Velocity-porosity Relationship Research Articles

Effects of overconsolidation on seismic rock physics — A comparative study between unconsolidated sands and weakly cemented sandstone

In seismic rock physics, models typically assume rocks are normally consolidated, often neglecting the effects of overconsolidation. Recent studies reveal that overconsolidated sands, resulting from stress release, show different physical property variations than normally consolidated sands. However, similar research is lacking for weakly cemented sandstones, a common reservoir analog. This study aims to systematically compare the effects of overconsolidation and stress direction on unconsolidated sandstones and weakly cemented sandstones. It also assesses the impact of overconsolidation on seismic interpretation, monitoring, and rock physics modeling applied to the two types of rocks. Experimental measurements of porosity, P-wave, and S-wave velocities were collected under different stress paths between loading and unloading. For weakly cemented sandstone, well-log data from the Norwegian Sea and Barents Sea were compared with experimental data. Analyses focused on the velocity-porosity relationship, VP/VS ratio vs. AI, and VP/VS ratio vs. effective stress.

ClinoformNet-1.0: stratigraphic forward modeling and deep learning for seismic clinoform delineation

Abstract. Deep learning has been widely used for various kinds of data-mining tasks but not much for seismic stratigraphic interpretation due to the lack of labeled training datasets. We present a workflow to automatically generate numerous synthetic training datasets and take the seismic clinoform delineation as an example to demonstrate the effectiveness of using the synthetic datasets for training. In this workflow, we first perform stochastic stratigraphic forward modeling to generate numerous stratigraphic models of clinoform layers and corresponding porosity properties by randomly but properly choosing initial topographies, sea level curves, and thermal subsidence curves. We then convert the simulated stratigraphic models into impedance models by using the velocity–porosity relationship. We further simulate synthetic seismic data by convolving reflectivity models (converted from impedance models) with Ricker wavelets (with various peak frequencies) and adding real noise extracted from field seismic data. In this way, we automatically generate a total of 3000 diverse synthetic seismic datasets and the corresponding stratigraphic labels such as relative geologic time models and facies of clinoforms, which are all made publicly available. We use these synthetic datasets to train a modified encoder–decoder deep neural network for clinoform delineation in seismic data. Within the network, we apply a preconditioning process of structure-oriented smoothing to the feature maps of the decoder neural layers, which is helpful to avoid generating holes or outliers in the final output of clinoform delineation. Multiple 2D and 3D synthetic and field examples demonstrate that the network, trained with only synthetic datasets, works well to delineate clinoforms in seismic data with high accuracy and efficiency. Our workflow can be easily extended for other seismic stratigraphic interpretation tasks such as sequence boundary identification, synchronous horizon extraction, and shoreline trajectory identification.

Petrophysics and sediment variability in a mixed alluvial to lacustrine carbonate system (Miocene, Madrid Basin, Central Spain)

AbstractThis study evaluates variations in petrophysical properties within a mixed alluvial to lacustrine carbonate system (Miocene, Madrid Basin, Central Spain). The transition from alluvial environments to lake margins settings displays a shift from alluvial, siliciclastic red sandstones and mudstones to palustrine–lacustrine mudstones to packstones. Fluctuations in lake‐water level enabled land plants to occupy the lake margins during periods of low lake levels. The palustrine carbonates include features like pseudo‐microkarst, nodular and mottled limestones; the lacustrine deposits include enlarged root cavities, desiccation cracks and channel bodies. Scarce fresh water biota comprises charophytes, gastropods and ostracods. The sediments possess high natural, irregular varying, gamma‐ray values at the alluvial–lacustrine transition, and low, but constant values at full lacustrine sites. Acoustic properties agree with lithological variations within individual facies. Porosity is the most important parameter influencing P‐wave and S‐wave velocities. The scatter in the velocity–porosity relationship links to the porosity type; macro‐porosity or microporosity. The wide range of pore types and pore sizes results in a weak porosity to permeability relationship for the carbonate‐dominated rocks with low permeability for microporous and high permeability for macro‐porous carbonates. The sandstones (probably only inhibiting interparticle porosity), and to a lesser extent the sandy wackestones to packstones, show quite a strong relationship between porosity and permeability. Elastic properties of mixed alluvial–lacustrine deposits (this study) and marine deposits (literature data) overlap as variations in pore structures and porosity values are similar. Only 16% of the marine and lacustrine carbonate sediments display Equivalent Pore Aspect Ratio values above 0.2. In travertine deposits, 83% of the samples exceed Equivalent Pore Aspect Ratio values above 0.2, which highlights that travertine deposits are dominated by larger Equivalent Pore Aspect Ratios compared to lacustrine and marine carbonate deposits. Travertines display other rock frameworks with different pore types, pore distribution and amount of porosity.

Prediction of porosity of pervious concrete based on its dynamic elastic modulus

In this research, we put forward a simple physical model of pervious concrete (PC) consisting of pore, aggregate and cement paste to evaluate theoretically the elastic modulus–porosity relationship. Also, the validity of the physical model was confirmed by conducting experiments on the elastic properties–porosity relationships (dynamic elastic modulus, natural frequency, and ultrasonic wave velocity–porosity relationships) of PC specimens with widely changed porosity. As a result, it was found that the dynamic elastic modulus–porosity relationship of PC can be represented by a linear function based on the simple physical models. Moreover, it was confirmed that the natural frequency–porosity relationship and ultrasonic wave velocity–porosity relationship can be expressed by a quadratic function based on the theory of elasticity and experimental evidence.

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.

Diagenetic controls on the elastic velocity of the early Triassic Upper Khartam Member (Khuff Formation, central Saudi Arabia)

The Permo-Triassic intervals of the Arabian Plate host the most important gas reservoirs in the world, the Khuff Formation and its equivalents. Understanding the main controls on the elastic properties of the Khuff carbonates is crucial for hydrocarbon exploration and quantitative interpretation of sonic and seismic data. In total, 88 samples were collected from the Upper Khartam Member of the Khuff Formation (central Saudi Arabia) to investigate the controls and variations in petrophysical properties and the associated acoustic velocities. Samples were analyzed using optical microscopy, XRD, and SEM to identify their texture, mineralogy and pore types. Porosity, permeability, and compressional and shear wave velocities were measured for all samples. A significant scatter is observed in the velocity-porosity relationship of the studied samples. Depositional environment, lithofacies and minerology show no clear impact on such observed scatter. Our results show that variations in pore types, predominantly of diagenetic origin, are the main factor controlling variations of velocity at any given porosity. Samples characterized by vuggy and non-cemented moldic porosity have a higher velocity when compared to samples characterized by infilled molds, interparticle and microporosity. The impact of pore types on velocity is investigated by means of velocity-porosity trajectories obtained by the differential effective medium (DEM) modeling, which incorporates variable equivalent pore aspect ratio (EPAR) values. Three main diagenetic processes, all being non-EPAR-preserving, contribute to the evolution of velocity and porosity: 1) dolomitization creating connected pore system between the euhedral dolomite rhombs which increases permeability (best reservoir unit) but decreases pore aspect ratio and thus velocity; 2) dissolution of microporous ooids and skeletal grains creating high EPAR molds and vugs at the expense of low EPAR micropores, 3) blocky calcite cementation that does not preserve the rounded shape of open oomolds reducing EPAR from more than 0.4 to less than 0.1 for extensively infilled molds. The established impedance-porosity trajectories in this study suggest that elastic properties can provide important insights about diagenetic overprints, pore types and reservoir quality in Khuff carbonates.

Grid-search inversion based on rock physics model for estimation of pore geometry and grain elastic moduli: application to hydrothermal ore deposits and basalt

ABSTRACTThe seismic velocity of rock material is sensitively affected by the pore geometry, and pore geometry is a key parameter related to the hydraulic properties of the rock. In this study, we propose a grid-search inversion method to estimate pore geometry and grain elastic moduli from observed velocity–porosity relationships. In our inversion, we compare laboratory-derived velocity–porosity relationships with the theoretical relationship calculated via the differential effective medium (DEM) model, assuming rock samples of the same lithology have the same crack aspect ratio. Compared with existing approaches to estimate elastic moduli and pore geometry, our approach is easy to apply because it can be applied to physical properties measured at atmospheric pressure without changing pressure. We tested our proposed inversion method using synthetic data, and successfully estimated the grain elastic moduli and crack aspect ratio. We also applied our inversion method to P-wave velocity and porosity measured in the laboratory on various rock samples acquired at the hydrothermal field and plate spreading centre, and found that the velocity–porosity relationship derived from DEM theory for the inverted model parameters agreed with the laboratory data. Using our proposed method, we estimate the average pore aspect ratio and grain bulk moduli for basaltic and hydrothermal ore deposit samples. Furthermore, the root mean square error (RMSE) distribution obtained in the grid-search inversion enables us to evaluate the uncertainty of the estimated values.

Rock physics-based carbonate pore type identification using Parzen classifier

Seismic velocity variation in carbonate rocks is a complicated function of different parameters such as mineral composition, porosity, pore type, saturation, and pore pressure. Among all, pore type is the main factor that affects reservoir permeability heterogeneity and change the velocity–porosity relationship. In this paper, a rock physics-based algorithm is presented to quantitatively identify three dominant pore types in a carbonate reservoir. The proposed algorithm is applied on data related to three wells drilled in a carbonate reservoir, southwest of Iran. We used the frame flexibility factor (γ), P-wave velocity–porosity and S-wave impedance–porosity trends as inputs of Parzen classifier to identify predominate pore type characterized by velocity-deviation log (VDL) in each depth. The results show that the proposed algorithm has high precision in classifying identified pore types with average accuracy of 76.7% throughout studied oil field.

The theory and application of DEM-Gassmann rock physics model for complex carbonate reservoirs

The storage spaces of carbonate reservoirs in the Tarim Basin are dominated by secondary pore porosity such as dissolution caves, holes, and cracks (Song et al., 2001). Research has shown that pore shapes can significantly influence the velocities of elastic waves (Eshelby, 1957; Kuster and Toksöz, 1974; Xu and White, 1995; Yan et al., 2002; Sun et al., 2004). Empirical [Formula: see text] relationships such as Castagna's (1985) mudrock line, Han's relations (1986), and Greenberg-Castagna's (1992) relationship that ignore the effect of pore geometry are not applicable to carbonates (Xu and White, 1995; Wang et al., 2009). Cheng and Toksöz (1979) imaged various pore space structures using SEM, and proposed a pore aspect ratio spectrum that can be used to explain velocity prediction. Han (2004) measured velocities of 52 different carbonate rocks, indicating that caves influence seismic velocities due to high rigidity while micropores or cracks significantly decrease velocities of rocks due to the low rigidity. Regarding carbonate reservoirs that are dominated by secondary pore porosity, Eberli et al. (2003) discussed the velocity-porosity relationship for microporosity rocks, moldic-porosity rocks, interparticle porosity rocks, and densely cemented rocks. Wang et al. (2009) analyzed the practicality of three published models (Wyllie time-average equation, Gassmann's equation, and Kuster-Toksöz model) on velocity prediction for carbonate reservoirs in the Tarim Basin, proving that Kuster-Toksöz model is the best one. Meanwhile, they also pointed out that the Kuster-Toksöz model is a very high-frequency model, and is limited to dilute concentrations of the pores. Based on effective medium theories of Norris et al. (1985), Berryman (1992) proposed a new differential effective medium (DEM) model. The matrix in this model begins as phase 1 and is updated at each step when a new increment of phase 2 (inclusions) is added; the process continues until the expected proportion of the inclusions is reached. In this process, the former incremental inclusion (phase 2) and the matrix phase are taken as a new matrix, which makes the inclusion added at each step “dilute.” Unfortunately, DEM is also a high-frequency model. At high frequencies, there is not enough time for wave-induced pore pressure to equilibrate, so it is not applicable to consider the effect of pore fluids on elastic properties. Wu's (1992) arbitrary aspect ratio and Berryman's (1995) 3D special pores are introduced into Berryman's (1992) DEM model to calculate the elastic moduli of dry rock in this paper. Spheres, needles, and penny-shaped cracks are used to represent dissolution vugs (small-sized caves), holes (needle-shaped), and cracks that have developed in the Tarim Basin. These “special” pores are incrementally added into the matrix of carbonate rocks so that the inclusion added at each step is dilute. Then, Gassmann's equation is employed to calculate the elastic properties of the saturated rocks. This rock physics model in this paper is called the DEM-Gassmann's model.

Rock-physics-based carbonate pore type characterization and reservoir permeability heterogeneity evaluation, Upper San Andres reservoir, Permian Basin, west Texas

In addition to mineral composition and pore fluid, pore type variations play an important role in affecting the complexity of velocity–porosity relationship and permeability heterogeneity of carbonate reservoirs. Without consideration of pore type diversity, most rock physics models applicable to clastic rocks for explaining the rock acoustic properties and reservoir parameters relationship may not work well for carbonate reservoirs. A frame flexibility factor ( γ ) defined in a new carbonate rock physics model can quantify the effect of pore structure changes on seismic wave velocity and permeability heterogeneity in carbonate reservoirs. Our study of an Upper San Andres carbonate reservoir, Permian Basin, shows that for core samples of given porosity, the lower the frame flexibility factor ( γ ), the higher the sonic wave velocity. For the studied reservoir, samples with frame flexibility factor ( γ ) < 3.85 represent either visible vuggy pore space in a dolopackstone or intercrystalline pore space in dolowackstone. On the other hand, samples with frame flexibility factor ( γ ) > 3.85 indicate either dominant interparticle pore space in dolopackstone or microcrack pore space in dolowackstone or dolomudstone. Using the frame flexibility factor ( γ) , different porosity–impedance and porosity–permeability trends can be classified with clear geologic interpretation such as pore type and rock texture variations to improve porosity and permeability prediction accuracy. New porosity–permeability relations with γ classification help delineate permeability heterogeneity in the Upper San Andres reservoir, and could be useful for other similar carbonate reservoir studies. In addition, results from analysis of amplitude variation with offset (AVO) and impedance modeling indicate that by combining rock physics model and pre-stack seismic inversion, simultaneous estimation of porosity and frame flexibility factor ( γ ) is quite feasible because of the strong influence of carbonate pore types on AVO especially when offset is large. ► A new rock physics model for evaluation of velocity and permeability heterogeneity. ► A rock-physics-based method to classify porosity–permeability trends. ► AVO and carbonate pore type estimation.

Acoustic Properties of Ancient Shallow-Marine Carbonates: Effects of Depositional Environments and Diagenetic Processes (Middle Jurassic, Paris Basin, France)

Abstract Examination of petrophysical properties (acoustic velocity, porosity, permeability, and density) and petrographical characteristics (texture, facies composition, and diagenesis) of more than 250 core plugs from the Middle Jurassic carbonates of the eastern Paris Basin provides insights into the parameters controlling acoustic velocities in relatively low-porosity carbonate rocks (Φ < 20%). The pore-type observations reveal distinct acoustic velocities in samples with intergranular macropores and samples with micropores in subhedral micrite, such that velocities in microporous mudstone–wackestone (lagoonal) deposits are greater than in macroporous grainstone (shoal) samples, at a given porosity range (15–20%). The standard Wyllie and Raymer transforms fit very well with the linear regression between acoustic velocity and porosity from mudstone or lagoonal facies. Marls and fine-grained deposits interpreted as lagoonal facies include statistically significant correlation (r = 0.9) between velocity and porosity. However, the data suggest that the wide scatter in velocity–porosity relationship from grainstones are not the result of different sorting, grain size, pore type, dolomite content, or clay content. Instead, early cementation greatly influences acoustic properties during diagenesis, and are interpreted to account for the high variability of velocities over a given porosity range. Specifically, at a given porosity, acoustic velocities in compacted grainstone that did not undergo early cementation are higher than in early-cemented grainstone. Petrographic observations suggest that early cementation limits mechanical compaction, creating a heterogeneous medium from the earliest stages of diagenesis (non-touching grains, preservation of intergranular macropores that are partially to totally filled by later blocky calcite cement). The abundant interfaces between micritized ooids, early cement fringes, and blocky calcites in grainstones may induce significant wave attenuation. As a result, the standard time-average equations fail to predict the effect of diagenetic features such as early cementation on sonic velocity. Conversely, an absence of early cementation favors mechanical compaction, grain-to-grain contact, and suturing. The result is a homogeneous micritized grain-supported network that may facilitate wave propagation. Through demonstration of the key role of early cementation in the explanation of variability in acoustic properties, the results of this study illustrate the complicated factors influencing velocity transforms in carbonates (Wyllie and Raymer), i.e., classical tools for predicting reservoir properties. These insights on the interpretation of Vp and the refinement of velocity–porosity transforms in grainstone units may be broadly applicable to enhancing seismic-based exploration in carbonate successions.

Velocity-porosity relationships in oceanic basalt from eastern flank of the Juan de Fuca Ridge: The effect of crack closure on seismic velocity

To construct in situ velocity-porosity relationships for oceanic basalt, considering crack features, P- and S-wave velocity measurements on basaltic samples obtained from the eastern flank of the Juan de Fuca Ridge were carried out under confining pressures up to 40 MPa. Assuming that the changes in velocities with confining pressures are originated by micro-crack closure, we estimated micro-crack aspect ratio spectra using the Kuster-Toksöz theory. The result demonstrates that the normalised aspect ratio spectra of the different samples have similar characteristics. From the normalised aspect ratio spectrum, we then constructed theoretical velocity-porosity relationships by calculating an aspect ratio spectrum for each porosity. In addition, by considering micro-crack closure due to confining pressure, a velocity-porosity relationship as a function of confining pressure could be obtained. The theoretical relationships that take into account the aspect ratio spectra are consistent with the observed relationships for over 100 discrete samples measured at atmospheric pressure, and the commonly observed pressure dependent relationships for a wide porosity range. The agreement between the laboratory-derived data and theoretically estimated values demonstrates that the velocity-porosity relationships of the basaltic samples obtained from the eastern flank of the Juan de Fuca Ridge, and their pressure dependence, can be described by the crack features (i.e. normalised aspect ratio spectra) and crack closure.

Velocity-Porosity relationship in clastic formations – a case study from some parts of Niger Delta, Nigeria

Velocity-Porosity relationship in some parts of Niger Delta was studiesd with a view to establish the velocity-porosity relationship and the generalized equation(s) that best describe this relationship in clastic formations. Five wireline logs were acquired for the study. Neutron porosity log data was converted to synthetic velocity (VTA) using time-average equation of Wyllie (1956), and the sonic porosity log was converted to sonic velocity (Vsonic). The results were presented as velocity-porosity crossplots with the trend line equations and the coefficient of correlation. The results give a distinct inverse velocity-porosity relationship; i.e. velocity decreasing with increasing porosity. The velocity-porosity relationships established from both sonic log (Vsonic) and time-average formulation are best described by polynomial fitting of 2nd order. Two generalized equations of high coefficient of correlation, which can be used to calculate compressional velocity (Vp) from porosity values in clastic formations, were established from these relationship. Keywords: porosity, velocity, compressional, polynomial and clastic Global Journal of Pure and Applied Sciences Vol. 12(1) 2006: 125-128

Revisiting the Wyllie time average equation in the case of near‐spherical pores

We suggest a generalized form of the Wyllie equation to better describe acoustic velocity variation with porosity in rocks with a mixture of intercrystalline and near‐spherical pores. Introducing a pore shape factor in the Wyllie equation allows different weights to be applied to the solid‐phase P‐wave velocity to account for rock frame stiffness. This is demonstrated in carbonate and igneous rocks having variable amounts of spherical porosity, ranging from 0% to 80% of the bulk porosity. The generalized equation describes a velocity–porosity envelope instead of the simple line given by the Wyllie equation. The lower limit of the velocity envelope is for rocks that have only interparticle or intercrystalline porosity (Wyllie equation behavior), and the upper limit is when all pores are spherical or near spherical. This upper limit corresponds to the Hashin‐Shtrikman upper bound for porosities up to 30%. The realization portrays Wyllie's velocity–porosity relationship as one particular case in which all pores are intercrystalline or interparticle with a pore shape factor equal to unity. An increase in the amount of high‐aspect‐ratio pores leads to higher pore shape factor. We suspect that this factor may be generalized to include fracture porosity with values less than unity. We suggest that this factor represents the acoustic equivalent of the cementation factor in Archie's law for resistivity measurements. The velocity calculated by the modified model correlates well with both the measured velocity and the calculated velocity using the Kuster‐Toksöz theoretical model. Various factors controlling acoustic velocity in carbonates can be quantified, based on this modification.

PETROPHYSICAL PROPERTIES DERIVED FROM X-RAY CT IMAGES

A micro-CT facility for imaging, visualising and modelling sedimentary rock properties in three dimensions (3D) is described. The facility is capable of acquiring 3D X-ray CT images of full-diameter cores and core plugs at up to 2,0003 voxels with resolutions down to 2μm. This allows the 3D pore-space of a rock to be imaged and, with the aid of SEM, to identify regions of different mineralogy. Computational results are presented which demonstrate that accurate predictions of petrophysical properties can be made directly from the digitised tomographic images. Computations of both formation factor and permeability from micro-tomographic images of Fontainebleau sandstone are shown to be in excellent agreement with experimental measurements over a wide range of porosities. Computed elastic properties for dry and water-saturated conditions are shown to be consistent with the exact Gassmann’s equations and are in excellent agreement with experimental measurements. Experimental measurements of Vp/Vs ratio for cemented sandstone morphologies are very noisy and cannot be used to infer relationships between elastic properties, mineralogy and rock microstructure. Computations on tomographic images show that the Vp/Vs ratio exhibits predictable limiting behavior which holds for any number of solid phases and is insensitive to the manner in which the phases are distributed. This allows the development of more accurate empirical methods for deriving the full velocity-porosity relationship for cemented sands. The results demonstrate the feasibility of combining digitised images with numerical calculations to accurately predict petrophysical properties of individual rock morphologies.

Wave scattering effects in elastic percolation models

The study of the propagation of waves in randomly diluted models is presented. Porosity (crack-like) models are simulated by constructing typical elastic percolation networks with random microscopic heterogeneities in order to resemble rock media. Central and bond-bending forces (Born Hamiltonian) models are considered. For each experimental case, the elastic energy of the system is relaxed in equilibrium and then the model is excited by a pulse source in order to produce wave propagation. First, a review is presented of the well established velocity-porosity relationship from rock physics, which shows a linear trend from small porosities up to the critical porosity (percolation threshold) where the rocks fall apart. From the wave propagation analysis a general trend is observed for the attenuation of waves, from the small to the large porosity models, suggesting multiple scattering effects similar to those reported from effective-medium approximations of wave scattering due to random heterogeneities. Finally, the results are compared with those obtained from laboratory experiments on dry rocks with different porosities and different applied stress regimes.

Gassmann Modeling of Acoustic Properties of Sand-clay Mixtures

—The feasibility of modeling elastic properties of a fluid-saturated sand-clay mixture rock is analyzed by assuming that the rock is composed of macroscopic regions of sand and clay. The elastic properties of such a composite rock are computed using two alternative schemes.¶The first scheme, which we call the composite Gassmann (CG) scheme, uses Gassmann equations to compute elastic moduli of the saturated sand and clay from their respective dry moduli. The effective elastic moduli of the fluid-saturated composite rock are then computed by applying one of the mixing laws commonly used to estimate elastic properties of composite materials.¶In the second scheme which we call the Berryman-Milton scheme, the elastic moduli of the dry composite rock matrix are computed from the moduli of dry sand and clay matrices using the same composite mixing law used in the first scheme. Next, the saturated composite rock moduli are computed using the equations of Brown and Korringa, which, together with the expressions for the coefficients derived by Berryman and Milton, provide an extension of Gassmann equations to rocks with a heterogeneous solid matrix.¶For both schemes, the moduli of the dry homogeneous sand and clay matrices are assumed to obey the Krief’s velocity-porosity relationship. As a mixing law we use the self-consistent coherent potential approximation proposed by Berryman.¶The calculated dependence of compressional and shear velocities on porosity and clay content for a given set of parameters using the two schemes depends on the distribution of total porosity between the sand and clay regions. If the distribution of total porosity between sand and clay is relatively uniform, the predictions of the two schemes in the porosity range up to 0.3 are very similar to each other. For higher porosities and medium-to-large clay content the elastic moduli predicted by CG scheme are significantly higher than those predicted by the BM scheme.¶This difference is explained by the fact that the BM model predicts the fully relaxed moduli, wherein the fluid can move freely between sand and clay regions. In contrast, the CG scheme predicts the no-flow or unrelaxed moduli. Our analysis reveals that due to the extremely low permeability of clays, at seismic and higher frequencies the fluid has no time to move between sand and clay regions. Thus, the CG scheme is more appropriate for clay-rich rocks.

Comparison of measured and BSR-derived heat flow values, Makran accretionary prism, Pakistan

During the German research cruise SO-124 on RV Sonne (fall 1997) on the Makran accretionary wedge off Pakistan, geophysical investigations were carried out to study the thermal regime at a gas hydrate bearing sediment in a tectonically deformed accretionary wedge. On a transect perpendicular to the strike of the deformation front 42 heat flow measurements were carried out, accompanied by seismic reflection experiments. The investigations start in the south in the abyssal plain and cover the continental slope up to 2300 m water depth. The aim of this study is to compare the BSR derived heat flow (denoted as estimated heat flow) with the values from measurements at the seafloor. This requires the calculation of sediment physical properties at depth using empirical relationships between velocity and porosity. The value measured and corrected for sedimentation of 47 mW/m 2 south of the deformation front is slightly higher than values reported by Hutchison et al. (Earth Planetary Sci. Lett. 56 (1981) 252–262). In all basins the estimated heatflow is significantly higher than the measured values. As a result, temperatures at the BSR extrapolated from seafloor measurements are 5–6 K lower than those taken from Gas hydrate stability considerations. As an overall trend the estimated as well as the measured heat flow show a small decrease from the deformation front to the northward thickening prism. A similar observation was made at other accretionary wedges and described by Wang et al. (J. Geophys. Res. 98 (B3) (1993) 4121–4142) and Ferguson et al. (J. Geophys. Res. 98 (B6) (1993) 9975–9984). Within the slope basins heat flow values show little variation, indicating predominantly conductive heat transport. Fluid flow might occur at the bounding faults where we have little control. The effect of rapid sedimentation on the dynamic behavior of the BSR might also have a significant influence on the estimated heat flow values. Our data set shows clearly that detailed seismic surveys and good control of the subsurface velocity are absolute necessities for the comparison of measured and BSR-derived heat flow values. However, the uncertainty of the velocity–porosity relationship together with a high and only approximately established sedimentation rate represent crucial but missing constraints which can be gained only by drilling.

Mass transfer to wall electrodes in a fluidised bed of inert particles

Mass transfer coefficients at electrodes positioned in the walls of a flow channel containing a fluidised bed of inert particles were determined electrochemically by measurement of limiting current for the diffusion controlled reduction of Fe(CN) 6 3−. The electrodes were positioned 30cm above the bed support thus minimising bed entrance effects and assuring only fluidisation enhancement of wall mass transfer rates. Spherical glass particles in the size range 0.6 to 1.5 mm were employed and data were correlated in the range 5 < Re dp (1 − ε) < 2000 by the equation J Dε = 0.28[Re dp (1 − ε)] −0.36 Comparison is made with data from several other sources. Experiments were also conducted in the packed bed condition and also for empty channel flow. Hydraulic aspects of fluidised bed performance were also investigated. The relative merits of the Zaki and Richardson and the Aerov and Todes equations for the superficial velocity—porosity relationship and minimum fluidisation velocity conditions being critically evaluated.

Method of estimating the amount of in situ gas hydrates in deep marine sediments

The bulk volume of gas hydrates in marine sediments can be estimated by measuring interval velocities and amplitude blanking of hydrated zones from true amplitude processed multichannel seismic reflection data. In general, neither velocity nor amplitude information is adequate to independently estimate hydrate concentration. A method is proposed that uses amplitude blanking calibrated by interval velocity information to quantify hydrate concentrations in the Blake Ridge area of the US Atlantic continental margin. On the Blake Ridge, blanking occurs in conjunction with relatively low interval velocities. The model that best explains this relation linearly mixes two end-member sediments: hydrated and unhydrated sediment. Hydrate concentration in the hydrate end-member can be calculated from a weighted equation that uses velocity estimated from the seismic data, known properties of the pure hydrate, and porosity inferred from a velocity-porosity relationship. Amplitude blanking can be predicted as the proportions of hydrated and unhydrated sediment change across a reflection boundary. Our analysis of a small area near DSDP 533 indicates that the amount of gas hydrates is about 6% in total volume when the interval velocity is used as a criterion and about 9.5% when amplitude information is used. This compares with a calculated value of about 8% derived from the only available measurement in DSDP 533.