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Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the 49th U.S. Rock Mechanics/Geomechanics Symposium, June 28–July 1, 2015

Paper Number: ARMA-2015-028

... upstream oil & gas rock salt axisymmetric compression us government displacement mpa compression test creep test mean stress reservoir geomechanics axisymmetric extension test sandia national laboratory

**invariant**axial stress extension test diameter reservoir characterization...
Abstract

Abstract A laboratory testing program was developed to examine the short-term mechanical and time-dependent (creep) behavior of salt from the Bayou Choctaw Salt Dome. Core was tested under creep and quasi-static constant mean stress axisymmetric compression, and constant mean stress axisymmetric extension conditions. Creep tests were performed at 38 degrees Celsius, and the axisymmetric tests were performed at ambient temperatures (22-26 degrees Celsius). The testing performed indicates that the dilation criterion is pressure and stress state dependent. It was found that as the mean stress increases, the shear stress required to cause dilation increases. The results for this salt are reasonably consistent with those observed for other domal salts. Also it was observed that tests performed under extensile conditions required consistently lower shear stress to cause dilation for the same mean stress, which is consistent with other domal salts. Young’s modulus ranged from 27.2 to 58.7 GPa with an average of 44.4 GPa, with Poisson’s ratio ranging from 0.10 to 0.43 with an average of 0.30. Creep testing indicates that the BC salt is intermediate in creep resistance when compared with other bedded and domal salt steady-state behavior. 1. INTRODUCTION Sandia National Laboratories, on behalf of The U.S. Department of Energy (DOE), is evaluating the mechanical integrity of the salt pillars surrounding existing petroleum storage caverns in the Bayou Choctaw Dome (Louisiana) that are part of the U.S. Strategic Petroleum Reserve (SPR). The purpose of this experimental effort is to better characterize the salt strength, dilational strength and creep in the salt section above Cavern 102 and below the overlying abandoned caverns, where casing issues have been observed [1]. The core used for this experimental study was obtained from a drill hole from depths of 325 to 335 meters below ground surface (bgs) and is above one of the Bayou Choctaw SPR caverns. For reference the top of the salt dome lies between 183 and 213 meters bgs, and the total depth is over 3050 meters bgs. The natural rock salt deposits used in the SPR are ideal for storage of crude oil because of their low (nearly zero) permeability, ease of mining, and proximity to shipping and refining operations. The mechanical behavior of rock salt is relatively unique when compared with other geologic media due to the well-known ability of salt to show significant time dependent deformation without fracturing when subjected to differential stresses [2]. This can result in the closure of caverns and mines over time, which results in reduced storage in the case of caverns. Under some differential stress states salt is known to dilate due to stress-induced microfracturing [3]. In this work elastic properties and dilation behavior were determined by performing constant mean stress axisymmetric compression (ASC) and axisymmetric extension (ASE) tests. Creep properties were determined using standard constant differential stress creep tests. While the composition of the salt used in this testing was not quantitatively determined, it was determined, from visual observation, that the salt is relatively pure halite with impurities comprising less than 2-4% by volume. Impurities appeared to be anhydrite.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the 47th U.S. Rock Mechanics/Geomechanics Symposium, June 23–26, 2013

Paper Number: ARMA-2013-656

... fluid modeling Upstream Oil & Gas Artificial Intelligence

**invariant**interaction term experiment reduction fiber matrix symmetry compliance model parameter elastic property stiffness Reservoir Characterization constraint tensor constitutive theory transverse isotropy anisotropy...
Abstract

Abstract: Geomaterials that are assumed to have symmetry about a single preferred direction have five independent transversely isotropic elastic constants. These elastic constants can be determined from data obtained through a series of macroscale calibration experiments, but only a subset of these five constants can be found directly from axial and lateral stressstrain measurements on a single cylindrical sample of material. Substructural axisymmetric inhomogeneities present in the material and decoupling methods used in modeling can imply constraints on transversely isotropic elastic constants, potentially reducing the number of macroscale experiments needed to characterize a geomaterial model. Morphology of substructural heterogeneities, such as distributions of microscale inclusions, cracks, pores and fibers, lead to homogenization or distribution parameters that affect the fourth-order elastic stiffness of the material. Constitutive models that decouple the elastic stiffness often neglect interaction components, which impose constraints on the transversely isotropic elastic constants. We consider the mathematically motivated decoupling of tensorially linear and non-linear functions of a structural or fabric tensor. Neglecting the non-linear components, as often done for rock models, imposes a constraint that the lateral shear modulus depends on the remaining elastic constants. We also consider the mathematically motivated decoupling of purely-volumetric and purely-deviatoric components, often used in the field of biomechanics. When the mixed volumetric-deviatoric components are neglected, the axial and lateral Poisson’s ratios are constrained to become dependent on the two tensile moduli and a new independent bulk modulus type parameter. The described constraints reduce the number of independent elastic constants from five to four. In biomechanics, the accuracy of the approximation from the constraints can be verified through knowledge that the substructural source of anisotropy is fibers embedded in a mostly incompressible water matrix. The potential for using similar techniques to investigate approximations that use constraints on elastic constants is discussed for geomaterials, specifically non-interacting cracked solids, with the goal of reducing the number of macroscale experiments needed to characterize a geomaterial model.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the Alaska Rocks 2005, The 40th U.S. Symposium on Rock Mechanics (USRMS), June 25–29, 2005

Paper Number: ARMA-05-818

... elastic homogeneous medium indicates that fractures evolve relative to three timescales associated with transitions between regimes characterized by large/small fluid lag, large/small effective fluid viscosity, and large/small °uid leak-o®. The three

**invariants**of the model are given by the ratio of the...
Abstract

ABSTRACT: Design of hydraulic fracturing laboratory experiments that capture similar phenomena to those expected at the field scale requires consideration of the scaling laws intrinsic to the mathematical model. Analysis of the model for a radial, Newtonian-fluid-driven fracture in an infinite elastic homogeneous medium indicates that fractures evolve relative to three timescales associated with transitions between regimes characterized by large/small fluid lag, large/small effective fluid viscosity, and large/small °uid leak-o®. The three invariants of the model are given by the ratio of the treatment time with these timescales, hence they provide the key for experimental design and interpretation that properly accounts for the deference between the field and laboratory scales. This paper presents a practical experimental design method based on these considerations. Experimental results are presented for which the invariant associated with °uid viscosity takes on deferent values. The results are in close agreement with a published solution that is based on modelling the crack tip using the classical Linear Elastic Fracture Mechanics when the viscosity invariant is small. However, when the viscosity invariant is O(1) the experimental results are in agreement with a published solution that utilizes a unique crack tip singularity associated with fluid-solid coupling in the tip region. INTRODUCTION Hydraulic fracturing has drawn hundreds of contributions over the last ¯fty years, many of which have involved laboratory investigation. However, the scale of laboratory fractures is always vastly different than the field applications to which they are supposed to bear relevance. The fundamental desire is to make some observations on laboratory- scale fractures, which permit measurements that are unavailable in the field, and then make some inference regarding the nature of field-scale fractures. However, it seems few authors give formal consideration to the difference of scale when de- signing or interpreting their experiments. The result is contradictions in the literature, particularly with regards to the relative importance of certain parameters. One example of such a contradiction concerns the viscosity of the fluid which is driving hydraulic fractures. Spence and Sharpe [1] and Barenblatt [2] have argued from the mathematical model that viscosity is expected to play a crucial role at the field-scale. However, laboratory verification of fracture behavior consistent with the so- called viscosity-dominated regime of propagation has proven elusive, and in fact, some laboratory studies are seemingly interpreted to downplay the role of viscosity altogether (e.g. [3]). Hence the hydraulic fracturing community remains divided on some important basic issues of parametric analysis. The way forward requires formal application of scaling principles to not only numerical and theoretical analysis of hydraulic fracturing, but also to design and interpretation of experimental investigations. This assertion was previously made by de Pater et al. [4], who derived invariants for essentially the same mathematical model considered here.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 30th U.S. Symposium on Rock Mechanics (USRMS), June 19–22, 1989

Paper Number: ARMA-89-0877

... drilling of oil and gas wells. Wellbore stability requires a proper balance between the in situ stresses, wellbore fluid pressure and mud chemical composition. Most oil field stability studies have used the von Mises failure criterion. This is based on the second

**invariant**of deviatoric stress and differs...
Abstract

ABSTRACT ABSTRACT An analysis of data of borehole breakouts as an indication of orientation of in-situ stresses is presented. Wellbores drilled in Alaska and Colorado provided data for this investigation. Two field cases illustrating borehole breakouts at opposing failure directions are discussed. The first case refers to an offshore well drilled in the Gulf of Alaska. The failure zone is predicted to take place centered on the diameter in the direction of the least horizontal principal stress. The second case refers to the failure in a coal seam in a wellbore drilled in the Piceance Basin (Colorado). The failure mode was located normal to the direction of the least horizontal principal stress. Both failures can be explained by the von Mises failure criteria. 1 INTRODUCTION Since the beginning of this decade breakouts have been used as indicators of the orientation of the principal stresses. Breakout (also referred as borehole ellipticity and borehole spalling) are zones of failure lying on opposite diameters of the wellbore. Failure leading to spalling results when the stresses at the borehole wall exceed or are equivalent to the local rock strength. Measurements of the spalled cross-sections, in vertical wells, with an ultrasonic televiewer[5] disclosed broad depressions aligned in the direction of the minimum principal stress. Other observations [4,6,7,10] also indicate that breakout azimuth is in the direction of the minimum principal stress. Breakouts aligned in the direction of the maximum principal stress were first reported by Jones, et. al.[7]. Breakouts in the direction of the maximum horizontal principal stress have been observed in friable rocks (e.g., coal seams) only. This paper describes an analysis of wellbore breakouts for boreholes drilled in Alaska and Colorado. The first well is an example of breakouts aligned with the direction of the minimum principal stress, while the spalled zones for the other well are aligned with the direction of the maximum principal stress. 2. FIELD SPALLING OBSERVATIONS Maintaining stable wellbore is of primary importance during drilling of oil and gas wells. Wellbore stability requires a proper balance between the in situ stresses, wellbore fluid pressure and mud chemical composition. Most oil field stability studies have used the von Mises failure criterion. This is based on the second invariant of deviatoric stress and differs from the shear stress by 0 to 15 percent. In the von Mises criteria the second invariant of the deviatoric stress (vJ 2 ) at the wellbore is obtained from: (available in full paper) and the mean effective stress, (P c - P o ), where (available in full paper) and P o is the pore pressure. In equations 1 and 2, s r , s ¿ and s z are the radial, tangential, and vertical stresses at the borehole wall, respectively. These parameters are obtained by superposition of the Kirsch [9] solution for biaxial far-field stresses and the solution for the stress distribution due to the application of a pressure (p) in the cylindrical cavity: (available in full paper)

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 30th U.S. Symposium on Rock Mechanics (USRMS), June 19–22, 1989

Paper Number: ARMA-89-0091

... Upstream Oil & Gas

**invariant**failure loci reservoir geomechanics criterion mohr-coulomb criterion nonlinear portion excavation strain rate parameter value failure data strength criteria Lode angle lode parameter saltrock specimen general failure criteria Rock Mechanics as a Guide...
Abstract

ABSTRACT ABSTRACT: Although under the majority of stress states found underground, saltrock yields and deforms viscoplastically and does not fail in a brittle manner, brittle failure does occur in the immediate vicinity of underground openings as a result of the high stress and strain rates induced by excavation. This paper examines the brittle failure behavior for saltrocks and evaluates the ability of several proposed failure criteria to predict this behavior. 1. INTRODUCTION It has long been recognized that the relationship between the shear stress and the normal stress for failure under compressive loading is linear only for relatively low normal stress levels. Nevertheless, the commonly-used Mohr-Coulomb and Drucker-Prager failure criteria are linear. While one or other of these criteria may be acceptable at low stresses, a criterion is also required t hat reasonably represents t \he non-linear locus obtained at higher stress levels. In addition, strength data obtained from true triaxial testing has shown that failure envelopes derived from conventional laboratory triaxial testing, where s 1 > s 2 = s 3 , do not represent failure in the more general case where s 1 >s 2 >s 3 . However, with a general failure criterion expressed in terms of the Lode parameter, µ , the material parameters could be obtained from conventional triaxial testing rather than using the less-common true triaxial testing. (It would be wise, however, to obtain the failure stresses for a few true triaxial loadings to verify the validity of the material parameters for general stress states.) Although masses of saltrock generally deform in a viscoelastic/viscoplastic manner, brittle failure does occur in the immediate vicinity of underground openings as a result of the dynamic stresses and strains caused by excavation. To evaluate the stability of pillars between openings in saltrock or to select pillar dimensions that will result in stable, but not overly conservative, pillars, an analyst must be able to predict the extent of this failure zone. To do so requires strength data for the saltrock of concern and failure criteria that cover the range of expected stress states. In the recent past, several general failure criteria have been proposed in an attempt to overcome the limitations of the conventional Mohr-Coulomb and Drucker-Prager criteria. The Mohr-Coulomb criterion neglects the influence of the intermediate principal stress (s 2 ), a situation that is unimportant when characterizing the behavior in conventional triaxial compressions tests( where s 2 =s 3 ) but which leads to incorrect predictions in the more general case of three unequal principal stresses. An extended Mohr-Coulomb criterion has been developed (Zienkiewicz, 1975; Senseny et al., 1983) that does account for general triaxial stress. However, the extended Mohr-Coulomb and the Drucker-Prager criteria each postulate a linear relationship between the octahedral normal and shear stresses at failure, a condition that exists only at relatively low confining stresses. A complication that cannot be overlooked in the case of saltrocks is the fact that the behavior depends on the strain rate as well as the confining stress.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 17th U.S. Symposium on Rock Mechanics (USRMS), August 25–27, 1976

Paper Number: ARMA-76-0419

... criteria that the mean stress (or first

**invariant**), satisfying Laplace's equation, remains unperturbed. As a consequence of not disturbing the mean stress of the original field, such shapes which will be termed "harmonic holes" also, apparently, produce a minimum stress concentration in any free field...
Abstract

ABSTRACT n Work by the author over the last four years on optimum shapes for unreinforced holes in stress fields [1] has created a new approach in this area of rock mechanics. Essentially, the problem is inverted so that geometry is left variable, and instead stresses around the eventual hole shape (and thereby in the entire field) are prescribed to satisfy a chosen design criteria. Through the use of the complex variable representation [4] [9], it is possible to develop a general functional equation in integral form for that hole geometry which will, in fact., satisfy the specific design criteria that the mean stress (or first invariant), satisfying Laplace's equation, remains unperturbed. As a consequence of not disturbing the mean stress of the original field, such shapes which will be termed "harmonic holes" also, apparently, produce a minimum stress concentration in any free field whether the hole boundary is loaded or not and are, therefore, optimum for design. s A description of the general design equation for the geometry of the optimum hole is presented in the Appendix. The optimum shapes for tunnels and cavities derived from it for the two basic situations of a biaxial field and an isotropic field with a gradient best illustrate its application to rock mechanics. However, since internal tractions either applied directly of through a suitably proportioned liner are also a variable in the general design equation, a great variety is possible within the two geometric families of shapes resulting from those two basic free-field site characterizations. For example, the harmonic holes in a particular biaxial stress field resulting from evaluation of the design equation for unloaded and uniformly loaded boundaries are the ellipses with the proportions shown in Figure 1 and 2. The geometry of these ellipses is such that the ratio of their major to minor axes satisfies the equation. Where s 1 and s 2 are the principal stresses such that |3C3; 1 =s 2 | and P is the magnitude of the uniform internal pressure (positive if suction). Also, the direction of the major axis must coincide with the direction of s 1 and equation (1) must be greater than or equal to one to insure existence. While this solution is amazingly simple it has never before been explicitly demonstrated. Furthermore, by fulfilling the design requirement of leaving the mean stress of the original field everywhere unperturbed, it can be proved [1] [2] for a biaxial field that the harmonic hole simultaneously produces the minimum possible stress concentration and is therefore optimum. In fact, since the first invariant remains unchanged, one can immediately determine the value of the tangential normal stress, s ¿ , everywhere on the hole boundary as the constant (mathematical equation)(available in full paper) Similarly, the shape of the "harmonic cavity" in a triaxial field would be an ellipsoid with axes proportional to the major, minor and intermediate principal stresses and coinciding with the principal axes. For the case of a linear gradient superimposed with anisotropic field (Figure 3) the stress components of the free field are, (mathematical equation)(available in full paper)