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

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.

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. D7-D12 ◽  
Author(s):  
Radim Ciz ◽  
Serge A. Shapiro

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.


2010 ◽  
Vol 13 (02) ◽  
pp. 265-274 ◽  
Author(s):  
Ashraf Al-Tahini ◽  
Younane Abousleiman

Summary In this study, we determine experimentally the effect of inherent and stress-induced anisotropy on stiffness components, elastic moduli, and Biot's pore-pressure coefficients (PPCs) for Lyons outcrop Colorado sandstone, which exhibits a clear transverse isotropic rock structure. Both dynamic and quasistatic methods were used under a nonhydrostatic state of stress to perform the measurements on dry core samples. Our assumption of apparent transverse anisotropy was confirmed initially with acoustic velocity measurements and at a later stage in the loading with experimental transverse anisotropic failure analysis. The objective of this study is to identify and isolate the effect of stress-induced anisotropy from the inherent transverse anisotropy on the measured stiffness components, elastic moduli, and Biot's PPCs. The effect of stress-induced anisotropy appears to have significant control on measured stiffness components, elastic moduli, and Biot's PPCs in comparison to the inherent-transverse-anisotropy effect. Our work shows that the stiffness components, Mij and thus the computed elastic moduli, are highly influenced by the stress-induced anisotropy, especially the off-diagonal stiffness components, M12 and M13, where the increase in their magnitudes from the dynamic measurements before failure is determined to be 100 and 81%, respectively. The difference in the magnitude between the axial and lateral Biot's PPCs in line with bedding planes and perpendicular to them is measured to be 24 and 16% from the quasistatic and dynamic methods, respectively; whereas, the effect of stress-induced anisotropy reduced the dynamic average magnitude of the Biot's PPCs along the bedding planes and transverse to these planes by 63% across a stress range of 145 MPa.


Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. L1-L11 ◽  
Author(s):  
M. Monzurul Alam ◽  
Ida Lykke Fabricius ◽  
Helle Foged Christensen

Deformation of a hydrocarbon reservoir can ideally be used to estimate the effective stress acting on it. The effective stress in the subsurface is the difference between the stress due to the weight of the sediment and a fraction (effective stress coefficient) of the pore pressure. The effective stress coefficient is thus relevant for studying reservoir deformation and for evaluating 4D seismic for the correct pore pressure prediction. The static effective stress coefficient [Formula: see text] is estimated from mechanical tests and is highly relevant for effective stress prediction because it is directly related to mechanical strain in the elastic stress regime. The corresponding dynamic effective stress coefficient [Formula: see text] is easy to estimate from density and velocity of acoustic (elastic) waves. We studied [Formula: see text] and [Formula: see text] of chalk from the reservoir zone of the Valhall field, North Sea, and found that [Formula: see text] and [Formula: see text] vary with differential stress (overburden stress-pore pressure). For Valhall reservoir chalk with 40% porosity, [Formula: see text] ranges between 0.98 and 0.85 and decreases by 10% if the differential stress is increased by 25 MPa. In contrast, for chalk with 15% porosity from the same reservoir, [Formula: see text] ranges between 0.85 and 0.70 and decreases by 5% due to a similar increase in differential stress. Our data indicate that [Formula: see text] measured from sonic velocity data falls in the same range as for [Formula: see text], and that [Formula: see text] is always below unity. Stress-dependent behavior of [Formula: see text] is similar (decrease with increasing differential stress) to that of [Formula: see text] during elastic deformation caused by pore pressure buildup, for example, during waterflooding. By contrast, during the increase in differential stress, as in the case of pore pressure depletion due to production, [Formula: see text] increases with stress while [Formula: see text] decreases.


2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yu Lu ◽  
Wenbin Fu ◽  
Danxuan Xue

Soft marine soil which could be found widely at the coastal and offshore areas is usually associated with high settlement and instability, especially under cyclic loading. Many research studies have been conducted on its deformation characteristics under the cyclic loading with high frequency, whereas few works have been reported on that under the low-frequency cyclic loading which largely existed in engineering. In this work, a comprehensive series of undrained triaxial tests under cyclic loading with low frequency was conducted to investigate the deformation characteristics of soft marine soil. The results demonstrate that soil specimens accumulate plastic deformation and pore pressure under cyclic loading. Specimens tested under conditions such as high confining stress, high-stress ratio, and long cyclic period generally reveal higher deformation and pore pressure. Meanwhile, the rectangular wave presents the largest contribution to plastic strain and pore pressure, followed by the trapezoidal and triangular waves, respectively, whereas the difference between the various waves decreased gradually with the increasing load level and cyclic period. The undisturbed specimens displayed lower deformations and pore pressures than the reconstructed specimens, whereas the differences are not significant when the confining stress is much higher than the structural yield stress. Furthermore, an empirical model for predicting the evolution of pore pressure is proposed and then validated against the experimental data in both this work and the literature.


Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. C201-C210 ◽  
Author(s):  
Viacheslav A. Sviridov ◽  
Sibylle I. Mayr ◽  
Serge A. Shapiro

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.


2000 ◽  
Vol 3 (06) ◽  
pp. 517-524
Author(s):  
J.K. Hughes

Summary The propagation of elastic waves in rocks is determined by the bulk modulus, shear modulus, and bulk density of the rock. In porous rocks all these properties are affected by the distribution of pore space, the geometry and interconnectivity of the pores, and the nature of the fluid occupying the pore space. In addition, the bulk and shear moduli are also affected by the effective pressure, which is equivalent to the difference between the confining (or lithostatic) pressure and pore pressure. During production of hydrocarbons from a reservoir, the movement of fluids and changes in pore pressure may contribute to a significant change in the elastic moduli and bulk density of the reservoir rocks. This phenomenon is the basis for reservoir monitoring by repeated seismic (or time-lapse) surveys whereby the difference in seismic response during the lifetime of the field can be directly related to changes in the pore fluids and/or pore pressure. Under suitable conditions, these changes in the reservoir during production can be quantitatively estimated by appropriate repeat three-dimensional (3D) seismic surveys which can contribute to understanding of the reservoir model away from the wells. The benefit to reservoir management is a better flow model which incorporates the information derived from the seismic data. What are suitable conditions? There are two primary factors which determine whether the reservoir changes we wish to observe will be detectable in the seismic data:the magnitude of the change in the elastic moduli (and bulk density) of the reservoir rocks as a result of fluid displacement, pressure changes, etc.;the magnitude of the repeatability errors between time-lapse seismic surveys. This includes errors associated with seismic data collection, ambient noise and data processing. The first is the signal component and the second the noise component. Previous reviews of seismic monitoring suggest that for 3D seismic surveys a signal-to-noise (S/N) ratio of 1.0 is sufficient for qualitative estimation of reservoir changes. Higher S/N ratios may allow quantitative estimates. After a brief examination of the rock physics affecting the seismic signal, we examine the second factor, repeatability errors, and use a synthetic seismic model to illustrate some of the factors which contribute to repeatability error. We also use two land 3D surveys over a Middle East carbonate reservoir to illustrate seismic repeatability. The study finds that repeatability errors, while always larger than desired, are generally within limits which will allow production-induced changes in seismic reflectivity to be confidently detected. Introduction Seismic data have been used successfully for many decades in the petroleum industry and have contributed significantly to the discovery of new fields throughout the world. Initially, seismic surveys were primarily an exploration tool, assisting in the identification of potential hydrocarbon structural and stratigraphic traps for drilling targets. With the introduction of 3D seismic surveys in the 1970's, accurate geological structural mapping became possible while the use of new seismic attributes as hydrocarbon indicators improved the success rate of discovery wells. More recently seismic data have also contributed to a better reservoir description away from the wells by making use of the correlation between suitable seismic attributes and petrophysical quantities such as porosity and net to gross, and by incorporating robust geostatistical methods for estimating the static reservoir model. Better seismic acquisition technology, improved seismic processing methods and an overall improvement in signal to noise have led to further 3D seismic surveys over producing fields primarily for better imaging of the reservoir and improved reservoir characterization. The concept of using repeated seismic surveys (time-lapse seismic) for monitoring changes in the reservoir due to production was suggested in the 1980's,1-3 and early tests were done by Arco in the Holt Sand fireflood4 from 1981-83. Over the last few years, the number of publications relating to time-lapse seismic [often referred to as four-dimensional (4D) seismic] has increased dramatically. Prior to time-lapse seismic monitoring, seismic data have been the domain of geologists and geophysicists, but the possibility of monitoring fluid displacements and pressure changes in a producing reservoir, away from the wells, has direct relevance to reservoir engineers and reservoir management. More exciting possibilities have been introduced by the use of time-lapse seismic data in combination with production history matching5 for greater refinement in optimization of the reservoir model. It is important, however, that reliable criteria are used to assess the feasibility of seismic monitoring.6


2021 ◽  
Vol 13 (14) ◽  
pp. 2684
Author(s):  
Eldert Fokker ◽  
Elmer Ruigrok ◽  
Rhys Hawkins ◽  
Jeannot Trampert

Previous studies examining the relationship between the groundwater table and seismic velocities have been guided by empirical relationships only. Here, we develop a physics-based model relating fluctuations in groundwater table and pore pressure with seismic velocity variations through changes in effective stress. This model justifies the use of seismic velocity variations for monitoring of the pore pressure. Using a subset of the Groningen seismic network, near-surface velocity changes are estimated over a four-year period, using passive image interferometry. The same velocity changes are predicted by applying the newly derived theory to pressure-head recordings. It is demonstrated that the theory provides a close match of the observed seismic velocity changes.


2006 ◽  
Vol 324-325 ◽  
pp. 951-954 ◽  
Author(s):  
Qing Min Yu ◽  
Zhu Feng Yue ◽  
Yong Shou Liu

Fracture along an interface between materials plays a major role in failure of material. In this investigation, finite element calculations with Kachanov–Rabotnov damage law were carried out to study the creep damage distribution near the interface cavity in bimaterial specimens. The specimens with central hole were divided into three types. The material parameters of K-R law used in this paper were chosen for a brittle material and ductile material. All calculations were performed under four load cases. Due to the difference between elastic moduli of the bounded materials, the elastic stress field as a function of the Young’s modulus ratio (R=E1/E2) was determined. At the same time, the influence of model type on elastic stress distribution near the cavity was considered. Under the same conditions, the material with larger modulus is subjected to larger stress. The creep damage calculations show that the location of the maximum damage is different for each model. The distributions of creep damage for all three models are dependent on the material properties and load cases.


2017 ◽  
Author(s):  
Kathleen Sell ◽  
Beatriz Quintal ◽  
Michael Kersten ◽  
Erik H. Saenger

Abstract. Sediments containing gas hydrate dispersed in the pore space are known to show a characteristic seismic anomaly which is a high attenuation along with increasing seismic velocities. Currently, this observation cannot be fully explained albeit squirt-flow type mechanisms at the microscale have been speculated to be the cause. Recent major findings from in-situ experiments coupled with high-resolution synchrotron-based X-ray micro-tomography revealed a systematic presence of thin water films between the quartz grains and the encrusting hydrate. In this study, the data was obtained from the experiments and underwent an image processing procedure to quantify the thicknesses and geometries of the aforementioned interfacial water films. Overall, the water films vary from sub-μm to a few μm in thickness where some of them are interconnected by water bridges. This geometrical analysis is then used to propose a new conceptual squirt flow model for hydrate bearing sediments. Subsequently the established model acts as a direct model input to obtain seismic attenuation. Our results support previous speculations that squirt flow can explain high attenuation at seismic frequencies in hydrate bearing sediments, but based on a conceptual squirt flow model which is different than those previously considered.


2021 ◽  
Author(s):  
Yasser Kholaif ◽  
Mahmoud Elmaghraby ◽  
Annick Nago ◽  
Jean-Michel Embry ◽  
Pramit Basu ◽  
...  

Abstract Drilling challenges in offshore Nile Delta have been largely documented in the literature. Operators are often confronted with drilling problems related to shale swelling, cavings, tight holes in combination with increased risks of lost circulation in some of the highly depleted formations. The Kafr El Sheikh shale in particular, has been linked to many instances of wellbore instability, due to its mineralogical composition (estimated to be mostly smectite, >70%). From offset well drilling experience, it could also be noticed that insufficient mud weight was often used to drill through the Kafr El Sheikh Shale, causing wellbore failure in shear due to lack of support of the wellbore wall. In the past, multiple mud weight designs have been implemented relying solely on pore pressure as lower bound of the mud window. With the increased use of geomechanics, it has been demonstrated that the lower bound should be taken as the maximum of the pore pressure and borehole collapse pressure, thus accounting for the effects of formation pressure, horizontal and vertical stresses, rock properties as well as wellbore trajectory. It has been proven that slight overpressure is often encountered halfway through the Kafr El Sheikh formation, which would typically result in slightly higher borehole collapse pressures. In the study fields, the operator expressed interest in drilling highly deviated wells (> 60-70 degrees). This raised concerns for increased drilling challenges, especially in the Kafr El Sheikh. A comprehensive and systematic risk assessment, design of a fit-for-purpose solution and its implementation during drilling took place in the fields of interest. Offset well data analytics from the subject fields supported a holistic evaluation of drilling risks associated with the Kafr El Sheikh, providing good understanding of stress sensitivity on deviation, azimuth and lithology. Upon building a robust geomechanical model, calibrated against offset well drilling experience, pre-drill mud weight and drilling practices recommendations were provided to optimize the drilling program. Near real-time geomechanical monitoring was implemented which helped to manage the model uncertainties. The implementation of a holistic risk assessment, including geomechanical recommendations and near real-time geomechanical monitoring, was effective to lead the drilling campaign successfully. As a result, three high angle wells (> 60-70 degrees) were drilled through the challenging Kafr El Sheikh formation without any hole instability. An integrated risk assessment of hole instability, managed in stages (pre-drill and during drilling), has helped to understand and simulate the behaviors of the formation. Proactive decisions have established a controlled drilling environment for successful operations.


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