Skip Nav Destination
Filter
Filter
Filter
Filter
Filter

Update search

Filter

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

### NARROW

Format

Subjects

Date

Availability

1-20 of 70

Jack Dvorkin

Close
**Follow your search**

Access your saved searches in your account

Would you like to receive an alert when new items match your search?

*Close Modal*

Sort by

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the SEG International Exposition and Annual Meeting, October 11–16, 2020

Paper Number: SEG-2020-3414427

Abstract

New experimental tests on 18 tight gas sandstone samples from a Saudi Arabia field show a strong dependence of both Vp and Vs on hydrostatic confining stress that varied from practically zero to 50 MPa. The absolute permeability k of the same samples was measured in the same stress range using a gas (nitrogen) permeameter. This Klinkenberg-corrected permeability also showed a dramatic stress dependence. It decreased by one to two orders of magnitude as the stress increased. Combined permeability velocity cross-plots can serve to estimate the permeability from the elastic property variations during time-lapse monitoring, as well as during fracking of these rocks. Theoretical simulations based on the inclusion-based differential effective medium theory confirm the experimental velocity-stress results. Note: This paperÂ wasÂ acceptedÂ into the Technical Program but was not presented at the 2020 SEG Annual Meeting.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016

Paper Number: SEG-2016-13951278

Abstract

ABSTRACT In this paper we demonstrate the use of the capillary pressure equilibrium theory (CPET) model to address the effects of partial saturation in order to estimate hydrocarbon saturation in a reservoir volume using acoustic impedances derived by seismic inversion. The data set used here has been donated by BHP Billiton, and is from an offshore oilfield called the Stybarrow field. The set comprises of a well with a 20-foot sandstone oil saturated pay section and 3D pre- and post-stack seismic volumes. Using the provided angle stacks and well log data, a statistical wavelet, and low impedance model, the final impedance model is computed. There are two final impedance models, derived from post-stack, and pre-stack data. The final impedance models are in agreement with one another at each of the well locations, with low impedance at the oil saturated well, and high impedance at the water saturated well. The corresponding CPET model is built based on the empirical porosity from the well log. The rock and fluid properties are available from the logs and petro physical reports provided by BHP Billiton. The CPET model has difficulty distinguishing between 0 and 30% water saturation. The impedances predicted by the CPET model are in good agreement at the two well locations (blind wells), predicting 98% oil saturation in the 97% oil saturated section, and 8% water saturation in the 5% water saturated section of the reservoir. Finally using the CPET workflow, a 3D distribution of saturation was computed from inversion derived acoustic impedance and the CPET model estimated from well log. Unlike conventional approaches of estimating saturation, our method is able to discriminate between patchy and uniform saturation. Our results on Stybarrow field data reveal that the Stybarrow field behaves in a manner very close to the uniform curve at low water saturation. However, starting at 30% water saturation or higher the distribution becomes slightly patchy. Presentation Date: Wednesday, October 19, 2016 Start Time: 3:35:00 PM Location: 167 Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016

Paper Number: SEG-2016-13688619

Abstract

ABSTRACT Four well datasets from a Saudi Arabian carbonate oil field were examined. These data helped to establish a rock physics transform between the P- and S-wave impedances and porosity. The key was finding appropriate elastic properties for the "zero-porosity" end member (i.e., pure mineral) for the field under examination. The resulting model was then used in synthetic seismic forward modeling, as well as seismic impedance inversion, to map porosity within the carbonate reservoir. Presentation Date: Wednesday, October 19, 2016 Start Time: 11:35:00 AM Location: 167 Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016

Paper Number: SEG-2016-13847246

Abstract

ABSTRACT Our goal is to accurately estimate attenuation from seismic data using model regularization in the seismic inversion workflow. One way to achieve this goal is by finding an analytical relation linking to . We derive an approximate closed-form solution relating to using rock physics modeling. This relation is tested on well data from a clean clastic gas reservoir. Next we create a 2D synthetic gas reservoir section populated with and and generate respective synthetic seismograms. The goal now is to invert this synthetic seismic section for . If we use standard seismic inversion based solely on seismic data, the inverted attenuation model has low resolution, incorrect position, and is distorted. However, adding our relation between velocity and attenuation, we obtain an attenuation model very close to the original section. Presentation Date: Wednesday, October 19, 2016 Start Time: 11:35:00 AM Location: 161 Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2013 SEG Annual Meeting, September 22–27, 2013

Paper Number: SEG-2013-0392

Abstract

Summary Modeling the effect of fluid saturation in reservoir rocks is essential for hydrocarbon reservoir characterization and monitoring of CO 2 during a sequestration experiment. Here we use the capillary pressure equilibrium theory to relate the saturation to the elastic properties of the host rock. This theory is based on the fact that natural rock is heterogeneous essentially at all scales. It requires that we break a volume of rock under examination into a number of subsamples, each with its own porosity, permeability, and elastic constants; vary the capillary pressure in the volume and observe how each subsample is saturated at fixed capillary pressure. Because the subsamples are different, the saturation will vary among them at each capillary pressure step. We compute the elastic properties of each subsample and then recombine them to obtain the effective elastic properties of the original volume. We also introduce the frequency dependence of the effective elastic properties. The example given includes a high-porosity sand dataset. Because this theory accounts for heterogeneity, it allows us to predict the mean as well as standard deviation of the elastic properties at given saturation. The results are always contained within the upper (patchy saturation) and lower (uniform saturation) bounds and allow us to narrow the range of anticipated responses.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2013 SEG Annual Meeting, September 22–27, 2013

Paper Number: SEG-2013-0073

Abstract

Summary Laboratory permeability data from a wet sandstone reservoir (the Tubåen formation, Hammerfest Basin, located in the Barents Sea) subject to CO 2 sequestration indicates an order of magnitude permeability variation at the same porosity. The velocity and density well data from the well, obtained prior to CO 2 injection, show that at the same porosity, the samples with higher permeability have higher elastic moduli (both compressional and shear) as compared to the samples with lower permeability. To understand and quantify this effect, we fit the elastic modulus versus porosity well data with the theoretical constant-cement model theoretical curves. This theoretical rock physics analysis shows that the lower-permeability, softer samples have less contact cement that their high-permeability, stiffer counterparts. One interpretation of this meaning is that in the lower-permeability samples, part of the pore space is filled with fines that do not contribute to the grain-to-grain cementation thus reducing the stiffness (as compared to the well-cemented samples). This means, in turn, that in the softer samples, the fines partly clog the pores thus reducing the permeability. This logic is supported by the geological character of the Tubåen formation where the tidal and marine influence acts to worsen the grain sorting compared to well-sorted distributary channel sediment.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2012 SEG Annual Meeting, November 4–9, 2012

Paper Number: SEG-2012-0861

Abstract

Summary The common properties of bitumen are: high specific gravity, low hydrogen to carbon ratios, high carbon residues, and high contents of asphaltenes, heavy metal, sulphur and nitrogen. Since it is very viscous, it does not flow so easily. Bitumen has gravity of about 10.3 API which translates into its density about 1.3 g/cc. Bitumen deposits mostly found at very shallow depth, where temperature doesn’t exceed 15°C. Therefore in-situ bitumen acts as a solid, since bitumen properties depend on temperature. The less temperature is in a formation the more viscous bitumen is. Hence velocities and modulus of bitumen will also depend on temperature.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2011 SEG Annual Meeting, September 18–23, 2011

Paper Number: SEG-2011-2161

Abstract

ABSTRACT Modeling the effect of fluid saturation in reservoir rocks is essential for hydrocarbon reservoir characterization and monitoring of CO2, during a sequestration experiment. In this paper we investigate the effect of CO2, injection in sandstone, where classically, the two limiting cases are saturations of gas and brine either uniformly distributed or located in large patches. In the patchy case, the saturated patches are large enough so that the effective elastic properties of partially saturated sand gently transition from those of gas sand to those of wet sand throughout the entire saturation range. We compare existing methods and explore a physically consistent way of assessing the elastic properties of sand at partial saturation based on the capillary pressure equilibrium assumption. In order to better understand the influence of water and gas saturation on seismic data, we compare four different methods of fluid substitution at the pore scale for the Oseberg sands. Our results show a range of variation in acoustic impedance, Poisson''s ratio, and reflection coefficient with saturation. These should aid in the interpretation of time-lapse seismic data.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2011 SEG Annual Meeting, September 18–23, 2011

Paper Number: SEG-2011-1769

Abstract

ABSTRACT The main objective of this work is to present a new methodology for seismic reservoir characterization that provides fine-scaled reservoir models of facies and reservoir properties, such as porosity, net-to-gross, and, possibly, fluid saturation. The proposed iterative methodology is based on sequential simulations of discrete variables, namely sequential indicator simulation, and a stochastic optimization technique called probability perturbation method. At each step of the optimization we generate a facies model, distribute reservoir properties, calculate the corresponding elastic attributes through a rock physics model, compute synthetic seismograms and, finally, compare these synthetic results with the real seismic amplitudes. The stochastic optimization technique perturbs the probability distribution used to generate the initial model and obtains the most probable facies model through a relatively small number of iterations. The method is applied to a real well profile, where three facies have been identified, and finally extended to a real 2D seismic section.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2011 SEG Annual Meeting, September 18–23, 2011

Paper Number: SEG-2011-2103

Abstract

ABSTRACT Well logs from deepwater Angola are texturally interpreted using a combination of petrophysical and rock physics models. The Thomas-Stieber model predicts the porosity resulting from various modes of sand-shale mixing. The Yin-Marion-Dvorkin-Gutierrez model predicts the associated P-wave velocities. Together, they offer a higher degree of constraint of formation properties.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010

Paper Number: SEG-2010-2441

Abstract

Summary Figure 1: The application of quantitative seismic interpretation techniques in poorly-calibrated basins where the nearest well control is some distance away is problematic. Quantitative seismic interpretation has been successfully applied to predicting lithology and fluids in areas with high-quality local-well control. By contrast, the application of the same techniques is problematic in frontier basins where the nearest well control is some distance away. The reason is when rock property models are extended out the range of calibration, seismic responses can not be always reliably predicted. Here we introduce an integrated methodology for frontier exploration that combines rock physics modeling and seismic-based evaluation, allowing the interpreter to consistently quantify seismic responses for a number of geologic scenarios. The key is to understand the underlying geological processes and, by so doing, focus on the main effects of geology on the seismic properties and variations thereof from a distant well to the prospect location. Stateof- art rock physics models have to be integrated with existing thermal, burial, and reservoir quality prediction models based on regional basin modeling and petrographic analysis. By combining geology and rock physics, this methodology helps generate a catalog of seismic responses of potential exploration successes and failures. From such catalogues, real seismic amplitudes are interpreted in terms of pore pressure, lithology, rock texture, fluid content, and porosity, thus providing a rock property-based seismic interpretation framework to de-risk exploration and support business decisions. Introduction Direct application of quantitative seismic interpretation techniques in frontier basins where the nearest well is far away can be problematic. Seismic responses cannot be reliably extrapolated and predicted without a clear understanding of the key geological and geophysical effects on the elastic properties and their variations from wells to lead locations (Figure 1). Here we describe how to use modern rock physics transforms that are consistently integrated with existing thermal, burial, and reservoir quality prediction models from regional basin modeling and petrographic analog data. These rock physics transforms link the rock elastic properties to their bulk properties (porosity, lithology), physical conditions (pressure, temperature, and pore fluid properties) and geological characteristics (texture and composition). Only the application of integrated rock physics workflow, that encompasses geological constrains, can provide robust predictions. Figures 2 and 3 show the generalized workflows that are applied to interpret the seismic amplitude anomalies in frontier basins. The interpretation framework includes the following tasks: (1) Log and seismic quality control and conditioning. (2) Time-depth calibrations. (3) Calibration of well and seismic processing velocities. (4) Rock typing and upscaling. (5) Rock property trend analysis, rock-physics diagnostic, and model formulation. (6) Integration with existing thermal, burial, and reservoir quality prediction models. Fluid acoustic properties modeling and extrapolation to the expected pressures and temperatures in prospect area. (7) Generation of synthetic seismograms for the key wells. Improvement of poor-quality logs using rock physics transforms. The basis of quantitative seismic interpretation is built upon quality-controlled seismic and borehole data. In order to illustrate these workflows, we have selected an example from a poorly-calibrated offshore deepwater Tertiary basin.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010

Paper Number: SEG-2010-2416

Abstract

Summary The objective of this study is to establish a rock physics model of North Sea Paleogene greensand. First, our approach is to develop a Hertz-Mindlin contact model for a mixture of quartz and glauconite. Next, we used this Hertz- Mindlin contact model of two types of grains as initial modulus for a soft-sand model and a stiff-sand model. By using these rock physics models, we examine the elastic modulus-porosity relationships of laboratory and logging measured data and link rock physics properties to greensand diagenesis. Results of rock physics modeling and thin section observations indicate that variations in elastic properties of greensand can be explained by two main diagenetic phases: microcrystalline quartz or silica cementation and berthierine cementation. These diagenetic phases dominate in separate parts of the greensand reservoir bodies. Initially greensand is a mixture of mainly quartz and glauconite; when weekly cemented, it has relatively low elastic modulus, and can modeled by a Hertz-Mindlin contact model of two types of grains. Microcrystalline quartz cemented greensand have relatively high elastic modulus and can be modeled by an intermediate-stiff-sand or a stiff-sand model. Berthierine cement has a different growth pattern in the greensand formation, resulting in a soft-sand model and an intermediate-stiff-sand model. Introduction Greensands are glauconite bearing sandstones composed of a mixture of stiff clastic quartz grains and soft glauconite grains. Glauconite grains are porous and composed of aggregates of iron-bearing clay. Porosity is thus found in two scales: macro-porosity between grains and microporosity within grains (Figure 1). Greensand petroleum reservoirs occur world-wide, however, evaluation of greensand reservoirs has challenged geologists, engineers and petrophysicsts. Glauconite has an effect on the elastic properties, porosity and permeability of reservoir rocks (Diaz et al., 2003). Glauconite is also ductile (Ranganathan and Ty, 1986) so it can cause non-elastic deformation of greensand (Hossain et al., 2009) which could affect reservoir quality. The Hertz-Mindlin contact model (Mindlin, 1949) is the most commonly used contact model for sandstone (Avseth et al., 2005). This model is used to calculate initial sandpack modulus of soft-sand (Dvorkin and Nur, 1996), of stiff-sand (Mavko et al., 2009), and of intermediate-stiffsand model (Mavko et al., 2009). For the initial sand-pack for sandstone it is assumed that only quartz grains are packed together and the normal and shear stiffness are calculated based on the contact of two quartz grains. However, for greensands the initial sand-pack is a mixture of quartz and glauconite and because both of them are load bearing, elastic properties between that of quartz and glauconite are anticipated. To address this, we present a Hertz-Mindlin contact model for mixtures of quartz and glauconite. Theory and Method We investigate the effective elastic properties of a granular pack of spheres, for which each pair of grains in contact under normal and tangential load determines the fundamental mechanics. Typically in granular media models for unconsolidated sand, the grains are taken to be of the same materials e.g. quartz.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010

Paper Number: SEG-2010-2709

Abstract

Summary At low porosity, the elastic moduli of the rock mineral matrix often dominates those of the whole rock. A sedimentary rock matrix may be considered as a composite and may include mineral constituents with very different moduli and shapes. To describe the fabric of these rocks, an unmanageable number of parameters may be needed. Understanding the elastic behavior of synthetic composites, which are easier to model, enables us to quantify the effect of each parameter on the elastic moduli of the rock matrix independently. We test whether the differential effectivemedium (DEM) and self-consistent (SC) models can accurately estimate the elastic moduli of a complex rock matrix and compare the results with the average of upper and lower Hashin-Shtrikman bounds (HS). The testing was conducted using data from the literature on composites, covering a wide range of inclusion concentrations, inclusion shapes, and elastic modulus contrasts. We find that when the material microstructure is consistent with the DEM approximation, DEM is more accurate than both SC and the bound-average method for a variety of inclusion aspect ratios, concentrations, and modulus contrasts. If relatively little information is known about the rock microstructure, DEM can estimate the elastic properties of complex mixtures of minerals more accurately than heuristic estimates, such as the arithmetic average of the upper and lower elastic bounds. Introduction Composites can be fabricated with several constituent phases. The simplest are two-phase composites. Two-phase composites, including granular aggregates such as polycrystalline aggregates, can be classified in terms of the phase continuity and connectivity. Three main composite categories have been suggested (Ji and Xia, 2003; Gurland, 1979): a) composites with a stiff-phase-supported frame (SPSF), in which the stiff phase is continuous, while the compliant phase is discontinuous in the direction of the applied load; b) composites with a compliant phasesupported- frame (CPSF), in which the stiff phase is discontinuous while the compliant phase is continuous in the loading direction; and c) composites with a transitional frame (TF), in which both the stiff and the compliant phases are continuous (TFC) or discontinuous (TFD) in the loading direction. When all phases are discontinuous, there is no well-defined matrix phase, such as in completely random polycrystalline materials. In this study, to model the elastic moduli of materials, we consider effectivemedium models, which are based on wave scattering theory. We test the effective-medium models on a large data set of CPSF and SPSF composites in order to evaluate their predictions for a wide range of elastic moduli contrasts and inclusion shapes, with the goal of finding which model will most accurately determine the effective elastic moduli of sedimentary rocks with complex matrices. For testing the accuracy of the DEM and CPA models, compared with the Hashin- Shtrikman bounds (Hashin and Shtrikman, 1963), we used twenty-three two-phase composite experimental data sets from the literature. These composites cover a wide range of inclusion concentrations and elastic-modulus contrasts. In order to formulate solvable equations, these theories are based on idealized assumptions about the material microstructures and mathematical approximations.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010

Paper Number: SEG-2010-1635

Abstract

Summary To predict the stress state as well as pore pressure in the Nankai accretionary prism southwest Japan, we estimated the ratio of P-wave velocity over S-wave velocity (Vp/Vs) and shear-wave splitting using multi-component ocean bottom seismometers (OBS) data. Because it is difficult to identify PS-converted reflection waveforms for each of the geological boundaries in the deep offshore region, we focused on the more easily identified PPS-refracted waveforms. We estimated the average Vp/Vs within the sedimentary section by using the time lag between P-refracted waves and PPSconverted waves. The estimated Vp/Vs changed abruptly at the trough axis, mainly because of compaction associated with the accretion process. Vp/Vs gradually increased landward from the trough axis to the mega-splay fault. The increase in Vp/Vs might indicate abnormal pore pressure below the mega-splay fault. To estimate the stress-induced fracture orientation, we computed the fast polarization direction and principal amplitude direction from PPSconverted waves. The anisotropic characteristics change at the mega-splay fault: the fast polarization direction and principal amplitude direction are parallel to the trough (transverse) landward of the mega-splay fault. Furthermore, we observe predominant velocity anisotropy around the mega-splay fault. These observations suggest that both the preferred fracture orientation and the principal stress orientation are oblique to the direction of subduction near the mega-splay fault. Introduction The Nankai Trough is a convergent plate margin where the Philippine Sea plate is subducting beneath southwestern Japan (Figure 1). This subduction zone has repeatedly generated great earthquakes in excess of Mw 8 (Ando 1975). Great earthquakes at convergent plate margins have been interpreted to occur along the subduction interface as well as mega-splay faults, and there have been many seismic studies of these seismogenic faults (e.g. Moore et al. 2009; Nakanishi et al. 2008). Because pore pressure near a fault influences the fault activities, several seismic studies estimated pore pressure as well as effective stress around the seismogenic faults (e.g., Tobin and Saffer 2009; Tsuji et al. 2008). Shear-wave velocity (Vs) is an important parameter in the determination of subsurface properties, including pore pressure and stress orientation (Takahashi et al., 2002). Dvorkin et al. (1999) demonstrated that Vp/Vs (Poisson’s ratio) is strongly dependent on pore pressure. However, Vs has not been accurately estimated around seismogenic faults in the Nankai Trough off Kii Peninsula because the characteristics of the deep offshore geology in this region make it difficult. Here we estimated the Vp/Vs in sediment in the Nankai accretionary prism by using multi-component OBS data acquired from the trench to the seismogenic zone. A recent drilling campaign of the Integrated Ocean Drilling Program (IODP) used borehole breakouts and core sample observations to show that the stress state (principal horizontal stress orientation) changes across the seismogenic megasplay fault (e.g., Kinoshita et al. 2008). Maximum horizontal stress is parallel to the direction of plate subduction seaward of the mega-splay fault, but perpendicular to the direction of subduction landward of the mega-splay fault. Here, we reveal further variations of stress state across the Nankai accretionary prism by using seismic anisotropy.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010

Paper Number: SEG-2010-2351

Abstract

SUMMARY We propose here a methodology for estimating reservoir properties, including porosity, clay content, hydrocarbon saturation, and pore pressure, from partial stacks of seismic traces recorded at the top of a reservoir. This methodology is probabilistic and includes two main steps: (a) the estimation of the probability distributions of elastic parameters (velocities and density) and (b) the estimation of the probability distributions of the underlying reservoir properties and conditions. This probabilistic approach is based on the assumption that reservoir properties occurrences obey a Gaussian mixture distribution (a linear combination of Gaussian components). Such assumption is needed to describe the generally non-Gaussian behavior of these properties in nature. To illustrate the utility of the proposed probabilistic approach, we created a synthetic reservoir model that reflects the complexity and heterogeneity of real earth. These synthetic results are encouraging and make us believe this methodology will work with real data. INTRODUCTION Recorded seismic amplitudes depend on the contrasts of the elastic properties in the subsurface as well as on the spatial geometry of these contrasts, the latter meaning that even very strong contrasts may be seismically invisible if spread over a small lateral area or thin vertical layer. At the same time, the physical properties and conditions of rock under examination are related to the absolute elastic properties rather than to their contrasts. Even if this dichotomy is resolved (e.g., by adding a low-frequency depth trend), we still face only three variables (e.g., elastic properties plus density, or near, mid and far stacks of seismic traces) that depend on five or more underlying rock properties and conditions (e.g., porosity, mineralogy, rock texture, saturation, pressure), all of which we aspire to resolve. To this end, the question is how to deal with this severe mathematical uncertainty. We recognize that in this case no deterministic solution can be found unless we introduce additional equations that link the underlying rock variables to each other. A mathematically different (but essentially physically the same) approach is to assume that the underlying variables obey certain probabilistic distributions and, moreover, these distributions are linked to each other or, in other words, the probability of finding certain porosity is linked to that of finding certain clay content and/or saturation. Following this concept, we adopt a probabilistic methodology for estimating reservoir properties from partial stack seismic data. This probabilistic approach to reservoir properties estimation (porosity, net to gross, fluids saturations and fluid pressure) starts with prestack seismic data and includes two main steps. First of all, a linearized AVO inversion technique (Buland and Omre, 2003) is applied to obtain elastic parameters from seismic seismic data. Following this, we perform a probabilistic estimation of reservoir properties from inverted seismic attributes. The inversion is based on a full Bayesian approach (Grana and Della Rossa, 2010), with the assumption that both elastic and petrophysical properties are distributed according to a Gaussian mixture. To test this method, a synthetic reservoir has been created based on plausible petrophysical, geological and pressure assumptions, within a geocellular grid.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010

Paper Number: SEG-2010-2452

Abstract

Summary The objective of this study was to experimentally revisit the relations among the resistivity, elastic-wave velocity, porosity, and permeability in Fontainebleau sandstone samples from the Ile de France region, around Paris, France. In our resistivity measurements, we partially saturated the samples with brine. We used Archie’s equation to estimate resistivity at 100% water saturation, assuming a saturation exponent of 2. Using self-consistent approximations (SC) 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. We also measured elastic-wave velocity on these dry samples for confining pressure between 0 and 40 MPa. We used a loading and unloading cycle and did not find any significant hysteresis in the velocity-pressure behavior. For the velocity data, using the self-consistent model with a grain aspect ratio 1 and pore aspect ratios 0.2, 0.1, and 0.05 fit our data at 40 MPa, while pores aspect ratios ranging between 0.1, 0.05, and 0.02 are a better fit for the data at 0 MPa. Both velocity and resistivity in clean sandstones can be modeled using SC approximation. In addition, we found a linear fit between the P-wave velocity and the decimal logarithm of the normalized resistivity, with deviations that correlate with differences in permeability. Introduction Velocity and resistivity of rocks depend on porosity, texture, mineralogy, and pore fluid. Studies by Wyllie et al. (1956, 1958) showed that porosity is the primary factor affecting P- and S- wave velocities. Later studies (Nur and Simmons, 1969; Domenico, 1976; Mavko, 1980; Murphy, 1984) have refined our understanding of rock properties showing how pore type and pore fluid distribution (i.e., saturation heterogeneity) may contribute to variations in the P- and S- wave velocities. Pore geometry, in particular, affects pore stiffness which, in turn, influences the velocity sensitivity to pressure (Mavko, 1980; Mavko and Nur, 1978; O’Connell and Budiansky, 1974) as well as to saturation (Mavko and Mukerji, 1995). In this study, we measure porosity, resistivity and velocity in Fontainebleau sandstones. We examine the porosity and resistivity relation using effective medium models, such as differential effective medium (DEM) (Bruggeman, 1935; Berryman, 1995) and self consistent (SC) (Landauer, 1952; Berryman, 1995), and a semi-empirical model by Archie (1942). We follow a similar procedure for P- and S-wave velocities as a function of porosity, using effective medium models, including also DEM and SC, and semi-empirical models, including the stiff sand model (Gal et al., 1998), the Raymer-Hunt-Gardner relation (Raymer et al., 1980), and Wyllie’s time-average equation (Wyllie et al., 1958). Elastic and electrical methods can contribute in different ways to characterizing rock. We examine the relation between resistivity and velocity. Both properties in this study were not measured in the same pressure, temperature, and saturation conditions due to limitations in the laboratory setups; therefore, the derived cross-property relations must be used with caution.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010

Paper Number: SEG-2010-2720

Abstract

Summary We propose an effective-medium model for estimating the elastic properties of a random aggregate of identical, spherical, cemented poroelastic grains. These estimates are achieved using a two-stage approach where the elastic properties of the porous grains are calculated first, followed by the elastic properties of an aggregate of the homogenized spherical grains. In the first stage, the effective elastic moduli of the poroelastic grains are calculated using an effective medium model or the combination of effective medium model with Gassmann’s equation, depending on the connectivity of the intragranular porosity. The intragranular pore space may be either air- or liquid-filled. In the second stage, we proceed to calculate the elastic properties of a dry aggregate of such grains using the cementation theory. In the third stage we use the self-consistent approximation to estimate the elastic properties of the aggregate at all cement concentrations. This model may be applied to diatomaceous and carbonate rocks. The microstructural parameters of our models can be associated to diagenesis and may be varied to mimic diagenetic processes of carbonates Introduction In this study we develop a methodology to determine the effective elastic moduli of porous grain aggregate with different textures. This work is an extension of the porousgrain model proposed by Ruiz and Dvorkin (2009). This extension combine the self-consistent approximation (Berryman, 1980) with the cementation theory (Dvorkin et al., 1994) to account for intergranular cement volume fractions from 0 to 1; and d) considering the effect of frequency. We treat a saturated porous-grain as an elastic solid with ellipsoidal inclusions filled with compressible fluid. This is achieved by introducing the porous grain concept into the cementation theory (Dvorkin et al., 1994). Then, by combining the cementation theory (Dvorkin et al., 1994) for porous grain material with a self-consistent approximation, specifically, the coherent potential approximation (CPA) (Berryman, 1980), we are allowed to estimate the elastic properties of cemented porous grain aggregates at all cement concentrations (Dvorkin et al. 1999). Our approach and models for non-cemented aggregates may be applied to sediment, such as calcareous and diatomaceous ooze, opal, and chalks. Our approach for cemented aggregates may be applied to carbonate rocks. The microstructural parameters of these models can be related to diagenesis and may be varied to mimic diagenetic processes of calcareous and diatomaceous ooze, and cemented and non-cemented carbonate rocks. Cemented aggregate of porous grains Cementation theory (Dvorkin et al., 1994) predicts that even a small amount of contact cement reinforces the grains contact, causing a large increase of the elastic moduli of the aggregate. The initial volume of cement added in the opening between grains is the most important. This theoretical prediction has been supported by several experiments (Ying, 1993; Tutuncu et al., 1997). Even by adding cement in the entire intergranular pore space, it is not possible to achieve the high relative stiffness increase produced by small volumes of cement at the grain contacts (Dvorkin et al., 1994; Dvorkin et al., 1999; Ying, 1993; Tutuncu et al., 1997).

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2009 SEG Annual Meeting, October 25–30, 2009

Paper Number: SEG-2009-2065

Abstract

Summary Elastic contrast in porous rock with fluid leads to irreversible seismic energy loss. This occurs in laminated intervals with individual layers much smaller than the seismic wavelength, even if the intrinsic attenuation in each single layer is zero. The proposed theoretical loss mechanism is macroscopic cross-flow between porous layers with differing elastic properties. A passing seismic wave creates deformation difference in this elastically heterogeneous body, hence encouraging viscous cross-flow and accompanying energy loss. Both the elastic and inelastic properties of this layered medium are anisotropic. The results indicate that the attenuation is larger in the direction perpendicular to the layers than parallel to the layers. Application of this theory to a gas hydrate well shows considerable attenuation anisotropy due to large contrast of elastic properties between hydrate-filled sand and surrounding shale. Introduction At least two reasons make the quantification of elastic anisotropy in earth relevant: (a) it has to be accounted for when analyzing far-offset seismic data and (b) if detected in seismic data, it may point to meaningful exploration and production related characteristics. We argue that assessing inelastic anisotropy is important as well. With this in mind, we offer a simple theory for calculating anisotropic inverse quality factor in a layered porous medium, based on an assumption that the irreversible seismic energy loss is due to viscous cross-flow between individual layers as they are deformed by a passing wave. Seismic waves in partially- or fully-saturated rock induce spatial and temporal variations of pore pressure. These variations result in oscillatory fluid flow. Viscous losses during this flow are one reason for irreversible energy loss and the resulting wave attenuation. The same induced fluid flow makes the elastic moduli (and elastic-wave velocity) in rock vary with frequency. The moduli are minimum at very low frequency when the pore fluid is relaxed, i.e., the spatial variations in the wave-induced pore pressure can equilibrate within the oscillation period. The moduli are maximum at very high frequency when the pore fluid is unrelaxed, which means that there is no immediate hydraulic communications between parts of the pore space. This modulus- and velocity-frequency dispersion is linked to attenuation via the causality condition. Therefore, if we can quantify how the elastic moduli vary with frequency, we can quantify attenuation. Dvorkin and Mavko (2006) show that the causality link between the modulus-frequency dispersion and attenuation can be used to estimate attenuation in fully-saturated rocks. In this work we extend their approach and assess attenuation anisotropy in a fully saturated layered medium. Attenuation estimation in finely layered media In a viscoelastic medium, the modulus-frequency dispersion and inverse quality factor are linked to each other by the causality Kramers-Kronig relations (Mavko et al., 1998). One example of this behavior is the standard linear solid where the elastic modulus M is related to linear frequency f as where M 0 is the low-frequency limit; M ¥is the high-frequency limit; and f CR is the critical frequency at which the transition occurs from the low- to high-frequency range. The corresponding maximum inverse quality factor at f = f CR is

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2009 SEG Annual Meeting, October 25–30, 2009

Paper Number: SEG-2009-2135

Abstract

Summary Basin-centered gas deposits are abundant in North America. Recently, such reservoirs have become attractive exploration and development targets because they contain vast domestic deposits of natural fuel. A key property required to plan and optimize production in these reservoirs is permeability. The latter is notoriously difficult to measure in a physical laboratory. Extremely low and often disconnected porosity results in small permeability, often in the nano-Darcy domain. This makes the standard steady-state flow approach virtually impossible to implement and calls for such intricate and lengthy techniques as pulse-decay flow measurement. An alternative to a physical measurement is a numerical simulation of fluid flow in a 3D digital pore space accurately imaged by high-resolution CT scanning. We present an example of this digital technique for two samples from the Williams Fork formation in Colorado Basin from one well drilled by Occidental Petroleum with the total porosity ranging from 0.01 to 0.10. The porosity of the first sample was about 0.08. It was dominated by fairly large pores connected by narrow conduits (Figure 2). This pore space was successfully imaged in a micro-CT machine with a voxel resolution of 2.2 microns. The simulated permeability was in the 1 to 5 mD range. The formation factor ranged from 600 to 2,000 (Table 1) The pore space of the second sample was not discernible at the micro-CT resolution. It was imaged in a nano-CT machine with a voxel resolution of 0.065 microns. Disconnected spherical pores of approximately 1 micron in size were discovered. These pores were predominantly located within calcite crystals, presumably due to secondary dissolution of carbonate inclusions. The Nano-CT x-ray system (Figure 1) has a copper target and a seventy-micron diameter focal spot. An elliptical capillary lens focuses the x-rays on to the sample. After the x-rays pass through the sample, a Fresnel zone plate, made with circular gold rings, refocuses the x-rays onto the detector. The system has two fields of view: 60 and 20 microns. SAMPLE B: Micro-CT Imaging The sample used in this study was extracted from a core (Figure 3) and was selected to represent the rock that was imaged with the micro-CT system, but did not allow determining porosity directly. The sample was mounted on a stem, and then placed in the scanner for the tomographic procedure. SAMPLE B: Nano-CT Imaging Calcite cement (Figure 4) can strongly control reservoir quality and usually reduces porosity and permeability. In this case the micro-porosity is associated with the calcite minerals. The nano- scale reveals the different crystal structures. The upper row in Figure 5 corresponds to three-dimensional views of the sample scanned with the nano-CT system. The matrix is made transparent to show a subregion selected for porosity calculations, shown in the small 20-micron cube shown in blue. The lower row corresponds to three-dimensional views of the sub-region of a 20-micron cube. The image on the left shows the solid phase in gray and the pore space in blue. The central figure shows only the pore space, and the image on the left shows the exterior bounding slices of the cube.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2009 SEG Annual Meeting, October 25–30, 2009

Paper Number: SEG-2009-1940

Abstract

Summary Rock properties, such as porosity, permeability, and elastic moduli, depend on the scale (volume) of measurement. They may spatially vary within millimeters and, certainly, within inches and feet. This natural variability renders meaningless the concept of a data point, simply because the datum will be different just a few inches away, or if averaged in a larger volume. However, some transforms from one property to another appear scale independent. Obtained at a microscale, they can be potentially applied at a larger scale in the field. This makes us believe that such transforms, stationary with respect to position and scale, should replace single-category properties (e.g., porosity) as the primary attributes of rock. Introduction Consider the Finney (1970) pack, a dense random pack of identical spheres, arguably one of the most homogeneous granular objects (Figure 1). This pack is comprised of about 4000 grains. Its porosity is about 0.36. Let us select a cube sub-volume at the center of this pack and further (evenly) divide this cube into eight sub-cubes (Figure 2). The porosity of these sub-volumes plotted in the same figure is not stationary in space: depending on the subsample, it can be as small as 0.32 or as large as 0.41, whereas the porosity of the larger volume is 0.36. We can reduce the porosity of the original pack by digitally expanding the radius of each sphere to 1.05 and 1.10 of its original size while keeping their centers fixed in space. Spatial non-stationarity of porosity persists in these altered samples (Figure 3). A question then is how the porosity (or any other rock property) measured at a given scale, be it in the lab or in the well, is relevant to forecasting and understanding processes at another scale (e.g., during reservoir simulation). One may argue of course, that the spatial non-stationarity can be alleviated by simply selecting a volume large enough, the so-called elementary representative volume (REV). This will certainly be the case in the Finney pack. We dispute this point by speculating that there is no REV to be found in natural rock (Figure 4 and 5) which is heterogeneous at all scales. This is demonstrated by many well data where rock properties can vary appreciably between two points just inches apart. Therefore, it may not be valid to assign a single porosity, permeability, resistivity, or velocity to a volume in the subsurface. What then should replace these traditional rock physics attributes? Using Trends instead of Data Points: Permeability It is reasonable to assume that if porosity is not stationary in space, neither will be the corresponding permeability. To measure permeability on samples and subsamples shown in Figure 2 and 4 is arguably impossible in the physical laboratory. However, it is definitely possible in the digital laboratory by simulating the Navier-Stokes flow through the digital pore space either constructed on the computer, as in the Finney pack example, or imaged, as in the oil sand in Figure 4. Such computer experiments have been robust and repeatable (Dvorkin et al., 2008; and Dvorkin and Nur, 2009).