Rock Physics Model Research Articles

Permeability prediction based on dual seismic pore structure factors

Pore structure, especially pore shape and size, is a key factor affecting reservoir permeability. There is a poor correlation between permeability and porosity when the pore structure is complex, which leads to the low accuracy of permeability prediction by using porosity. In view of the preceding problems, six factors related to pore structure are summarized from rock physical models and entitled seismic pore structure factors (SPSFs), and the sensitivity of SPSF to permeability is analyzed with the data of two groups of clastic rock cores. The results find that the shear Lee factor is most sensitive to permeability, followed by the shear flexibility factor. In addition, there are good linear correlations between the shear Lee factor and pore size and between the shear flexibility factor and pore aspect ratio. Therefore, the combination of the shear Lee factor and pore aspect ratio can better characterize pore structure, and thus reservoir permeability. A seismic permeability prediction method based on pore aspect ratio, the shear Lee factor, and lithofacies is developed and applied to the Jurassic tight sandstone reservoirs of the Sichuan Basin. The results find that the permeability prediction accuracy is within half an order of magnitude, which is five times higher than the single-factor method of the shear flexibility factor. Compared with porosity, permeability distribution is more consistent with the measured productivity, which confirms the effectiveness of the method. It also provides a new way to predict the spatial distribution of reservoir permeability.

An empirical elastic anisotropy prediction model in self-sourced reservoir shales and its influencing factor analysis

Organic shales can split into laminae or thin layers due to their fissility and are usually characterized as transverse isotropic media. Understanding their elastic and anisotropic properties plays a significant role in geophysical modeling and imaging, reservoir geomechanics, and reservoir characterization. One can obtain their velocity anisotropy through laboratory and field measurements or rock-physics models. However, the measurements are scarce, and theoretical modeling of Thomsen’s anisotropy parameters generally requires extra inputs, which are sometimes difficult to obtain. We have compiled ultrasonic data from 159 self-sourced reservoir shale samples from the literature and our own measurements. Simple exponential models can capture the trends of the P- and S-wave anisotropy parameters [Formula: see text] and [Formula: see text] decreasing with the increasing vertical P- and S-wave velocities, with [Formula: see text] being above 0.84. The error in estimated anisotropy is small for high-velocity ([Formula: see text]) shales but relatively large for low-velocity ([Formula: see text]) shales. We analyze the influence of multiple geologic factors on the proposed anisotropy-velocity relationships. We observe that velocity anisotropy generally increases with clay content. In addition, mature shales (0.6 < Ro (%) < 1.4) generally have stronger anisotropy strength spreading in a broader range than overmature shales (Ro (%) > 1.4). Overall, no single parameter dominates the source of velocity anisotropy, which is jointly affected by the coupled factors of clay content, organic matter, porosity, maturity level, and geologic history. The empirical model has the potential to offer a fast and straightforward method of predicting P- and S-wave anisotropy strength from vertical P- and S-wave velocities.

The investigation of multiple factors on elastic anisotropy of artificial shale based on the orthogonal experiment

Elastic anisotropy of shales is critical to accurate constraints for rock physical models, quantitative interpretation and hydraulic fracturing. However, the causes of elastic anisotropy of shales are very complicated, and the understanding of how multiple influence factors affect the elastic anisotropy of shales is still not clear. Hence, the orthogonal experiment, as an effective multiple factors experimental method, is adopted in this study to analyze the effect of multiple factors for shale elastic anisotropy. Three factors, clay content, organic matter (OM) content and compaction stress are selected as independent variables, the orthogonal test table L16(43) with four levels for each factor is adopted. According to the designed orthogonal table, sixteen artificial shales are constructed based on the cold-pressing method, and all the dry artificial shales are measured by the ultrasonic measurements. The influence of each factor on the elastic anisotropy and the sensitivity orders of three factors are obtained using the range analysis. The orders of sensitivity for selected factors follow the sequence clay content > compaction stress > OM content for velocity anisotropy parameters. The compaction mechanism of artificial shales is also discussed by the compaction factor, which are positively correlated with the velocity anisotropy parameters. The clay platelets orientation distribution function (ODF) of samples is evaluated by a theoretical model, the ODF coefficients are significantly affected by the clay content and compaction stress, and W200 are much more sensitive to these factors than W400. The results can provide a critical rock physics basis for quantitative interpretation and reservoir prediction of the low-maturity or maturity shale reservoir.

The effects of clay mineralogy and crack properties on elastic properties of dry and water-saturated transversely isotropic rocks

The causes of the intrinsic elastic anisotropy of shales are very complicated, and clay mineralogy and crack properties are critical for rock-physics models and geomechanics applications in shales, but they are still poorly understood. Further, it is difficult to directly measure the elastic properties of single-crystal clays due to their small particle size. To reduce the multiparametric influence factors caused by complex components in natural shales, two sets of artificial rocks with different clay minerals are fabricated, and their porosity, permeability, and ultrasonic velocities are measured under different pressure conditions. The results suggest that clay mineralogy can significantly affect physical and elastic properties and their pressure sensitivity, and the permeabilities of the sample composed of kaolinite are much higher than those of the sample composed of smectite due to the larger particle size of kaolinite compared with smectite. Further, the type of clay can cause a difference in “intrinsic” velocity and anisotropy. The microcrack can enhance the velocity anisotropy on the basis of intrinsic anisotropy, and crack properties such as maximum dip angle and normal-to-tangential compliance ratio are obtained by a theoretical model, which is also affected by clay type, causing the difference in the pressure sensitivity of elastic properties. Water has a significant influence on the elastic properties and anisotropy of artificial clay samples, which can reduce the S-wave velocity and increase the P-wave velocity driven by multiple competing factors. Water reduces the velocity anisotropy because the presence of water narrows the difference between the velocity parallel and perpendicular to the axis of symmetry. The normal-to-tangential compliance ratio of cracks is also affected by water as a stiffer fluid can reduce the normal compliance of cracks at the grain scale.

Decorrelated linearized seismic-petrophysics inversion

Seismic model and rock-physics models (RPMs) are of significance in petrophysics inversion to estimate petrophysical properties from seismic data. Nevertheless, the prediction of petrophysical properties is commonly restricted by two issues. One is that computationally intensive algorithms are required to invert petrophysical parameters coupled in most nonlinear RPMs. Another is that statistical error caused by correlation characterization between different petrophysical parameters can affect the accuracy of inverted results. To solve these two issues, a decorrelated linearized seismic-petrophysics inversion (DLSPI) based on a linearized seismic-petrophysics model is proposed. First, a novel linearized seismic-petrophysics model is constructed based on the Taylor first-order approximate RPMs including Nur's critical porosity model and Gassmann's equation. Next, a linearized seismic-petrophysics inversion (LSPI) is proposed under the linear Bayesian framework. This approach can estimate petrophysical parameters from seismic data directly and efficiently. Then, a decorrelation strategy based on principal component analysis (PCA) is introduced to the LSPI to form the DLSPI, which can avoid the effect of the statistical correlation between different petrophysical parameters and improve inversion accuracy. Finally, the proposed method is validated both on synthetic seismic data and real seismic data from a sandstone reservoir. The inverted results indicate the efficiency and stability of the proposed method.

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

Rock physics models are predictive tools used to estimate the velocity, or elastic properties of formations, based on strong theoretical foundations, as opposed to some of the simple empirical correlations that have been developed for specific regional formations. While the basic rock physics models use simplified assumptions and involve less input, more complex models, such as inclusion-based models, estimate velocity-porosity relation as function of different parameters including pore's fluid saturation and type, cementation, confining pressure and diagenesis. The downside is that these models require performing tedious calculations and in some cases solving complex differential equations. These models may also differ depending on the type of formation, for example, separate models may be used for shales compared to the siliciclastic or carbonate formations.In this paper, we present newly developed correlations that can substitute the rock physics modeling. The developed velocity-porosity correlationsare based on the mineralogical data from the Bakken formation in the Williston Basin, North Dakota, however, they can be used with good accuracy for other formations too. These models were developed based on large volumes of data from simulation of many cases using the differential effective medium (DEM) theory, a commonly used rock physics model. DEM models were developed for composite rock, but assuming single mineral type constituting the rock. The inclusion phase was incrementally added to the matrix phase. The pores were then modeled with three phase fluid (water, oil, and gas) at different saturation levels and finally, different pore's aspects ratios (AR) were assumed to simulate pores heterogeneity (i.e., crack, intraparticle, intergranular and moldic type pore geometries). The correlations constants were extracted for different key minerals in the Bakken, including quartz, calcite, dolomite, anhydrite, illite and kerogen. Having the volume fraction of minerals from lab-based XRD or Elemental Capture Spectroscopy (ECS) logs, linear averaging was applied to estimate the equivalent velocity and elastic properties of the formations.The correlations were applied to several case studies in the Bakken and also compared with the existing lab data, which showed a good agreement with the DEM model. The simplicity of using the correlations consists of simply entering the input values in an excel template that accounts for the constant parameters, using a single approach for different type of formations. This offers a great advantage for their applications. The workflow of developing the correlations and its applications in one case stduy using data from a Well in the Mountrail County will be presented.

Estimation of pore pressure considering hydrocarbon generation pressurization using Bayesian inversion

Undercompaction and hydrocarbon generation are the main factors affecting pore pressure. The current seismic pore-pressure prediction (PPP) method is to obtain the overpressure trend by estimating the normal compaction trend (NCT) to predict the physical parameters during normal compaction and comparing the measured parameters. However, selecting a single parameter to indicate overpressure may cause insufficient consideration of factors, such as hydrocarbon generation. Because hydrocarbon generation requires specific temperature and other conditions, pore pressure is divided into two parts: undercompaction in the early stage and hydrocarbon generation after reaching the hydrocarbon generation threshold. A rock-physical model is established for estimating the NCT before hydrocarbon generation to modify the bulk modulus of the model and calculate the pressure generated by undercompaction; the pressure generated by hydrocarbon generation is added to obtain the final pore pressure. In the shale gas work area in the Sichuan Basin, the prediction results are more in line with the actual situation, and the petrophysical analysis indicates that the ratio of free hydrocarbon content and kerogen to water is the influencing factor indicating pore pressure. The practicality of the PPP formula considering hydrocarbon generation in oil and gas sweet spots is illustrated through an example in the research area.

Shear-wave velocity estimation based on rock physics modelling of a limestone gas reservoir in the Pannonian Basin

In the Pannonian Basin, especially in Croatia, there are a small number of wells for which acquired shear-wave (S-wave) velocities have been obtained. Often, quantitative interpretation relies only on compressional-wave (P-wave) velocity data, and S-wave velocity must be modelled. S-wave velocity estimation in combination with other petrophysical data is essential for detailed reservoir characterization. P- and S-wave velocities enable seismic modelling of different saturation states in a reservoir. This paper demonstrates a workflow for S-wave velocity estimation where S-wave velocity data are absent in the gas field and neighbouring fields with the same lithology, based on the Kuster–Toksöz and Xu–Payne models applied to the Pannonian Basin limestone reservoir. The results are calibrated with the P-wave velocity obtained from borehole data and the vertical seismic profile (VSP) S-wave interval velocity. Although rock physics models are idealized analogues of real rocks, a very good correlation was obtained between the modelled and measured P-wave velocity, as well as between the modelled S-wave velocity and the VSP interval velocity. The study also illustrates the problem of defining the pore aspect ratio in zones of increasing shale content. Due to the limited research on the limestones of the Pannonian Basin, these results enable a better understanding of the seismic parameters of the Pannonian Basin limestones. The results indicate that the proposed workflow gives an adequate estimation of S-wave velocities.

Seismic Tiles, a data format to facilitate analytics on seismic reflectors

Seismic Tiles is a new concept for representing seismic reflectors and attributes derived from seismic data, which makes it easy to automate seismic interpretation and analysis in general. Many subsurface problems can now be solved mostly automatically by computers, instead of mostly manually by humans, enabling the disruption of seismic interpretation at a scale similar to the disruption of road navigation facilitated by the closely analogous Google Map-style data structure. Some examples where this has been successfully implemented include screening for amplitude-variation-with-offset anomalies to identify prospects, automatic characterization of 4D effects according to rock physics modeling, and identifying faults and horizons verified by structural logic. Automation takes place not via machine learning but by direct and transparent application of well-known geophysical and geologic logic. This is achieved by automatically detecting all reflectors in the seismic data set and representing them by a set of tiles, which are small rectangular surfaces typically 200 m × 200 m in size. Tiles are calculated on a regular grid in lateral coordinates via a local 3D linear Radon transform. A set of tiles combine to describe a reflector surface, similar to how tiles in a bathroom combine to describe the walls and floor. Any attribute, from any seismic cube or other data sets, can be automatically extracted and assigned to the tiles and thus used in the logic. This logic can include the geometry of the tile itself and how it relates to tiles in the neighborhood, thus allowing easy implementation of any kind of interpretation logic that involves seismic reflectors. As the tile geometry and attributes are exposed to man and machine in a simple tabular data format, implementing logic using Seismic Tiles is easy, and much easier than applying logic directly on input in the form of raw seismic data.

Integrated petrographical and petrophysical evaluation for reservoir management of the Upper Miocene Qawasim sandstones in West Dikirnis, onshore Nile Delta, Egypt

The Upper Miocene Qawasim Formation is an important hydrocarbon reservoir of the West Dikirnis field, onshore Nile Delta. Here we present a detailed assessment of the Qawasim reservoir by integrating petrographical thin sections, SEM, XRD, wireline logs, and routine core analysis. Eight different lithofacies have been distinguished from cores, which are grouped as four facies associations: massive sandstone (FA-1), massive, gravelly and pebbly sandstone (FA-2), silty laminated sandstone (FA-3) and mudstone (FA-4). FA-4 occurs at the top and bottom of the reservoir interval. The reservoir consists dominantly of massive subfeldspathic arenites (FA-1, FA-2 and FA-3) and exhibits fine to coarse-grained, poorly to moderately sorted and subangular to subrounded texture. The reservoir has high intergranular porosity with good pore connectivity. The feldspar grains are partly leached or near completely dissolved indicating dissolution as a reservoir quality enhancing diagenetic agent. Calcite cementation, authigenic kaolinite precipitation, and minor quartz overgrowth are observed as the porosity destroying processes. Cementation has severe local effects on the reservoir quality of FA-3. The reservoir is dominated by megaporosities (mostly isotropic pore system), exhibits 20–33% porosity,>100 mD horizontal permeability, and a wide range of permeability anisotropy (0.60–24.74). Six hydraulic flow units are identified. Based on the RQI, FZI, and RPI metrics, these flow units are ranked in terms of reservoir quality and vertical permeability baffles are identified. The massive sandstones in the Middle Qawasim flow units are inferred to have superior reservoir quality contributing to 35% of the cumulative storage capacity and ∼75% of the cumulative flow capacity. We employed rock physics models to infer the effects of diagenesis on reservoir petrophysical characteristics. Sediments of constant shale content fall within the constant and contact-cement models and we infer that the velocity-porosity variation in the studied reservoir formation is mainly due to the pore-filling material and less due to the fluid effects. Based on our analyses, we drew inferences on drilling, completion, and optimum reservoir management strategies.

The Application of Support Vector Machine to Estimate Synthetic Shear Sonic Log

Abstract – Rock physics modelling is commonly applied to characterize the subsurface. Sonic log provides the elastic properties in advanced petrophysics modelling or rock physics modelling. Although it is very important, to obtain shear sonic measurement results is very expensive. Therefore, empirical and artificial intelligence allow some solutions to estimate synthetic shear sonic log. This study applicate PCA as feature selection and SVM as the regressor with TAF as the target interval for well NEGF1P. The results of feature selection are GR, DTC, and MSF log as selected features. GS optimizes the SVM kernel parameter using selected features. The best parameters for each kernel (linear and rbf) and selected feature are the input to estimate synthetic shear sonic log. The estimation result using linear kernel has R2 0.845 and root mean square error (RMSE) 15.132 and using rbf kernel has R2 0.886 and RMSE 12.989. The estimation results construe that rbf kernel estimates the synthetic sonic log with more precision than the linear kernel and indicates the linear relation between the estimated and origin log. The three other wells apply SMV with rbf kernel best parameters and selected features to estimation the synthetic shear sonic in similar interval and younger interval (GUF).

Introducing realistic distributions of gas bubble size and inclusion aspect ratio to model the coexistence of gas hydrate and free gas

The coexisting free gas within the hydrate stability zone is recognized by laboratory and field studies. The conventional resistivity method fails to obtain hydrate saturation in the sediment with gas hydrate and free gas because both of them are electrical insulators. Hydrate saturation can be obtained from a velocity log based on a certain rock physics model. However, few studies of rock physics have been conducted on gas and hydrate coexistence. In this study, a more realistic distribution of gas bubble size and inclusion aspect ratio was introduced into an effective medium model to elucidate how such coexistence affects velocity and attenuation at a broad-band frequency. The modeling results obtained indicate that such coexistence decreases P-wave velocity at low frequencies, while increases P- and S-wave velocities at high frequencies. The velocity decrease of P-wave at low frequencies is attributed to the overwhelming effect of gas bubble vibration, while it seems not to affect P-wave velocity at high frequencies significantly. Moreover, coexisting gas hydrate and free gas may strengthen P-wave attenuation at the broad-band frequency range. It is found that the damping of oscillating gas bubbles dominates P-wave attenuation at low frequencies, while squirt flow in the porous hydrate is more likely to contribute to P-wave attenuation at high frequencies. Hydrate morphology is also a significant factor affecting P-wave velocity and attenuation at high frequencies. This research reveals that rock physics modeling can provide insight into how to characterize the coexisting gas hydrate and free gas as referring to the acoustic velocity and attenuation at seismic, sonic, and ultrasonic frequencies.

Rock physics model for velocity—pressure relations and its application to shale pore pressure estimation

Acoustic wave velocity has been commonly utilized to predict subsurface geopressure using empirical relations. Acoustic wave velocity is, however, affected by many factors. To estimate pore pressure accurately, we here propose to use elastic rock physics models to understand and analyze quantitatively the various contributions from these different factors affecting wave velocity. We report a closed-form relationship between the frame flexibility factor (γ) in a rock physics model and differential pressure, which presents the major control of pressure on elastic properties such as bulk modulus and compressional wave velocity. For a gas-bearing shale with abundant micro-cracks and fractures, its bulk modulus is much lower at abnormally high pore pressure (high γ values) where thin cracks and flat pores are open than that at normal hydrostatic pressure (low γ values) where pores are more rounded on average. The developed relations between bulk modulus and differential pressure have been successfully applied to the Upper Ordovician Wufeng and Lower Silurian Longmaxi formations in the Dingshan area of the Sichuan Basin to map the three-dimensional spatial distribution of pore pressure in the shale, integrating core, log and seismic data. The estimated results agree well with field measurements. Pressure coefficient is positively correlated to gas content. The relations and methods reported here could be useful for hydrocarbon exploration, production, and drilling safety in both unconventional and conventional fields.

Optimized rock physics model implementation to characterize the heterogeneous B-interval reservoir facies in the petro-elastic domain, mubarak block, lower indus basin, Pakistan

Rock physics abridges geological and reservoir parameters to quantify the heterogeneous hydrocarbon reservoir facies in the petro-elastic domain. The widely distributed Lower Goru sands across the Lower Indus Basin are proven hydrocarbon reservoirs and exhibit heterogeneity due to their complex depositional environment. Diagenetic detrital quartz overgrowth cementation, sand, shale intercalation, and various fluids add more challenges to characterize facies in the petro-elastic domain. For precise petro-elastic relationship establishment, an extended cemented sandstone rock physics model for B-Interval sands of the Lower Goru Formation was developed. It produced conclusive elastic properties by optimizing the density log and synthesizing the missing shear sonic log. The accuracy of the selected model was authenticated by statistical measures, i.e., good prediction quality, high correlation coefficient, along with less normalized root mean square error for modeled Vp, Vs and density. This comprehensive approach adheres to the interrelationship between pores, minerals, cementation effects and fluids to address reservoir heterogeneity, facies classification and tight sand. Furthermore, these parameters are translated in a ubiquitous way in the petro-elastic domain, illuminating the sweet spots within the reservoir.

The role of calcite mineral elastic moduli in carbonate rock physics

Rock-physics models for carbonate reservoirs assume that the mineral elastic moduli are known variables. A review of publications reveals a range of values for calcite that are out of date and misleading. We present a robust compilation for future investigations. We subsequently discuss the application of calcite elastic moduli for rock-physics modeling and interpretation of wireline data through a case study data set from an offshore Canada carbonate reservoir. The data set exhibits an offset between the zero-porosity intercept and the calcite elastic moduli values. Our experience indicates that this phenomenon is present in many wireline data sets from carbonate reservoirs around the world. We demonstrate that the data can be reconciled to the mineral elastic moduli through the interpretation of microcracks in the formation (defined by a crack density of 0.06). Understanding the microcrack effect in relatively low-porosity formations is important for the correct calibration of pore microstructure parameters and for fluid-substitution calculations. Results in the case study data set show a relatively high sensitivity to changes in fluid saturation. The sensitivity can be reduced through the use of effective mineral elastic moduli that are derived from the data. We justify the effective mineral elastic moduli as a representation of the mineral moduli plus microcracks. The effective mineral elastic moduli are proposed as a relatively simple method to constrain the fluid substitution calculations in low-porosity formations where microcracks are present.

Seismic prediction of shale reservoir quality parameters: A case study of the Longmaxi–Wufeng formation in the WY area

Shale is a crucial natural gas resource, attracting global exploration and development interest. China has abundant shale gas resources that will drive future oil and gas exploration advances by increasing reserves and production. The WY shale gas field is the most productive and has the greatest potential for exploration and development. This study analyzed high-quality shale logging response characteristics and drilling logging, seismic, and analytical test data in the WY area to establish a rock physical model of seismic attribute parameters and shale reservoir quality parameters. Seismic elastic parameters were converted into indicators that directly reflect shale reservoir quality, such as total organic carbon (TOC), high-quality reservoir thickness, porosity, brittleness index, and crack development strength. Corresponding regression equations were established to predict quality parameters.The results showed that shale reservoir quality parameters have a good correlation with seismic parameters. The TOC distribution ranged from 2% to 5% in the study area and was generally high in the north but low in the south. The high-quality shale reserve had a thickness of over 40 meters, and except for the northwest region, the porosity was nearly over 4%. The overall brittleness of the study area was favorable, and the brittleness index was over 35%, which is suitable for network fractures formation in subsequent fracturing operations. The anisotropy of shale in S1l1I was small, and the overall fractures were underdeveloped in the study area. Drilling verifications showed that the prediction results of the quality parameters of high-quality shale reservoirs were consistent with actual drilling test results with high reliability. This study provides guidance for comprehensive prediction of sweet spots and subsequent fracturing and well location deployment.In summary, this study provides valuable insights into shale gas exploration and development in the WY area by establishing a rock physical model, predicting quality parameters, and offering guidance for fracturing and well location deployment.

Morphology identification of gas hydrate based on a machine learning method and its applications on saturation estimation

SUMMARY Proper identification of hydrate morphology is an essential pre-condition for the quantification and exploitation of gas hydrate resources. However, the morphology results from core-based analysis and resistivity-based imaging could be discontinuous in hydrate-bearing intervals. Rock physical model-based methods could predict morphology within complete hydrate-bearing intervals, but the accuracy is not much satisfactory in some cases. In this study, we propose a machine learning (ML) method using the wavelet twin support vector machine (WTWSVM) to accurately differentiate the pore-filling and grain-displacing hydrate. By employing different combinations of well logs as the inputs of the WTWSVM, we find the optimal one for the data set in Hydrate Ridge, offshore Oregon is the combination of gamma-ray, resistivity, compressional and shear wave velocity logs, with an accuracy of 88.6 per cent and F1-score of 82.89 per cent. Compared with the two traditional rock-physics-based methods and three typical ML algorithms, the WTWSVM with those optimal inputs performs better in terms of accuracy and F1-score. We then use the WTWSVM to predict the hydrate morphology in the hydrate-bearing intervals at an unlabelled (i.e. unidentified hydrate morphology) site 1250F and a partially labelled (i.e. only a portion of the hydrate and its morphology is identified by IR images) site 1247B at Hydrate Ridge. Finally, the hydrate-morphology-related rock physics models are employed to construct 3-D crossplots of density, compressional and shear wave velocity, on which hydrate concentration, as well as other reservoir parameters, are estimated through projecting. The proposed WTWSVM method and workflow are proved to be valid based on the good agreement between the reservoir parameters from core measurement and elastic properties.

Using a Synthetic Borehole Model to Determine the Pore Aspect Ratio Dependence of Velocities from Acoustic Well-Logging Data

Revealing the elastic wave properties of carbonate rocks with complex pore structures and improving the reliability of carbonate reservoir descriptions have always been a global challenge in the field of carbonate geophysical exploration. In this study, we established a synthetic borehole model by selecting different particle sizes of cement, carbonate cuttings, and micro-silicon as the matrix, and silicon disks as the pores in carbonate rocks. We conducted four sets of low-porosity (0-3%) borehole models with different pore aspect ratios (ARs) and measured the P- and S-wave velocities ( V P and V S ) at the well-logging scale obtained from an acoustic logging system with one source and two receivers. The results indicate that the relationship between velocities and porosities in these borehole models follows a linear relation, with the pore AR significantly influencing the velocities at any given porosity. The velocity variation caused by pore AR reaches 560 m/s and 410 m/s at 3% porosity for the P-wave and S-wave within the AR range of 0.017-0.13. The theoretical DEM models provide a high and broad estimation of V P and V S at the well-logging scale in our measurement. They could perform better in fractured formation than in dissolved porous formation in carbonate reservoirs. The linear relation of V P and V S is independent of the pore AR and is effective for both fractured and dissolved porous formations. The change of V P / V S in different pore AR is more responsive to porosity and nonlinear dependent on the pore AR. The relationship between the defined normalized V P and V S indicates the pore AR has a more significant effect on V S than V P in our model. The constructed borehole models provide a unique opportunity for evaluating the availability of rock physics models at an acoustic logging scale. The study’s findings have significant implications for improving the reliability of carbonate reservoir descriptions and enhancing the accuracy of geophysical exploration in carbonate rocks with complex pore structures.

Measurements of Wave‐Induced Attenuation in Saturated Metapelite and the Band‐Limitation of Low‐Frequency Earthquakes

AbstractThe most common explanation for the depletion of high frequency waves that defines low‐frequency earthquakes (LFEs) and very low‐frequency earthquakes (VLFEs) is that fault rupture and slip are slower than typical earthquakes. However, it is difficult to rule out the possibility that the high frequency waves are produced during slip, but attenuated near the LFE source. One reason this hypothesis has been poorly tested is that there are no measurements of attenuation on the relevant rocks. We present the results of forced oscillation experiments that measure the frequency‐dependent attenuation of a chlorite‐rich metapelitic schist, a lithology found along the subduction plate boundary where LFEs and VLFEs have been documented. Experiments were run on dry and water‐saturated schist at effective pressures of 2–10 MPa and at frequencies of 2 × 10−5–30 Hz. We find that pore fluids and low effective pressure result in the attenuation of high frequencies. The frequency‐dependent attenuation is consistent with the concomitant operation of two wave‐induced fluid flow mechanisms, squirt flow, and patchy saturation. When the effects of these mechanisms are extrapolated to geologic conditions using rock physics models, our results predict that attenuation is capable of completely diminishing the frequencies depleted in LFEs and VLFEs. Therefore, LFEs and VLFEs may not necessarily record slow fault slip, but possibly the presence of high fluid pressure.

Seismic rock-physics linearized inversion for reservoir-property and pore-type parameters with application to carbonate reservoirs

Carbonate reservoirs hold promising potential for hydrocarbon exploration, but they usually exhibit complex pore structures, which lead to difficulties in the seismic/elastic prediction via conventional rock physics modeling, and in turn, hinder an accurate estimation of reservoir properties from seismic observations. This work presents a seismic rock-physics inversion method to jointly estimating reservoir-property (porosity and fluid saturation) and pore-type (pore aspect ratio) parameters in carbonates from seismic/elastic data. The method considers the aspect ratio as a pending parameter, which favors the pore-type variation so as to describe the structure complexity. To achieve the joint estimation, we derive a linearized rock physics model based on the differential effective medium model and the Biot-Gassmann equation that relate porosity, water saturation, and aspect ratio to elastic parameters. Moreover, to realize the estimation with computational efficiency, we derive the analytical solution to the inversion with the linearized model based on the Bayesian inverse theory. We estimate the pore aspect ratio at a well location to provide prior information for the inversion and employ an iterative inversion strategy with piecewise linearization to improve the result. The proposed method is applied to two carbonate reservoirs including 2D and 3D field data sets. Compared with the conventional rock physics inversion scheme with a constant aspect ratio, the application demonstrates that the method achieves better accuracy for reservoir property estimation, which can be a good indicator for the potential target areas of complex reservoirs.