timerecords, we submit that breakdown occurs before peak pressurePp in the first cycle. In a series of tests in which σσσσh, σσσσv, and Po werekept constant throughout, breakdown pressure Pc increased sig-nificantly with wellbore pressurization rate, and appeared to asymp-totically approach to an upper and lower bound corresponding tofast and slow rates, respective1y as expected by Detournay andCheng (1992). Another series of tests conducted at a preset pres-surization rate in unjacketed specimens (σσσσh=Po) revealed that(Pc−Po) increased with confining/pore pressure, contrary to theconstant (Pc−Po) based on the Terzaghi’s effective stress law. Wemodified the Detournay−Cheng criterion by replacing the Terza-ghi's effective stress with a general effective stress. More series ofhydraulic fracturing tests in jacketed specimens reinforced theapplicability of the modified Detournay−Cheng criterion to Table-rock sandstone in terms of correctly estimating the relationshipbetween the unknown far-field stress and the typically known testparameters: breakdown pressure, initial pore pressure and pres-surization rate.

Key words: hydrofracturing test, in situ stress measurement, pres-surization rate, pore pressure, breakdown pressure

1. INTRODUCTION

Hydraulic fracturing (HF) tests for the determination of insitu stress magnitudes and directions consist of injectingfluid into an isolated segment of a wellbore until a tensilefracture develops. Breakdown pressure, Pc, is defined as thewellbore pressure necessary to induce the hydraulic frac-ture. If one of the far-field principal stresses acts along thevertical wellbore, a vertical fracture develops typically alongthe direction of the maximum horizontal principal stress.The Pc is given in the closed-form of analytic solution interms of the far-field horizontal principal stresses.

There are two classical (or conventional) HF criteria toestablish equations between Pc and in situ horizontal prin-cipal stresses; one based on e1astic theory for impermeable

rocks (Hubbert and Willis, 1957) and the other based poroelastic theory considering the poroelastic stress inducethe fluid permeation into rocks (Haimson and Fairhurst, 196The Hubbert and Willis (H−W) HF criterion is given by:

(1)

The Haimson and Fairhurst (H−F) HF criterion is written as:

(2)

where σh and σH are the least and the maximum horizontprincipal stresses, respectively. Po is initial pore pressure inthe rock formation. Thf is hydraulic fracturing tensile strengthand η is poroelastic parameter given by:

(3)

where α is the Biot parameter (Biot and Willis, 1957) and νis the Poisson’s ratio. Two assumptions were made in bH−W and H−F criteria. One is that a tensile fracture occuwhen the effective tangential stress at wellbore wall reacthe HF tensile strength (Thf) of the rock. The other assumption is that Terzaghi’s (1943) effective stress law governs effect of pore fluid on rock stress, i.e.

(i, j=1, 2, 3) (4)

where is the effective stress and δij is the Kroneckerdelta (δij=1 for i=j and δij=0 for i � j).

There are several issues that are not satisfactorily descrby the two classical criteria. Firstly, there is no obvious dtinction between permeable and impermeable rocks. Pmeability varies from rock to rock so that it is impossible determine whether a given rock is permeable or impermable. Secondly, the H−F criterion (equation 2) does nodegenerate towards the H−W criterion (equation 1) as thepermeability/porosity (corresponding toα) becomes zero

Pc Po– Thf 3σh– σH 2Po–+=

Pc Po–Thf 3+ σh σH– 2Po–

2 2η–-----------------------------------------------=

η α 1 2ν–( )2 1 ν–( )

----------------------- 0 η 0.5≤ ≤=

σ i jeff σij δ ijPo–=

σ i jeff

264 Insun Song, Mancheol Suh, Kyoung Sik Won and Bezalel Haimson

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(α→0). Thirdly, neither H−W nor H−F criterion incorporatesthe effects of the wellbore pressurization rate and wellboresize, which are substantial in some experimental resultssuch as those by Haimson and Zhao (1991), Ito and Hayash(1991) and Schmitt and Zoback (1992). Efforts to figure outthese ambiguities have been limited to theoretical analyses(Detournay and Cheng, 1992; Detournay and Carbonell,1994), while laboratory verifications have been rare.

In little permeable rocks, the effect of wellbore pressur-ization rate may be less important because the wellborepressure can be raised in quasi-static condition. The pres-surization rate effect, however, becomes more important inhigh1y permeable rocks because it is indispensable to speedup the injection flow rate or to increase the fluid viscosityto overcome losses due to leak-off into rock pores (Songand Haimson, 2000). We carried out laboratory hydrofrac-turing simulations in hollow cylinders of highly permeableTablerock sandstone. The general objective of our researchwas to assess the potential for estimating in situ stress mag-nitudes from HF pressures in the high porosity sandstones,with particular reference to (1) the determination of Pc, (2)injection pressurization rate effect on Pc, and (3) pore pressureeffect on Pc. The ultimate goal of our project is to establishwhether HF technique is appropriate for estimating in situstress magnitudes in highly permeable sandstones based onexperimental results.

2. ROCK TYPE TESTED

For hydraulic fracturing experiments, we have obtainTablerock sandstone from a group of sandstone layers withe lower Idaho Group, upper Miocene in age (Wood aBurnham, 1987). The rock is classified as arkosic sandstdue to high content of K−feldspar (Prothero and Schwab, 1966The formation varies stratigraphically in terms of colorock texture and mineral composition. The sandstone ufor HF tests is ‘tan’-colored, composed of angular to suangular grains with 0.2 mm of mean diameter and is cosidered homogeneous with minor bedding and occasiothin seams of mica. Rock blocks for HF tests were obtainfrom the area where rock formation is relatively homogneous and uniform. Some important mechanical properof the rock were measured and are listed in Table 1.

3. EXPERIMENTAL SETUP AND PROCEDURE

We carried out experimental hydrofracturing tests in thiwalled, hollow cylinders of Tablerock sandstone with a hodiameter of 1.3 cm, an external diameter of 10.2 cm anlength of 13 cm (Fig. la). Specimens were placed in a axial pressure chamber and subjected to predetermined fining pressure Pconf (representing uniform horizontal stresσh), vertical load (simulating vertical far-field stress σv) and

Table 1. Physical and mechanical properties of the Tablerock sandstone tested.

Porosity Permeability Uniaxial Brazilian Tangential Poisson’s BiotCompressive Tensile Young’s ratio parameter

strength strength Modulus(%) (Darcy) (MPa) (MPa) (GPa) ν α

26.0±0.9 0.12 42.0±1.0 4.4±0.22 15.3 0.2 0.71

Fig. 1. (a) Prepared specimen for hydrofracturing test and (b) schematic of experimental setup.

A laboratory study of hydraulic fracturing breakdown pressure in tablerock sandstone 265

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uniform fluid pressure through pore spaces (pretending for-mation pore pressure Po). Fluid pressure for pore spaceswas applied through the saw-cut slots (1 mm width and 3mm depth) every 20o in axial direction on the outer surfaceof the hollow cylinder (Fig. la). Control of pore pressure atthe outer radius of specimen allowed the radial fluid flowwhen the wellbore was pressurized. Borehole fluid (viscos-ity: 2.5 Pa s at 20oC) which was the same as the pore fluidwas injected at a constant flow rate until a peak pressurewas reached. Fluid injection was stopped as soon as bore-hole pressure ceased to increase. Pressure cycles were repeatedseveral times. A four-channel servo-control system enabledthe continuous control the pressures applied (σh, σv and Po)and the borehole injection-fluid flow rate (Fig. 1b). A com-mercial software and a personal computer equipped withdigitatl-to-analog and analog-to-digital converters were employedfor test control and data acquisition. The entire loading pro-cess and borehole pressurization were automated includinginjection halting upon hydraulic fracturing and pressure decline.

4. APPEARANCE OF HYDROFRACTURES

The pressurization of wellbore always resulted in thedevelopment of vertical to subvertical brittle tensile frac-tures, confirming that conventional hydrofracing in highlyporous sandstone is feasible as long as appropriate fluidsand flow rates are used. SEM analysis revealed that hydrof-

ractures developed along grain boundaries (Fig. 2). Tintergranular crack propagation is so dependent upon grbond strength that often hydrofractures develop a tortupath that strays considerably from a straight plane (Fig.

5. ANALYSIS OF PRESSURE-TIME CURVES

A typical pressure-time record is shown in Figure 4. Tfluid injection with a constant flow rate brought abouincreasing in wellbore pressure and eventually peak prsures in all four cycles. Acoustic emission activities thappeared around each peak representing rock fracturinfracture reopening. In those tests peak pressures of suquent cycles are typically lower than that of the first one. soon as the wellbore pressure reaches a peak, fluid injechalted and the wellbore pressures rapidly decayed duehigh permeation and equalized to the initial pore pressthat was controlled at the outer surface of hollow cylind

For the more detailed view of fracture-inducing and fra

Fig. 2.Micrograph showing one complete branch of an intergran-ular hydrofracture propagating along grain boundaries. Wellbore islocated in the left side.

Fig. 3.Detail of a section of the hydrofracture, showing the tortous path of the fracture due to different grain-bond strengths (white arrow heads).

Fig. 4.Typical borehole pressure-timeand flowrate-time test record.


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ture-reopening pressure-time curves, the ascending portionof the first pressure cycle is superimposed on that of a sub-sequent cycle (Fig. 5a). The figure shows that the slope ofeach cycle is identical in the beginning stages of pressur-ization as expected if the flow rate is maintained constantfrom cycle to cycle (Haimson, 1980; Zoback et al., 1980),and if the fracture closes completely between cycles (Leeand Haimson, 1989). The peak pressure Pp of the first cycleis typically taken as the breakdown pressure. The pointwhere the slope of the subsequent pressurization deviatesfrom that of the first cycle is commonly taken as equal tothe reopening pressure Pr (Hickman and Zoback, 1983; Leeand Haimson, 1989). The hydrofracturing tensile strength as

obtained from Thfp−r=Pp−Pr (Haimson, 1980) varies betwee

9.1~35.5 MPa (average; 23.2±7.33 MPa), obviously too highfor such a sandstone (refer to Table 1 for mechanical prerties). This result probably comes from the overestimabreakdown pressure as equitable with the peak presrather than from the underestimated reopening pressThe technique of reopening pressure determination is qlogical and consistent (Hickman and Zoback, 1983; Lee aHaimson, 1989). In addition, in many cases acoustic emsion activities preceded the peak pressure as shown in5a. This result also implies that the peak pressure of the cycle is a post event appearing after fracture initiation.

The ascending portion of the pressure-time curve is clenon-linear (Fig. 5a), showing deceleration of the pressincrease with time (Fig. 5b). This is reasonable becawellbore fluid would leak through pore spaces to specimouter surface where the fluid pressure was maintainedequal as the initial pore pressure Po. According to Darcy’slaw, the outflow from the hole to the outer surface is liearly proportional to the pressure difference if the permability is constant. As outflow increases while the inflow constant, a gradual decline of wellbore pressurization incment (dP/dt) takes place due to the loss of borehole fluiwhich linearly increases with the wellbore pressure P.Eventually the injection fluid flow and outgoing flow willbe in equilibrium, and then dP/dt approaches 0, i.e. P sta-bilizes at a certain level if breakdown does not occur shown in Figure 6. In a test where the flow rate was too lto pressurize the wellbore until hydrofracing, the fluid flowbecame in steady state condition as P approaches a certainlevel (Fig. 6a). Figure 6b shows that the dP/dt linearlydecreases all the way to 0. Note that the dP/dt is a linearfunction of P as far as the specimen is intact.

In Figure 5b, however, at a point the pressure rate deates from the linear approximation, and becomes evfaster slow down. That is the point where we believe ththe permeability suddenly changes due to the tensile frturing. We call the deviation point Pc (Fig. 5b), and refer toit as the ‘apparent breakdown pressure’. Obtaining Pc directlyfrom a pressure-time curve such as Figure 5a is often ficult. Rather we were able to determine the Pc from plotsrepresenting the experimental data in the form of dP/dt asa function of P such as Figure 5b. The apparent breakdopressure determined from this technique often coincides wthe beginning of acoustic emission activity. This methworks not only for obtaining Pc but also for determining Pr.As shown in Figure 5, in most cases Pr obtained from thedeviation point in the pressure-time record closely coincwith the value read from the deviation point from the lineapproximation of the subsequent cycles in dP/dt versus Pdomain. Thus this technique could be used for back up dor sometimes yield better results. Now we recalculate hydrlic tensile strength Thf

c−r from the difference between Pc andPr. These values vary from 3.7 through 11.0 MPa and av

Fig. 5. (a) The ascending segment of the first pressure cycle super-imposed on that of a subsequent cycle showing the similar non-lin-earity of the two curves. Note that acoustic emission activitiesprecede the peak pressures. (b) Replotting of the ascending seg-ment of the pressure-time curves in the form of dP/dt as a functionof P, and the selection of the breakdown pressure Pc and reopeningpressure Pr as the respective inflection points.


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age 8.0±2.33 MPa. These values are much more reasonablefor hydrofracturing tensile strength than those calculatedfrom Thf

p−r=Pp−Pr (average: 23.2 MPa). Secondly, Thfp−r is

not only too high but also linearly increases with the pres-surization rate dP/dt (Fig. 7). The tensile strength is a mate-rial property that does not change so much with loadingcondition. On the other hand, Thf

c−r is more convincing as atensile strength because it is much more constant (Fig. 7).

6. RESULTS FROM UNJACKETED HYDROFRAC-TURING TESTS

Two series of HF tests were conducted on unjacketedspecimens, where fluid was free to move radially in and outof the hollow cylinders so that during test the initial porepressure Po was equal to the confining pressure (Po=Pcon�

σh) at the outer surface. In one series, fluid was injecteddifferent pressurization rate (dP/dt), resulting from differentflow rate, from test to test, while all specimens used wesubjected to the same level of confining/pore pressure aMPa. In the other series, the injection flow rate was tsame at 5 m3/sec in all tests yielding the same dP/dt ( 15�20 MPa/sec at breakdown) but in each test different cfining/pore pressures, 0 through 30 MPa, were applied. Tformer series was aimed to determine the pressurization effect on breakdown pressure Pc. The latter was to examinethe pore pressure effect on rock stress. If the effective stis given by Terzaghi’s law (equation 4), Pc−Po should beconstant because the effective confining stress (σh−Po)becomes zero. The reason that we used unjacketed smens was that the boundary condition was so clear atouter surface of hollow cylinder.

The former series of HF tests revealed that Pc−Po increasedsignificantly with the wellbore pressurization rate dP/dt(Fig. 8a). This behavior suggests that classical HF crite(Hubbert and Willis, 1957; Haimson and Fairhurst, 196were unsuitable for Tablerock sandstone since they disgard the effect of dP/dt. In the second series of HF tesconducted in unjacketed specimens, where a preset preization rate was used, Pc−Po appeared to linearly increasewith confining/pore pressure (Fig. 8b), contrary to the costant values predicted by both classical elastic and poroetic criteria. In both criteria, Pc−Po should be constant irrespectivof the magnitude of confining/pore pressure because σh=Po

in unjacketed specimens (see equations 1 and 2). Thibecause we used Terzaghi’s effective stress law (equatioto obtain the effective stress on tensile failure. Thus t

≅

Fig. 6. (a) A pressure cycle in which the rock specimen was nothydrofractured. (b) Replotting of the ascending segment of thepressure-time curves in the form of dP/dt as a function of P show-ing that dP/dt is approximated with a linear function all the way tothe peak pressure.

Fig. 7.Hydraulic fracture tensile strength Thf computed based ontwo different assumptions. Open circles were calculated from difference between the peak pressure (Pp) and the fracture reopen-ing pressure (Pr) showing linear function with dP/dt, and the otherone based Pc−Pr is independent of dP/dt.


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contrast implies that the Terzaghi’s effective stress law isnot suitable for tensile failure in Tablerock sandstone.

7. A NEW HYDROFRACTURING CRITERION

Conventional elastic and poroelastic models for hydraulicfracturing employed continuum mechanics and the maxi-mum tensile stress theory; a tensile fracture initiates at thelocation of the greatest local tensile stress and propagateperpendicular to its orientation once the material strength isexceeded. Neither elasticity nor poroelasticity describestime and size effects on rock behavior. However, those effectshave been repeatedly reported in laboratory experimentsincluding current our results from unjacketed tests. These

ambiguities arising in the classical hydrofracturing theoriare from the assumption that breakdown is characterizedthe failure of elastic regime at wellbore wall (Detournaand Carbonell, 1994). Several theoretical attempts wmade to interpret some of these problems by introducfracture mechanics (Whitney and Nuismer, 1974; AboSayed et al., 1978; Ito and Hayashi, 1991; Detournay anCarbonell, 1994).

The natural presence of miniature cracks in rocks hlong been considered as an origin of fracture propagatsince the works of Inglis (1913) and Griffith (1921). A basassumption is that hydraulic fracturing will initiate whethe stress intensity factor KI at a microcrack tip at wellborewall reaches the material toughness KIc (Abou-Sayed et al.,1978; Rummel and Winter, 1982; Detournay and Carbon1994). KI is partly dependent upon the pore pressure witthe cracks, which is a function of the wellbore pressuriztion rate dP/dt. As shown in Figure 3, however, there is ncrack tip because pores between grains are all inter-cnected. Instead of employing fracture mechanics, Detonay and Cheng (1992) introduced a lengthscale aroundwellbore to propose a model that breakdown takes plawhen the average effective hoop stress over the lengthsreaches the critical value Thf. In their approach, the averageffective stress was considered to induce a tensile faiinitiation. Pore pressure distribution over the length givby diffusion equation is also dependent upon the wellbpressurization rate. The Detournay and Cheng (D−C) HFcriterion is expressed as:

(5)

where γ is a dimensionless pressurization rate given by:

(6)

where A, λ and c are borehole pressurization rate, microrack lengthscale and diffusivity coefficient, respectively, aS is a stress quantity equal to the numerator of D−C crite-rion: S =Thf+3σh−σH−2Po. h(γ) is derived from diffusionequation representing pore pressure distribution in the vicity of wellbore. Figure 9a shows an example of functioh(γ), where η=0.27. As shown in the figure, h(γ) variesbetween 0 for γ=� ; the fast limit of wellbore pressurizationrate, and 1 forγ=0; the slow limit, so that equation 5 degenerates to either the H−W or the H−F criteria correspondingrespectively to the fast and slow limits of the pressurizatregimes. The D−C model implies that the condition of tensile failure initiation depends strongly on the wellbore presurization rate rather than on impermeable or permearocks (Fig. 9b). The theoretical breakdown pressure curvea function of γ is coincident with the variation of measurevalues shown in Figure 8a (Song and Haimson, 2001).

We still have a problem to explain the influence of po

Pc Po–Thf 3σh σH 2Po––+

1 1 2η–( )h γ( )+-----------------------------------------------=

γ Aλ2

4cS--------- 0 γ ∞≤ ≤=Fig. 8. (a) Hydrofracturing test results under identical sigma_h

(=Po) but different flow rates in unjacketed specimens. (b) Hydrof-racturing test results under a constant flow rate but various σh

(=Po) in unjacketed specimens.


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pressure. According to equation 5, Pc−Po should be con-stant for unjacketed tests regardless the magnitude of con-fining/pore pressure once if h(γ) is given. However, ourresult shows that Pc−Po linearly increases with the confin-ing/pore pressure (Fig. 8b). This discrepancy comes fromthe employment of Terzaghi’s effective stress law in the D−C theory. We considered a more general effective stress lawfor tensile failure as proposed by Schmitt and Zoback (1989):

(0≤β≤1) (7)

where β is an effective stress parameter depending on rocktype. We modified D−C HF criterion based on an assump-tion that a breakdown occurs when the effective stress gov-erned by the generalized effective stress law (equation 7)

equals the HF tensile strength. The modified D−C hydraulicfracturing model is expressed as:

(8)

For HF tests in unjacketed hollow cylinder, equationwill be:

(9)

Comparing this equation with the linear approximation experimental data (Fig. 8b) yields:

(10)

We determined independently η and h(γ) from equation 3and Figure 8a based on correspondent dP/dt, respectively;η=0.27 and h(γ)=0.82. Plugging these values in equation10, Thf and β come to 13.5 MPa and 0.72, respectively.

The effective stress coefficient β could be estimated froma series of hydrofracturing tests in unjacketed specimenshown above or in jacketed specimens without pore prsure (Schmitt and Zoback, 1989). We believe that the efftive stress hypothesis for tensile failure of equation 8 shobe true not only in hydraulic fracturing but also in any othconditions. One of the suggested methods to determinβmay be Bridgman-type pinch-off tests in which uniformconfining pressures were applied over the central sectionthe unjacketed rock cylinders with or without axial loads the ends (Jaeger, 1963; Jaeger and Cook, 1963). They fothat in a series of tests significantly higher confining/popressures than ones calculated by the Terzaghi effectivewere necessary for tensile failure. Other source that β maybe less than unity in some case is provided by pore presinduced failure experiments on sandstone.

8. RESULTS FROM JACKETED HYDROFRACTUR-ING TESTS

We conducted several series of hydrofracturing testsjacketed specimens. The uniform far-fie1d horizontal streapplied was kept in the range of 15−45 MPa; the pore pres-sure was between 1−20 MPa; wellbore pressurization ratwas between 10 and 60 MPa/sec. First we plotted all expimental data in the domain of [Pc−Po] versus [σh−Po] employ-ing the D−C criterion (Fig. l0a). In the figure data are scattervertically for the given effective confining stress (σh−Po).On the other hand, in the plot of [Pc−Po] versus [2 σh−(1+β)Po],where β=0.72 (as determined from the unjacketed testthey fit rather well a linear relationship (Fig. 10b). The sloof the linear approximation of experimental data in Figu9b yields h(γ)=0.75 when η=0.27 (from equation 3) and Thf

=8.0±2.3 (MPa) for Tablerock sandstone.

σ i jeff σij δij βPo–=

Pc Po–Thf 3σh σH 1 β+( )Po––+

1 β 2η–( )h γ( )+------------------------------------------------------------=

Pc Po–Thf 1 β–( )σh+

1 β 2η–( )h γ( )+--------------------------------------=

Thf

1 β 2η–( )h γ( )+-------------------------------------- 11.77

1 β–( )1 β 2η+( )h γ( )+--------------------------------------- 0.242=,=

Fig. 9. (a) Function h(γ) derived from diffusion equation where ηis 0.27. (b) The Detounay and Cheng hydrofracturing model as afunction of γ when the stress condition is given.


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9. CONCLUSIONS

We carried out laboratory hydraulic fracturing tests inhollow cylinders of Tablerock sandstone for the purpose ofestablishing a correct relationship between the breakdownpressure and the far-filed stress in high porosity sandstones.Based on a series of tests in which we examined wellborepressurization rate effect on breakdown pressure, the Detour-nay-Cheng (1992) hydrofracturing criterion was deemed asuniquely suitable because it implicitly incorporates thateffect. However, another series of tests in which the con-fining/pore pressure was varied from test to test for a givenpressurization rate revealed that the D−C criterion requires

a modification in order to appropriately interpret our hydrfracturing test results. Incorporating a general effectistress law into the D−C criterion, we were able to correctlydescribe the relationship between breakdown pressure the far-field stress in high-porosity Tablerock sandstonOur results are of significance in the petroleum industry, sinmany reservoirs are found in high-porosity sandstones, knowledge of the in situ stress conditions gained fromhydrofracturing tests is essential to borehole stability andfield design.

ACKNOWLEDGEMENTS: This work is supported by tile Geo-sciences Research Program, Office of Basic Energy Research, Department of Energy Grant DE-FGO2-98ER14850.

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Fig. 10.Compilation of all test result in jacketed specimens plotted(a) as Pc−Po versus σh−Po where the Terzaghi’s effective stresslaw was applied, and (b) as Pc−Po versus 2 σh−(1+β)Po where β=0.72.


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Manuscript received May 9, 2001Manuscript accepted July 10, 2001

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