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#### Reflection/transmission coefficients at small angles and magnitude

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Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the SEG International Exposition and Annual Meeting, October 11–16, 2020

Paper Number: SEG-2020-3424753

... We consider a horizontal interface bounded by two triclinic half-spaces to derive the

**reflection**and**transmission**(R/T)**coefficient**approximations. To accommodate media where strong anisotropy and/or strong contrasts can present, we consider the second-order approximations and anisotropic...
Abstract

We consider a horizontal interface bounded by two triclinic half-spaces to derive the reflection and transmission (R/T) coefficient approximations. To accommodate media where strong anisotropy and/or strong contrasts can present, we consider the second-order approximations and anisotropic background medium. The pseudo-wave projection (PWP) method is extended to the triclinic media to obtain appropriate approximations for S1, S2 and converted waves. The proposed approximations are tested numerically. Presentation Date: Wednesday, October 14, 2020 Session Start Time: 1:50 PM Presentation Time: 3:05 PM Location: Poster Station 7 Presentation Type: Poster

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-2015-245

... Abstract Crack initiation, propagation and coalescence, from pre-cracked rock specimens, were detected in the laboratory using elastic wave

**transmission**and**reflection**signals. The experiments were conducted on prismatic Indiana limestone specimens with two parallel pre-existing flaws...
Abstract

Abstract Crack initiation, propagation and coalescence, from pre-cracked rock specimens, were detected in the laboratory using elastic wave transmission and reflection signals. The experiments were conducted on prismatic Indiana limestone specimens with two parallel pre-existing flaws subjected to uniaxial compression. Digital image correlation was used to monitor the cracking process around the tips of the flaws by imaging surface displacements. Compressional and shear wave pulses were transmitted and reflected continuously through the specimen while the uniaxial compressive load increased. The normalized amplitude of transmitted waves (shear waves with horizontal polarization) was observed to decrease with increasing uniaxial load, which was associated with the elastic deformations of the specimen. However, prior to tensile crack initiation, a large reduction in amplitude occurred. In addition, an additional decrease in amplitude was observed close to crack coalescence. These changes in amplitude occurred at least 1.3 MPa before the detection of damage by DIC imaging. The normalized amplitude of reflected signals (from the flaw tips) also increased significantly before the initiation of new cracks. These experimental results indicate that changes in transmitted and reflected seismic waves provide a potential method to detect crack initiation inside rock, as well as to determine the location of new cracks. 1. OVERVIEW A large number of experimental studies have been conducted on crack initiation, propagation, and coalescence in pre-cracked brittle materials. In most of these studies, the pre-existing crack (flaw) has been subjected to mixed mode loading (mode I: opening or tensile and mode II: in plane shear) [1–11]. Two types of cracks have been observed in these experiments: tensile (wing) and shear (secondary) cracks, which are shown in Fig. 1. Tensile cracks initiate at or near the tip of the flaw. They propagate toward the direction of maximum compression and they are stable (i.e. further propagation of these cracks require application of additional load). These cracks are also characterized by a plumose structure on their surface. Shear cracks initiate from the tips of the flaws, they are initially stable, but they may be unstable close to crack coalescence or specimen failure. These cracks have been classified into two groups: coplanar or quasi-coplanar (making an angle of 45° or less with the flaw plane) and oblique (with an initiation angle larger than 45° with the flaw plane). The shear cracks are formed in areas of high compression and/or shear stress. They are characterized by pulverized material on the surface and by high roughness [12]. Park and Bobet [12] performed laboratory uniaxial compression tests on gypsum specimens with two, three, and 16 parallel flaws. They identified eight types of coalescence based on different flaw geometries (see Table 1 in [12]). Observations in the laboratory have relied on visual inspection using optical magnification and high-speed cameras. While these techniques have been instrumental in the understanding of cracking phenomena at the macroscopic scale, what is needed, is a local or microscopic characterization of new cracks forming inside the brittle materials.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Annual Technical Conference and Exhibition, October 26–29, 2020

Paper Number: SPE-201275-MS

... slightly higher than that of the MLPNN model

**at**0.9931. The k-fold cross validation results also show the stability of the two models. These ML models are 5 to 6 orders of**magnitude**faster than CFD models with similar accuracy therefore significantly saving time and cost. We further built a web application...
Abstract

Predicting CO 2 corrosion in fluid transmission pipelines is crucial for oil/gas company in upstream applications. This paper applies Light Gradient Boosting Machine (LightGBM) and Multiple Layer Perceptron Neural Network (MLPNN) models for the prediction of CO 2 corrosion in aqueous pipelines with different pipe bending angles. To build the predictive models, a data set with total of 77,745 data points was generated parametrically by a computational fluid dynamics (CFD) model. Since different environmental conditions and geometries of the pipeline may cause non-uniform corrosion, a total of seven variables, including flow velocity, pH value, CO 2 concentration, pipe inner diameter, pipe bend angle, radius and temperature are taken as the input features with the corrosion rate as the target variable. The CFD model was then used to compute the electrochemical processes occurring at the metal surfaces to predict the corrosion rate. Knowing that these features have nonlinear relationship with the target, tree based LightGBM, and neural network based MLPNN were chosen. LightGBM can control the overfitting issues, deal with comparative scales of the features and learn non-linear decision boundaries via boosting. The most significant findings are that these two types of machine learning (ML) algorithms have higher efficiency and can predict new results in microseconds in contrast to hours or even days using CFD. The R square of the LightGBM model is 0.9985, which is slightly higher than that of the MLPNN model at 0.9931. The k-fold cross validation results also show the stability of the two models. These ML models are 5 to 6 orders of magnitude faster than CFD models with similar accuracy therefore significantly saving time and cost. We further built a web application based on these predictive models as a tool for pipeline design and monitoring applications.

Proceedings Papers

Paper presented at the The 29th International Ocean and Polar Engineering Conference, June 16–21, 2019

Paper Number: ISOPE-I-19-133

... submerged barrier in presence of

**small**forward and reversed currents using hydraulic model tests, to understand the analysis and prediction of wave**reflection**,**transmission**and loss**coefficient**under the influence of the existing currents with different directions. The wave attenuation and**reflection**...
Abstract

ABSTRACT This paper investigates the wave attenuation and reflection induced by a submerged barrier in presence of small forward and reversed currents using hydraulic model tests, to understand the analysis and prediction of wave reflection, transmission and loss coefficient under the influence of the existing currents with different directions. The wave attenuation and reflection induced by a submerged barrier in presence of small forward and reversed currents is experimentally discussed by using both the regular and irregular wave. Wave attenuation of the embankments affected by external current are also discussed and compared with those of cases without current. The results indicated that the influence of present current on wave reflection is slightly larger for irregular waves than that of regular waves. INTRODUCTION In coastal protection technology, artificial structures such as seawalls, jetty, armor units, and detached breakwaters are traditionally adopted as absorbing facilities to eliminate wave energies. Scholars have studied various offshore embankments, including changing the shape of the submerged embankment (Shih and Weng, 2016), the permeability characteristics of the submerged embankment, the number of submerged embankments and the distance between the submerged structures (Shih et al., 2013, 2014), to explore the interaction between waves and structures and their dissipation effectiveness. Traditionally, coastal protective was achieved by applying the constructions of armor units and rubble mound breakwater, etc., with the change of leisure patterns and the demand for activity spaces, many dissipation technologies and new energy-dissipation structures have been extensively developed and investigated to reduce wave energy, that provided the maintenance of natural ecology and landscape. The applications of the stepped rough surface on coastal structures has been studied by Krecic et al. (2004), and Lokesha et al. (2015), they explored the effect of smooth and stepped submarine embankment on the wave transmission characteristics with hydraulic model tests. The investigations on stepped revetments were limited in the past. Kerpen et al. (2014) conducted a series of experiments using 2D hydraulic model tests. Three different breakwater heights and breakwater widths consisting 18 sets of stepped and smooth breakwaters. Detailed descriptions of the roughness slopes for different types of revetments can be found in EurOtop (2018).

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015

Paper Number: SEG-2015-5859284

...

**reflection****coefficient**zoeppritz equation sin? 0**coefficient**reservoir characterization gradient variation viscous parameter intercept upstream oil & gas equation amplitude three-term approximation incident**angle****magnitude**approximation frequency-dependent**reflection****coefficient**...
Abstract

Summary The frequency-dependent seismic anomalies related to hydrocarbon reservoirs have lately attracted wide interests. The diffusive-viscous model was proposed to explain these anomalies. When an incident diffusive-viscous wave strikes a boundary between two different media, it is reflected and transmitted. The equation of the reflection coefficient is quite complex and laborious, so it does not provide an intuitive understanding of how different amplitude relates to the parameters of the media and how variation of a particular parameter affects the reflection coefficient. In this abstract, we first derive the two-term (interceptgradient) and three-term (intercept-gradient-curvature) approximations to the reflection coefficient of the plane diffusive-viscous wave without any assumptions. Then, we give the limitations of the obtained approximations by comparing the approximate value of the reflection coefficient with its exact value. Finally, we analyze the impacts of parameters of the media on the intercept, gradient and curvature terms in the approximations. The results show that the diffusive parameter in the diffusiveviscous wave equation has a big impact on the them, while the viscous parameter is insensitive to them. Introduction The amplitude variation with offset/angle of incidence (AVO/AVA) has been a powerful technique for geoscientists to extract fluid and lithology information from the analysis of prestack seismic amplitudes. When an incident plane wave strikes a boundary between two media, it will be reflected and transmitted. The theory of obtaining the reflection coefficient and transmission coefficient is Zoeppritz equations in elastic media. Zoeppritz equations give exact values of the amplitudes of the reflected and transmitted plane waves. However, they do not support an intuitive understanding of the effects of the parameter changes on the seismic amplitudes. In the past few decades, many linear approximations to the Zoeppritz equations have been derived to give an intuitive relationship between the parameters of the media and the seismic amplitudes. The first approximation to the Zoeppritz equations was obtained by Bortfeld (1961), who linearized the equations by dividing the major subsurface interfaces into a group of layers under the assumptions of small changes of the elastic parameters in the transition layers.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016

Paper Number: SEG-2016-13781169

...

**angle**. Therefore, the ratios of numerator to denominator are stable and reliable**at****small**incident**angles**except when it is less than about . 01 Conclusions In this paper, we present the explicit expression between uniaxial stress and the**coefficients**of P-wave**reflection**for a boundary an isotropic...
Abstract

ABSTRACT The investigation of subsurface stress is most important for geophysical exploration. In this paper, we present the expression of inverted uniaxial stress by P-wave reflection coefficients for a boundary between an isotropic overburden and a horizontal uniaxial stressed medium based on the weak-anisotropy approximations in stressed media and coefficients of approximate P-wave reflection in anisotropic media. We inverse the magnitudes of uniaxial stress according to the presented expression by P-wave reflection coefficients and compare the inversed results with those from coefficients of S-wave reflection. The results show the simple formulations given in this paper are stable and useful except incident degree is close to zero, and the precisions of inversed stress become better than those from unrevised relationships of coefficients of S-wave reflection. Therefore, the expression of inverted uniaxial stress by P-wave reflection coefficients may be helpful to us to estimate the magnitude of stress using P-wave data. Presentation Date: Tuesday, October 18, 2016 Start Time: 1:25:00 PM Location: 150 Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2009 SEG Annual Meeting, October 25–30, 2009

Paper Number: SEG-2009-3495

...:

**Magnitude**of the exact PP-wave**reflection**coef- ficient**at**a VTI/isotropic interface for different inhomo- geneity**angles**. The quality factors are Q = QP0,1 = 2QS0,1 = 2QP0,2 = 4QS0,2; the other model parameters are listed in Table 1. The asymmetry of the**reflection****coefficient**with respect to = 0...
Abstract

ABSTRACT Such reservoir rocks as heavy oils are characterized by significant attenuation and, in some cases, attenuation anisotropy. Here, we discuss the influence of attenuation on PP- and PS-wave reflection coefficients for anisotropic media with the main emphasis on models with VTI (transversely isotropic with a vertical symmetry axis) symmetry. Concise analytic solutions obtained by linearizing exact plane-wave reflection coefficients are verified by numerical modeling. To make a substantial contribution to reflection coefficients, attenuation has to be strong, with the quality factor Q, not exceeding 10. For such highly attenuative media, it is also necessary to take attenuation anisotropy into account if the magnitude of the Thomsen-style attenuation-anisotropy parameters is relatively large. Our formalism also helps to evaluate the influence of the inhomogeneity angle (the angle between the real and imaginary parts of the slowness vector) on reflection coefficients. A nonzero inhomogeneity angle of the incident wave introduces additional terms into both PP- and PS-wave reflection coefficients, which makes conventional AVO (amplitude-variation-with-offset) analysis inadequate for strongly attenuative media. The linearized solutions developed here can be used in AVO inversion for highly attenuative reservoirs.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015

Paper Number: SEG-2015-5924279

..., 2009) can be constructed so as to respond to

**small**-**angle**backscattered data, e.g., pre-critical specular**reflections**, in a manner consistent with linearized inverse scattering and AVO inversion (Innanen, 2014). This means a multi-parameter**reflection**FWI updating scheme can be protected against...
Abstract

Summary In standard seismic full waveform inversion updates (e.g., of Gauss- Newton type) small angle, backscattered amplitudes are incorporated linearly. Making an effort to include nonlinearity in each update may be useful, however, both for estimation of difficult-to-discriminate parameters such as density, and for improvement of convergence rates. We consider, in a theoretical scalar environment, one possible approach to including nonlinearity, wherein sensitivities at iteration n are computed by varying the field associated with the n+1th, rather than nth, model iterate. This produces an extended, series form, sensitivity expression. To understand the basic character of updates based on these revised sensitivities, the expression is truncated at second order, and the resulting Gauss-Newton-like updates are analyzed to expose their use of 1st and 2nd order reflectivity information. Differences between standard and nonlinear updates suggest that the latter may hold promise for the effective incorporation of high angle and high contrast reflectivity information in FWI. Introduction Seismic full waveform inversion updates (Lailly, 1983; Tarantola, 1984; Virieux and Operto, 2009) can be constructed so as to respond to small-angle backscattered data, e.g., pre-critical specular reflections, in a manner consistent with linearized inverse scattering and AVO inversion (Innanen, 2014). This means a multi-parameter reflection FWI updating scheme can be protected against parameter cross-talk to the same degree as AVO and linear inverse scattering. However, it also means that linearization error will be present to the same degree as it is in those other methods, and concern registered in those domains (e.g., Weglein et al., 1986) is equally applicable to FWI. Backscattered wave amplitudes are generally nonlinear in medium property variations. In the special case of two elastic half-spaces, for instance, the Zoeppritz equations define a highly nonlinear relationship between reflection coefficients and relative changes in elastic properties across a reflecting boundary. The relationship is often linearized; in the two half-space example, the Aki-Richards approximation, which is linear in the relative changes (Aki and Richards, 2002; Castagna and Backus, 1993; Foster et al., 2010), is commonly used in AVO inversion. Linearization error takes the form of a decrease in accuracy with an increase of incidence angle and/or magnitude of relative changes. This is one reason in AVO/AVAZ inversion why density is difficult to separate from VP (e.g., Stolt, 1989), and why certain anisotropic parameters are difficult to determine (e.g., Mahmoudian et al., 2013). These parameters are best distinguished at high angle, where the Aki- Richards formula and its extensions are insufficiently accurate. In FWI, nonlinearity is primarily accommodated through iteration. Nevertheless, mitigating linearization error within individual FWI updates could play an important role, in principle making available to FWI both (1) the improved parameter discrimination known to be possible at large scattering angles, and (2) an uplift in convergence rate. Linearization error has been mitigated in inverse scattering environments (Weglein et al., 2003; Zhang and Weglein, 2009a,b) and AVO environments (e.g., Stovas and Ursin, 2001; Innanen, 2011, 2013). In this paper we consider means by which nonlinearity can also be at least partially accommodated during FWI iterations—specifically, if it is possible to make changes to the basic ingredients of FWI such that an update naturally accommodates nonlinearity in the reflectivity/ step length relationship. General nonlinear sensitivity formalisms have been discussed in the literature, in a seismic context by Wu and Zheng (2014) and elsewhere (e.g., in optical tomography by Kwon and Yazici, 2010). Here we will discuss the construction of very particular, analyzable FWI update formulas that have direct expression in terms of nonlinear operations on the residuals.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, January 24–26, 2017

Paper Number: SPE-184873-MS

... in Fig. 15 (Case 3-1) and Fig. 16 (Case 3-2), the fracture propagates by following the pre-damage zone in calcite in both the stress initialization settings. A pre-damage zone appears in calcite when the fracture approaches the clay-calcite interface

**at**a right**angle**( Fig. 15 (a), (d) and Fig...
Abstract

Most hydraulic fracturing models assume that the rock is homogeneous at a pore scale. However, reservoirs are highly heterogeneous at all length scales. Pore scale heterogeneity is evident from thin sections and scanning electron microscopic images (SEM). Heterogeneity at larger length scales is evident from logs and cores. In this paper, the effect of micro-scale (pore and core scale) heterogeneities caused by varying mineral composition and the presence of pores and microfractures, on fracture propagation has been investigated. A model that solves the solid displacements and fluid pressures both inside and outside the fracture and allows for the creation and propagation of multiple fractures is presented. This peridynamics-based hydraulic fracturing model is used to model the growth of multiple, complex fractures in a heterogeneous rock. Thin section and SEM images of rocks are used to represent the geometry of the rock grains and the pores in several rock samples. Far-field stresses are then applied and a fluid induced fracture is propagated in the rock matrix. The results of the model reveal that the stress distribution and the fracture geometry can be quite complex at the micro-scale. Fracture branching and turning is induced by variations in elastic moduli and stress concentration at the grain scale. The microstructure of the fracture is, therefore, determined by the geometry and distribution of mineral grains, their mechanical properties, and the initial stress anisotropy due to the co-existence of different mineral grains. A similar effect is observed at the core scale where differences in the microstructure of the rock can result in stress concentration at layer boundaries. For example, we show that the presence of a brittle mineral like calcite in the rock matrix causes fractures to branch at the mineral interface. Multiple fractures are shown to open, some that may not be in hydraulic contact with each other. As the fracture propagation continues, only the least tortuous path remains open. All other branches are bypassed hydraulically and are eventually closed. This fracture complexity occurs despite macroscopic stress anisotropy. Several examples of fracture propagation in rocks that are heterogeneous at a pore scale are provided to show that such fracture complexity should be expected in most lithologies. These results clearly show that while we have traditionally represented fractures as planes perpendicular to the minimum horizontal stress, the fracture surfaces may indeed be much more complex due to existence of different minerals grains with widely different mechanical properties. Cracks can form away from the crack tip along planes of weakness. These damage zones resulting from strains induced by fracture propagation may explain the creation of the stimulated reservoir volume (regions of enhanced permeability) around fractures in shale reservoirs.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2013 SEG Annual Meeting, September 22–27, 2013

Paper Number: SEG-2013-0842

...-

**angle**-depended**reflection**and**transmission**in three classes reservoirs To systemically illustrate dispersion effects on**reflection**and**transmission****coefficient****at**arbitrary incident**angles**, we chose three reservoir models correspond to class I, II and III AVO anomalies. Following Ren et al. (2009...
Abstract

Summary Frequency-angle-dependent reflection and transmission at an interface between a non-dispersive medium and patchy-saturated dispersive medium are analyzed on three reservoir models, which correspond to AVO Class I, II and III. The reflection and transmission of PP and PS wave show district behavior in frequency domain and incident-angle domain. Amplitude versus frequency variation (AVF) depends much on velocity dispersion and attenuation rather than impedance contrast. P-wave reflection is also investigated for fluid-saturated porous rock in presence of planar fractures. Numerical example reveals that fractures can affect the AVO classification, and soft fracture can cause velocity dispersion and AVF anomalies. These features may be helpful for characterization of fractured reservoirs.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2000 SEG Annual Meeting, August 6–11, 2000

Paper Number: SEG-2000-2020

...

**transmission**filtering effect introduced by the presence of high amplitude coal reflectors. Results indicate that the amount of variation in the**transmission**filters with**angle**(or offset) is**small**compared to the**magnitude**of the basic spectral notching effect common to all offsets. Comparison of**transmission**...
Abstract

Summary Reflectivity modeling is performed using well log data from several Western Canadian Basin (WCB) wells in order to investigate the angle-dependent transmission filtering effect introduced by the presence of high amplitude coal reflectors. Results indicate that the amount of variation in the transmission filters with angle (or offset) is small compared to the magnitude of the basic spectral notching effect common to all offsets. Comparison of transmission filters computed using acoustic and elastic algorithms indicates that both interbed multiples and mode conversions contribute to the observed offset variation. While spiking deconvolution succeeds in removing the transmission filter effects on clean synthetics, it may break down in the presence of moderate random noise.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 5–8, 2020

Paper Number: PSIG-2002

... material, as presented, does not necessarily

**reflect**any position of the Pipeline Simulation Interest Group, its officers, or members. Papers presented**at**PSIG meetings are subject to publication review by Editorial Committees of the Pipeline Simulation Interest Group. Electronic reproduction, distribution...
Abstract

Pipeline capacity results derived from any hydraulic models are heavily dependent on several assumptions including ambient ground temperature and heat transfer. This paper presents a simplified approach to identify and validate ambient soil temperatures along with determining the heat transfer coefficient to be utilized in transient hydraulic models. The proposed method entails linear regression and statistical analysis of empirical ground temperature data, as well as utilization of parametric modeling techniques to adjust heat transfer coefficients by comparing results with SCADA data.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2007 SEG Annual Meeting, September 23–28, 2007

Paper Number: SEG-2007-0254

... the AVO response (AVOaz response) of fractured reservoirs is usually modeled using equations for

**reflection****coefficients**obtained for plane waves. However, the plane wave approximation can break down**at**long offsets where incidence**angle**approaches the critical**angle**. Since azimuthal variation of AVO...
Abstract

Summary Azimuthal variation of the AVO response (AVOaz response) of fractured reservoirs is usually modeled using equations for reflection coefficients obtained for plane waves. However, the plane wave approximation can break down at long offsets where incidence angle approaches the critical angle. Since azimuthal variation of AVO response is often more noticeable at large offsets (and can be rather weak), spherical wave effects must be carefully analysed and taken into account. In order to analyse these effects quantitatively we performed an AVOaz laboratory experiment under fully controlled conditions, and then numerically simulated this experiment. The AVOaz response of a physical model is studied in the laboratory with finely layered Plexiglas simulating vertical fractures. Transmission measurements are performed to construct the elasticity tensor for the HTI model. This elasticity tensor is used as an input into numerical simulations which are performed using an anisotropic full-wave reflectivity algorithm. The comparison of the experimental data with simulations shows a very good match for the isotropic case and good qualitative agreement for the azimuthal variations. The agreement is especially good for critical angles extracted by picking inflection points on AVO curves for at each azimuth. This shows that (1) reflection measurements are consistent with the transmission measurements; (2) the anisotropic numerical simulation algorithm is capable of simulating subtle azimuthal variations with excellent accuracy; (3) the methodology of picking critical angles on seismograms using the inflection point is robust, even in the presence of random and/or systematic noise. Introduction In recent years variations of the AVO response with azimuth (AVOaz response) have been increasingly used for the characterisation of fractured reservoirs. However up until now in many cases the interpretation of such multiazimuthal data set has been qualitative, and focused on estimating fracture and/or stress direction. With novel processing methods which enable preservation of the long offset data, quantitative interpretation becomes feasible. Quantitative interpretation requires a good understanding of the AVOaz response as a function of medium parameters. Behaviour of plane-wave reflection coefficients in anisotropic media and their azimuthal variations can be analysed using an extension of the Zoeppritz equations to anisotropic media (Musgrave, 1970; Schoenberg and Potazio, 1992), and is well understood. More recently, Tsvankin (1996) and Rüger (1997) have derived concise and robust approximate relationships for reflection coefficients, which extend to anisotropy from the wellknown isotropic AVO approximations. While the theory has been derived for plane waves it is known that seismic surveys utilise localised sources which produce spherical, rather than plane waves. Nevertheless, the plane wave approximation for reflection coefficients is assumed to be quite accurate for typical hydrocarbon exploration target depths and is routinely used in isotropic AVO analysis and inversion. However, it is well known that plane wave approximations can break down at long offsets where the incidence angle approaches the critical angle. Since azimuthal variation of AVO response is often more noticeable at large offsets (and can be rather weak), spherical wave effects must be carefully analysed and taken into account.

Proceedings Papers

Paper presented at the The 27th International Ocean and Polar Engineering Conference, June 25–30, 2017

Paper Number: ISOPE-I-17-659

... is the depth

**at**the seaward toe of the structures. From the results, which include**reflection**and**transmission****coefficients**and velocity and vorticity fields, it is revealed that the crest width affects the wave and flow behavior in the leeward side of LC breakwaters. KEY WORDS: Low-Crested...
Abstract

ABSTRACT Low-crested (LC) rubble mound breakwaters, whose crest level is at the still water level (SWL), represent an environmentally friendly method for shore protection. Numerical simulations of the flow field induced by wave overtopping over these structures were performed. Three different cases of breakwaters were examined with crest width equal to d , 2 d and 3 d , where d is the depth at the seaward toe of the structures. From the results, which include reflection and transmission coefficients and velocity and vorticity fields, it is revealed that the crest width affects the wave and flow behavior in the leeward side of LC breakwaters. INTRODUCTION LC rubble mound breakwaters, which are characterized by frequent overtopping, are widely used for coastal protection. The main advantage of these structures is their mild aesthetic impact on the natural environment. As the waves approach and transmit over these structures, significant hydrodynamic processes occur in their proximal area. In the seaward side, the most important processes are wave breaking and reflection, while in the leeward side wave overtopping and transmission (Garcia et al., 2004). Many researchers have studied the hydrodynamics of flow in the vicinity of such structures, as well as the influence of their geometrical characteristics on the flow field. However, most of these structures are either emerged or submerged, while the case in which the crest level of the breakwaters is at the still water level has to be further investigated. Losada et al. (1996) examined the effect of the incident wave obliqueness of a non-breaking wave on a porous breakwater, placed on a sloped bottom, as well as the effect of the geometrical characteristics of the breakwater and porosity on the kinematic and dynamic characteristics of the flow around the breakwater. More specifically, they studied the influence of the above parameters on wave reflection, transmission and energy dissipation, assuming ideal flow. From their results, it was indicated that wave reflection was significantly affected by the obliqueness of the incident waves, while wave transmission was not. Regarding the geometry of the structures, it was found that the crest width influences the processes of reflection and transmission of waves, while the effect of the sloped bottom (where the breakwater is placed) is negligible. It is important to note that this behavior might change under the influence of breaking waves. Finally, it was also found that porosity affects wave transmission significantly.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Annual Technical Conference and Exhibition, October 26–29, 2020

Paper Number: SPE-201563-MS

... modify the

**transmissibility**in the advective flux for the fracture blocks. The fracture deformation is implicitly combined with the matrix deformation, and the fracture effect is**reflected**through the pore pressure changes of the matrix gridblocks intersected by the fracture segments.**At**a given time...
Abstract

The depletion of producing layers leads to significant stress changes in adjacent targets, especially when complex natural fractures are present. Due to weak bedding interfaces or small stress barriers, hydraulic fractures can easily penetrate neighboring layers, and this further increases the chance of multilayer stress disturbance. In this work, we investigate the effects of vertical fracture complexity, i.e., hydraulic fracture penetration and interlayer natural fracture existence, on stress interference between different layers using a data set from a typical shale gas well in the Sichuan Basin. Two geological contexts, i.e., without interlayer natural fractures (w/o INF) and with interlayer natural fractures (w/ INF), are considered under different degrees of fracture penetration and interlayer connectivity. An in-house iteratively coupled geomechanics and compositional reservoir simulator is used to model the three-dimensional pressure and stress changes. The non-uniform hydraulic fractures and stochastic natural fractures are incorporated in our coupled simulation with an embedded discrete fracture model (EDFM). Comprehensive spatial-temporal stress analysis quantifies the approximate range of orientation change of S Hmax and magnitude change of S hmin under various reservoir conditions. Numerical results indicate that the presence of natural fractures in the interlayer upgrades the risk of stress interference between different pay zones. A larger hydraulic fracture penetration increases gas production, but also exerts a significant impact on stress reorientation and redistribution in the upper potential layer. The orientation change of S Hmax along the prospective infill location is below 10 degrees in the w/o INF cases but up to 30 degrees in the w/ INF cases with a moderate number of interlayer natural fractures. The average magnitude change of S hmin is within 3.5 MPa along the prospective infill location for most w/o INF cases, whereas that in the w/ INF cases is above 10 MPa at most times. Moreover, the existence of natural fractures in the interlayer brings forward the occurrence of maximum orientation change in the upper layer by around one year. While inducing non-negligible stress drop in the upper layer, higher interlayer matrix permeability does not significantly reorient the horizontal principal stresses. Varying the density of interlayer natural fractures not only affects the stress magnitude but also causes considerable orientation change in the upper layer. The findings from this work help understand the extent of stress interference in the upper potential layer of the Sichuan Basin under different vertical fracture complexities. It is of guiding significance for future hydraulic fracture design and child-well operations in similar highly fractured tight formations.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2008 SEG Annual Meeting, November 9–14, 2008

Paper Number: SEG-2008-0269

... intercept and gradient, which satisfies the inversion precision only

**at****small**incidence**angles**. However, this may not be the optimum approach for converted-wave AVO analysis since the signal to noise (S/N) ratio is often very low for converted waves**at****small**incidence**angles**, and the concept of intercept...
Abstract

Summary Using the empirical Gardner equation describing the relationship between density and compressional wave velocity, we propose converted wave reflection coefficient extreme attributes for AVO analysis and derive relations between the extreme position and amplitude, average velocity ratio across the interface, and shear wave reflection coefficient. The extreme position is a monotonically decreasing function of average velocity ratio, and the extreme amplitude is a function of average velocity ratio and shear wave reflection coefficient. For theoretical models, the average velocity ratio and shear wave reflection coefficient are inverted from the extreme position and amplitude obtained from fitting a power function to converted wave AVO curves. Shear wave reflection coefficient sections have clearer physical meaning than conventional converted wave stacked sections and establish the theoretical foundation for geological structural interpretation and event correlation. The method of inverting average velocity ratio and shear wave reflection coefficient from the extreme position and amplitude obtained from fitting a power function is applied to real CCP gathers. Introduction Amplitude versus Offset (AVO) is used to analyze the relationship between seismic amplitude, lithology and pore fluid properties in order to invert reservoir elastic parameters and predict hydrocarbon distributions. The foundation of the AVO technique is based on the Zoeppritz equations (Zoeppritz, 1919), but though these equations can describe the variation of PP (incident P wave, reflected P wave) and PS (incident P wave, reflected S wave) reflection coefficients, they are mathematically complex and are usually not applied directly in practice. With the development of converted wave exploration, AVO analysis of PS waves is extensively used to describe and predict reservoirs. In contrast to compressional (PP) waves, the amplitude variation with offset for converted (PS) wave data is related only to the contrast of density and shear wave velocity as well as the average velocity ratio. The significance of this result is that it is possible to estimate the density of the rock in a reservoir directly from PS AVO inversion. Currently, one common simplification for P-wave AVO analysis is to use a two-term approximation which consists of an intercept and gradient, which satisfies the inversion precision only at small incidence angles. However, this may not be the optimum approach for converted-wave AVO analysis since the signal to noise (S/N) ratio is often very low for converted waves at small incidence angles, and the concept of intercept and gradient is not really applicable. At middle to far offset the converted wave amplitude reaches an extreme, and the S/N ratio is higher. Therefore, we propose to make use of the extreme position and amplitude to perform converted-wave AVO analysis. This utilizes the best of high S/N ratio data within the middle offset range, and makes it possible to invert for the average velocity ratio and shear wave reflection coefficient from the extreme position and amplitude. AVO Attributes of Converted Waves Aki and Richards (1980) showed an AVO approximation to the Zoeppritz equations (Zoeppritz, 1919) which are derived on the assumption of small contrasts in elastic properties across an interface.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the 54th U.S. Rock Mechanics/Geomechanics Symposium, June 28–July 1, 2020

Paper Number: ARMA-2020-1734

... errors because the borehole tele-viewer is unable to monitor the fracture initiation

**at**the moment of rock fracture. Thus, the new constraint model is proposed to calculate the**magnitude**of SHmax in this study. Given that in-situ stress in the crust is limited by the frictional**coefficient**of faults...
Abstract

The oilfield micro-seismic tests showed that the occurrences and forms of hydraulic fractures near the fault plane were ambiguous when the fracturing stimulations operations were carried out in the conglomerate reservoirs in Karamay city, Xinjiang province, China. The original rock stress controls the fracture propagation and the effect of hydraulic fracturing. In this study, the magnitudes and orientations of principal horizontal stresses were calculated by the newly established lateral pressure coefficient polygon and borehole image logging data. The results showed that principal vertical stress Sv was not always the minimal principal stress under the reverse fault stress regime because of the lithological interface, it explained that the initiation and propagation of hydraulic fractures are inconclusive in fault-block reservoirs. Furthermore, sandstone formation in the hanging wall and footwall tends to form horizontal fractures, while mudstone formation tends to produce vertical fractures. The proposed method could figure out the stress field orientation and magnitude around a reverse fault plane effectively in fault-block reservoirs and predict the fracture morphology and propagation path. Results could provide insight for preventing drilling fluid losses and casing damage in fault-developed reservoirs, optimizing borehole azimuth, and improving fracturing design. 1. INTRODUCTION The knowledge of stress magnitudes and orientations at great depth is of considerable interest in both the geologic science and engineering application. One of the most important uses of the in-situ stress data in the petroleum industry associates with wellbore instability (Zoback et al. 2003). How to characterize the in-situ stress in fault-block reservoirs is a challenging task. Fault structure, topographic loading, buried depth, sedimentary structure, disconnection with basement, geological structure (anticlines, salt domes, joints), and formation lithology changes have significant influence on local variations in the measurement of in-situ stress orientation (Yale. 2003). Zoback et al (1987) propose an analytical method in delimiting the range of in-situ stress in terms of stress polygon, which defines the possible stress regimes at a particular depth for given pore pressure ( p p ) and assumes coefficient of fault friction µ (usually taken to be 0.6). These stresses regimes are sensitive to unconfined compressive strength (UCS), breakout width (BOs), overpressure ratio, and friction coefficient (Huffman and Saffer. 2015; Zoback. 2007). A poroelastic method is raised to predict the 3D in-situ stress and pore pressure fields in shale reservoir with finite faults, which have reservoir stratigraphy as well as fault dimension and slip acquired from the interpretation of the seismic profile (Lin et al., 2018). Studies on in-situ stress orientation and magnitude along the San Andreas Fault and other major continental transforms provide key evidence that shear stress resolved on the fault are far lower than those predicted by the typical rock friction coefficients (Mount and Suppe. 1987). The oilfield measurements of in-situ stress show that the horizontal stresses are highly dependent on lithology, Coal seams and shales have much higher the minimum horizontal stress S hmin than the adjacent sandstones (Gunzburger and Magnenet. 2014). Previous studies focus on the analysis of the magnitude and orientation of in-situ stress, but few mentioned the law of fracture occurrences and propagation near the fault plane.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, January 23–25, 2018

Paper Number: SPE-189901-MS

... samples for a 30° fault orientation. The variation of μ with respect to the fault orientation is also summarized in Figure 2 . The

**coefficient**of friction for both PMMA and Solnhofen limestone tends to slightly reduce as the fault**angle**approaches 60° and becomes less steep. The reduction in μ**at**less...
Abstract

Enhanced reservoir connectivity generally requires maximizing the intersection between hydraulic fracture (HF) and preexisting underground natural fractures (NF), while having the hydraulic fracture cross the natural fractures (and not arrest). We have studied the interaction between a hydraulic fracture and a polished saw-cut fault. The experiments include a hydraulic fracture initiating from a pressurized axial borehole (using water) that approaches a dry fault that is inclined at an angle θ with respect to the borehole axis. The experiments are conducted on Poly(methyl) Meta Acrylate (PMMA) and Solnhofen limestone, a finely grained (<5 μm grain), low permeability (<10 nD) carbonate. The confining pressure in all experiments is 5 MPa, while the differential stress (1-80 MPa) and approach angle, θ (30, 45, 60, 90°) are experimental variables. During the hydraulic fracture, acoustic emissions (AE), slip velocity, slip magnitude, stress drop and pore pressure are recorded at a 5 MHz sampling rate. A Doppler laser vibrometer measures piston velocity outside the pressure vessel to infer fault slip duration and a strain gauge adjacent to the saw-cut provides a near-field measure of axial stress. For PMMA, the coefficient of friction was 0.30 and sliding was unstable (stick-slip). The approaching HF in PMMA created a tensile fracture detected by AE transducers ~100 μs before the significant stick-slip event (45% stress drop and slip velocity of ~60 mm/s) and was arrested by the fault at all fault orientations and differential stresses, even at 90° fault orientation and 80 MPa differential stress. For Solnhofen limestone, we observed stable sliding at a coefficient of friction of 0.12. In contrast to PMMA, the HF in Solnhofen consistently crossed to the other side of the fault. When the HF crossed the fault, it produced a small stress drop (<10%) and slip velocity of only 0.5 mm/s. Theoretical models by Blanton (1986) and Renshaw and Pollard (1995) predict that HF will be arrested for Solnhofen limestone and cross PMMA 90° fault at 80 MPa differential stress. Although the exact cause for the discrepancy between experiments and the theory is not known, one feature present in the experiments but not considered in the models, is the diffusion of fluid driven by the fault slip. Thus, the formation of a "fluid-filled patch" on the fault surface as it is intersected by the HF may substantially impact the crossing/arrest behavior. The approach angle and differential stress also influence the HF initiation azimuth and breakdown pressure. In most cases, the HF initiation azimuth was normal to the fault strike. These observations suggest that the presence of natural fractures could result in rotation of hydraulic fractures to be more normal to their strike and a subsequent change in the downhole pressure recordings. The latter could be used as a diagnostic tool for predicting this interaction.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Western Regional Meeting, April 23–26, 2019

Paper Number: SPE-195344-MS

...). The value of maximum principal stress was then determined from the value of friction

**coefficient**used in that simulation. To allow the initial fracture**transmissivity**to vary over several orders of**magnitude**, e 0 was scaled such that the logarithm of e 0 3 /12 varied uniformly between -17 and...
Abstract

Productive zones or "sweet spots" in unconventional reservoirs depend on their geomechanical and petro-physical rock properties. Machine learning algorithms can significantly improve workflows used for evaluating sweet-spots in such complex reservoirs. The objectives of this paper are to: (i) quantity the effects of rock mechanical properties on fracturing treatments using data analytics and (ii) use regression-based machine learning algorithms and improve sweet-spot assessment in complex mudrock reservoirs. We used a hydraulic fracturing simulator that couples fluid-flow with fracture deformation in discrete fracture networks to model field-scale hydraulic fracturing treatments. First, we selected several geomechanical properties related to rock fracability. We obtained wide variation in aforementioned properties using a quasi-random design approach. Then, we performed 200 slick-water fracturing simulations with quasi-random distribution of design parameters using the hydraulic fracturing simulator. We quantified the performance of fracture treatments by calculating the effective short- and long-term Stimulated Reservoir Volume of the reservoir (SRV). We finally analyzed the results of numerical simulations by applying regression analysis to improve the assessment of sweet-spots in complex reservoirs. The regression analysis involved the following simulation variables: shear modulus, poisson's ratio, fracture friction coefficient, principal horizontal stress anisotropy, fracture toughness, fracture closure stress, shear dilation angle, and initial fracture aperture. The SRV results were analyzed using: linear regression, linear regression with beta coefficients, ridge and lasso regression, and principal component regression algorithms. The regression analysis revealed that linear models can explain 73.1% and 59.2% variance in short- and long-term SRV values, respectively. The ridge and lasso regression and beta linear regression analysis revealed that stress anisotropy, fracture dilation angle, and fracture friction coefficient show the highest effect on the aforementioned SRV values. In all the regression models, shear modulus and critical fracture toughness did not have a significant effect on SRV but these parameters are important as they are correlated to other parameters that directly impact fluid flow. The results of using data analytic approaches demonstrated that factors related to unpropped fracture conductivity play a critical role in success of hydraulic fracturing treatments. We have also introduced and compared the performances of different machine learning algorithms that might be used to assess the impact of geomechanical properties on fracturing treatments. Such supervised and unsupervised machine learning algorithms can help in integrating legacy field data in the analysis of productive zones in complex reservoirs. Such analysis can also be used to develop data-based models that might improve the study of sweet-spot and fracturing treatment performance assessment in complex reservoirs.

Proceedings Papers

Publisher: NACE International

Paper presented at the CORROSION 2021, April 19–30, 2021

Paper Number: NACE-2021-16404

..., Ni increases the low-temperature fracture toughness due to grain refinement and modification of the ferrite properties. 6 Furthermore, Ni has a low impact on weldability as

**reflected**by its carbon equivalent**coefficient**, which is the lowest compared with other alloying elements. 1 16404...
Abstract

Abstract Low Alloy steels (LASs) are, by volume, the most widely used alloy family in critical oil & gas (O&G) components. However, the strength and hardness of LASs for sour environments are limited to prevent different forms of hydrogen embrittlement, such as hydrogen stress cracking (HSC) and sulfide stress cracking (SSC). Moreover, ISO 15156-2 (1) restricts LASs to a maximum of 1 wt% Ni due to SSC concerns. In the present work, the hydrogen diffusivity of the nuclear-grade ASTM(2) A508 Gr.4N LAS was measured using the hydrogen permeation method. Results are linked to quenched and tempered (Q&T) microstructure features characterized by transmission electron microscopy (TEM). Additionally, a comparison was made between the A508 Gr.4N and a ferritic-pearlitic steel with similar Ni content. This work is connected with the HSC evaluation of the same alloy by slow strain rate testing (SSRT) described in a separate publication. Material requirements for unconventional Oil and Gas environments Due to the progressive depletion of conventional oil and gas (O&G) reserves, the energy demand drifts its attention to unconventional reservoirs. 1 These new O&G fields pose challenges to the materials used that are often associated with high-pressure (>103 MPa) and high temperature (>177 °C) or, in arctic service, temperatures as low as -60°C. 1-3 Moreover, the presence of atomic hydrogen produced either from corrosion reactions or by cathodic protection can lead to hydrogen stress cracking (HSC). In sour environments, the cracking mechanism is referred to as sulfide stress cracking (SSC) in which H 2 S acts as a hydrogen recombination poison and increases severity. Materials susceptible to hydrogen embrittlement (HE)—by either HSC or SSC—characterized by ductile behavior under normal circumstances, can fracture in a brittle mode in the presence of atomic hydrogen. Therefore, materials selection is paramount to reduce possible catastrophic failures. Use of high strength low alloy steels for sour service applications Low alloy steels (LASs) are widely used because of their low cost and good mechanical properties. 1 By appropriate heat treatment processing, a high yield strength (e.g., 690 MPa (100 ksi)) can be achieved while retaining adequate toughness. The hardenability can be enhanced by the addition of alloying elements such as molybdenum, chromium, and nickel. 4 Nickel additions produce an increase in yield strength (YS) due to solid solution strengthening and subgrain size reduction. 1, 5 Hardenability is improved with Ni as it stabilizes the austenite phase, delaying the austenite to martensite transformation. 1 Additionally, Ni increases the low-temperature fracture toughness due to grain refinement and modification of the ferrite properties. 6 Furthermore, Ni has a low impact on weldability as reflected by its carbon equivalent coefficient, which is the lowest compared with other alloying elements. 1

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