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Published laboratory elastic-wave velocity versus porosity data in carbonate rocks exhibit significant scatter even at a fixed mineralogy. This scatter is usually attributed to the strong variability in the rock-frame or pore-space geometry, which, in turn, is driven by the richness and complexity of diagenetic alteration in these very reactive sediments. Yet, by examining wireline data from oil-bearing high-to-medium porosity chalk deposits, we find surprisingly tight velocity–porosity trends. Moreover, these trends are continued into the low-porosity domain by data from a location thousands of miles away from the chalk field. This congruence implies a universality of diagenetic trends, at least in the massive deposits under examination. We also find that the elastic bulk and shear moduli of the pure-calcite end member are somewhat smaller than such values reported in the literature. Using the end-member elastic constants relevant to the data under examination, we establish a theoretical rock physics model to match and generalize these data. [ABSTRACT FROM AUTHOR]

Ultrasonic elastic‐wave velocities, as well as the stress‐strain behavior, were measured on dry dune sand from Saudi Arabia under hydrostatic loading from 0 to 50 MPa. The samples came from the dune's crest, limb, and base. The experiments included several loading and unloading cycles. All samples exhibited irreversible deformation and porosity reduction during the tests due to grain repacking in low‐stress regimes and grain breakage at higher stress. The loading behavior was plastic, while the unloading/reloading behavior was elastic. In spite of noticeable porosity variations during the experiments, the elastic‐wave velocities mainly depended on the stress rather than on porosity. Our velocity versus stress data is very close to earlier published results, although the provenance of the sand is very different, pointing at a universality of such behavior in loose sand. Our results were matched by the contact Hertz‐Mindlin theory with varying coordination number and shear‐stiffness adjustment. We also offer a new theoretical model for the static bulk modulus measured in these experiments. This model is based on the concept of stress heterogeneity (stress chains or patches) in a granular pack and uses elastic bound averaging of the respective moduli of stressed and unstressed parts of the pack. The same model is used to describe the velocity versus stress behavior. These results and theory constitute a new installment into the published sparse data of the mechanical properties of unconsolidated sand as well as theoretical analyses thereof and are the first ever such data generated in Saudi Arabia. Key Points: New dataset on dune sand, velocity and deformationNew theory for elastic‐wave velocityNew theory for static bulk modulus [ABSTRACT FROM AUTHOR]

ABSTRACT: We explore a package of parallel porous layers, each filled with a different fluid. Assume that this package is sampled by an elastic wave with the wavelength much larger than the thickness of an individual layer. Also assume that the layers are hydraulically isolated from each other, meaning that the diffusion length is smaller than that of the individual layer. This assumption is relevant to a patchy saturation scenario. Suppose that we wish to conduct the fluid substitution operation on this package treated as a single porous elastic body. What is the effective bulk modulus of the pore fluid to be used in this operation that will result in the same elastic modulus as computed by Backus averaging the individual moduli of the layers? We address this question analytically by assuming that the porosity, dry frame, and the mineral matrix properties of the individual layers are the same for all layers. The only difference between the layers is the pore fluid. We find that the resulting effective bulk modulus of the fluid thus derived falls between the arithmetic and harmonic averages of the fluid bulk moduli in the layers. It can be approximated by a linear combination of these two bounds where the weights are 0.50 and 0.50 or 0.75 for the arithmetic average and 0.25 for the harmonic average, depending on the elastic moduli of the dry frame, the mineral, and the pore fluids. This solution also provides a relation between the effective bulk modulus of the pore fluid in the system under examination and water saturation to be used in the fluid substitution operation at a coarse spatial scale. [ABSTRACT FROM AUTHOR]

Laboratory permeability data from the brine-filled Tubaen Formation in the Snøhvit field show an order of magnitude permeability variation for approximately the same porosity. This variation in permeability is explained by a modified Kozeny-Carman equation that exploits the relationships among permeability, porosity, cementation, and pore geometry. The expression correlates the slope in a logarithmic plot of porosity versus permeability with the amount of contact cement and sorting, and the intercept with the grain size. Additional information about sorting and/or cementation can be used to better constrain the slope of the plot. Based on this equation, we found that the grain size and the amount of contact cement increased with depth in the lowermost Tubaen 1-3 sandstone units, this led to an increasing permeability with depth, in the same porosity range. The permeability variation in the shallowest Tubaen 4 sandstone unit was affected by sorting to a larger degree than the remaining Tubaen intervals, which influenced the cementation factor, porosity, and permeability simultaneously. These findings were supported by the depositional environment of the formation, a petrology study of grain size and sorting and a rock-physics study. The rock-physics study indicated that the samples with higher permeability had higher elastic moduli compared with the samples with lower permeability. This correlation between permeability and elastic moduli can be explained by the increasing amount of contact cement for the stiffer, high-permeability samples. [ABSTRACT FROM AUTHOR]

We studied the heterogeneity of natural rocks with respect to their pore-size distribution, obtained from mercury-intrusion capillary pressure (MICP) tests, at a scale about one-fifth of the standard plug size (2.5 cm). We investigated two Fontainebleau sandstone and two limestone samples. We found that at the scale of the MICP tests, heterogeneities are practically nonexistent. Still, there are large differences in the capillary curves from one rock type to another. Also, carbonate rocks, unlike Fontainebleau sandstone, show heterogeneities at a scale smaller than the scale used in MICP tests, as seen by the complexity in the mercury saturation versus pressure curves. We used this diversity between the capillary curves and this complexity within a single capillary curve to obtain information about the movement and chemical reactivity of CO2 in carbonates. The method consists of three steps: first, subdividing the carbonate pore system into microstructural facies, each of them having a specific range of pore throat size (e.g., tight micrite, microporous rounded micrite, small vugs, ...); second, getting a characteristic value of their petrophysical properties (namely porosity, effective surface area, and permeability) from the collected MICP data; and third, computing, for experimental conditions corresponding to a transport-controlled system, the dimensionless Peclet and Damkb'hler numbers, expressed as a function of the aforementioned permeability and effective surface area. These numbers allowed us to infer the dominant process (i.e., diffusion, advection, or kinetics) controlling the dissolution/precipitation reaction induced by the carbonic acid. Because of heterogeneities in the pore microstructure, we found that either diffusion or advection is locally the dominant mechanism, which renders some zones (e.g., vugs or, to a lesser extent, microporous rounded micrite) chemically more reactive than others (e.g., tight micrite or spar cement). [ABSTRACT FROM AUTHOR]

Seismic reservoir characterization requires a transform of seismically derived properties such as P- and S-wave velocities, acoustic impedances, elastic impedances, or other seismic attributes into parameters describing lithology and reservoir conditions. A large number of different rock physics models have been developed to obtain this link. Their relevance is, however, constrained by the type of lithology, porosity range, textural complexity, saturation conditions, and the dynamics of the pore fluid. Because the number of rock physics parameters is often higher than the number of seismic parameters, this is known to be an underdetermined problem with nonunique solutions. We have studied the framework of inverse rock physics modeling which aims at direct quantitative prediction of lithology and reservoir quality from seismic parameters, but where nonuniqueness and data error propagation are also handled. The procedure is based on a numerical reformulation of rock physics models so that the seismic parameters are input and the reservoir quality data are output. The modeling procedure can be used to evaluate the validity of various rock physics models for a given data set. Furthermore, it provides the most robust data parameter combinations to use for either porosity, lithology, and pore fluid prediction, whenever a specific rock physics model has been selected for this cause. [ABSTRACT FROM AUTHOR]

We presented a new methodology for seismic reservoir characterization that combined advanced geostatistical methods with traditional geophysical models to provide fine-scale reservoir models of facies and reservoir properties, such as porosity and net-to-gross. The methodology we proposed was a stochastic inversion where we simultaneously obtained earth models of facies, rock properties, and elastic attributes. It is based on an iterative process where we generated a set of models of reservoir properties by using sequential simulations, calculated the corresponding elastic attributes through rock-physics relations, computed synthetic seismograms and, finally, compared these synthetic results with the real seismic amplitudes. The optimization is a stochastic technique, the probability perturbation method, that perturbs the probability distribution of the initial realization and allows obtaining a facies model consistent with all available data through a relatively small number of iterations. The probability perturbation approach uses the Tau model probabillistic method, which provides an analytical representation to combine single probabilistic information into a joint conditional probability. The advantages of probability perturbation method are that it transforms a 3D multiparameter optimization problem into a set of 1D optimization problems and it allowed us to include several probabilistic information through the Tau model. The method was tested on a synthetic case where we generated a set of pseudologs and the corresponding synthetic seismograms. We then applied the method to a real well profile, and finally extended it to a 2D seismic section. The application to the real reservoir study included data from three wells and partially stacked near and far seismic sections, and provided as a main result the set of optimized models of facies, and of the relevant petrophysical properties, to be the initial static reservoir models for fluid flow reservoir simulations. [ABSTRACT FROM AUTHOR]

The equations for fluid substitution in a sample with known porosity and the mineral's and pore-fluid's elastic moduli are well-documented. Discussions continue on how to conduct fluid substitution in practical situations where more than one fluid phase is present and the porosity and mineralogy are not precisely defined. We pose a different question: If we agree on a fluid substitution method, and also agree that at partial saturation the bulk modulus of the "effective" pore fluid is the harmonic average of those of the components, can we conduct fluid substitution directly on the seismic reflection amplitude? To address this question, we conducted forward modeling synthetic exercises: We systematically varied the porosity, clay content, and thickness of the reservoir and assumed that the properties of the bounding shale are fixed. Next, we used a velocity-porosity model to compute the elastic properties of the dry-rock frame and applied Gassmann's equation to compute these properties in wet rock as well as at partial gas saturation. After that, we generated prestack synthetic seismic reflections at the top of the reservoir at full saturation and at partial saturation, and related one to the other. We found that within our assumption framework, there is an almost linear relation between the intercepts of the P-to-P reflectivity for the wet and gas reservoir. The same is true for the gradients. We have provided best-linear-fit equations that summarize these results. We applied this technique to field data and found that we can approximately predict the seismic amplitude at a gas reservoir from that measured at a wet reservoir, given that all other properties of the rock remain fixed. The solution given here should be treated as a method, meaning it should be tested and modified for various rock types and textures. [ABSTRACT FROM AUTHOR]

The tight trends (transforms) between two rock physical properties obtained in the physical or digital laboratory on cm- or mm-sized samples may hold for a composite constructed of these samples. One requirement is that all the elements of the composite obey the same trend. Another requirement is that the composite is spatially uncorrelated and, hence, approximately isotropic. The final requirement is that the underlying elemental transforms are approximately linear. The methods we use to address this exportability of trends for the dynamic elastic moduli (or the elastic-wave impedance) versus porosity, permeability versus porosity, and electrical resistivity versus porosity are, respectively, theoretical elastic bounding, numerical reservoir-scale fluid flow, and electrical current simulations. A practical implication is that if an elastic property of a large volume is determined from remote sensing, be it seismic or cross-well data, its average porosity can be estimated using the transforms established at a much smaller scale. Then, this average porosity can be translated into the hydraulic and electrical properties once again, using the elemental transforms established in the physical or digital laboratory. [ABSTRACT FROM AUTHOR]

We tested computational benchmarking data for the absolute permeability, electrical formation factor, and elastic moduli based on the Finney pack, a physical dense random pack of identical spheres digitally rendered into a 3D rectangular coordinate system, as the starting digital object. It is altered by (a) changing the radius of each sphere and (b) geometrically inverting these new packs by swapping grains and pores. Porosity, the absolute permeability, electrical formation factor, and elastic moduli are computed for all these alterations. The direct (grain-based) objects are relevant to clastic rock, and the inverse objects are proxies for carbonates with moldic pores. To corroborate these computational results, we matched the permeability versus porosity, formation factor versus porosity, and elastic moduli versus poros- ity Wends they form by established theoretical rock physics models. These trends persisted when we reduced the scale of investigation by subsampling some of the digital objects under examination. [ABSTRACT FROM AUTHOR]

The objective of this study was to establish a rock physics model of North Sea Paleogene greensand. The Hertz-Mindlin contact model is widely used to calculate elastic velocities of sandstone as well as to calculate the initial sand-pack modulus of the soft-sand, stiff-sand, and intermediate-stiff-sand models. When mixed minerals in rock are quite different, e.g., mixtures of quartz and glauconite in greensand, the Hertz-Mindlin contact model of single type of grain may not be enough to predict elastic velocity. Our approach is first to develop a Hertz-Mindlin contact model for a mixture of quartz and glauconite. Next, we use this Hertz-Mindlin contact model of two types of grains as the initial modulus for a soft-sand model and a stiff-sand model. By using these rock physics models, we examine the relationship between elastic modulus and porosity in laboratory and. logging data and link rock-physics properties to greensand diagenesis. Calculated velocity for mixtures of quartz and glauconite from the Hertz-Mindlin contact model for two types of grains are higher than velocity calculated from the Hertz-Mindlin single mineral model using the effective mineral moduli predicted from the Hill's average. Results of rock-physics modeling and thin-section observations indicate that variations in the elastic properties of greensand can be explained by two main diagenetic phases: silica cementation and berthierine cementation. These diagenetic phases dominate the elastic properties of greensand reservoir. Initially, greensand is a mixture of mainly quartz and glauconite; when weakly cemented, it has relatively low elastic modulus and can be modeled by a Hertz-Mindlin contact model of two types of grains. Silica-cemented greensand has a relatively high elastic modulus and can be modeled by an intermediate-stiff-sand or a stiff-sand model. Berthierine cement has different growth patterns in different parts of the greensand, resulting in a soft-sand model and an intermediate-stiff-sand model. [ABSTRACT FROM AUTHOR]

To validate the transport (fluid and electrical) and elastic properties computed on CT scan pore-scale volumes of natural rock, we first contrast these values to physical laboratory measurements. We find that computational and physical data obtained on the same rock material source often differ from each other. This mismatch, however, does not preclude the validity of either of the data type -- it only implies that expecting a direct match between the effective properties of two volumes of very different sizes taken from the same heterogeneous material is generally incorrect. To address this situation, instead of directly comparing data points generated by different methods of measurement, we compare trends formed by such data points. These trends include permeability versus porosity; electrical formation factor versus porosity; and elastic moduli (elastic-wave velocity) versus porosity. In the physical laboratory, these trends are generated by measuring a significant number of samples. In contrast, in the computational laboratory, these trends are often hidden inside a very small digital sample and can be derived by subsampling it. Hence, we base our validation paradigm on the assumption that if these computational trends match relevant physical trends and/or theoretical rock physics transforms, the computational results are correct. We present examples of such validation for clastic and carbonate samples, including drill cuttings. [ABSTRACT FROM AUTHOR]

To estimate variation of stress state and sediment consolidation in the Nankai plate subduction zone off southwest Japan, we measured the P-wave to S-wave velocity ratio (VP,/VS) and S-wave splitting along the seismic line extending from th trench to the seismogenic zone. For this purpose, we used active-source seismic data recorded by multicomponent ocean bottom seismoineters (OBS). Because it is difficult to identify the PS-converted reflection waveforms for each of the geological boundaries in this deep offshore region, we focused on the more easily identified PPS-refracted waveforms that register the conversion of the up-going P-waves to S-waves at the igneous crust surface. We estimated the average VP/VS ratio within the sedimentary section by using the time lag between the P-refracted waves and PPS-converted waves. This VP/VS ratio changes abruptly at the trough axis (i.e., the deformation front of the accretionary prism) arguably because of compaction associated with the accretion process. We observed relatively high VP/VS around the seismogenic megasplay fault, which may partially indicate the abnormal pore pressure and intensive fractures associated with the fault. To estimate the stress-induced fracture orientation and stress magnitude, we computed the fast S-wave polarization direction and estimated S-wave velocity anisotropy by applying the crosscorrelation method to the PPS-converted waves. To improve signal-to-noise ratio of the waveform for S-wave splitting analysis, we stacked PPS-converted waveforms on receiver gather. These anisotropic characteristics change at the seismogenic megasplay fault: the fast polarization direction is nearly parallel to the subduction direction seaward of the megasplay fault and is perpendicular to the subduction direction landward of the megasplay fault. This velocity anisotropy is especially strong around the megasplay fault. These results imply that the preferred fracture orientation, as well as the principal stress orientation, is oblique to the direction of plate subduction near the megasplay fault. [ABSTRACT FROM AUTHOR]

The relations among the resistivity, elastic-wave velocity, porosity, and permeability in Fontainebleau sandstone samples from the Ile de France region, around Paris, France were experimentally revisited. These samples followed a permeability-porosity relation given by Kozeny-Carman's equation. For the resistivity measurements, the samples were partially saturated with brine. Archie's equation was used to estimate resistivity at 100% water saturation, assuming a saturation exponent, n = 2. Using self-consistent (SC) approximations modeling with grain aspect ratio 1, and pore aspect ratio between 0.02 and 0.10, the experimental data fall into this theoretical range. The SC curve with the pore aspect ratio 0.05 appears to be close to the values measured in the entire porosity range. The elastic-wave velocity was measured on these dry samples for confining pressure between 0 and 40 MPa. A loading and unloading cycle was used and did not produce any significant hysteresis in the velocity-pressure behavior. For the velocity data, using the SC model with a grain aspect ratio 1 and pore aspect ratios 0.2, 0.1, and 0.05 fit the data at 40 MPa; pore aspect ratios ranging between 0.1, 0.05, and 0.02 were a better fit for the data at 0 MPa. Both velocity and resistivity in clean sandstones can be modeled using the SC approximation. In addition, a linear fit was found between the P-wave velocity and the decimal logarithm of the normalized resistivity, with deviations that correlate with differences in permeability. Combining the stiff sand model and Archie for cementation exponents between 1.6 and 2.1, resistivity was modeled as a function of P-wave velocity for these clean sandstones. [ABSTRACT FROM AUTHOR]

Rock physics has evolved to become a key tool of reservoir geophysics and an integral part of quantitative seismic interpretation. Rock-physics models adapted to site-specific deposition and compaction help extrapolate rock properties away from existing wells and, by so doing, facilitate early exploration and appraisal. Many rock-physics models are available, each having benefits and limitations. During early exploration or in frontier areas, direct use of empirical site-specific models may not help because such models have been created for areas with possibly different geologic settings. At the same time, more advanced physics-based models can be too uncertain because of poor constraints on the input parameters without well or laboratory data to adjust these parameters. A hybrid modeling approach has been applied to siliciclastic unconsolidated to moderately consolidated sediments. Specifically in sandstones, a physical-contact theory (such as the Hertz-Mindlin model) combined with theoretical elastic bounds (such as the Hashin-Shtrikman bounds) mimics the elastic signatures of porosity reduction associated with depositional sorting and diagenesis, including mechanical and chemical compaction. For soft shales, the seismic properties are quantified as a function of pore shape and occurrence of cracklike porosity with low aspect ratios. A work flow for upscaling mterbedded sands and shales using Backus averaging follows the hybrid modeling of individual homogenous sand and shale layers. Different models can be included in site-specific rock-physics templates and used for quantitative interpretation of lithology, porosity, and pore fluids from well-log and seismic data. [ABSTRACT FROM AUTHOR]