Bounds of elastic parameters characterizing transversely isotropic media: Application to shales

Several rocks, and in particular shales, are often described as transversely isotropic (TI) materials. Geophysical data coverage does not always permit reliable determination of all five elastic parameters, neither in seismic and sonic data from the field nor in laboratory measurements. Data may, however, be constrained by the existence of bounds on elastic moduli, derived from the fundamental requirement of positive elastic energy. Conditioned bounds are described for engineering parameters such as Poisson’s ratios as well as anisotropy coefficients such as the moveout parameter δδ and the anellipticity parameter ηη. “Conditioned bounds” means bounds that in general depend on some of the other elastic moduli: The bounds we have evaluated are controlled primarily by P- and S-wave moduli obtained from wave propagation along a symmetry axis and to some extent by P- and S-wave anisotropies. Such data may be acquired more easily from geophysical measurements. We have inspected the laboratory data obtained with various types of shales under different testing conditions, and none of them failed to adapt to the bounds. The data indicate, for instance, clear distinctions between how the proximity to bounds is driven by stress changes for saturated versus nonsaturated shales

The impact of saturation on seismic dispersion in shales — Laboratory measurements

Previous studies found a significant increase of acoustic velocities between seismic and ultrasonic frequencies (seismic dispersion) for shales, which would have to be taken into account when comparing seismic or sonic field data with ultrasonic measurements in the laboratory. We have executed a series of experiments performed with a partially saturated Mancos shale and a Pierre shale I in which the influence of water saturation on acoustic velocities and seismic dispersion was investigated. The experiments were carried out in a triaxial setup allowing for combined measurements of quasistatic rock deformation, ultrasonic velocities, and dynamic elastic stiffness at seismic frequencies under deviatoric stresses. Prior to testing, the rock samples were preconditioned in desiccators at different relative humidities. For both shale types, we present and analyze the experimental results that demonstrate strong saturation and frequency dependence of dynamic Young’s moduli, Poisson’s ratios, and Thomsen’s anisotropy parameters, as well as P- and S-wave velocities at seismic and ultrasonic frequencies. The observed effects can be attributed to water adsorption and capillary pressure that are functions of several factors including water saturation. Water adsorption results in a reduction of surface energy and grain-contact stiffness. The capillary pressure affects the effective stress and possibly also the effective pore-fluid modulus, which may be approximated by Brie’s empirical model. Reasonable fits to the low-frequency seismic data are obtained by accounting for these two effects and applying the anisotropic Gassmann model. The strong increase in dispersion with increasing water saturation is attributed to local flow involving adsorbed (bound) water, but a quantitative description is yet to be provided.acceptedVersio

Comparing mechanical and ultrasonic behaviour of a brittle and a ductile shale: Relevance to prediction of borehole stability and verification of shale barriers

Borehole collapse during drilling operations in shale formations is a well-known and costly problem within the petroleum industry. Recently it has become evident that shales may also form sealing barriers around the casing, reducing the need for cement jobs on new wells, and reducing costs for plugging and abandonment of old wells. The forming of such barriers involves large deformations of shale through creep and plastic processes. Hence, it is important to be able to characterize to what extent shales may fail in a brittle or ductile manner, in both cases causing possible hole instabilities during drilling, and in the case of ductile shales, enabling permanent sealing barriers. Triaxial failure tests, creep tests and tests tailored to follow the failure envelope under simulated borehole conditions have been performed with two soft shales. One shale fails in a more brittle manner than the other and fails to form a sealing barrier in the laboratory. The more ductile shale has been proved to form barriers both in the laboratory and in the field. By comparing their behavior, it is seen that the ductile shale exhibits normally consolidated behaviour, while the more brittle shale is overconsolidated. This points to the stress history and possibly cementation as keys in determining the failure mode. In addition, porosity, clay content, ultrasonic velocities, unconfined strength and friction angle may be used as indicators of brittle or ductile post-failure behaviour. Ultrasonic velocity and in particular attenuation measurements are shown to be sensitive to the failure initiation process, although stress sensitivity is much lower in the ductile than in the brittle case. The experiments provide values for anisotropic velocities as well as P-wave impedances that are necessary for open as well as cased hole log interpretation, in particular for barrier verification and possibly for monitoring of barrier formationpublishedVersio

Fracture Assessment of Quasi-brittle Rock Simulated by Modified Discrete Element Method

New developments of an in-house hybrid code, named Modified Discrete Element Method (MDEM) are presented in the paper. The new developments are on the treatment of pre-existing and propagating fractures in quasi-brittle materials. These developments are the embedment of Linear Elastic Fracture Mechanics (LEFM) and elastic-softening crack band model -based methodologies in the MDEM and their application in lab and reservoir scale. Using the first methodology, MDEM can calculate stress intensity factors, �I and �II using the internal contact forces of particles. �I and �II are calculated independent of boundary conditions and geometrical configuration with acceptable accuracy level. The methodology has been also used in reservoir scale to study the rupture likelihood of faults and fractures due to fluid injection. This methodology enables the code to model mode I and mode II failures and propagation direction based on the fracturing model proposed by Rao et al. (Int J Rock Mech Min Sci 40(3): 355–375, 2003). Using the second methodology, the MDEM can model nonlinear behavior of quasi-brittle materials including or excluding preexisting cracks based on fracture energy. A model was verified against an experiment of a three point bend test with a notch. The numerically obtained force-crack mouth opening curve was reasonably comparable to the experimental test. The analysis was repeated for three other mesh sizes and the results are less mesh size dependent. Finally, it was shown that MDEM has the potential in studying fracture mechanics of quasi-brittle materials both in lab and large-scale investigations

The impact of saturation on seismic dispersion in shales — Laboratory measurements

Previous studies found a significant increase of acoustic velocities between seismic and ultrasonic frequencies (seismic dispersion) for shales, which would have to be taken into account when comparing seismic or sonic field data with ultrasonic measurements in the laboratory. We have executed a series of experiments performed with a partially saturated Mancos shale and a Pierre shale I in which the influence of water saturation on acoustic velocities and seismic dispersion was investigated. The experiments were carried out in a triaxial setup allowing for combined measurements of quasistatic rock deformation, ultrasonic velocities, and dynamic elastic stiffness at seismic frequencies under deviatoric stresses. Prior to testing, the rock samples were preconditioned in desiccators at different relative humidities. For both shale types, we present and analyze the experimental results that demonstrate strong saturation and frequency dependence of dynamic Young’s moduli, Poisson’s ratios, and Thomsen’s anisotropy parameters, as well as P- and S-wave velocities at seismic and ultrasonic frequencies. The observed effects can be attributed to water adsorption and capillary pressure that are functions of several factors including water saturation. Water adsorption results in a reduction of surface energy and grain-contact stiffness. The capillary pressure affects the effective stress and possibly also the effective pore-fluid modulus, which may be approximated by Brie’s empirical model. Reasonable fits to the low-frequency seismic data are obtained by accounting for these two effects and applying the anisotropic Gassmann model. The strong increase in dispersion with increasing water saturation is attributed to local flow involving adsorbed (bound) water, but a quantitative description is yet to be provided

Offset dependence of overburden time-shifts from ultrasonic data

Depletion or injection into a reservoir implies stress changes and strains in the reservoir and its surroundings. This may lead to measurable time-shifts for seismic waves propagating in the subsurface. To better understand the offset dependence of time-shifts in the overburden, we have systematically quantified the time-shifts of three different overburden shales in controlled laboratory tests. These experiments may be viewed as an analogue to the time-shifts recorded from seismic field surveys. For a range of different stress paths, i.e. the ratio between the horizontal and the vertical stress changes, the changes of the P-wave velocities in different directions were measured such that the offset dependence of time-shifts for different stress paths could be studied. The time-shifts are stress path dependent, which is particularly pronounced at large offsets. For all stress paths the time-shifts exhibit a linearly decreasing trend with increasing offset, i.e. a negative offset-gradient. At zero offset, for which the ray path is normal to the bedding, the time-shifts are similar for all investigated stress paths. The isotropic stress path is associated with the smallest offset-gradient of the time-shifts. Contrary, the constant-mean-stress path shows the largest gradient with a flip in the polarity of the time-shifts for the largest offsets. The separate contributions from the strain and velocity changes to the time-shift were also quantified. The time-shifts for the isotropic stress path are dominated by the contribution from velocity changes at all offsets. Contrary, the strain contributes significantly to the time-shifts at small offsets for the constant-mean-stress path. This shows that the offset dependence in pre-stack seismic data may be a key to understand the changes of subsurface stresses, pore pressure and strain upon depletion or injection. To utilize this knowledge from laboratory experiments, calibrated rock physics models and correlations are needed to constrain the seismic time-shifts and to obtain an adequately updated geological model reflecting the true anisotropic nature of the subsurface. This may have important implications for improved recovery and safety, particularly in mature fields.publishedVersio

Influence of subsurface injection on time-lapse seismic: laboratory studies at seismic and ultrasonic frequencies

Seismic monitoring of reservoir and overburden performance during subsurface CO2 storage plays a key role in ensuring efficiency and safety. Proper interpretation of monitoring data requires knowledge about the rock physical phenomena occurring in the subsurface formations. This work focuses on rock stiffness and elastic velocity changes of a shale overburden formation caused by both reservoir inflation induced stress changes and leakage of CO2 into the overburden. In laboratory experiments, Pierre shale I core plugs were loaded along the stress path representative for the in situ stress changes experienced by caprock during reservoir inflation. Tests were carried out in a triaxial compaction cell combining three measurement techniques and permitting for determination of (i) ultrasonic velocities, (ii) quasistatic rock deformations, and (iii) dynamic elastic stiffness at seismic frequencies within a single test, which allowed to quantify effects of seismic dispersion. In addition, fluid substitution effects connected with possible CO2 leakage into the caprock formation were modelled by the modified anisotropic Gassmann model. Results of this work indicate that (i) stress sensitivity of Pierre shale I is frequency dependent; (ii) reservoir inflation leads to the increase of the overburden Young's modulus and Poisson's ratio; (iii) in situ stress changes mostly affect the P‐wave velocities; (iv) small leakage of the CO2 into the overburden may lead to the velocity changes, which are comparable with one associated with geomechanical influence; (v) non‐elastic effects increase stress sensitivity of an acoustic waves; (iv) and both geomechanical and fluid substitution effects would create significant time shifts, which should be detectable by time‐lapse seismic

Anisotropic poroelasticity – Does it apply to shale?

Shale plays an important role as cap rock above oil and gas reservoirs and above e.g. CO2 storage sites, as well as being source and reservoir rock in development of so-called unconventional reserves. Shale anisotropy needs to be accounted for in geophysical as well as geomechanical applications. This paper presents a brief description of anisotropic poroelasticity theory, and compares it to its more familiar isotropic counterpart. Experiments performed with field shales are presented, and the static mechanical behavior in terms of drained versus undrained moduli, Skempton parameters and Biot coefficients are shown to be consistent with the poroelastic approach. The necessary steps to provide static properties from seismic data and further link these measurements to laboratory ultrasonic data are briefly discussed

Stress-dependent elastic properties of shales—laboratory experiments at seismic and ultrasonic frequencies

Knowledge about the stress sensitivity of elastic properties and velocities of shales is important for the interpretation of seismic time-lapse data taken as part of reservoir and caprock surveillance of both unconventional and conventional oil and gas fields (e.g. during 4-D monitoring of CO2 storage). Rock physics models are often developed based on laboratory measurements at ultrasonic frequencies. However, as shown previously, shales exhibit large seismic dispersion, and it is possible that stress sensitivities of velocities are also frequency dependent. In this work, we report on a series of seismic and ultrasonic laboratory tests in which the stress sensitivity of elastic properties of Mancos shale and Pierre shale I were investigated. The shales were tested at different water saturations. Dynamic rock engineering parameters and elastic wave velocities were examined on core plugs exposed to isotropic loading. Experiments were carried out in an apparatus allowing for static-compaction and dynamic measurements at seismic and ultrasonic frequencies within single test. For both shale types, we present and discuss experimental results that demonstrate dispersion and stress sensitivity of the rock stiffness, as well as P- and S-wave velocities, and stiffness anisotropy. Our experimental results show that the stress-sensitivity of shales is different at seismic and ultrasonic frequencies, which can be linked with simultaneously occurring changes in the dispersion with applied stress. Measured stress sensitivity of elastic properties for relatively dry samples was higher at seismic frequencies however, the increasing saturation of shales decreases the difference between seismic and ultrasonic stress-sensitivities, and for moist samples stress-sensitivity is higher at ultrasonic frequencies. Simultaneously, the increased saturation highly increases the dispersion in shales. We have also found that the stress-sensitivity is highly anisotropic in both shales and that in some of the cases higher stress-sensitivity of elastic properties can be seen in the direction parallel to the bedding plane

Stress Path Dependent Velocities in Shales: Impact on 4D Seismic Interpretation

Overburden stresses and pore pressure are altered by depletion or inflation of a subsurface reservoir, leading to seismic travel time and reflectivity changes that may be interpreted as footprints of reservoir drainage or injection. Our objective is to contribute to the quantification of expected 4D seismic timeshifts and reflectivities by understanding how overburden stresses and strains change, and how seismic velocities depend on these stress and strain changes. Stress sensitivity of ultrasonic velocities has been obtained from controlled laboratory experiments where field shale cores are brought to in situ conditions, and then probed with different stress paths, i.e. different ratios between horizontal and vertical stress change. The tests are performed in undrained conditions, and pore pressure changes are recorded. The experiments show that both velocity and pore pressure changes depend linearly on the stress path. The latter is a verification of the applicability of Skempton’s law from soil mechanics for shales. Overburden stress paths are, through analytical and numerical geomechanical modelling, seen to depend on the aspect ratio of the depleting or inflating zone, on elastic contrast between the overburden and the reservoir, and on reservoir tilt. By combining laboratory data and simulated overburden stress paths, the response of in situ wave velocities to reservoir pore pressure change can be estimated. Calculated in situ stress dependence of the vertical P-wave velocity shows significant dependence on stress path. The strain sensitivity, expressed by the dilation parameter, or R-factor, increases strongly with stress path. This expresses the explicit sensitivity of R to vertical in situ strain. The results also show that time-lapse overburden response may be significantly influenced by pore pressure changes in the overburden