ALBERT

Description: The shear motion in Newtonian fluids, that is, the fluid vorticity, represents an intrinsic loss mechanism governed by a diffusion equation. Its description involves the trace-free part of the fluid viscous stress tensor. This part is missing in the Biot theory of poroelasticity. As a result, the fluid vorticity is not captured and only one shear wave (S-wave) is predicted. The missing fluid vorticity has implications for the propagation of S-waves across discontinuities. This becomes most apparent in the problem of S-wave propagation across the welded contact of an elastic solid with a porous medium. At such a contact, the no-slip condition between the elastic solid and the constituent parts of the porous medium, the solid frame and the pore fluid, must hold. This requirement translates into a vanishing relative motion of the fluid with respect to the solid frame, that is, the filtration field, at the contact. Nevertheless, our analysis indicates that for the Biot theory, in the low-frequency regime, a nonzero, although insignificantly small, filtration field exists at the contact. However, more importantly, the filtration field is noticeable when the transition to the high-frequency regime occurs. This constitutes a disagreement with the requirement of a no-slip boundary condition and renders the prediction unphysical. This shortcoming is circumvented by including the fluid viscous stress tensor into the poroelastic constitutive relations, as stipulated by the de la Cruz-Spanos poroelasticity theory. Then, a second S-wave is predicted that manifests as the fluid vorticity at the macroscale. This process is distinct from the fast S-wave, the other predicted S-wave akin to the Biot S-wave. We find that the generation of this process at the contact induces a filtration field equal and opposite to that associated with the fast S-wave. Therefore, the no-slip condition is satisfied and the S-wave reflection/transmission across a discontinuity becomes physically meaningful.

Description: Tight-gas sandstone reservoirs of the Ordos Basin in China are characterized by high rock-fragment content, dissimilar pore types, and a random distribution of fluids, leading to strong local heterogeneity. We model the seismic properties of these sandstones with the double-double porosity theory, which considers water saturation, porosity, and the frame characteristics. A generalized seismic wavelet is used to fit the real wavelet, and the peak frequency-shift method is combined with the generalized S-transform to estimate attenuation. Then, we establish rock-physics templates (RPTs) based on P-wave attenuation and impedance. We use the log data and related seismic traces to calibrate the RPTs and generate a 3D volume of rock-physics attributes for the quantitative prediction of saturation and porosity. The predicted values are in good agreement with the actual gas production reports, indicating that the method can be effectively applied to heterogeneous tight-gas sandstone reservoirs.

Description: The complete characterization of a reservoir requires accurate determination of properties such as the porosity, gamma ray, and density, among others. A common workflow is to predict the spatial distribution of properties measured by well logs to those that can be computed from the seismic data. In general, a high degree of scatter of data points is seen on crossplots between P-impedance and porosity, or P-impedance and gamma ray, suggesting great uncertainty in the determined relationship. Although for many rocks there is a well-established petrophysical model correlating the P-impedance to porosity, there is not a comparable model correlating the P-impedance to gamma ray. To address this issue, interpreters can use crossplots to graphically correlate two seismically derived variables to well measurements plotted in color. When there are more than two seismically derived variables, the interpreter can use multilinear regression or artificial neural network analysis that uses a percentage of the upscaled well data for training to establish an empirical relation with the input seismic data and then uses the remaining well data to validate the relationship. Once validated at the wells, this relationship can then be used to predict the desired reservoir property volumetrically. We have described the application of deep neural network (DNN) analysis for the determination of porosity and gamma ray over the Volve field in the southern Norwegian North Sea. After using several quality-control steps in the DNN workflow and observing encouraging results, we validate the final prediction of the porosity and gamma-ray properties using blind well correlation. The application of this workflow promises significant improvement to the reservoir property determination for fields that have good well control and exhibit lateral variations in the sought properties.

Description: The mercury injection capillary pressure (MICP) method and nuclear magnetic resonance (NMR) relaxometry provide insight into the pore radius distribution (PRD) either of pore throats (MICP) or pore bodies (NMR) of rocks. One variety of permeability ( k) prediction models is based on the knowledge of the PRD. We have evaluated the quality of k-prediction models using a sample set of Eocene sandstones with known values of measured permeability. The Swanson method relates the apex point of the capillary pressure curve to k. Although this widely acknowledged method uses only a single point of the PRD, it provides a predictive quality with an average ratio between the measured and predicted permeability lower than a factor of three. The pore throat radius of the apex point proves to be a good proxy of the effective hydraulic radius. We determine that an improved k prediction can be achieved if a larger section of the PRD is considered in our generalized model. Using reliable values of surface relaxivity, the NMR relaxation time distribution is transformed into a PRD. We find that a characteristic apex point can be determined from NMR data, too. This characteristic point enables a good k prediction for the set of Eocene sandstone samples. In contrast to MICP, the predictive quality cannot be improved by applying an integration over a larger section of the PRD. Further tests with samples of different pore structure and lithology should demonstrate the potential of our models.

Description: Nowadays, there are many unsupervised and supervised machine learning techniques available for performing seismic facies classification. However, those classification methods either demand high computational costs or do not provide an accurate measure of confidence. Probabilistic neural networks (PNNs) overcome these limitations and have demonstrated their superiority among other algorithms. PNNs have been extensively applied for some prediction tasks, but they have not been well studied regarding the prediction of seismic facies volumes using seismic attributes. We have explored the capability of the PNN algorithm when classifying large- and small-scale seismic facies. In addition, we evaluate the impact of user-chosen parameters on the final classification volumes. After performing seven tests, each with a parameter variation, we assess the impact of the parameter change on the resultant classification volumes. We find that the processing task can have a significant impact on the classification volumes, but we also find how the most geologically complex areas are the most challenging for the algorithm. Moreover, we determine that even if the PNN technique is performing and producing considerably accurate results, it is possible to overcome those limitations and significantly improve the final classification volumes by including the geologic insight provided by the geoscientist. We conclude by proposing a new workflow that can guide future geoscientists interested in applying PNNs, to obtain better seismic facies classification volumes by considering some initial steps and advice.

Description: The mechanical nature of fluid-substitution models has always been recognized as a major cause of their limited predictive power. For instance, saturants are typically treated as simple fluids characterized only by their densities, viscosities, and moduli of elasticity; their chemistry is just ignored, even when that fluid is crude oil. However, crude oil is a complex mixture of several thousand organic compounds characterized by a variety of molecular weights, polarities, and polarizabilities, and the response of its rheological behavior to acoustic wave propagation is difficult to predict, especially when it resides in the pore space of rocks. We have performed ultrasonic-velocity measurements on carbonate core plugs saturated with a brine and with a light crude oil that are mechanically similar (i.e., having comparable densities, viscosities, and moduli of elasticity) and that show a significant and consistent excess of hardening when the saturant is oil. Dispersion and wettability are excluded as explanations for the data. We hypothesize that asphaltene aggregation and adsorption as well as paraffin-wax crystallization (and possibly volumetric expansion) combine to cause crude oil to exhibit a dilatant-like behavior within the pore space of carbonates at ultrasonic frequencies. In general, the observed effect would be similar to the hardening of ooblek at high deformation rates. This hypothesis could be tested in the future by an adequate combination of high-resolution imaging and microfluidic setups. This and similar studies would be beneficial in developing physical fluid-substitution models with a more consistent predictive power.

Description: Gas-bearing prediction of tight sandstone reservoirs is significant but challenging due to the relationship between the gas-bearing property and its seismic response being nonlinear and complex. Although machine learning (ML) methods provide potential for solving the issue, the major challenge of ML applications to gas-bearing prediction is that of generating accurate and interpretable intelligent models with limited training sets. The k nearest neighbor ( kNN) method is a supervised ML method classifying an unlabeled sample according to its k neighboring labeled samples. We have introduced a kNN-based gas-bearing prediction method. The method can automatically extract a gas-sensitive attribute called the gas-indication local waveform similarity attribute (GLWSA) combining prestack seismic gathers with interpreted gas-bearing curves. GLWSA uses the local waveform similarity among the predicting samples and the gas-bearing training samples to indicate the existence of an exploitable gas reservoir. GLWSA has simple principles and an explicit geophysical meaning. We use a numerical model and field data to test the effectiveness of our method. The result demonstrates that GLWSA is good at characterizing the reservoir morphology and location qualitatively. When the method applies to the field data, we evaluate the performance with a blind well. The prediction result is consistent with the geologic law of the work area and indicates more details compared to the root-mean-square attribute.

Description: Seismic amplitude-variation-with-offset (AVO) inversion from prestack seismic data plays a significant role in estimating elastic parameters and characterizing reservoir properties. In general, sparse regularization is widely used to solve ill-posed inverse problems by reducing the solution space of subsurface parameters, which makes seismic AVO inversion more stable. However, the traditional sparse constraint inversion only focuses on the vector sparsity of reflectivity, instead of the structural sparse characteristics of the estimated parameters. Consequently, various elastic parameters demonstrate different formation structural features in the same location of stratum. In this study, we have developed a novel approach that combines the structural sparsity and the vector sparsity of the model reflectivity to establish the posterior probability density distribution and solve the objective function of the model parameters. Based on the relationship among multiple elastic parameters, we divide the model parameters to be inverted into several groups according to intrinsic structural sparse characteristics of elastic parameters. In this case, all of the model parameters at the same sampling point are classified into the identical group, which ensures that different estimated parameters indicate the same characteristic in terms of stratigraphic structure. From the perspective of Bayesian inference, we use the modified Cauchy probability density function (PDF) to characterize the group sparsity and describe the relationship among model parameters in the same group by Gaussian PDF. Furthermore, we estimate the optimum solution corresponding to the maximum a posteriori probability under Bayesian inference. Synthetic experiments on a Marmousi model prove that the estimated P-velocity, S-velocity, and density are consistent with those of the real models, and the application of field data confirms the availability and feasibility of group sparse inversion.

Description: Compaction effects can obscure the impedance separation between hydrocarbon-bearing and fully brine-saturated sandstones. We have improved their discrimination by removing depth-related trends from inverted seismic impedance. Although the ratio of compressional- to shear-wave velocity versus seismic compressional-wave impedance crossplots shows differences among pay, brine sand, and shale trends, using absolute inverted impedances only imperfectly distinguishes hydrocarbon sands from brine sands due to outliers. In a given locality, statistical comparison of well log and seismic-derived impedances enables us to obtain a shale impedance model for a lithology baseline to detrend the impedance from the effects of burial and overburden. This has the effect of unmasking anomalies associated with hydrocarbon-bearing sands and serves as a reliable fluid discriminator. For an offshore Gulf of Mexico data set on the flank of a salt dome, with pay occurring over a wide range of depths, we identify hydrocarbon-bearing sands with a greater success rate after detrending the absolute seismic impedance.

Description: Instrumenting wells with distributed acoustic sensors (DAS) and illuminating them with passive or active seismic sources allows precise tracking of temporal variations of direct-wave traveltimes and amplitudes, which can be used to monitor variations in formation stiffness and density. This approach has been tested by tracking direct-wave amplitudes and traveltimes as part of a CCS project where a 15 kt supercritical CO2 injection was monitored with continuous offset VSPs using nine permanently mounted surface orbital vibrators (SOVs) acting as seismic sources and several wells instrumented with DAS cables cemented behind the casing. The results show a significant (from 15 to 30%) increase of strain amplitudes within the CO2 injection interval, and travetime shifts of 0.3 to 0.4 ms below this interval, consistent with full-wave 1.5D numerical simulations and theoretical predictions. The results give independent estimates of the CO2 plume thickness and P-wave velocity reduction within it.