Romain Prioul

Nonlinear rock physics model for estimation of 3D subsurface stress in anisotropic formations: Theory and laboratory verification

We develop a rock physics model based on nonlinear elasticity that describes the dependence of the effective stiffness tensor as a function of a 3D stress field in intrinsically anisotropic formations. This model predicts the seismic velocity of both P- and S-waves in any direction for an arbitrary 3D stress state. Therefore, the model overcomes the limitations of existing empirical velocity-stress models that link P-wave velocity in isotropic rocks to uniaxial or hydrostatic stress. To validate this model, we analyze ultrasonic velocity measurements on stressed anisotropic samples of shale and sandstone. With only three nonlinear constants, we are able to predict the stress dependence of all five elastic medium parameters comprising the transversely isotropic stiffness tensor. We also show that the horizontal stress affects vertical S-wave velocity with the same order of magnitude as vertical stress does. We develop a weakanisotropy approximation that directly links commonly measured anisotropic Thomsen parameters to the principal stresses. Each Thomsen parameter is simply a sum of corresponding background intrinsic anisotropy and stressinduced contribution. The stress-induced part is controlled by the difference between horizontal and vertical stresses and coefficients depending on nonlinear constants. Thus, isotropic rock stays isotropic under varying but hydrostatic load, whereas transversely isotropic rock retains the same values of dimensionless Thomsen parameters. Only unequal horizontal and vertical stresses alter anisotropy. Since Thomsen parameters conveniently describe seismic signatures, such as normal-moveout velocities and amplitudevariation-with-offset gradients, this approximation is suitable for designing new methods for the estimation of 3D subsurface stress from multicomponent seismic data.

Forward modeling of fracture-induced sonic anisotropy using a combination of borehole image and sonic logs

We develop a methodology to model and interpret borehole dipole sonic anisotropy related to the effect of geologic fractures, using a forward-modeling approach. We use a classical excess-compliance fracture model that relies on the orientation of the individual fractures, the elastic properties of the host rock, and the normal and tangential fracture-compliance parameters. Orientations of individual fractures are extracted from borehole-image log analysis. The model is validated using borehole-resistivity image and sonic logs in a gas-sand reservoir over a 160-ft (50 m) vertical interval of a well. Significant amounts of sonic anisotropy are observed at three zones, with a fast-shear azimuth (FSA) exhibiting 60° of variation and slowness difference between 2% and 16%. Numerous quasivertical fractures with varying dip azimuths are identified on the image log at the locations of strong sonic anisotropy. The maximum horizontal-stress direction, given by breakouts and drilling-induced fractures, is shown not ...

Fracture characterization at multiple scales using borehole images, sonic logs, and walkaround vertical seismic profile

We present a quantitative forward-modeling methodology to link and interpret several measurements relevant to mechanical properties of fractures such as borehole images, sonic anisotropy logs, and borehole seismic anisotropy. The analysis is applied to a case study from a north African tight gas field using data from a vertical well. Two studies are conducted independently using the same geological fracture data to model fracture-induced anisotropy. In the first study, we use the orientation of the natural and drilling-induced fractures interpreted on the image log to model the azimuthal fracture-induced anisotropy at the sonic scale. The mechanical effects of natural and drilling-induced fractures are treated using different compliance parameters for each fracture type. We show that modeled sonic fast shear azimuths could be biased by the presence of noncompliant fractures in each fracture type, and we propose an empirical selection criterion to reject noncompliant fractures prior to compliance estimation. Then, we estimate the fracture compliances and confirm that natural open fractures have larger compliances than drilling-induced fractures. In the second study, we apply interpreted borehole images toward modeling of the azimuthal vertical seismic profile (VSP) attributes as a function of source azimuthal position. Natural fractures inside a window of height, h, and located at depth, d, are included, and several volume sizes and positions (i.e., h and d) are considered. We find a good agreement between modeled and observed transverse-over-radial displacement trends using natural fractures within windows located at the depth of the VSP receiver, and having window heights on the order of one to two VSP shear wavelengths.

Hydraulic Fracture Propagation Across a Weak Discontinuity Controlled by Fluid Injection

We investigated the problem of a hydraulic fracture propagation through a weakly cohesive frictional discontinuity for different conditions of fracture toughness, in situ stresses, fracture intersection angle, injection parameters and permeability of the pre-existing fracture. The parametric sensitivity of the fracture interaction process, in terms of crossing versus arresting of the hydraulic fracture at the discontinuity, was performed using numerical simulations through an extensive parameter space representative of hydraulic fracturing field conditions. The effect of the pre-existing fracture permeability on the crossing behavior was analyzed using a simple analytical model. We showed that the injection rate and viscosity of fracturing fluid are the key parameters controlling the crossing/non-crossing interaction behavior, in addition to already known fracture interaction angle and in-situ stress parameters. We have also found that the pre-existing fracture hydraulic aperture, when as large as that of the hydraulic fracture aperture, has significant influence on the interaction and may more likely cause the hydraulic fracture to arrest.

Incremental linear-elastic response of rocks containing multiple rough fractures: Similarities and differences with traction-free cracks

Fractures in the subsurface serve as conduits for fluids and gas, connecting remote hydrocarbon reservoir sections to production wells. Seismic and sonic data are popular sources for information on fracture properties. The most commonly used model to extract fracture information from such data is based on the paradigm of the displacement discontinuity interface, without a direct link to relevant characteristics such as the surface roughness properties of a fracture. Indeed, fractures can be modeled as displacement discontinuity surfaces, and in this sense they resemble traction-free cracks. In literature, cracks and fractures are not always properly distinguished, perhaps because the terms are often perceived as synonyms. However, microstructural parameters that control magnitudes of the discontinuities — and thus the effective stiffnesses — are entirely different: statistics of contacts for fractures versus crack density for traction-free cracks. We explore the effective elasticity of rocks containing multiple fractures using a model of a fracture as two rough surfaces with isolated contacts. This is done in the context of the incremental, linear elastic response to small stress changes, typical in wave-propagation problems. Fractures are dry or may have diverse orientations, and contacts may or may not be Hertzian. A link exists between contact characteristics and effective stiffness of single and multiple fractures. Our work examines and accounts for the strong effect of interactions between individual contacts by means of a double sum over mutual positions as well as outlines the differences and similarities between theories for cracks and fractures.

Effect of Flow Rate and Viscosity on Complex Fracture Development in UFM Model

A recently developed unconventional fracture model (UFM*) is able to simulate complex fracture networks propagation in a formation with pre-existing natural fractures. Multiple fracture branches can propagate at the same time and crisscross each other. The behaviour of a hydraulic fracture when it intersects a natural fracture, whether being arrested, cross‐ ing, creating an offset, or dilating the natural fracture, plays a key role in predicting the re‐ sulting fracture footprint, microseismicity, and improving production evaluation. It is therefore critical to properly model the fracture interaction in a complex fracture model such as UFM. A new crossing model, called OpenT, taking into account the effect of flow rate and fluid viscosity on the hydraulic/natural fracture crossing behaviour is integrated in UFM simula‐ tor. The previous fracture crossing model is primarily based on the stress field at the ap‐ proaching hydraulic fracture tip and its interaction with the natural fracture. A new elasticity solution for the fracture contact has been developed. The new OpenT semi-analyti‐ cal crossing model quantifies the localized stress field induced in the natural fracture and in the rock and evaluates the size and length of open and shear slippage zones along the natu‐ ral fracture. The natural fracture activation and stress field near the intersection point are strongly dependent on the contacting hydraulic fracture opening and thus on fluid flow rate and viscosity. This new model is validated against laboratory experimental results and an advanced numerical model. In this paper we present the results of several test cases showing the influence of injection rate and fluid viscosity on the generated hydraulic fracture footprint in formations with pre© 2013 Kresse et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. existing natural fractures. The influence of the stress field anisotropy, intersection angle, as well as natural fractures properties are also important and are discussed. The results are then compared with the simulations using the previous crossing model which does not ac‐ count for the influence of fluid properties.

Relating shear sonic anisotropy directions to stress in deviated wells

We develop a model that relates the polarization direction of a dipole sonic fast shear wave propagating along the borehole (hereafter called FSA) to the relative deviatoric stress tensor for arbitrary well orientations. We first define stress quantities, or “subsidiary principal stress,” relevant for sonic dipole shear characterized sufficiently far away into the formation to be unaffected by borehole stress concentration. Next, we show analytically for wells oriented within principal stress planes and numerically for wells outside principal stress planes that the stress-induced FSA coincides with the maximum normal stress direction orthogonal to the borehole (“maximum subsidiary principal stress”) using a nonlinear elastic model for isotropic unstressed background media and plane wave solutions. This model is independent of stress sensitivity parameters. This result is a consequence of, first, the direct relationship between the stressellipsoid factor and the shear stiffness difference ratio, R≡ ( σ2 − ...

Calibration of Velocity-stress Relationships Under Hydrostatic Stress For Their Use Under Non-hydrostatic Stress Conditions

We have computed stress sensitivity parameters for intrinsically transverse isotropic (TI) shales and sandstones under hydrostatic stress using literature data from Wang (2002b). We use the three-parameter non-linear model that relates the whole stiffness tensor and the whole stress tensor. We introduce physical and empirical constraints in the inversion of parameters c111, c112, c123 to compensate for the absence of non-hydrostatic stress data. The constraints c111 < c112 and c155 < c144 ensure respectively that P-waves are dominated by the stress in the polarization direction and S-waves by stresses in the polarization and propagation direction. We confirm the validation of the model for all 16 shale samples and 10 out of 20 sandstone samples (35 MPa stress range) when intrinsic anisotropy is present and greater than 4.5 %. Sand samples show higher stress sensitivity than shale samples. With this methodology, we suggest that velocity-stress relationships can be calibrated in the lab under hydrostatic stress and then used under non-hydrostatic stress conditions.

Limited Height Growth and Reduced Opening of Hydraulic Fractures due to FractureOffsets: An XFEM Application

Note: SPE 168622 Reference EPFL-CONF-212821 Record created on 2015-10-08, modified on 2016-08-09

Fracture compliance estimation using a combination of image and sonic logs

We estimate fracture elastic compliances using a combination of image and sonic logs from a typical borehole survey in a naturally fractured reservoir. Borehole dipole sonic anisotropy related to the effect of drilling-induced (DI) and natural fractures is modeled using a classical excess-compliance fracture model. We extract the orientation of individual fractures from borehole image log analysis. The analysis is focused on the log depth interval where fracture-induced anisotropy is observed, and where the maximum horizontal stress direction is not aligned with the strike of natural fractures. Fracture compliances are estimated in two steps by first selecting the fractures that honor the fast-shear azimuth, and second by using a grid search method minimizing the sonic slowness anisotropy difference. Two fracture compliance parameters are used, one per fracture type (natural and DI). We first model the effect of natural and DI fractures including all fractures observed on the images. Predicted fast-shear azimuths are shown to be slightly biased by the presence of non-compliant fractures in each fracture type. Next, we introduce a selection criteria based on the fast-shear azimuth to reject non-compliant fractures. Finally, we estimate fracture compliances using sonic slowness difference before and after the selection process and discuss the results.