Stress-dependent anisotropy in transversely isotropic rocks: Comparison between theory and laboratory experiment on shale

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. D7-D12 ◽  
Author(s):  
Radim Ciz ◽  
Serge A. Shapiro
Keyword(s):  
Effective Stress ◽  
Elastic Moduli ◽  
Pore Space ◽  
Transversely Isotropic ◽  
Stress Sensitivity ◽  
Seismic Velocities ◽  
The North ◽  
Compliance Tensor ◽  
Stress Dependent ◽  
Deformation Approach

Understanding the effect of stress and pore pressure on seismic velocities is important for overpressure prediction and for 4D reflection seismic interpretation. A porosity-deformation approach (originally called the piezosensitivity theory) and its anisotropic extension describe elastic moduli of rocks as nonlinear functions of the effective stress. This theory assumes a presence of stiff and compliant parts of the pore space. The stress-dependent geometry of the compliant pore space predominantly controls stress-induced changes in elastic moduli. We show how to apply this theory to a shale that is transversely isotropic (TI) under unloaded conditions. The porosity-deformation approach shows that components of the compliance tensor depend on exponential functions of the principal components of the effective stress tensor. In the case of a hydrostatic loading of a TI rock, only the diagonal elements of this tensor, expressed in contracted notation, are significantly stress dependent. Two equal shear components of the compliance will depend on a combination of two stress exponentials. Exponents of the stress exponentials are controlled by components of the stress-sensitivity tensor. This tensor is an important physical characteristic directly related to the elastic nonlinearity of the porous rock. We simplify the porosity-deformation theory for TI rocks and provide corresponding explicit equations. We apply this theory to ultrasonic measurements on saturated shale samples from the North Sea. We show that the theory explains the compliance tensor, anellipticity, and three anisotropic parameters under a broad range of loads.

Porosity and elastic anisotropy of rocks under tectonic stress and pore-pressure changes

Geophysics ◽  
2005 ◽  
Vol 70 (5) ◽  
pp. N27-N38 ◽  
Author(s):  
Serge A. Shapiro ◽  
Axel Kaselow
Keyword(s):  
Pore Pressure ◽  
Elastic Moduli ◽  
Elastic Anisotropy ◽  
Pore Space ◽  
Tectonic Stress ◽  
Stress Sensitivity ◽  
Seismic Velocities ◽  
Confining Stress ◽  
The Difference ◽  
Stress Dependent

Elastic properties of rocks depend on tectonic stress. Using the theory of poroelasticity as a constraint, we analyze features of these dependencies related to changes in rock pore-space geometry. We develop a formalism describing elastic moduli and anisotropy of rocks as nonlinear functions of confining stress and pore pressure. This formalism appears to agree with laboratory observations. To a first approximation, elastic moduli and seismic velocities as well as porosity depend only on the difference between the confining tectonic stress and pore pressure. However, in general, both the confining stress tensor and the pore pressure must be taken into account as independent variables. The stress-dependent geometry of the pore space fully controls the stress-induced changes in elastic moduli and seismic velocities. Specifically, the compliant porosity plays the most important role, despite the fact that in many rocks the compliant porosity is a very small part of total porosity. Changes in compliant porosity with pressure and stress explain the often observed behavior of elastic moduli: in the low compressive stress regime — say, below 50 to 100 MPa — moduli increase rapidly and then taper exponentially into a flat and linear increase with increasing load. Taking into account the strain of the compliant pore space, we introduce a tensor quantity defining the sensitivity of elastic moduli of rocks to the difference between confining stress and pore pressure. We call it the stress sensitivity tensor. This tensor is an important physical characteristic directly related to elastic nonlinearity of rocks. The stress sensitivity tensor governs the changes in elastic anisotropy of a drained poroelastic system as it depends upon the applied load.

Elastic properties of two VTI shale samples as a function of uniaxial stress: Experimental results and application of the porosity-deformation approach

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. C201-C210 ◽  
Author(s):  
Viacheslav A. Sviridov ◽  
Sibylle I. Mayr ◽  
Serge A. Shapiro
Keyword(s):  
Elastic Properties ◽  
Pore Space ◽  
Uniaxial Stress ◽  
Data Sets ◽  
Seismic Velocities ◽  
Transverse Isotropic ◽  
Compliant Parts ◽  
Stress Dependent ◽  
Deformation Approach ◽  
Stress Dependency

Shale is a complex medium composed of clay, other mineral phases, and a pore space. The combined elastic properties of these components control the effective (anisotropic) properties of the composite solid. The factor that is the most dependent on the stress field is the structure of the pore space, which greatly influences the elastic properties of the medium. We have further developed and experimentally validated the porosity deformation approach (PDA) for understanding and modeling stress-dependent changes of the elastic properties of sedimentary rocks. PDA separates the pore space into stiff and compliant parts. The load dependencies of the elastic properties have linear contributions due to the former and exponential contributions due to the latter. We evaluate data sets of elastic properties of two vertical transverse isotropic shale samples measured under uniaxial stress. Then we apply the PDA and our optimization algorithm to the measured data sets to model the stress dependency of the seismic velocities and validate the modeling with experimentally obtained results. We have developed for the first time the constant anellipticity approach (CAN), which estimates the off-axis velocity (in an inclined direction relative to the symmetry axis direction) as a function of stress. Measurements of off-axis velocities are often missing information, and CAN permits us to fill this gap. This provides further background for the reconstruction of the stress dependency of the compliance tensor from acoustic log data.

scholarly journals Stress-Dependent Permeability of Fractures in Tight Reservoirs

Energies ◽  
2018 ◽  
Vol 12 (1) ◽  
pp. 117 ◽  
Author(s):  
Nai Cao ◽  
Gang Lei ◽  
Pingchuan Dong ◽  
Hong Li ◽  
Zisen Wu ◽  
...  
Keyword(s):  
Effective Stress ◽  
Influencing Factor ◽  
Quantitative Model ◽  
Stress Sensitivity ◽  
Gas Production ◽  
Fracture System ◽  
Permeability Model ◽  
Fracture Systems ◽  
Tight Reservoirs ◽  
Stress Dependent

Permeability is one of the key factors involved in the optimization of oil and gas production in fractured porous media. Understanding the loss in permeability influenced by the fracture system due to the increasing effective stress aids to improve recovery in tight reservoirs. Specifically, the impacts on permeability loss caused by different fracture parameters are not yet clearly understood. The principal aim of this paper is to develop a reasonable and meaningful quantitative model that manifests the controls on the permeability of fracture systems with different extents of fracture penetration. The stress-dependent permeability of a fracture system was studied through physical tests and numerical simulation with the finite element method (FEM). In addition, to extend capability beyond the existing model, a theoretical stress-dependent permeability model is proposed with fracture penetration extent as an influencing factor. The results presented include (1) a friendly agreement between the predicted permeability reduction under different stress conditions and the practical experimental data; (2) rock permeability of cores with fractures first reduces dramatically due to the closure of the fractures, then the permeability decreases gradually with the increase in effective stress; and (3) fracture penetration extent is one of the main factors in permeability stress sensitivity. The sensitivity is more influenced by fracture systems with a larger fracture penetration extent, whereas matrix compaction is the leading influencing factor in permeability stress sensitivity for fracture systems with smaller fracture penetration extents.

Stress sensitivity of sandstones

Geophysics ◽  
1996 ◽  
Vol 61 (2) ◽  
pp. 444-455 ◽  
Author(s):  
Jack Dvorkin ◽  
Amos Nur ◽  
Caren Chaika
Keyword(s):  
Elastic Modulus ◽  
Effective Stress ◽  
Elastic Moduli ◽  
Hydrostatic Stress ◽  
Clay Content ◽  
Stress Sensitivity ◽  
High Porosity ◽  
Effective Pressure ◽  
Critical Porosity ◽  
Difference Formula

Our observations made on dry‐sandstone ultrasonic velocity data relate to the variation in velocity (or modulus) with effective stress, and the ability to predict a velocity for a rock under one effective pressure when it is known only under a different effective pressure. We find that the sensitivity of elastic moduli, and velocities, to effective hydrostatic stress increases with decreasing porosity. Specifically, we calculate the difference between an elastic modulus, [Formula: see text], of a sample of porosity ϕ at effective pressure [Formula: see text] and the same modulus, [Formula: see text], at effective pressure [Formula: see text]. If this difference, [Formula: see text], is plotted versus porosity for a suite of samples, then the scatter of ΔM is close to zero as porosity approaches the critical porosity value, and reaches its maximum as porosity approaches zero. The dependence of this scatter on porosity is close to linear. Critical porosity here is the porosity above which rock can exist only as a suspension—between 36% and 40% for sandstones. This stress‐sensitivity pattern of grain‐supported sandstones (clay content below 0.35) practically does not depend on clay content. In practical terms, the uncertainty of determining elastic moduli at a higher effective stress from the measurements at a lower effective stress is small at high porosity and increases with decreasing porosity. We explain this effect by using a combination of two heuristic models—the critical porosity model and the modified solid model. The former is based on the observation that the elastic‐modulus‐versus‐porosity relation can be approximated by a straight line that connects two points in the modulus‐porosity plane: the modulus of the solid phase at zero porosity and zero at critical porosity. The second one reflects the fact that at constant effective stress, low‐porosity sandstones (even with small amounts of clay) exhibit large variability in elastic moduli. We attribute this variability to compliant cracks that hardly affect porosity but strongly affect the stiffness. The above qualitative observation helps to quantitatively constrain P‐ and S‐wave velocities at varying stresses from a single measurement at a fixed stress. We also show that there are distinctive linear relations between Poisson’s ratios (ν) of sandstone measured at two different stresses. For example, in consolidated medium‐porosity sandstones [Formula: see text], where the subscripts indicate hydrostatic stress in MPa. Linear functions can also be used to relate the changes (with hydrostatic stress) in shear moduli to those in compressional moduli. For example, [Formula: see text], where [Formula: see text] is shear modulus and [Formula: see text] is compressional modulus, both in GPa, and the subscripts indicate stress in MPa.

scholarly journals Influence of microheterogeneity on effective stress law for elastic properties of rocks

Geophysics ◽  
2008 ◽  
Vol 73 (1) ◽  
pp. E7-E14 ◽  
Author(s):  
Radim Ciz ◽  
Anthony F. Siggins ◽  
Boris Gurevich ◽  
Jack Dvorkin
Keyword(s):  
Effective Stress ◽  
Seismic Data ◽  
Elastic Moduli ◽  
Seismic Velocity ◽  
Time Lapse ◽  
Seismic Velocities ◽  
Laboratory Measurements ◽  
Hydrocarbon Production ◽  
Stress Coefficient ◽  
Seismic Measurements

Understanding the effective stress coefficient for seismic velocity is important for geophysical applications such as overpressure prediction from seismic data as well as for hydrocarbon production and monitoring using time-lapse seismic measurements. This quantity is still not completely understood. Laboratory measurements show that the seismic velocities as a function of effective stress yield effective stress coefficients less than one and usually vary between 0.5 and 1. At the same time, theoretical analysis shows that for an idealized monomineral rock, the effective stress coefficient for elastic moduli (and therefore also for seismic velocities) will always equal one. We explore whether this deviation of the effective stress coefficient from unity can be caused by the spatial microheterogeneity of the rock. The results show that only a small amount (less than 1%) of a very soft component is sufficient to cause this effect. Such soft material may be present in grain contact areas of many rocks and may explain the variation observed experimentally.

Source-rock seismic-velocity models: Gassmann versus Backus

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. N37-N45 ◽  
Author(s):  
José M. Carcione ◽  
Hans B. Helle ◽  
Per Avseth
Keyword(s):  
Oil And Gas ◽  
Seismic Velocity ◽  
Transversely Isotropic ◽  
Source Rocks ◽  
Seismic Velocities ◽  
Fluid Mixture ◽  
Data Set ◽  
Velocity Models ◽  
The North ◽  
Anisotropic Case

Source rocks are described by a porous transversely isotropic medium composed of illite and organic matter (kerogen, oil, and gas). The bulk modulus of the oil/gas mixture is calculated by using a model of patchy saturation. Then, the moduli of the kerogen/fluid mixture are obtained with the Kuster and Toksöz model, assuming that oil is the inclusion in a kerogen matrix. To obtain the seismic velocities of the shale, we used Backus averaging and Gassmann equations generalized to the anisotropic case with a solid-pore infill. In the latter case, the dry-rock elastic constants are calculated with a generalization of Krief equations to the anisotropic case. We considered 11 samples of the Bakken-shale data set, with a kerogen pore infill. The Backus model provides lower and upper bounds of the velocities, whereas the Krief/Gassmann model provides a good match to the data. Alternatively, we obtain the dry-rock elastic moduli by using the inverse Gassmann equation, instead of using Krief equations. Four cases out of 11 yielded physically unstable results. We also considered samples of the North Sea Kimmeridge shale. In this case, Backus performed as well as the Krief/Gassmann model. If there is gas and oil in the shale, we found that the wave velocities are relatively constant when the amount of kerogen is kept constant. Varying kerogen content implies significant velocity changes versus fluid (oil) saturation.

scholarly journals Local radon flux maxima in the quaternary sediments of Schleswig–Holstein (Germany)

2021 ◽  
Author(s):  
Johannes Albert ◽  
Maximilian Schärf ◽  
Frieder Enzmann ◽  
Martin Waltl ◽  
Frank Sirocko
Keyword(s):  
Water Content ◽  
Pore Space ◽  
Mineralogical Composition ◽  
Fault System ◽  
Near Surface ◽  
Salt Diapirism ◽  
The North ◽  
Radon Flux ◽  
Published Evidence ◽  
Tectonically Active

AbstractThis paper presents radon flux profiles from four regions in Schleswig–Holstein (Northern Germany). Three of these regions are located over deep-rooted tectonic faults or salt diapirs and one is in an area without any tectonic or halokinetic activity, but with steep topography. Contrary to recently published studies on spatial patterns of soil radon gas concentration we measured flux of radon from soil into the atmosphere. All radon devices of each profile were deployed simultaneously to avoid inconsistencies due to strong diurnal variations of radon exhalation. To compare data from different seasons, values had to be normalized. Observed radon flux patterns are apparently related to the mineralogical composition of the Quaternary strata (particularly to the abundance of reddish granite and porphyry), and its grain size (with a flux maximum in well-sorted sand/silt). Minimum radon flux occurs above non-permeable, clay-rich soil layers. Small amounts of water content in the pore space increase radon flux, whereas excessive water content lessens it. Peak flux values, however, are observed over a deep-rooted fault system on the eastern side of Lake Plön, i.e., at the boundary of the Eastholstein Platform and the Eastholstein Trough. Furthermore, high radon flux values are observed in two regions associated with salt diapirism and near-surface halokinetic faults. These regions show frequent local radon flux maxima, which indicate that the uppermost strata above salt diapirs are very inhomogeneous. Deep-rooted increased permeability (effective radon flux depth) or just the boundaries between permeable and impermeable strata appear to concentrate radon flux. In summary, our radon flux profiles are in accordance with the published evidence of low radon concentrations in the “normal” soils of Schleswig–Holstein. However, very high values of radon flux are likely to occur at distinct locations near salt diapirism at depth, boundaries between permeable and impermeable strata, and finally at the tectonically active flanks of the North German Basin.

scholarly journals Stress sensitivity of porosity and permeability under varying hydrostatic stress conditions for different carbonate rock types of the geothermal Malm reservoir in Southern Germany

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Daniel Bohnsack ◽  
Martin Potten ◽  
Simon Freitag ◽  
Florian Einsiedl ◽  
Kai Zosseder
Keyword(s):  
Effective Stress ◽  
Hydraulic Properties ◽  
Rock Strength ◽  
Pore Network ◽  
Stress Sensitivity ◽  
Stress Conditions ◽  
Rock Matrix ◽  
Effective Stresses ◽  
Rock Types ◽  
Porosity And Permeability

AbstractIn geothermal reservoir systems, changes in pore pressure due to production (depletion), injection or temperature changes result in a displacement of the effective stresses acting on the rock matrix of the aquifer. To compensate for these intrinsic stress changes, the rock matrix is subjected to poroelastic deformation through changes in rock and pore volume. This in turn may induce changes in the effective pore network and thus in the hydraulic properties of the aquifer. Therefore, for the conception of precise reservoir models and for long-term simulations, stress sensitivity of porosity and permeability is required for parametrization. Stress sensitivity was measured in hydrostatic compression tests on 14 samples of rock cores stemming from two boreholes of the Upper Jurassic Malm aquifer of the Bavarian Molasse Basin. To account for the heterogeneity of this carbonate sequence, typical rock and facies types representing the productive zones within the thermal reservoir were used. Prior to hydrostatic investigations, the hydraulic (effective porosity, permeability) and geomechanical (rock strength, dynamic, and static moduli) parameters as well as the microstructure (pore and pore throat size) of each rock sample were studied for thorough sample characterization. Subsequently, the samples were tested in a triaxial test setup with effective stresses of up to 28 MPa (hydrostatic) to simulate in-situ stress conditions for depths up to 2000 m. It was shown that stress sensitivity of the porosity was comparably low, resulting in a relative reduction of 0.7–2.1% at maximum effective stress. In contrast, relative permeability losses were observed in the range of 17.3–56.7% compared to the initial permeability at low effective stresses. Stress sensitivity coefficients for porosity and permeability were derived for characterization of each sample and the different rock types. For the stress sensitivity of porosity, a negative correlation with rock strength and a positive correlation with initial porosity was observed. The stress sensitivity of permeability is probably controlled by more complex processes than that of porosity, where the latter is mainly controlled by the compressibility of the pore space. It may depend more on the compaction of precedented flow paths and the geometry of pores and pore throats controlling the connectivity within the rock matrix. In general, limestone samples showed a higher stress sensitivity than dolomitic limestone or dolostones, because dolomitization of the rock matrix may lead to an increasing stiffness of the rock. Furthermore, the stress sensitivity is related to the history of burial diagenesis, during which changes in the pore network (dissolution, precipitation, and replacement of minerals and cements) as well as compaction and microcrack formation may occur. This study, in addition to improving the quality of input parameters for hydraulic–mechanical modeling, shows that hydraulic properties in flow zones largely characterized by less stiff, porous limestones can deteriorate significantly with increasing effective stress.

scholarly journals Parameterization of elastic stress sensitivity in shales

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA147-WA155 ◽  
Author(s):  
Marina Pervukhina ◽  
Boris Gurevich ◽  
Pavel Golodoniuc ◽  
David N. Dewhurst
Keyword(s):  
Elastic Properties ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
Bedding Plane ◽  
Stress Sensitivity ◽  
Crack Orientation ◽  
Fluid Identification ◽  
Orientation Anisotropy ◽  
Characteristic Pressure ◽  
Stress Dependency

Stress dependency and anisotropy of dynamic elastic properties of shales is important for a number of geophysical applications, including seismic interpretation, fluid identification, and 4D seismic monitoring. Using Sayers-Kachanov formalism, we developed a new model for transversely isotropic (TI) media that describes stress sensitivity behavior of all five elastic coefficients using four physically meaningful parameters. The model is used to parameterize elastic properties of about 20 shales obtained from laboratory measurements and the literature. The four fitting parameters, namely, specific tangential compliance of a single crack, ratio of normal to tangential compliances, characteristic pressure, and crack orientation anisotropy parameter, show moderate to good correlations with the depth from which the shale was extracted. With increasing depth, the tangential compliance exponentially decreases. The crack orientation anisotropy parameter broadly increases with depth for most of the shales, indicating that cracks are getting more aligned in the bedding plane. The ratio of normal to shear compliance and characteristic pressure decreases with depth to 2500 m and then increases below this to 3600 m. The suggested model allows us to evaluate the stress dependency of all five elastic compliances of a TI medium, even if only some of them are known. This may allow the reconstruction of the stress dependency of all five elastic compliances of a shale from log data, for example.

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