Differential Effective Medium Theory Research Articles

Deep Dive into the factors influencing acoustic velocity in the Dalan-Kangan formations, the central Persian Gulf

The propagation of acoustic waves in rocks is directly influenced by the rocks’ elastic properties. To evaluate petrophysical properties from acoustic data, it is essential to understand the factors that influence the variations in acoustic velocity of sedimentary rocks. Carbonate reservoirs are heterogeneous, and their evaluation is complicated. A closer look at the factors affecting the elastic properties of these rocks is essential because they reveal important information about the reservoir properties and their formation evaluation. Rock physics modeling relies on laboratory-measured acoustic data. This study, however, employs acoustic logs to elucidate the key factors influencing sonic velocity, offering a more comprehensive and field-applicable perspective. Samples were prepared from the Permian–Triassic Upper Dalan and Kangan formations. Porosity, permeability, sedimentary textures, mineralogy, and pore types were investigated. Furthermore, compressional, shear, and Stoneley well-logs data were recorded and converted to acoustic velocity in the sampled interval. Porosity-velocity modeling based on the differential effective medium (DEM) theory was performed for different values of equivalent pore aspect ratio (EPAR). The results show that there is a strong inverse relationship between acoustic velocities and porosity. Acoustic velocities also exhibit an inverse correlation with permeability, but the strength of these relationships is relatively weak. Acoustic velocities are not affected by carbonate textures. A specific texture may exhibit different velocities due to the influence of diagenetic processes. Mineralogy has only a minor influence on acoustic velocities. Dolostones have a slightly higher velocity than limestones, but the difference is insignificant. Stoneley log values are slightly different in limestone and dolostone, because this wave propagates along the mud-borehole interface. The velocities were affected by the variations in pore types within the studied formations. Therefore, in carbonate rocks, porosity, and the pore types play a significant role in controlling acoustic velocities. The value of EPAR = 0.15 can be considered as the boundary between stiff pores (moldic and vuggy) and soft pores (interparticle, intercrystalline, micro-intercrystalline, and microporosity). The lower EPAR value of interparticle pores in limestones compared to dolostones can be attributed to diagenetic processes such as dolomitization and compaction. The findings of this study can help to better understand what factors affect acoustic velocity in carbonate rocks. This study also shows that acoustic logs data can be effectively used in rock physics modeling and pore type identification. By identifying the pore types, it is possible to recognize diagenetic processes and determine the rock types to control the heterogeneity and estimate reservoir quality.

Effect of temperature and fluid on rock microstructure based on an effective-medium theory

Abstract Temperature and pressure variations during the geologic diagenesis process can lead to complex pore structures in tight rocks. The effective-medium theory, based on the stress–strain relationship in combination with pore structure parameters, can be used to describe the elastic-wave responses of rocks. In this work, the differential effective medium (DEM) and self-consistent approximation (SCA) models are combined to invert the pore-crack spectrum. The Voigt–Reuss–Hill average is used to estimate the elastic moduli of the minerals. Then, based on SCA, the pore structures are incorporated into the rock matrix to create a new host phase. Subsequently, the DEM theory is used to add cracks with different volume fractions and aspect ratios to the host phase. To predict the structure of pores and cracks (crack density and aspect ratio), an objective function is defined as the sum of variances between experimentally measured and predicted wave velocities. The results show that the modeling predictions of P- and S-wave velocities at different temperatures and pressure ratios agree well with the experimental measurements. Variations in pore structure are determined at a zero effective pressure and different temperatures. We analyze the characteristics of how cracks change with variations in temperature and confining pressure, providing a theoretical basis for characterizing the structure of tight rocks.

Investigation of mechanical properties of garnet structured Li7La3Zr2O12 under Al3+ and Ta5+ co-substitutions

The influence of co-substitutions on the structural and mechanical properties of garnet structured Li7La3Zr2O12 (LLZO) is investigated. Ab initio simulations of the cubic phase under Al and Ta substitutions are performed for an analysis of substitution dependencies on lattice constants, elastic moduli and hardness. The use of the differential effective medium theory methods enables a scale bridging description towards porous LLZO, with a 27% decay of Young's modulus for a porosity of 10%, compared to dense LLZO.

Excluding quartz content from the estimation of saturated soil thermal conductivity: Combined use of differential effective medium theory and geometric mean method

Saturated soil thermal conductivity (λsat) is the maximum soil thermal conductivity value of a given soil. Although it can be determined accurately with a heat pulse sensor, there are challenges to prepare fully saturated soil samples. Numerous models have been developed to estimate λsat, and among these, the geometric mean method (GMM) generally performs well. The GMM requires soil mineral composition or quartz content information, which is unavailable for most soils. Earlier studies commonly used assumed that quartz content (fquartz) was equal to sand content (fsand) or to 0.5 × fsand, which led to significant λsat estimation errors especially on coarse-textured soils. We derived a novel method to estimate λsat from soil porosity (ϕ) based on a combination of the GMM and differential effective medium theory (DEM). The new DEM-GMM approach has a single parameter, cementation exponent (m). Using a calibration dataset of 43 soils, we determined best fit m values for soils in three groups: 1.66 for Group I (fsand < 0.4), 1.62 for Group II (0.4 <= fsand < 1) and m = -1.34ϕ+1.70 for Group III (fsand = 1). Using best fit m values for different groups, the new model can estimate λsat values from ϕ. Independent validation results on another 46 soils showed that the new model outperformed the GMM method with the assumption that fquartz = fsand or fquartz = 0.5 × fsand. The mean RMSE, Bias and R2 values of the DEM-GMM approach were 0.202 W m−1 K−1, 0.013 W m−1 K−1 and 0.89, respectively, and corresponding values of the GMM with the two assumptions were 0.295 and 0.476 W m−1 K−1, 0.056 and -0.28 W m−1 K−1, 0.80 and 0.82, respectively. The robust performance of the DEM-GMM approach suggests that it can be incorporated into thermal conductivity models to accurately estimate the thermal conductivity of unsaturated soils.

Rock-physics modeling of elastic properties of multiscale fractured rocks

Fractures, often existing across various scales, control the mechanical and fluid flow properties of upper crustal rocks. Inferring fracture properties at different scales from multiband geophysical measurements is essential for many fields of earth and energy sciences. Under the framework of multiscale homogenization, we develop a rock-physics model to characterize the elastic and anisotropic properties of multiscale fractured rocks following a certain statistical law. The isotropic differential effective medium theory is used to model the elasticity of randomly oriented microcracks, and the linear slip theory is used to model the elasticity of oriented or randomly oriented macroscale fractures. For a multiscale fractured rock covered by six orders of fracture length (10−4 m to 102 m), it is found that velocity exhibits a decreasing trend with the increment of scale. Nevertheless, the different statistical distribution of multiscale fractures significantly affects the velocity and anisotropy variation pattern with scale. The velocity for the fractal distribution decreases significantly at the seismic scale, whereas, for the log-Gaussian distribution, the dramatic change in velocity occurs more at the ultrasonic and logging scales, depending on the length of the dominant fractures. We apply our methodology to interpret a set of multiscale geophysical data of P-wave velocity in a fractured carbonate formation and estimate that the multiscale fracture is possibly distributed in a log-Gaussian manner. Our elastic and anisotropic modeling strategy has the potential to predict the distribution pattern of fractures, especially by reconciling the multifrequency geophysical measurements (e.g., ultrasonic, logging, and seismic data).

Design and development of polymer composite heat exchanger tubes using an integrated thermal-hydraulic and material design framework

In the current study, thermal-hydraulic design of the heat exchanger and composite material design are integrated to develop polymer composite tube materials for heat exchanger applications. For preliminary analysis, the scheme utilizes basic thermal resistance equations, Kern and Bell-Delaware methods for the design of baffled shell and tube heat exchangers, and differential effective medium theory for the design of composite materials. The preliminary analysis clarifies that the thermal conductivity of tubes is a performance-limiting parameter in the case of liquid-liquid applications. The heat exchanger's design imposes that the tubes' thermal conductivity must be enhanced to ≥8.5 W/m.K for achieving heat transfer comparable to those of metal counterparts. To attain the threshold thermal conductivity, the design of polymer composites employing differential effective medium theory requires that high volume fractions (> 0.3) of high effective aspect ratio (> 10 or 0.1) thermally conductive fillers be incorporated in a polymer matrix. Finally, the samples are fabricated of polypropylene matrix and expandable graphite filler with variable volume fractions (0.1–0.4). The highest thermal conductivity of 8.3 W/m.K was achieved in a 40 vol% sample. The comparison of measured and computed thermal conductivity values shows an acceptable agreement supported by electron microscopy and thermal images.

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.

Effect of mineralogy on elastic properties of the Bakken formation: A lab scale rock physics modelling

The Bakken formation in the Williston Basin, is one of the largest tight oil reserves in the U.S.A. and is currently the second largest oil producer in the nation. The Bakken formation is divided into the upper and lower shale members which comprise the source rocks, while the middle Bakken, which is a fractured silicious-carbonate formation, is the main producer. The Bakken has a complex mineralogy, composed of mainly quartz and clay in the two shale members and quartz, calcite, dolomite, and anhydrite in the middle member, along with several other minerals with lower volume fractions. Past studies have reported the importance of mineral composition in development, completion, and production from shales.In this study, the effect of mineral composition of the three Bakken members on rock elastic and velocity properties are investigated. Rock physics models were developed at macro (core) scales from data in Dunn and Mountrail Counties. The minerals' volume fractions from core XRD data were used for estimation of rock stiffness and velocities. The calculations were performed for the upper and lower Bakken (UB, LB) shales as well as the clastic and carbonate intervals of the middle Bakken (MB). Hill averaging was used to mix the non-clay members. Clays were added using both Kuster-Toksoz (K-T) model and differential effective medium (DEM) theory. The effect of fluid phase (assuming both homogeneous and patchy fluids) was applied using K-T (Kuster and Toksöz, 1974) and Gassmann equations (Gassmann, 1951) for frequency-dependent velocity estimation. For shales, Backus averaging (Backus, 1962) captured the upper and lower bounds of the data, whereas the K-T model developed for parallel and perpendicular to the laminations, allowed accurate curve fits to the lab data by changing the pore's aspect ratios to capture the pores heterogeneity exhibited in Bakken. The results showed that, In overall, the UB and LB shales, due to the presence of clay minerals, show lower properties than the MB and composed mainly of microfracures (pores). The MB is shown to have more intraparticle pores with stiffer properties. The estimated stiffness and velocity properties are valuable input data for the development, completion and production planning from future wells.

The heterogeneity of petrophysical and elastic properties in carbonate rocks controlled by strike-slip fault: A case study from yangjikan outcrop in the tarim basin

The petrophysical and elastic properties of the carbonate rocks controlled by strike-slip fault are still poor understood due to their significant complexities and strong heterogeneities, causing challenges for the exploitation and development of these carbonate reservoirs. To better comprehend the heterogeneity of petrophysical and elastic properties of the fault-controlled carbonate rocks, a small carbonate strike slip fault zone is selected, which is located in Yangjikan section in the Tarim basin. We combine the geostatistical, microscopic observation, petrophysical and ultrasonic analyses to characterize and understand the complexities and heterogeneity of petrophysical and elastic properties with different distance to the main fault core. The results show significant complexities and heterogeneities of petrophysical and elastic properties, and the variations of rocks drilled from the fault core are relatively drastic compared to those from the damage zone. The equivalent pore aspect ratios of the rocks are calculated from the differential effective medium theory, the values in the fault core are much higher compared to those from the damage zone, which can discriminate the pore network architectures and can represent reference for determination of the boundary of fractured damage zone. The controlling factors on the heterogeneity of the petrophysical and elastic properties for the selected fault zone are discussed, which mainly include the influence of fault structure position on fracture development, fluid selective filling on effective fracture and pore development, and the sequence on pore development. The results can contribute to the recognition and prediction of the petrophysical and elastic properties and hydrocarbon exploration in carbonate strike-slip fault zone in the Tarim Basin, and can provide reference for the construction of integrate multiscale heterogeneities models.

Factors controlling sonic velocity in dolostones

Although the impact of rock texture and crystal size on porosity and permeability of dolostones is well documented, the impact of such factors on the sonic velocity of these sedimentary rocks remains poorly understood. In this study, 100 samples from five formations outcropping along the Arabian Plate, were analyzed to investigate the main factors controlling the sonic velocity in dolostones. The study integrates results obtained using different techniques including: thin-section petrography, SEM, XRD, digital image analysis, porosity and permeability measurements, velocity measurements, in addition to rock physics modeling. Results indicate that porosity is a major factor in controlling the sonic velocity in dolostone where the porosity-velocity relationship shows a determination coefficient (R2) of 0.82. The scatter in the porosity-velocity relationship can be mainly attributed to variations in the dolostone texture (fabric preserving, FP, versus non-fabric preserving, NFP) and the associated pore types. FP dolostones (characterized by macro interparticle, moldic and shelter pores inherited from the precursor limestone) show higher velocities than NFP dolostones (dominated by intercrystalline pores) at a given porosity. The experimental porosity-velocity data, and the rock texture and pore types observations are consistent with rock-physics modeling incorporating variable equivalent pore aspect ratio (EPAR) values in the differential effective medium (DEM) theory. FP dolostones display higher EPAR values (>0.15) compared to NFP dolostones; a criterion that can be used to differentiate between the two dolostone textures. When classifying data based on texture (FP versus NFP), we observe strong porosity-impedance relationship (R2 > 0.95) for both the studied samples, and literature datasets (regional and global) following a consistent distinct trend for each texture. This implies a universality of the porosity-impedance trends observed here, which when combined with the presented rock physics analysis, can inform the modeling and quantitative interpretation of sonic logs and seismic data in dolostone strata.

Borehole Geophysical Joint Inversion to Fully Evaluate Shaly Sandstone Formations

Simultaneous inversion of sonic, density, and electrical resistivity borehole-derived well logs, has been addressed in literature in recent years. However, this problem is not broadly studied for dual-porosity sandstone formations. In addition, most authors presumed salinity and matrix properties as known parameters in their studies. We integrate the conservation of mass to model density, a differential effective medium theory for elastic modeling, and a laboratory-supported model for electrical resistivity of dual-porosity sandstones. Utilizing this methodology, we simulate electrical resistivity, sonic, and density well-log data. We develop a stochastic global search engine to jointly invert petrophysical properties. We build a dual-porosity formation with associated petrophysical properties and show the proposed workflow accurately replicates true well-log responses in the oil column, water leg, and transition zone. Local petrophysical properties (microporosity, intergranular porosity, total porosity, and water saturation) and global model parameters (salinity, matrix properties, critical porosity, resistivity lithology exponents, and sonic length scales for different pore networks) are all well recovered. The developed multiphysics calibrated rock models will assist petrophysicists and seismic analysts to identify and distinguish sandstone facies characteristics from well-log and prestack seismic data.

Brittle mineral prediction based on rock-physics modelling for tight oil reservoir rocks

AbstractThe reservoir rocks from Chang-7 member of Yanchang Formation of Ordos Basin are characterised with heterogeneous fabric structures at the pore scale, and low porosity/permeability is exhibited at the macro scale. Precise prediction of reservoir brittleness is of great significance to oil production. Ultrasonic experiments are performed on tight sandstones collected from the target formation. A rock-physics model (RPM) is presented based on the Voigt–Reuss–Hill average (VRH), self-consistent approximation (SCA) and differential effective medium (DEM) theory. The brittleness characteristics relying on mineral composition, porosity and microcrack properties are explored by using the RPM. The Young's modulus increases and Poisson ratio decreases with increasing quartz content. Based on experimental, log and seismic data, brittle mineral analysis of rock physical model is performed at multiple scales. The model accuracy is verified by experimental data and well log data. The brittleness distribution is predicted on the basis of log and seismic data, which can be instructive for the reservoir rock fracturing in actual engineering operations.

Multi-physics rock templates to seismically characterise complex carbonates

Single-physics rock templates have been widely addressed in the literature especially for sandstone reservoirs. Nevertheless, multi-physics rock templates (MPRT) have not been broadly studied to characterise complex carbonates. Multi-physics measurements lead to generate MPRTs which provide visual aid to petrophysicists and seismic rock physicists to classify facies and determine reservoir rock and fluids. Our research is oriented around two sequential stages. In the first stage, we make three independent porosity measurements (Archimedes, µCT and NMR) on core carbonate plugs from northern Niagaran reef. Resistivity, P&S-wave ultrasonic measurement and joint modelling of the same brine saturated plugs help us to fine-tune the model parameters through a global optimisation algorithm. Optimisation algorithm provides vuggy and micro-porosities close to independently measured porosities using NMR and µCT. In the second stage, we extend the technique from core data to well logs. We integrate mass balance equations to model bulk density and staged differential effective medium (SDEM) theory to model elastic and electrical resistivity of dual-porosity carbonates. Then, we design a stochastic global algorithm to simultaneously invert petrophysical properties. The inversion algorithm iteratively recovers the petrophysical properties including intergranular porosity, vuggy porosity, water saturation, salinity and matrix properties. Critical porosity, resistivity lithology exponents and sonic length scales for different pore systems are also estimated with meaningful accuracy.

Effects of material texture and packing density on the interfacial polarization of granular soils

Many electrical and electromagnetic (EM) methods operate at MHz frequencies, at which the interfacial polarization occurring at the solid-liquid interface in geologic materials may dominate the electrical signals. To correctly interpret electrical/EM measurements, it is therefore critical to understand how the interfacial polarization influences the effective electrical conductivity and permittivity spectra of geologic materials. We have used pore-scale simulation to study the role of material texture and packing in interfacial polarization in water-saturated granular soils. Synthetic samples with varying material textures and packing densities are prepared with the discrete element method. The effective electrical conductivity and permittivity spectra of these samples are determined by numerically solving the Laplace equation in a representative elementary volume of the samples. The numerical results indicate that the effective permittivity of granular soils increases as the frequency decreases due to the polarizability enhancement from the interfacial polarization. The induced permittivity increment is mainly influenced by the packing state of the samples, increasing with the packing density. Material textures such as the grain shape and size distribution may also affect the permittivity increment, but their effects are less significant. The frequency characterizing the interfacial polarization (i.e., the characteristic frequency) is mainly related to the electrical contrast of the solid and water phases. The model based on the traditional differential effective medium (DEM) theory significantly underestimates the permittivity increment by a factor of more than two and overestimates the characteristic frequency by approximately 1 MHz. These inaccurate predictions are due to the fact that the electrical interactions between neighboring grains are not considered in the DEM theory. A simple empirical equation is suggested to scale up the theoretical depolarization factor of grains entering the DEM theory to account for the interaction of neighboring grains in granular soils.

Geophysical pore type inversion in carbonate reservoir: Integration of cores, well logs, and seismic data (Yadana field, offshore Myanmar)

Detection of pore types and diagenetic features from seismic data is a major challenge for the evaluation of carbonate reservoirs in the subsurface. Based on a detailed petrographical and petrophysical analysis of carbonate rock using optical and scanning electron microscopy, mercury-injection measurements, digital image analysis, and well logs, we have determined the potential of the geophysical pore type ([Formula: see text]) inversion — a rock physics inversion scheme based on the differential effective medium theory—to quantitatively and qualitatively characterize the pore type distribution from acoustic data in the Yadana carbonate gas field (Early Miocene, offshore Myanmar). The geophysical pore type ([Formula: see text]) is revealed to be an upscalable parameter, whose depositional/diagenetic interpretation may be performed at well log and at seismic scales. We apply the inversion method on a 3D seismic data to map the reservoir-scale distribution and highlight the occurrence of laterally extended (100–1000 m) subseismic- to seismic-scale (thickness [Formula: see text]) geologic bodies. From this approach, two main reservoir geobodies are discriminated and interpreted in terms of depositional and diagenetic fabrics: (1) highly microporous, decameter-scale reservoir units (approximately 80% of the reservoir), mainly consisting of foraminiferal, red algae floatstone to rudstone with vuggy moldic porosity and characterized by moderate to high [Formula: see text] (0.11–0.20) and (2) thin, stratiform, cemented scleractinian floatstone/brecciated units (5–10 m; approximately 20% of the reservoir) with low microporosity and macroporosity and exhibiting low [Formula: see text] values ([Formula: see text]).

Wave Propagation in Infinituple‐Porosity Media

AbstractThe fractal texture (or fabric) of porous media, which supports fluid flow at different scales, is the main cause of wave anelasticity (dispersion and attenuation) on a wide range of frequencies. To model this phenomenon, we develop a theory of wave propagation in a fluid saturated infinituple‐porosity media containing inclusions at multiple scales, based on the differential effective medium (DEM) theory of solid composites and Biot‐Rayleigh theory for double‐porosity media. The dynamical equations are derived from first principles, that is, based on the strain (potential), kinetic, and dissipation energies, leading to generalized stiffness and density coefficients. The scale of the inclusions can be characterized by different distributions. The theory shows that the anelasticity depends on the size (radius) of the inclusions, parameter θ (exponential distribution), mean radius r0 and variance σr2 (Gaussian distribution) and the fractal dimension Df (self‐similar distribution). When Df = 2, θ = 1 and σr2 = 4, the three distributions give the same P‐wave velocities and attenuation, since each added inclusion phase has nearly the same volume fraction. For the modeling results, the range of anelasticity of Df = 2.99/θ = 1/σr2 = 4 is broader than that of Df &lt; 2.99/θ &lt; 1/σr2 &lt; 4. To confirm the validity of the model, we compare the results with laboratory measurements on tight sandstone and carbonate samples in the range 1 Hz–1 kHz, Fox Hill sandstone (5 Hz–800 kHz) and field measurements of marine sediments (50 Hz–400 kHz). This comparison shows that the model successfully describes the observed anelasticity.

Physical properties of Cretaceous to Eocene platform-to-basin carbonates from Albania

Understanding acoustic velocities of sedimentary deposits is crucial for realistic subsurface imaging. The velocities rely on mineralogy, density, as well as pore volume (porosity) and pore structure. In carbonate rocks, both depositional and diagenetic histories exert a significant control on these characteristics. In order to determine this control, petrographic analysis (thin sections) associated with the analysis of the carbonate content, grain density, permeability, porosity, and acoustic measurements were performed on samples from Cretaceous to Eocene carbonate platform-to-basin series of Albania. Rock facies showed two depositional associations and four pore-type associations. Very low average permeability (<1 mD) and variable porosity values (0–14%) characterize the samples. Pore type and diagenetic alteration steered the porosity-permeability distribution. Modelling of the velocity-porosity relationship, using the differential effective medium theory (DEM), revealed that variations in the acoustic velocity were mainly driven by variations in porosity and pore type, while facies and mineralogy were of minor importance.The Albanian dataset was compared with petrophysical data retrieved from time- and deep-water facies equivalent carbonate series of the Gargano Promontory in Italy. The comparison demonstrates that the variation in acoustic velocity is limited within the Albanian samples due to the pronounced infill of primary and secondary pores. Acoustic velocity data, on the other hand, are more scattered for the Gargano and this is essentially related to the higher porosity due to the preserved primary macro-intergranular and micro-intercrystalline pores, and/or to significant development of secondary mouldic pores.This study contributes to the understanding of heterogeneities and spatial distribution of pore types resulting in different petrophysical signatures of Cretaceous platform to deep-water carbonates. The data provide a better insight into possible variations in reservoir quality and seismic signature of these types of carbonates in subsurface reservoirs.

Application of the differential effective medium theory to determine fluid saturation and crack density from measured P- and S-wave velocities

SUMMARY The differential effective medium (DEM) theory studied in this paper describes elastic moduli of a fractured medium with help of differential equations, where crack density is the independent variable and fluid saturation is a parameter. The effective medium is isotropic for randomly oriented flat ellipsoidal cracks and thus fully characterized by two elastic constants. In this article we derive an analytical solution of the equation for Poisson’s ratio and we transform the differential equation for Young’s modulus into a non-linear algebraic equation. Fluid saturation and crack density can then be determined from measured wave propagation velocities by a simple algorithm. We also derive approximate solutions for elastic moduli as a function of crack density and saturation, which allows to quantify the uncertainty of the result due to measurement errors. The DEM theory leads to higher crack densities than the self-consistent method and to lower crack densities than the non-interacting theory for measured elastic moduli, while all three methods give similar fluid saturation fractions. As an example of application of our theoretical results, we study weathered granite in the Strengbach water catchment in the Vosges mountains in France. We have performed full waveform sonic logging measurements in an 86-m-deep borehole located at an altitude of 1130 m above sea level, which is used for hydrogeophysical and geochemical studies of a granitic aquifer. The logging data allows us to investigate P and S waves in the depth range between 40 and 80 m. The P- and S-wave propagation velocities take average values of 5.0 and 2.7 km s–1, respectively, with the highest values of 5.8 and 3.2 km s–1 at 75–80 m depth. From these velocities we obtain a water saturation of 75 ± 25 per cent. The crack density describes the degree of weathering of the granite, which generally decreases with depth, but takes high values near layers of strongly weathered granite. Crack density is on average 0.5, with the highest value of 1.0 at 65 m and the lowest value of 0.2 at 75 m depth. The analysis of the full waveform logging data by the DEM method supports results from previous geochemical and hydrological studies in the Strengbach catchment which concluded that water is stored in deeper layers of the granitic aquifer.

Investigating hydrate formation rate and the viscosity of hydrate slurries in water-dominant flow: Flowloop experiments and modelling

Water dominated flow is typically encountered in mature oil and gas fields after water breakthrough has occurred; gas hydrate formation in these systems is generally associated with a high risk of flowline blockage. With the move towards production of natural hydrate deposits as an abundant source of gas, understanding water dominated flow will become increasingly important, particularly as these systems inherently operate near or within the hydrate equilibrium region. In this work, we present an improved mass-transfer limited hydrate growth rate model, which includes the effect of hydrate slurry viscosification on formation. This is validated through several methane hydrate formation experiments employing a 10 mm ID flowloop operating at high water cut (100 vol% water).The model is based on understanding mass transfer limitations for hydrate slurry systems; the mass transfer coefficient itself was estimated by the small eddy cell model and considers changes in the viscosity and diffusion coefficient due to an increase in hydrate volume fraction. Further, differential effective medium theory was employed to predict the viscosity of the hydrate slurry. The gas-water interfacial area was directly estimated (without any correlations) by employing high quality images captured through an in-line camera instrumented on the flowloop. Experimental results obtained from the flowloop were used to validate the overall growth rate predictions of our model. Overall, this work offers a pathway to improve predictive capabilities for the coming generation of natural gas hydrate production, and to increase confidence in our ability to actively manage hydrate formation for water dominant systems.

Elastic Anisotropy Modeling of Organic-Rich Lower Gondwana Shale in Eastern India

Analysis of cores from the Lower Gondwana basin in eastern India confirms the presence of abundant organic matter, indicating a high shale gas prospective zone. Shale is intrinsically (transversely) anisotropic due to the preferential orientation of anisotropic clay platelets depending on the geological processes of deposition. Such anisotropy needs to be incorporated in modeling for an accurate explanation of observed seismic anisotropy in shale. Combined anisotropic formulations of self-consistent approximation (SCA) and differential effective medium (DEM) theory is the most suitable among existing theories to deal with the complex microstructure of shale. We start by predicting the bulk and rigidity moduli of clay mineral aggregates as 21 GPa and 10 GPa from our model, which are difficult to measure in the laboratory due to the small crystal size of clay. A concept of host medium (HM) is presented here, which is constituted of clay mineral aggregates, kerogen, and unconnected pores. Other minerals are added in the biconnected composite constituted of HM and connected pores filled with water. An orientation distribution function (ODF) of clay particles is determined using the combined SCA-DEM theory from the observed ultrasonic velocity measurements. Our model shows strong intrinsic anisotropy at the shallow depth that decreases with depth because of the changes in the microstructure of the shale. The P-velocity predicted from our model, widely used Biot–Gassmann theory (BGT) and Biot–Gassmann theory modified by Lee (BGTL) match well with the measured data where P-wave anisotropy is insignificant. We also predict from our model the volume of kerogen and total organic carbon as 26–43% and 6–8%, respectively.