Bezalel C. Haimson

THE HYDROFRACTURING STRESS MEASURING METHOD AND RECENT FIELD RESULTS

Abstract The hydrofracturing technique is a recent development in the area of stress measurements in rock. Unlike most other methods, it does not measure strain at a point through the use of delicate instrumentation in the test-hole. Rather, it directly determines average stresses over large areas by recording two hydraulic pressures, one necessary to crack open a segment of the test-hole and the other required to keep the fracture open. To do so, it uses simple down-hole mechanical tools so that the method can be employed at any depth from the surface. Elementary elastic relationships exist between recorded pressures and in-situ stresses, and between fracture direction and stress orientation. Our laboratory experiments have confirmed these relationships, and in the last five years we have conducted a number of successful field measurements throughout the United States and elsewhere, at depths between very near the surface and 5000 m . The results of these measurements, details of which are given in the paper, have been used in studying earthquake control problems (Rangely, Colorado), underground power station design (California, South Carolina), hard rock tunnel design (Wisconsin), and geology and plate tectonics (all the measurements and particularly those in Michigan and Iceland). A general uniformity of maximum principal stress direction throughout the continental United States has been established. Stress magnitudes are affected by regional geologic conditions but generally show linear increases with depth.

True triaxial strength and deformability of the German Continental Deep Drilling Program (KTB) deep hole amphibolite

We designed and fabricated a true triaxial loading system and used it to determine deformational and strength characteristics of the amphibolite penetrated by the superdeep hole drilled in the Bohemian massif of southeastern Germany under the German Continental Deep Drilling Program (KTB). Amphibolite is found between 3200 and 7300 m and thus the dominant rock in this 9100-m boring. Our loading system enables the application of three unequal principal stresses to a rectangular prismatic rock specimen. During a test we maintained the least principal (σ3) and the intermediate (σ2) stresses constant and increased the major principal stress (σ1) until brittle failure occurred, in the form of a fracture steeply dipping in the σ3 direction. Typically, for the same σ3 level the amphibolite compressive strength increased substantially with the magnitude of σ2, demonstrating the inadequacy of Mohr-like failure criteria that ignore the effect of the intermediate principal stress on rock strength. We found that a general criterion for the amphibolite could be expressed in the form of a power function relating the octahedral shear stress at failure to the mean normal stress acting on the plane containing the fracture. With respect to deformation, we established that for the same σ3 the onset of dilatancy increases significantly with the magnitude of σ2. Thus the intermediate principal stress appears to extend the elastic range of the stress-strain behavior for a given σ3 and hence to retard the onset of the failure process. Scanning electron microscopy observations of the failure process reveal that microcracks develop mainly parallel to σ2 direction, as the intermediate stress grows beyond σ3, localizing in close proximity of the eventual main fracture.

Statistical evaluation of hydraulic fracturing stress measurement parameters

Statistical analysis of hydraulic fracturing field data enhances the objectivity of determining shut-in and fracture reopening pressures and fracture orientations. Using nonlinear regression analysis (NLRA), we isolate the closed-fracture segment of the pressure-time curve by fitting it to an exponential decay model. The shut-in pressure (Ps) is expected to be in the range between Psepd−1 (the onset of the post fracture-closure segment) and Psepd−u (the pressure level of the best-fitting exponential curve extrapolated to the time of pump shut-off). We employ bilinear regression analysis to improve the objectivity of selecting Ps from the pressure-decay rate vs pressure plot. The same analysis helps to identify Ps in the pressure vs flowrate record obtained during steprate pressurization of the hydrofractured interval. We identify unambiguously the fracture reopening pressure (Pr) by superposing the ascending portion of the pressure-time curves in the fracture-inducing cycle and a subsequent cycle. Pr is the onset of deviation between the two curves, defined as the point where the difference in pressures is larger than a statistical “reference threshold”, provided the difference continues to increase from there on. Circular statistics and a sinusoidal curve-fitting method provide the means of objectively delineating the complete trace of induced hydrofractures from fragmented or splaying traces on the impression packer or on the borehole televiewer photograph. Examples of field hydraulic fracturing data and statistically determined pressures and fracture orientations are presented. A startling discovery was made in the course of determining Pr, with our new technique: it appears to be very nearly equal to the estimated Ps. A review of the literature shows that in a great number of cases Pr and Ps are indeed close to each other, which raises the question whether we are in fact reading the correct fracture reopening pressure.

Laboratory study of borehole breakouts in Lac du Bonnet granite: a case of extensile failure mechanism

Abstract We subjected boreholes drilled vertically in the center of cubical specimens of Lac du Bonnet granite to constant vertical (S v ) and least horizontal (S h ) farfield stresses, and increased the maximum horizontal stress (S H ) until breakouts occurred. A thin section study revealed that extensile cracking behind the borehole in two zones aligned with S h preceded the development of breakouts. Progressive detachment of thin long flakes bounded by these densely spaced subparallel cracks led to ‘dog ear’ shaped breakouts. Breakout mechanism and appearance match those found in the field. Results also suggest the potential for using breakout occurrence to estimate S H if S h is known or vice versa.

Laboratory study of borehole breakouts in Cordova Cream: a case of shear failure mechanism

Abstract We subjected vertical boreholes drilled in cubical specimens of Cordova Cream to a 3-dimensional stress field, and increased one or both of the horizontal principal stresses until breakout failure occurred. Acoustic emission, borehole strain, and visual monitoring of the borehole wall during testing revealed four stages of breakout development: crack initiation, extension, breakout formation, and stabilization. Thin section analysis suggests that breakout formation in Cordova Cream is the result of shear failure mechanism. The relationships at breakout stabilization between the two horizontal principal stresses and between the span at the borehole wall and the least horizontal stress suggest a potentially simple method of estimating the far-field state of stress if ‘breakouted’ borehole geometry is accurately mapped.

True Triaxial Stresses and the Brittle Fracture of Rock

This paper reviews the efforts made in the last 100 years to characterize the effect of the intermediate principal stress r2 on brittle fracture of rocks, and on their strength criteria. The most common theories of failure in geomechanics, such as those of Coulomb, and Mohr, disregard r2 and are typically based on triaxial testing of cylindrical rock samples subjected to equal minimum and intermediate principal stresses (r3=r2). However, as early as 1915 Böker conducted conventional triaxial extension tests (r1=r2) on the same Carrara marble tested earlier in conventional triaxial compression by von Kármán that showed a different strength behavior. Efforts to incorporate the effect of r2 on rock strength continued in the second half of the last century through the work of Nadai, Drucker and Prager, Murrell, Handin, Wiebols and Cook, and others. In 1971 Mogi designed a high-capacity true triaxial testing machine, and was the first to obtain complete true triaxial strength criteria for several rocks based on experimental data. Following his pioneering work, several other laboratories developed equipment and conducted true triaxial tests revealing the extent of r2 effect on rock strength (e.g., Takahashi and Koide, Michelis, Smart, Wawersik). Testing equipment emulating Mogi’s but considerably more compact was developed at the University of Wisconsin and used for true triaxial testing of some very strong crystalline rocks. Test results revealed three distinct compressive failure mechanisms, depending on loading mode and rock type: shear faulting resulting from extensile microcrack localization, multiple splitting along the r1 axis, and nondilatant shear failure. The true triaxial strength criterion for the KTB amphibolite derived from such tests was used in conjunction with logged breakout dimensions to estimate the maximum horizontal in situ stress in the KTB ultra deep scientific hole.

Characteristics of shut‐in curves in hydraulic fracturing stress measurements and determination of in situ minimum compressive stress

Characteristics of pressure decay curves obtained after shut-in in hydraulic fracturing stress measurements are studied in detail in an effort to enhance the reliability of the minimum compressive in situ stress determination. The analysis utilizes linear theory of elasticity, fracture mechanics, and global mass balance of fracturing fluid after shut-in. A small amount of crack growth takes place almost instantaneously just after shut-in due to equilibration of injected-fluid pressure within the fracture. Thereafter, the fracture gradually closes commensurate with the amount of fluid leakage into the rock and the net compliance of the pressured system consisting of the rock, the fracture, and the tubing conveying pressurized fluid from the surface to the depth of testing. Theoretical considerations and laboratory and field data suggest the closure process after shut-in can be considered to consist of three major stages: from cessation of fracture growth until fracture tip closure (stage I), from just after fracture tip closure until complete fracture closure (stage II), and from just after complete fracture closure until the test is stopped (stage III). An analysis of these stages reveals that the inverse of the pressure decrease rate is linear with respect to the fluid pressure in stages I and III. It is also shown that the far-field minimum compressive stress can be determined on the basis of these characteristics. The method of determination of the in situ minimum compressive stress is successfully applied to a sampling of shut-in curves obtained in laboratory and field experiments.

Fracture-like borehole breakouts in high-porosity sandstone: Are they caused by compaction bands?

Abstract We induced borehole breakouts in a 25%-porosity Berea sandstone by drilling 23 mm diameter holes into 152×152×229 mm blocks subjected to constant true triaxial far-field stresses. BSen5 consists of large quartz grains (0.5 mm) cemented mainly by sutured grain contacts. Breakouts in BSen5 are demonstratively different from those observed in granite, limestone, and lower porosity sandstones. Rather than the typically short ‘V’-shaped breakouts, BSen5 displays long fracture-like tabular slots, which counterintuitively, develop orthogonally to σH. These breakouts originate at the points of highest compressive stress at the borehole wall, along the σh spring line. Micrographs of BSen5 breakouts show an apparent compaction band created just ahead of the breakout tip in the form of a narrow layer of grains that are compacted normal to σH. The compaction band characteristics are nearly identical to those observed in the field. The mechanism leading to fracture-like breakouts is seen as anti-dilatant, and related directly to grain debonding and porosity reduction accompanying the formation of the compaction band. Some compacted grains at the borehole wall are expelled as a result of the line of tangential loading and the radial expansion of adjacent grains. The circulating drilling fluid flushes out the remaining compacted loose grains at the borehole-rock interface. As the breakout tip advances, the stress concentration ahead of it persists, extending the compaction band, which in turn leads to additional grain removal and breakout lengthening. By extrapolation, this process may continue for considerable distance (at least several times the wellbore diameter) in field situations, leading potentially to substantial sand production.

An investigation of the mechanics of rock joints—Part I. Laboratory investigation

Abstract In this paper, which is the first of a two-part series, a laboratory investigation of the mechanical behavior of initially closely mated joints in rock undergoing small sliding displacements is undertaken. The goal is to elucidate important features of joint behavior such as dilatancy, damage of surface roughness, cyclic sliding behavior and the dependence of these phenomena on stress level and sliding history. Testing was carried out in a specially designed and fabricated servo-controlled direct shear machine. Most tests employed artificial joint samples with saw-tooth shaped asperities molded of hydrostone which replicates soft natural rock. Use of molded samples allowed tests to be conducted on simulated joints which for our purposes, could be considered to be identical. Tests on natural joints in dolomite were also carried out. This testing program provided the guidance and data base necessary for the development of a quantitative theory and constitutive model for rock joint behavior, which is described in Part II.

Borehole Breakouts in Berea Sandstone Reveal a New Fracture Mechanism

Vertical drilling experiments in high-porosity (22% and 25%) Berea sandstone subjected to critical true triaxial far-field stresses, in which ay (maximum horizontal stress) > a, (vertical stress) > ah (least horizontal stress), revealed a new and non-dilatant failure mechanism that results in thin and very long tabular borehole breakouts that have the appearance of fractures, and which counterintuitively develop orthogonally to a y .These breakouts are fundamentally different from those induced in crystalline rocks, as well as limestones and medium-porosity Berea sandstone. Breakouts in these rocks are typically dog-eared in shape, a result of dilatant multi-cracking tangential to the hole and subparallel to the maximum far-field horizontal stress a y , followed by progressive buckling and shearing of detached rock flakes created by the cracks. In the high-porosity sandstone a narrow layer of grains compacted normal to a n is observed just ahead of the breakout tip. This layer is nearly identical to “compaction bands” observed in the field. It is suggested that when a critical tangential stress concentration is reached along the a y , spring line at the borehole wall, grain bonding breaks down and a compaction band is formed normal to ay Debonded loose grains are expelled into the borehole, assisted by the circulating drilling fluid. As the breakout tip advances, the stress concentration ahead of it persists or may even increase, extending the compaction band, which in turn leads to breakout lengthening