Tangential Fracture Weaknesses Research Articles

Inversion of fracture weakness parameters based on 3C vertical seismic profile data — Part I: Horizontal transversely isotropic media composed of a single fracture set in the isotropic background media

Natural fractures in oil and gas reservoirs are a crucial factor that cannot be ignored because they significantly influence the reservoir’s petrophysical properties and hydrocarbon development. A horizontal transversely isotropic (HTI) medium composed of a single fracture set in an isotropic background is a typical anisotropic medium. Meanwhile, the S-wave splitting is a sensitive response of such anisotropic media, resulting in the generation of fast and slow S waves. The normal and tangential fracture weaknesses are crucial parameters that characterize the anisotropy of fractured media. We develop an inversion method for fracture weakness based on 3C vertical seismic profiling (3CVSP) data. First, assuming weak anisotropy and an HTI medium containing a single fracture set, we derive a first-order linear approximation of the traveltimes of the converted fast and slow S waves (PS1 and PS2 waves) with respect to fracture weakness parameters in the phase velocity domain. By solving for the horizontal projection of the slowness vector, approximate equations of the traveltimes of the PS1 and PS2 waves are converted from the phase velocity domain to the group velocity domain. Furthermore, we devise an inversion workflow consisting of three primary steps: (1) preprocessing the VSP data to derive the traveltimes and azimuth of the HTI medium, (2) constructing a forward model with undetermined fracture weakness parameters, and (3) following the establishment of the objective function, conducting the inversion for the fracture weakness parameters. We demonstrate the reliability of the method through numerical examples and synthetic 3CVSP data. The inversion errors are primarily influenced by the azimuth angle, with minimal influence from the receiver depth. Furthermore, a collective set of inverted results derived from all geophones is more stable and accurate than individual geophones. The application to actual 3CVSP data further confirms the effectiveness of our approach.

Estimating two groups of fracture weaknesses using azimuthal differences in partially incidence-angle-stacked seismic amplitudes

Geophysical and geologic data, e.g., results obtained using rock cores, outcrops, and borehole images, reveal the presence of multiple sets of fractures in rock. To analyze how fracture interactions affect seismic anisotropy and dispersion, we consider an effective model that contains two sets of orthogonal fractures. In seismic amplitude analysis, we focus on the case of subsurface target zones containing a fracture network composed of primary and secondary fracture sets. Focusing on gas-bearing rocks with small fracture densities, we formulate simplified stiffness parameters in terms of two groups of fracture weaknesses, which are related to the primary and secondary fractures, respectively. Using the simplified stiffness parameters, we derive the PP-wave reflection coefficient and the azimuthal elastic impedance (AEI) as functions of the two groups of normal and tangential fracture weaknesses. Based on the derived PP-wave reflection coefficient and AEI, we propose a method and workflow in which the azimuthal variations of the partial incidence-angle-stacked seismic data are used to estimate the AEI and differences in AEI (which we refer to as DEI) is input to a nonlinear inversion for two groups of fracture weaknesses. In the nonlinear inversion, the initial values of fracture weaknesses are obtained based on a two-term approximation of the PP-wave reflection coefficient. First- and second-order derivatives of DEI with respect to fracture weakness parameters are calculated to generate the update in the unknown parameter vector. Synthetic seismic gathers with varying signal-to-noise ratios are used to validate the robustness of the estimation. Applying the inversion method to a real data set, we obtain what we interpret to be reliable fracture weakness estimates that produce azimuthal amplitude differences matching those extracted from real seismic data. The results provide a potential tool for determining if two sets of fractures have developed in a reservoir.

Seismic characterization of fractured reservoirs with elastic impedance difference versus angle and azimuth: A low-frequency poroelasticity perspective

PP-wave azimuthal elastic impedance (EI) data inverted from azimuthal prestack seismic reflection data can be theoretically and practically used for fluid- and fracture-property discrimination in naturally porous and fluid-saturated fractured reservoirs within the exploration seismic frequency band. From the perspective of the low-frequency Biot-Gassmann theory, Russell’s fluid indicator can be stably applied to fluid identification in hard-rock fractured reservoirs. Based on the low-frequency anisotropic poroelasticity theory, we first derive an azimuthal PP-wave reflection coefficient and an azimuthal EI equation in terms of Russell’s fluid indicator (a combination of acoustic impedances and dry-rock velocity ratio without the effect of squirt flow in the seismic frequency range) and two fracture indicators (i.e., normal and tangential fracture weaknesses). Using azimuthal differences in EI data, we then develop a three-step inversion method of EI difference versus angle and azimuth. It can be used accurately to estimate the fluid and fracture indicators and characterize the sensitive properties of saturated fractured porous reservoirs. Noisy synthetic data are used to verify the stability and robustness of the proposed hierarchical impedance inversion approach. A real data set acquired over a gas-bearing fractured reservoir is also used to obtain the sensitive indicators of the fluid and fracture properties, which agree well with the well-log data. Thus, our hierarchical inversion approach provides a more straightforward and efficient manner to characterize the porous and fluid-saturated fractured reservoirs.

Azimuthal amplitude variation with offset parameterization and inversion for fracture weaknesses in tilted transversely isotropic media

The characterization of fracture-induced tilted transverse isotropy (TTI) seems to be more suitable to actual scenarios of geophysical exploration for fractured reservoirs. Fracture weaknesses enable us to describe fracture-induced anisotropy. With the incident and reflected PP-wave in TTI media, we have adopted a robust method of azimuthal amplitude variation with offset (AVO) parameterization and inversion for fracture weaknesses in a fracture-induced reservoir with TTI symmetry. Combining the linear-slip model with the Bond transformation, we have derived the stiffness matrix of a dipping-fracture-induced TTI medium characterized by normal and tangential fracture weaknesses and a tilt angle. Integrating the first-order perturbations in the stiffness matrix of a TTI medium and scattering theory, we adopt a method of azimuthal AVO parameterization for PP-wave reflection coefficient for the case of a weak-contrast interface separating two homogeneous weakly anisotropic TTI layers. We then adopt an iterative inversion method by using the partially incidence-angle-stacked seismic data with different azimuths to estimate the fracture weaknesses of a TTI medium when the tilt angle is estimated based on the image well logs prior to the seismic inversion. Synthetic examples confirm that the fracture weaknesses of a TTI medium are stably estimated from the azimuthal seismic reflected amplitudes for the case of moderate noise. A field data example demonstrates that geologically reasonable results of fracture weaknesses can be determined when the tilt angle is treated as the prior information. We determine that the azimuthal AVO inversion approach provides an available tool for fracture prediction in a dipping-fracture-induced TTI reservoir.

Estimating tilted fracture weaknesses from azimuthal differences in seismic amplitude data

Tilted transverse isotropy (TTI) provides a useful model for the elastic response of a medium containing aligned fractures with a symmetry axis oriented obliquely in the vertical and horizontal coordinate directions. Robust methods for determining the TTI properties of a medium from seismic observations to characterize fractures are sought. Azimuthal differencing of seismic amplitude data produces quantities that are particularly sensitive to TTI properties. Based on the linear slip fracture model, we express the TTI stiffness matrix in terms of the normal and tangential fracture weaknesses. Perturbing stiffness parameters to simulate an interface separating an isotropic medium and a TTI medium, we derive a linearized P-to-P reflection coefficient expression in which the influence of tilt angle and fracture weaknesses separately emerge. We formulate a Bayesian inversion approach in which amplitude differences between seismic data along two azimuths, interpreted in terms of the reflection coefficient approximation, are used to determine fracture weaknesses and tilt angle. Tests with simulated data confirm that the unknown parameter vector involving fracture weakness and tilted fracture weaknesses is stably estimated from seismic data containing a moderate degree of additive Gaussian noise. The inversion approach is applied to a field surface seismic data acquired over a fractured reservoir; from it, interpretable tilted fracture weaknesses, consistent with expected reservoir geology, are obtained. We determine that our inversion approach and the established inversion workflow can produce the properties of systems of tilted fractures stably using azimuthal seismic amplitude differences, which may add important information for characterization of fractured reservoirs.

Azimuthal Attenuation Elastic Impedance Inversion for Fluid and Fracture Characterization Based on Modified Linear-Slip Theory

The seismic attenuation should be considered while accounting for the effect of anisotropy on the seismic wave propagating through a saturated fractured porous medium. Based on the modified linear-slip theory and anisotropic Gassmann’s equation, we derive an analytical expression for a linearized PP-wave reflection coefficient and an azimuthal attenuation elastic impedance (AAEI) equation in terms of fluid/porosity term, shear modulus, density, dry normal and tangential fracture weaknesses, and compressional (P-wave) and shear (S-wave) attenuation parameters in a weak-attenuation isotropic background rock containing one single set of vertical aligned fractures. We then propose an AAEI inversion method to characterize the characteristics of fluids and fractures using two kinds of constrained regularizations in such a fractured porous medium. The proposed approach is finally confirmed by both the synthetic and real data sets acquired over a saturated fractured porous reservoir.

Azimuthally anisotropic elastic impedance inversion for fluid indicator driven by rock physics

The normal-to-tangential fracture compliance ratio is usually used as a fracture fluid indicator (FFI) for fluid identification in fractured reservoirs. With a new parameterization for fracture weaknesses, we have defined a new FFI based on azimuthally anisotropic elastic impedance (EI) inversion and fractured anisotropic rock-physics models. First, we derived a new azimuthally anisotropic EI equation with a similar expression for the isotropic and anisotropic EI parts to remove the exponential correction of EI that is attributable to weak anisotropy. Then, we built a fractured anisotropic rock-physics model used for the estimation of well-log parameters for the normal and tangential fracture weaknesses, which built the initial background low-frequency trend of fracture weaknesses. Finally, based on the azimuthally anisotropic EI inversion method with the Cauchy-sparse and low-frequency information regularization, we estimated an FFI applied to fluid identification in fractured reservoirs. Tests on the synthetic and real data demonstrate that the anisotropic parameters related to fracture weaknesses can be estimated reasonably and stably and that our method appears to provide an alternative available for fluid identification in fractured reservoirs.

McMC-based nonlinear EIVAZ inversion driven by rock physics

A single set of vertically aligned fractures embedded in a purely isotropic background medium may be considered as a long-wavelength effective transversely isotropic medium with a horizontal symmetry axis (HTI). The estimation of fracture weaknesses is essential for characterizing the anisotropy in HTI media. Using the fractured anisotropic rock-physics models and the wide-azimuth seismic data, elastic impedance inversion variation with incident angle and azimuth, or simply 'EIVAZ' for short, can be carried out for the estimation of the normal and tangential fracture weaknesses with the nonlinear Markov chain Monte Carlo (McMC) strategy. Firstly, an inversion method of nonlinear anisotropic elastic impedance (AEI) with the McMC algorithm was proposed, which is used for the inversion of nonlinear AEI information with different angles of incidence and azimuth. Then we extracted the normal and tangential fracture weaknesses directly using the ratio differences of inverted nonlinear AEI data. So we can eliminate the influence of the isotropic background elastic impedance on the anisotropic perturbation elastic impedance and obtain the normal and tangential fracture weaknesses more stably. A test on a 2D over-thrust model shows that the fracture weaknesses are still estimated reasonably with moderate noise. A test on a real data set demonstrates that the estimated results are in good agreement with the results of the well log interpretation, and our McMC-based nonlinear AEI approach appears to be a stable method for predicting fracture weaknesses.

McMC-based AVAZ direct inversion for fracture weaknesses

Considering that wide-azimuth seismic data contains abundant azimuthal amplitude information about the fractured reservoir with obvious characteristics of amplitude variation with incident angle and azimuth (AVAZ), azimuthal seismic data can be used for the inversion of anisotropic parameters in fractured reservoir. Fractured reservoir with a single set of vertically aligned fractures embedded in a purely isotropic background medium may be considered as a long-wavelength effective transversely isotropic medium with a horizontal symmetry axis (HTI). The normal and tangential fracture weaknesses are two key parameters to the evaluation of fracture properties in HTI media, thus the inversion of fracture weaknesses may be used for characterizing the anisotropy in fractured reservoir. The elastic properties of background isotropic media without fractures, however, do not cause azimuthal changes in AVAZ data compared to the fracture anisotropic properties, therefore simultaneous inversion for the background elastic parameters and fracture anisotropic parameters may be not stable. Thus we propose a method of azimuth-difference-based AVAZ direct inversion for fracture weaknesses. First, we extract the fracture symmetry axis azimuth based on the least square ellipse fitting (LSEF) method to obtain a linear AVAZ approximation. Then we build a fractured anisotropic rock-physics model for the estimation of anisotropic well-log information, building the initial background low-frequency trend of fracture weaknesses. Finally, an AVAZ direct inversion method of normal and tangential fracture weaknesses is proposed with the nonlinear Markov chain Monte Carlo (McMC) strategy. So we can eliminate the influence of isotropic background elastic properties on the fracture weakness properties and obtain the normal and tangential fracture weaknesses more stably. Tests on both 2D over-thrust model and real data demonstrate that the normal and tangential fracture weaknesses may be estimated more stably, and it turns out that fracture-developed zones can be identified using the estimated fracture weaknesses.

Azimuthal Seismic Amplitude Difference Inversion for Fracture Weakness

Fracture weakness prediction is an important task in fractured reservoir analysis. We propose a new method to use seismic amplitude differences between azimuths to estimate the normal and tangential fracture weaknesses under the assumption that the anisotropic perturbation of the reflection coefficient is mainly induced by fractures. We first derive an expression of the reflection coefficient in terms of the normal and tangential fracture weaknesses for the case of an interface separating two fractured media. Then we use the linear fitting method to get the relationship between the two fracture weaknesses, and change the variables to precondition the inversion problem. The Bayesian framework, under the hypothesis of a Cauchy distribution prior information and a Gaussian distribution likelihood function, is employed to construct the objective function, and an initial low-frequency constraint is introduced to the objective function to make the inversion more stable. The conjugate gradient algorithm is adopted to solve the inverse problem. Tests on both synthetic and real data demonstrate that the normal and tangential fracture weaknesses can be estimated reasonably in the case of seismic data containing a moderate noise, and our inversion approach appears to be a stable method for predicting the fracture weaknesses.

Azimuthal reflectivity inversion

Seismic fracture prediction is becoming a more important exploration and development problem with the growing focus on unconventional reservoirs. A non-linear inversion technique is presented to estimate layer-based fracture parameters and velocities based on azimuthal reflectivity data. The earth model assumes a single set of vertical fractures per layer parameterized in terms of linear slip parameters - the normal and tangential fracture weaknesses - and fracture strike. In addition, the background P-wave and S-wave impedances are estimated. Either the exact Zoeppritz equation or some linearization thereof is used in a convolutional modelling scheme to estimate seismic amplitude data. The inverse problem is solved in a nonlinear fashion using simulated annealing. The new technique has several advantages over performing azimuthal amplitude versus angle analysis (AVAz). The reflectivity calculation used in the new technique is more theoretically correct, allowing for the symmetry plane to change as a function of layer. The 90 degree ambiguity in estimating the symmetry plane typical of the near offset approximation also disappears. Further, there is an improvement in the isotropic parameter estimates compared to isotropic inversion since the bias introduced by neglecting anisotropy has been removed by incorporating it into the forward model. The azimuthal inversion is demonstrated on both synthetic and real seismic data.

Use of AVOA data to estimate fluid indicator in a vertically fractured medium

Microstructural attributes of cracks and fractures, such as crack density, aspect ratio, and fluid infill, determine the elastic properties of a medium containing a set of parallel, vertical fractures. Although the tangential weakness [Formula: see text] of the fractures does not vary with the fluid content, the normal weakness [Formula: see text] exhibits significant dependence on fluid infill. Based on linear-slip theory, we used the ratio [Formula: see text] — termed the fluid indicator — as a quantitative measure of the fluid content in the fractures, with g representing the square of the ratio of S- and P-wave velocity in the unfractured medium. We used a Born formalism to derive the sensitivity to fracture weakness of PP- and PS-reflection coefficients for an interface separating an unfractured medium from a vertically fractured medium. Our formulae reveal that the PP-reflection coefficient does not depend on the 2D microcorrugation/surface roughness with ridges and valleys parallel to the fracture strike, whereas the PS-reflection coefficient is sensitive to this microstructural property of the fractures. Based on this formulation, we developed a method to compute the fluid indicator from wide-azimuth PP-AVOA data. Inversion of synthetic data corrupted with 10% random noise reliably estimates the normal and tangential fracture weaknesses and hence the fluid indicator can be determined accurately when the fractures are liquid-filled or partially saturated. As the gas saturation in the fractures increases, the quality of inversion becomes poorer. Errors of 15%–20% in g do not affect the estimation of fluid indicator significantly in case of liquid infill or partial saturation. However, for gas-saturated fractures, incorrect values of g may have a significant effect on fluid-indicator estimates.