A Decoupled Fracture- and Stress-Induced PP-wave Reflection Coefficient Approximation for Azimuthal Seismic Inversion in Stressed Horizontal Transversely Isotropic Media

Anisotropy is widespread in the Earth’s crust, and VTI (vertical axis symmetry transverse isotropy) anisotropy is common due to stratigraphic pressure. Disregarding anisotropy leads to inaccurate inversion results in VTI media. To estimate accurate elastic parameters, the exact reflection coefficient equation of VTI media should be used. This equation is nonlinear and more accurate than the commonly used linear reflection coefficient equation. Although the inversion based on the VTI anisotropy exact reflection coefficient equation is a complex nonlinear inversion problem, it is still computable. Therefore, for VTI media, we derive the objective function combining Bayesian theory and use the iterative reweighted least squares method for a fast and stable solution. Adding Bayesian theory can improve the robustness of the algorithm. The accuracy and noise immunity of the method is tested with synthetic data. Finally, the method is applied on field data and obtains accurate elastic parameters. The results can provide an understanding of subsurface formations and serve as the base data for calculating fluid and fracture distribution.

/pdf/a-vti-anisotropic-media-inversion-method-based-on-the-exact-2ogpt5er.pdf

A VTI anisotropic media inversion method based on the exact reflection coefficient equation

/pdf/rock-physics-based-velocity-porosity-correlations-developed-164o9oa6.pdf

Rock physics based velocity-porosity correlations developed for estimation of the elastic properties of the Bakken formations of the Williston Basin, North Dakota

Abstract In this study, the elastic characteristics of reservoir rocks and their relationship to porosity and pore fluid were predicted using the fluid substitution method in combination with machine learning techniques. We first discarded the data at gas points to remove the erroneous effect of gas on the prediction process of Poisson’s ratio using the three proposed machine learning models. Then, the prediction was carried out after substituting the gas zones by oil and by water. As a result, the prediction was enhanced and showed stronger correlation coefficient values. The integration of fluid substitution and machine learning methods was applied in the reservoir of Scarab field as a case study from the Eastern Mediterranean to detect the effect of different pore fluids (gas, oil, and water) on Poisson's ratio estimation. The main objective of the study was to analyze the seismic and well log data to estimate and predict the Poisson’s ratio in four fluid-content cases; these are gas-bearing reservoir, reservoir after removal of log data of gas-bearing zones, and reservoirs after gas-substitution with oil and with water. These four cases were dealt with directly and by using the machine learning algorithms based on the proposed model of random vector functional link (RVFL), which was enhanced by the Cheetah optimizer (CO). This study shows how the performance of RVFL is affected by the presence or absence of gas zones. It is shown that the Poisson’s ratio value increases when gas is substituted with water more than when gas is substituted with oil. For validation of these results, regression analysis technique was used and the correlation coefficient of the CO–RVFL model increased after removing well log data of gas zones and was more enhanced after fluid substitution from gas to oil or to water. 

/pdf/contribution-of-fluid-substitution-and-cheetah-optimizer-395gb8gd.pdf

Contribution of Fluid Substitution and Cheetah Optimizer Algorithm in Predicting Rock-Physics Parameters of Gas-Bearing Reservoirs in the Eastern Mediterranean Sea, Egypt

The acoustical-electrical (AE) properties of reservoir rocks are affected by their microstructure (pores, microfractures, cracks and their geometry) and saturating fluids. To aid the interpretation, digital rock physics (DRP) is a useful technique to characterize this microstructure, as well as equivalent petrophysical models (EPM) to obtain joint AE properties. We perform thin-section analysis on rocks from tight-oil reservoirs, along with X-ray diffraction (XRD) and computed tomography (CT) to study rock lithology and minerals. We also perform porosity, permeability, ultrasound, and electrical conductivity experiments as a function of confining pressure to analyze pore structure. First, the 3D digital multicomponent cores are created based on a geology-driven multiphase segmentation workflow and images of the samples, and verified based on the porosity and minerals. Then, the AE properties and permeability are calculated by using numerical simulations (finite difference and finite volume methods). Next, the rigid and microcracked (soft) porosities are determined by using the Shapiro model to create the rock skeleton. We develop a joint EPM based on the effective medium AE and the Biot-Rayleigh equations with double porosity to describe the rock properties. The ultrasonic, sonic and seismic multiple data are used to compare and analyze the two approaches. The results show that the DRP techniques based on real cores are effective in characterizing the microstructure and the proposed EPM can describe the AE properties of real rocks, indicating a potential for quantitative characterization of reservoirs. 

Acoustical-electrical models of tight rocks based on digital rock physics and double-porosity theory

Fluid Discrimination Based on Inclusion-Based Method for Tight Sandstone Reservoirs

Seismic Characterization of Naturally Fractured Reservoirs with Monoclinic Symmetry Induced by Horizontal and Tilted Fractures from Amplitude Variation with Offset and Azimuth

Horizontally transverse isotropy (HTI) induced by vertical or subvertical, aligned fractures is common for unconventional fractured porous shale oil or gas reservoirs. Compared with the unfractured rocks, the seismic response characteristics of PP-wave azimuthal amplitudes are usually disturbed by the fractures and the in-situ stresses. Knowledge of fracture properties, as well as in-situ stresses, is required to optimize horizontal well planning and hydraulic fracturing during production, and seismic inversion for in-situ stresses from the PP-wave azimuthal amplitude data in fracture-induced anisotropic media is an essential step. Using the linear-slip theory and the effective stress law, we derive the fluid-saturated effective elastic stiffness tensors parameterized by background elastic moduli, the effective stress coefficient of isotropic host rocks, fluid modulus, porosity, and fracture parameters based on the anisotropic Gassmanns fluid substitution equation. Combining the perturbations in saturated stiffness tensors and scattering theory, we formulate the reflection coefficient equation of PP-wave data as a function of background porosity-related stress parameter, and two (i.e., normal and shear) fracture weakness parameters. Following Bayes rule, we estimate the porosity-related stress parameter and fracture weaknesses using the inversion method of azimuthal Fourier coefficients. We finally compute the effective horizontal and vertical in-situ stresses using the estimated elastic moduli, porosity-related stress parameter and fracture weaknesses. Synthetic and real data sets demonstrate that our proposed inversion approach based on the derived reflection equation provides us another way to obtain reasonable estimates of in-situ stresses in a complex fractured porous shale reservoir.

Estimation of in-situ stresses from PP-wave azimuthal seismic data in fracture-induced anisotropic media

Seismic inversion is an effective way to investigate the lithology and fluid in hydrocarbon-bearing reservoirs. In addition to obtaining inversion results, probabilistic seismic prediction can be used for uncertainty evaluation. Its prior probability is usually assumed to follow a specific distribution, which limits the prediction accuracy. By considering both the p-norm and total variation (TV) constraints, an improved prior is proposed. The p-norm constraint is first introduced into the probabilistic seismic prediction, which can be reduced to other probability distribution forms. With the p-norm constraint, the probability density function is updated. Then, the posterior probability (PP) with both the p-norm and TV constraints is re-derived. By analysis, the proposed approach helps to preserve the boundary and highlight the sparsity. Compared with a specific prior distribution, the proposed prior is more flexible and can effectively improve the prediction accuracy. The proposed approach is discussed in detail in terms of probabilistic prediction by using synthetic data. Both synthetic data and field data tests demonstrate the superiority of the proposed prior. The construction of the prior with p-norm and TV constraints is of great help to improve probabilistic prediction.

Improved Prior Construction for Probabilistic Seismic Prediction

Fracture weakness is one of the most important anisotropic parameters used to characterize the fractures and identify the fluids. The model of horizontal transversely isotropic (HTI) medium is usually utilized in seismic azimuthal inversion for the fracture weaknesses. Low-frequency component of fracture weaknesses plays a significant role in seismic fracture characterization and fluid identification due to the deficiency of low-frequency component in acquired seismic azimuthal data. The commonly used approaches to estimate low-frequency component include the smoothing model constraints and the damped wave field in complex-frequency domain. Following the Bayesian framework, we propose a novel approach used for compensating the low-frequency component of fracture weaknesses in Laplace–Fourier domain. First, we reconstruct the seismic forward solver in Laplace–Fourier domain to obtain the low-frequency component of fracture weaknesses. Then, we propose a method of seismic azimuth-difference inversion for fracture weaknesses in Laplace–Fourier domain in a Bayesian framework. Finally, both synthetic and field data examples are used to demonstrate the superiority and stability of the proposed inversion approach. Compared with the conventional inversion approach, the proposed approach can reduce the dependence on the initial model of model parameters and weaken the effect of missing low-frequency components of fracture weaknesses in azimuthal seismic data, and it may help to improve the inversion accuracy of fracture weaknesses and reduce the uncertainty of inversion results.

Bayesian Seismic Azimuth-Difference Inversion of Horizontal Transversely Isotropic Media for Low-Frequency Component of Fracture Weaknesses in Laplace-Fourier Domain

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