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1
Li, Yongyi, Lev Vernik, Mark Chapman, and Joel Sarout. "Introduction to this special section: Rock physics." Leading Edge 38, no. 5 (May 2019): 332. http://dx.doi.org/10.1190/tle38050332.1.
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Rock physics links the physical properties of rocks to geophysical and petrophysical observations and, in the process, serves as a focal point in many exploration and reservoir characterization studies. Today, the field of rock physics and seismic petrophysics embraces new directions with diverse applications in estimating static and dynamic reservoir properties through time-variant mechanical, thermal, chemical, and geologic processes. Integration with new digital and computing technologies is gradually gaining traction. The use of rock physics in seismic imaging, prestack seismic analysis, seismic inversion, and geomechanical model building also contributes to the increase in rock-physics influence. This special section highlights current rock-physics research and practices in several key areas, namely experimental rock physics, rock-physics theory and model studies, and the use of rock physics in reservoir characterizations.
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Grana, Dario. "Multivariate probabilistic rock-physics models using Kumaraswamy distributions." GEOPHYSICS 86, no. 5 (August 30, 2021): MR261—MR270. http://dx.doi.org/10.1190/geo2021-0124.1.
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Rock-physics models are physical equations that map petrophysical properties into geophysical variables, such as elastic properties and density. These equations are generally used in quantitative log and seismic interpretation to estimate the properties of interest from measured well logs and seismic data. Such models are generally calibrated using core samples and well-log data and result in accurate predictions of the unknown properties. Because the input data are often affected by measurement errors, the model predictions are often uncertain. Instead of applying rock-physics models to deterministic measurements, I have applied the models to the probability density function (PDF) of the measurements. This approach has been previously adopted in the literature using Gaussian distributions, but for petrophysical properties of porous rocks, such as volumetric fractions of solid and fluid components, the standard probabilistic formulation based on Gaussian assumptions is not applicable due to the bounded nature of the properties, the multimodality, and the nonsymmetric behavior. The proposed approach is based on the Kumaraswamy PDF for continuous random variables, which allows modeling double-bounded nonsymmetric distributions and is analytically tractable, unlike beta or Dirichlet distributions. I have developed a probabilistic rock-physics model applied to double-bounded continuous random variables distributed according to a Kumaraswamy distribution and derived the analytical solution of the probability distribution of the rock-physics model predictions. The method is evaluated for three rock-physics models: Raymer’s equation, Dvorkin’s stiff sand model, and Kuster-Toksöz’s inclusion model.
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Mur, Alan, and Lev Vernik. "Testing popular rock-physics models." Leading Edge 38, no. 5 (May 2019): 350–57. http://dx.doi.org/10.1190/tle38050350.1.
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In the spirit of classic rock physics, and as an ideal foundation for conventional quantitative interpretation workflows, we consider several popular models relating elastic rock properties to their composition, microstructure, and effective stress on the background of a worldwide log data set, incorporating sands and shales characterized by the maximum dynamic impedance range. We demonstrate that the patchy cement model, ellipsoidal inclusion model, and siliciclastic diagenesis model may be calibrated successfully against the world data set and used in seismic rock property log restoration/editing. We also demonstrate that some of these models present obvious challenges in terms of the information derived from quantitative seismic interpretation. Notably, the key input parameters used in these rock-physics models may show little resemblance to the rock parameters actually observed in geologic studies. Replacing the true rock parameters with the effective ones may do disservice to the science of rock physics in general.
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Khadeeva, Yulia, and Lev Vernik. "Rock-physics model for unconventional shales." Leading Edge 33, no. 3 (March 2014): 318–22. http://dx.doi.org/10.1190/tle33030318.1.
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Grana, Dario. "Bayesian linearized rock-physics inversion." GEOPHYSICS 81, no. 6 (November 2016): D625—D641. http://dx.doi.org/10.1190/geo2016-0161.1.
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The estimation of rock and fluid properties from seismic attributes is an inverse problem. Rock-physics modeling provides physical relations to link elastic and petrophysical variables. Most of these models are nonlinear; therefore, the inversion generally requires complex iterative optimization algorithms to estimate the reservoir model of petrophysical properties. We have developed a new approach based on the linearization of the rock-physics forward model using first-order Taylor series approximations. The mathematical method adopted for the inversion is the Bayesian approach previously applied successfully to amplitude variation with offset linearized inversion. We developed the analytical formulation of the linearized rock-physics relations for three different models: empirical, granular media, and inclusion models, and we derived the formulation of the Bayesian rock-physics inversion under Gaussian assumptions for the prior distribution of the model. The application of the inversion to real data sets delivers accurate results. The main advantage of this method is the small computational cost due to the analytical solution given by the linearization and the Bayesian Gaussian approach.
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Vlahou, I., and M. G. Worster. "Freeze fracturing of elastic porous media: a mathematical model." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2175 (March 2015): 20140741. http://dx.doi.org/10.1098/rspa.2014.0741.
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We present a mathematical model of the fracturing of water-saturated rocks and other porous materials in cold climates. Ice growing inside porous rocks causes large pressures to develop that can significantly damage the rock. We study the growth of ice inside a penny-shaped cavity in a water-saturated porous rock and the consequent fracturing of the medium. Premelting of the ice against the rock, which results in thin films of unfrozen water forming between the ice and the rock, is one of the dominant processes of rock fracturing. We find that the fracture toughness of the rock, the size of pre-existing faults and the undercooling of the environment are the main parameters determining the susceptibility of a medium to fracturing. We also explore the dependence of the growth rates on the permeability and elasticity of the medium. Thin and fast-fracturing cracks are found for many types of rocks. We consider how the growth rate can be limited by the existence of pore ice, which decreases the permeability of a medium, and propose an expression for the effective ‘frozen’ permeability.
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Grana, Dario. "Probabilistic approach to rock physics modeling." GEOPHYSICS 79, no. 2 (March 1, 2014): D123—D143. http://dx.doi.org/10.1190/geo2013-0333.1.
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Rock physics modeling aims to provide a link between rock properties, such as porosity, lithology, and fluid saturation, and elastic attributes, such as velocities or impedances. These models are then used in quantitative seismic interpretation and reservoir characterization. However, most of the geophysical measurements are uncertain; therefore, rock physics equations must be combined with mathematical tools to account for the uncertainty in the data. We combined probability theory with rock physics modeling to make predictions of elastic properties using probability distributions rather than definite values. The method provided analytical solutions of rock physics models in which the input is a random variable whose exact value is unknown but whose probability distribution is known. The probability distribution derived with this approach can be used to quantify the uncertainty in rock physics model predictions and in rock property estimation from seismic attributes. Examples of fluid substitution and rock physics modeling were studied to illustrate the application of the method.
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Ruiz, Franklin, and Arthur Cheng. "A rock physics model for tight gas sand." Leading Edge 29, no. 12 (December 2010): 1484–89. http://dx.doi.org/10.1190/1.3525364.
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Rasolofosaon, Patrick N. "Unified phenomenological model for the mechanical behavior of rocks." GEOPHYSICS 74, no. 5 (September 2009): WB107—WB116. http://dx.doi.org/10.1190/1.3169505.
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Various types of experiments are used to interrogate the mechanical behavior of rocks. The whole experimental spectrum covers many orders of magnitude in frequency (roughly ten orders of magnitude) and in strain (approximately eight orders of magnitude). These experimental studies have established unambiguously a certain number of robust results, namely, frequency dependence, dependence on stress-strain level (nonlinearity), eventually the presence of hysteresis (stress is not an analytic function of strain), and dependence on the direction of observation (anisotropy). These four behaviors are synthesized in a single model. The model allows direct comparison of the magnitude of the different phenomena (dispersion, nonlinearity, anisotropy) and their combinations in rocks. The frequency dependence of the mechanical properties should not be neglected, but another fundamental parameter, namely, the strain level, is important to explain the mismatch between the “static moduli,” measured with a press in rock mechanics, and the “dynamic moduli,” measured with ultrasonic devices in rock physics, which commonly is not appreciated. Such a unified model helps to make the link between different communities (e.g., rock physics, seismology, applied seismics, and rock mechanics) by using the same mathematical tool, and it could contribute to mutual fertilization among these communities.
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Chen, Jinsong, and G. Michael Hoversten. "Joint inversion of marine seismic AVA and CSEM data using statistical rock-physics models and Markov random fields." GEOPHYSICS 77, no. 1 (January 2012): R65—R80. http://dx.doi.org/10.1190/geo2011-0219.1.
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Joint inversion of seismic AVA and CSEM data requires rock-physics relationships to link seismic attributes to electric properties. Ideally, we can connect them through reservoir parameters (e.g., porosity and water saturation) by developing physical-based models, such as Gassmann’s equations and Archie’s law, using nearby borehole logs. This could be difficult in the exploration stage because information available is typically insufficient for choosing suitable rock-physics models and for subsequently obtaining reliable estimates of the associated parameters. The use of improper rock-physics models and the inaccuracy of the estimates of model parameters may cause misleading inversion results. Conversely, it is easy to derive statistical relationships among seismic and electric attributes and reservoir parameters from distant borehole logs. In this study, we developed a Bayesian model to jointly invert seismic AVA and CSEM data for reservoir parameters using statistical rock-physics models; the spatial dependence of geophysical and reservoir parameters were carried out by lithotypes through Markov random fields. We applied the developed model to a synthetic case that simulates a CO2 monitoring application. We derived statistical rock-physics relations from borehole logs at one location and estimated seismic P- and S-wave velocity ratio, acoustic impedance, density, electric resistivity, lithotypes, porosity, and water saturation at three different locations by conditioning to seismic AVA and CSEM data. Comparison of the inversion results with their corresponding true values showed that the correlation-based statistical rock-physics models provide significant information for improving the joint inversion results.
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Dupuy, Bastien, Stéphane Garambois, Amir Asnaashari, Hadi M. Balhareth, Martin Landrø, Alexey Stovas, and Jean Virieux. "Estimation of rock physics properties from seismic attributes — Part 2: Applications." GEOPHYSICS 81, no. 4 (July 2016): M55—M69. http://dx.doi.org/10.1190/geo2015-0492.1.
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The estimation of quantitative rock physics properties is of great importance for reservoir characterization and monitoring in [Formula: see text] storage or enhanced oil recovery as an example. We have combined the high-resolution results of full-waveform inversion (FWI) methods with rock physics inversion. Because we consider a generic and dynamic rock physics model, our method is applicable to most kinds of rocks for a wide range of frequencies. The first step allows determination of viscoelastic effective properties, i.e., quantitative seismic attributes, whereas the rock physics inversion estimates rock physics properties (porosity, solid frame moduli, fluid phase properties, or saturation). This two-step workflow is applied to time-lapse synthetic and field cases. The sensitivity tests that we had previously carried out showed that it can be crucial to use multiparameter inputs to accurately recover fluid saturations and fluid properties. However, due to the limited data availability and difficulties in getting reliable multiparameter FWI results, we are limited to acoustic FWI results. The synthetic tests are conclusive even if they are favorable cases. For the first time-lapse fluid substitution synthetic case, we first characterize the rock frame parameters on the baseline model using P-wave velocity estimations obtained by acoustic FWI. Then, we obtain an accurate estimation of fluid bulk modulus from the time-lapse P-wave velocity. In the Marmousi synthetic case, the rock frame properties are accurately recovered for the baseline model, whereas the gas saturation change in the monitor model is not estimated correctly. On the field data example (time-lapse monitoring of an underground blowout in the North Sea), the estimation of rock frame properties gives results on a relatively narrow range, and we use this estimation as a starting model for the gas saturation inversion. We have found that the estimation of the gas saturation is not accurate enough, and the use of attenuation data is then required. However, the uncertainty on the estimation of baseline rock frame properties is not critical to monitor gas saturation changes.
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Zhang, Lin, Jing Ba, and José M. Carcione. "A rock-physics model to determine the pore microstructure of cracked porous rocks." Geophysical Journal International 223, no. 1 (July 7, 2020): 622–31. http://dx.doi.org/10.1093/gji/ggaa327.
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SUMMARY Determining rock microstructure remains challenging, since a proper rock-physics model is needed to establish the relation between pore microstructure and elastic and transport properties. We present a model to estimate pore microstructure based on porosity, ultrasonic velocities and permeability, assuming that the microstructure consists on randomly oriented stiff equant pores and penny-shaped cracks. The stiff pore and crack porosity varying with differential pressure is estimated from the measured total porosity on the basis of a dual porosity model. The aspect ratio of pores and cracks and the crack density as a function of differential pressure are obtained from dry-rock P- and S-wave velocities, by using a differential effective medium model. These results are used to invert the pore radius from the matrix permeability by using a circular pore model. Above a crack density of 0.13, the crack radius can be estimated from permeability, and below that threshold, the radius is estimated from P-wave velocities, taking into account the wave dispersion induced by local fluid flow between pores and cracks. The approach is applied to experimental data for dry and saturated Fontainebleau sandstone and Chelmsford Granite.
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Nie, Xin, Chi Zhang, Chenchen Wang, Shichang Nie, Jie Zhang, and Chaomo Zhang. "Variable secondary porosity modeling of carbonate rocks based on μ-CT images." Open Geosciences 11, no. 1 (October 25, 2019): 617–26. http://dx.doi.org/10.1515/geo-2019-0049.
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Abstract As an essential carbonate reservoir parameter, porosity is closely related to rock properties. Digital rock physics (DRP) technology can help us to build forward models and find out the relationship between porosity and physical properties. In order to prepare models for the rock physical simulations of carbonate rocks, digital rock models with different porosities and fractures are needed. Based on a three-dimensional carbonate digital rock image obtained by X-ray microtomography (μ-CT), we used erosion and dilation in mathematical morphology to modify the pores, and fractional Brownian motion model (FBM) to create fractures with different width and angles. The pores become larger after the erosion operation and become smaller after the dilation operation. Therefore, a series of models with different porosities are obtained. From the analysis of the rock models, we found out that the erosion operation is similar to the corrosion process in carbonate rocks. The dilation operation can be used to restore the matrix of the late stages. In both processes, the pore numbers decrease because of the pore surface area decreases. The porosity-permeability relation of the models is a power exponential function similar to the experimental results. The structuring element B’s radius can affect the operation results. The FBM fracturing method has been proved reliable in sandstones, and because it is based on mathematics, the usage of it can also be workable in carbonate rocks. We can also use the processes and workflows introduced in this paper in carbonate digital rocks reconstructed in other ways. The models we built in this research lay the foundation of the next step physical simulations.
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Nababan, Benyamin Elilaski, Eliza Veronica Zanetta, Nahdah Novia, and Handoyo Handoyo. "ESTIMASI NILAI POROSITAS DAN PERMEABILITAS DENGAN PENDEKATAN DIGITAL ROCK PHYSICS (DRP) PADA SAMPEL BATUPASIR FORMASI NGRAYONG, CEKUNGAN JAWA TIMUR BAGIAN UTARA." Jurnal Geofisika Eksplorasi 5, no. 3 (January 17, 2020): 34–44. http://dx.doi.org/10.23960/jge.v5i3.34.
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Reservoir rock permeability and porosity are physical properties of rocks that control reservoir quality. Conventionally, rock porosity and permeability values are obtained from measurements in the laboratory or through well logs. At present, calculation of porosity and permeability can be calculated using digital image processing / Digital Rock Physics (DRP). Core data samples are processed by X-ray diffraction using CT-micro-tomography scan. The result is an image model of the core sample, 2D and 3D images. The combination of theoretical processing and digital images can be obtained from the value of porosity and permeability of rock samples. In this study, we calculated porosity and permeability values using the Digital Rock Physics (DRP) approach in sandstone samples from the Ngrayong Formation, North East Java Basin. The results of the digital image simulation and processing on the Ngrayong Formation sandstone samples ranged in value from 33.50% and permeability around 1267.02 mDarcy.
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Hossain, Zakir, Tapan Mukerji, Jack Dvorkin, and Ida L. Fabricius. "Rock physics model of glauconitic greensand from the North Sea." GEOPHYSICS 76, no. 6 (November 2011): E199—E209. http://dx.doi.org/10.1190/geo2010-0366.1.
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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.
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Xu, Miaomiao, Xingyao Yin, Zhaoyun Zong, and Haitao Li. "Rock-physics model of volcanic rocks, an example from Junggar Basin of China." Journal of Petroleum Science and Engineering 195 (December 2020): 107003. http://dx.doi.org/10.1016/j.petrol.2020.107003.
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Sengupta, Mita, and Shannon L. Eichmann. "Computing elastic properties of organic-rich source rocks using digital images." Leading Edge 40, no. 9 (September 2021): 662–66. http://dx.doi.org/10.1190/tle40090662.1.
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Digital rocks are 3D image-based representations of pore-scale geometries that reside in virtual laboratories. High-resolution 3D images that capture microstructural details of the real rock are used to build a digital rock. The digital rock, which is a data-driven model, is used to simulate physical processes such as fluid flow, heat flow, electricity, and elastic deformation through basic laws of physics and numerical simulations. Unconventional reservoirs are chemically heterogeneous where the rock matrix is composed of inorganic minerals, and hydrocarbons are held in the pores of thermally matured organic matter, all of which vary spatially at the nanoscale. This nanoscale heterogeneity poses challenges in measuring the petrophysical properties of source rocks and interpreting the data with reference to the changing rock structure. Focused ion beam scanning electron microscopy is a powerful 3D imaging technique used to study source rock structure where significant micro- and nanoscale heterogeneity exists. Compared to conventional rocks, the imaging resolution required to image source rocks is much higher due to the nanoscale pores, while the field of view becomes smaller. Moreover, pore connectivity and resulting permeability are extremely low, making flow property computations much more challenging than in conventional rocks. Elastic properties of source rocks are significantly more anisotropic than those of conventional reservoirs. However, one advantage of unconventional rocks is that the soft organic matter can be captured at the same imaging resolution as the stiff inorganic matrix, making digital elasticity computations feasible. Physical measurement of kerogen elastic properties is difficult because of the tiny sample size. Digital rock physics provides a unique and powerful tool in the elastic characterization of kerogen.
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Shegelski, Mark R. A., and Ross Niebergall. "The Motion of Rapidly Rotating Curling Rocks." Australian Journal of Physics 52, no. 6 (1999): 1025. http://dx.doi.org/10.1071/ph98064.
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We present a physical model that accounts for the motion of rapidly rotating curling rocks. By rapidly rotating we mean that the rotational speed of the contact annulus of the rock about the centre of mass is large compared with the translational speed of the centre of mass. The principal features of the model are: (i ) that the kinetic friction induces melting of the ice, with the consequence that there exists a thin film of liquid water lying between the contact annulus of the rock and the ice; (ii ) that the curling rock drags some of the thin liquid film around the rock as it rotates, with the consequence that the relative velocity between the rock and the thin liquid film is significantly different to the relative velocity between the rock and the underlying solid ice surface. Since it is the former relative velocity which dictates the nature of the motion of the curling rock, our model predicts some interesting differences between the motions of slowly versus rapidly rotating rocks. Of principal note is that our model predicts, and observations confirm, that rapidly rotating curling rocks stop moving translationally well before rotational motion ceases. This is in sharp contrast to the usual case of slow rotation, where both rotational and translational motion cease at the same instant. We have verified this and other predictions of our model by careful comparison with the motion of actual curling rocks.
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Yuan, Hemin, De-Hua Han, and Weimin Zhang. "Heavy oil sands measurement and rock-physics modeling." GEOPHYSICS 81, no. 1 (January 1, 2016): D57—D70. http://dx.doi.org/10.1190/geo2014-0573.1.
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Heavy oil reservoirs are important alternative energy resources to conventional oil and gas reservoirs. However, due to the high viscosity of heavy oil, much production of heavy oil reservoirs involves injecting steam, and determining the temperature distribution is significant for production. To do this, time-lapse inversion is commonly used to derive the change of the oil sand properties during steam injection, and rock-physics models are used to link the properties and temperature. Many people have done research on simulating variations of the oil sand properties with temperature; however, the previous models fail to adequately represent our experimental data, and they overestimate their values. The errors between previous models’ predictions and measurements are quite large, especially at low temperatures. To study the oil sand properties, we first measured eight oil sand samples including five presteam samples and three poststeam samples, and we experimentally quantified the pressure sensitivity of velocity, the temperature sensitivity of velocity, and the corresponding [Formula: see text] ratios. Then we developed a new model, introducing a frame damage parameter and a solid oil proportion parameter. This model integrates the solid oil into the sand frame, and it incorporates the temperature-dependent frame damage to characterize the frame moduli variations with increasing temperature. The solid-Gassmann equation was then applied to saturate the sands’ frame with heavy oil. Our simulation results determined that the errors at low temperature and high temperature were both compensated, and the new model fitted better than previous models over the whole measurement temperature range. The modeling was also extended to the thermal production temperature range, and the phase transition of water was considered, which provided a useful indicator of the steam.
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Lubis, L. A., and Z. Z. T. Harith. "Integration of Rock Digital Images to Improve Carbonate Rock Physics Model of Offshore Sarawak." Journal of Applied Sciences 14, no. 23 (November 15, 2014): 3354–58. http://dx.doi.org/10.3923/jas.2014.3354.3358.
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Arévalo-López, Humberto S., and Jack P. Dvorkin. "Rock-physics diagnostics of a turbidite oil reservoir offshore northwest Australia." GEOPHYSICS 82, no. 1 (January 1, 2017): MR1—MR13. http://dx.doi.org/10.1190/geo2016-0083.1.
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Interpreting seismic data for petrophysical rock properties requires a rock-physics model that links the petrophysical rock properties to the elastic properties, such as velocity and impedance. Such a model can only be established from controlled experiments in which both groups of rock properties are measured on the same samples. A prolific source of such data is wellbore measurements. We use data from four wells drilled through a clastic offshore oil reservoir to perform rock-physics diagnostics, i.e., to find a theoretical rock-physics model that quantitatively explains the measurements. Using the model, we correct questionable well curves. Moreover, a crucial purpose of rock-physics diagnostics is to go beyond the settings represented in the wells and understand the seismic signatures of rock properties varying in a wider range via forward seismic modeling. With this goal in mind, we use our model to generate synthetic seismic gathers from perturbational modeling to address “what-if” scenarios not present in the wells.
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Durrani, Muhammad Z. A., Keith Willson, Jingyi Chen, Bryan Tapp, and Jubran Akram. "Rational Rock Physics for Improved Velocity Prediction and Reservoir Properties Estimation for Granite Wash (Tight Sands) in Anadarko Basin, Texas." International Journal of Geophysics 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/209351.
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Due to the complex nature, deriving elastic properties from seismic data for the prolific Granite Wash reservoir (Pennsylvanian age) in the western Anadarko Basin Wheeler County (Texas) is quite a challenge. In this paper, we used rock physics tool to describe the diagenesis and accurate estimation of seismic velocities of P and S waves in Granite Wash reservoir. Hertz-Mindlin and Cementation (Dvorkin’s) theories are applied to analyze the nature of the reservoir rocks (uncemented and cemented). In the implementation of rock physics diagnostics, three classical rock physics (empirical relations, Kuster-Toksöz, and Berryman) models are comparatively analyzed for velocity prediction taking into account the pore shape geometry. An empirical (VP-VS) relationship is also generated calibrated with core data for shear wave velocity prediction. Finally, we discussed the advantages of each rock physics model in detail. In addition, cross-plots of unconventional attributes help us in the clear separation of anomalous zone and lithologic properties of sand and shale facies over conventional attributes.
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Yan, Fuyong, De-Hua Han, and Qiuliang Yao. "Rock-physics constrained seismic anisotropy parameter estimation." GEOPHYSICS 86, no. 4 (July 1, 2021): MR247—MR253. http://dx.doi.org/10.1190/geo2019-0153.1.
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Compared with isotropic media, at least two extra parameters are involved in common P-wave seismic data processing and interpretation for transversely isotropic media. Previous synthetic model testing has shown that it is challenging to estimate anisotropy parameters even using extremely low noise level seismic data from a simple geologic setting. Although theoretically independent, anisotropy parameters are not free variables for organic-rich mudrocks whose elastic properties are often approximated by transverse isotropy. One potential approach to improve the accuracy in the estimated anisotropy parameters is to consider the physical relationships between them during the inversion process. To test this proposition, we first modify a commonly used nonhyperbolic reflection moveout equation as a function of the interval anisotropy velocities so that rock-physics constraints could be effectively applied to each layer. The rock-physics constraints are established from data analysis of selected laboratory anisotropy measurement data. The laboratory data are then used to parameterize hundreds of 15-layer transverse isotropy models using a Monte Carlo simulation. The synthetic model testing indicates that the accuracy of the estimated anisotropy parameters can be improved if the relationships between the anisotropy parameters are considered during the inversion process.
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Ganikhodjaev, Nasir, and Pah Chin Hee. "Rock-Paper-Scissors Lattice Model." Malaysian Journal of Fundamental and Applied Sciences 16, no. 4 (August 17, 2020): 400–402. http://dx.doi.org/10.11113/mjfas.v16n4.1726.
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In this work, we introduce Rock-Paper-Scissors lattice model on Cayley tree of second order generated by Rock-Paper-Scissors game. In this strategic 2-player game, the rule is simple: rock beats scissors, scissors beat paper, and paper beats rock. A payoff matrix of this game is a skew-symmetric. It is known that quadratic stochastic operator generated by this matrix is non-ergodic transformation. The Hamiltonian of Rock-Paper-Scissors Lattice Model is defined by this skew-symmetric payoff matrix . In this paper, we discuss a connection between three fields of research: evolutionary games, quadratic stochastic operators, and lattice models of statistical physics. We prove that a phase diagram of the Rock-Paper-Scissors model consists of translation-invariant and periodic Gibbs measure with period 3.
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Lissa, Simón, Matthias Ruf, Holger Steeb, and Beatriz Quintal. "Digital rock physics applied to squirt flow." GEOPHYSICS 86, no. 4 (July 1, 2021): MR235—MR245. http://dx.doi.org/10.1190/geo2020-0731.1.
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We have developed a workflow for computing the seismic-wave moduli dispersion and attenuation due to squirt flow in a numerical model derived from a micro X-ray computed tomography image of cracked (through thermal treatment) Carrara marble sample. To generate the numerical model, the image is processed, segmented, and meshed. The finite-element method is adopted to solve the linearized, quasistatic Navier-Stokes equations describing laminar flow of a compressible viscous fluid inside the cracks coupled with the quasistatic Lamé-Navier equations for the solid phase. We compute the effective P- and S-wave moduli in the three Cartesian directions for a model in dry conditions (saturated with air) and for a smaller model fully saturated with glycerin and having either drained or undrained boundary conditions. For the model saturated with glycerin, the results indicate significant and frequency-dependent P- and S-wave attenuation and the corresponding dispersion caused by squirt flow. Squirt flow occurs in response to fluid pressure gradients induced in the cracks by the imposed deformations. Our digital rock-physics workflow can be used to interpret laboratory measurements of attenuation using images of the rock sample.
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Ke, Ganpan, Merrick Johnston, and Hefeng Dong. "Rock-physics models for bitumen-saturated sands: Fractional gradient model and Hashin-Shtrikman iterative model." GEOPHYSICS 77, no. 2 (March 2012): D7—D15. http://dx.doi.org/10.1190/geo2011-0338.1.
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Rock-physics modeling of heavy-oil-saturated sands requires adjustments and new approaches to the available fluid-substitution schemes used on conventional reservoirs. This paper introduces two models: the fractional-gradient model (FGM) for simulating the frequency dispersion of the shear modulus of pure bitumen and the Hashin-Shtrikman iterative model (HSIM) for modeling the moduli of bitumen-saturated sands as a function of frequency and temperature. Taylor expansion shows that the first-order FGM has higher resolution than the Maxwell model and lower complexity than the Cole-Cole model. In addition, FGM is superior to Maxwell and Cole-Cole models in that viscosity modeling does not need to be done prior to shear-modulus modeling. The building of HSIM is based on observations of the microstructure of the bitumen-saturated sands. Three main characteristics in the sands are observed in the simplified model, producing a range of stiff, medium, and soft effective matrices. Bitumen can dominate the matrix as if the quartz grains were suspended in it (soft); quartz grains can surround the bitumen (stiff); and a bitumen layer can form around the quartz grain (medium). The quartz grains are assumed to be statistically spherical. HSIM is obtained by iteratively calculating the HS bounds of the stiff and soft parts of the sands. The measured shear modulus of pure bitumen and bitumen-saturated sands at different frequencies and temperatures verify the validity of these two models. The combination of these two models gives a novel fluid-substitution routine for modeling the time-lapse response during steam-assist gravity draining thermal production of bitumen. The limitations of the two models also are discussed.
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Shegelski, Mark R. A., Ross Niebergall, and Mark A. Walton. "The motion of a curling rock." Canadian Journal of Physics 74, no. 9-10 (September 1, 1996): 663–70. http://dx.doi.org/10.1139/p96-095.
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We present a plausible physical model that accounts for the motion of a curling rock. The principal features of the model are (i) that the kinetic friction induces melting of the ice with the consequence that the curling rock experiences both "dry friction," when encountering solid ice, as well as "wet friction," for contact areas that pass over the thin film of liquid water lying above the ice; (ii) that the wet friction is velocity dependent; and (iii) that the curling rock is able, in its last stages of motion, to drag some of the thin liquid film part way around the rock, which significantly enhances the curl of the rock. We compare the model to actual trajectories of curling rocks.
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Wollner, Uri, Yunfei Yang, and Jack P. Dvorkin. "Rock-physics diagnostics of an offshore gas field." GEOPHYSICS 82, no. 4 (July 1, 2017): MR121—MR132. http://dx.doi.org/10.1190/geo2016-0390.1.
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Seismic reflections depend on the contrasts of the elastic properties of the subsurface and their 3D geometry. As a result, interpreting seismic data for petrophysical rock properties requires a theoretical rock-physics model that links the seismic response to a rock’s velocity and density. Such a model is based on controlled experiments in which the petrophysical and elastic rock properties are measured on the same samples, such as in the wellbore. Using data from three wells drilled through a clastic offshore gas reservoir, we establish a theoretical rock-physics model that quantitatively explains these data. The modeling is based on the assumption that only three minerals are present: quartz, clay, and feldspar. To have a single rock-physics transform to quantify the well data in the entire intervals under examination in all three wells, we introduced field-specific elastic moduli for the clay. We then used the model to correct the measured shear-wave velocity because it appeared to be unreasonably low. The resulting model-derived Poisson’s ratio is much smaller than the measured ratio, especially in the reservoir. The associated synthetic amplitude variation with offset response appears to be consistent with the recorded seismic angle stacks. We have shown how rock-physics modeling not only helps us to correct the well data, but also allows us to go beyond the settings represented in the wells and quantify the seismic signatures of rock properties and conditions varying in a wider range using forward seismic modeling.
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Ayani, Mohit, and Dario Grana. "Statistical rock physics inversion of elastic and electrical properties for CO2 sequestration studies." Geophysical Journal International 223, no. 1 (July 16, 2020): 707–24. http://dx.doi.org/10.1093/gji/ggaa346.
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SUMMARY We present a statistical rock physics inversion of the elastic and electrical properties to estimate the petrophysical properties and quantify the associated uncertainty. The inversion method combines statistical rock physics modeling with Bayesian inverse theory. The model variables of interest are porosity and fluid saturations. The rock physics model includes the elastic and electrical components and can be applied to the results of seismic and electromagnetic inversion. To describe the non-Gaussian behaviour of the model properties, we adopt non-parametric probability density functions to sample multimodal and skewed distributions of the model variables. Different from machine learning approach, the proposed method is not completely data-driven but is based on a statistical rock physics model to link the model parameters to the data. The proposed method provides pointwise posterior distributions of the porosity and CO2 saturation along with the most-likely models and the associated uncertainty. The method is validated using synthetic and real data acquired for CO2 sequestration studies in different formations: the Rock Springs Uplift in Southwestern Wyoming and the Johansen formation in the North Sea, offshore Norway. The proposed approach is validated under different noise conditions and compared to traditional parametric approaches based on Gaussian assumptions. The results show that the proposed method provides an accurate inversion framework where instead of fitting the relationship between the model and the data, we account for the uncertainty in the rock physics model.
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Shegelski, Mark R. "Maximizing the lateral motion of a curling rock." Canadian Journal of Physics 79, no. 8 (August 1, 2001): 1117–20. http://dx.doi.org/10.1139/p01-076.
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A simplified version of a previously proposed model captures the salient features of the motion of a slowly rotating curling rock. The model is used to suggest how standard curling rocks may be modified to maximize the net lateral displacement of a slowly rotating curling rock. PACS No.: 46.00
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Sayers, Colin M., and Sagnik Dasgupta. "A predictive anisotropic rock-physics model for estimating elastic rock properties of unconventional shale reservoirs." Leading Edge 38, no. 5 (May 2019): 358–65. http://dx.doi.org/10.1190/tle38050358.1.
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This paper presents a predictive rock-physics model for unconventional shale reservoirs based on an extended Maxwell scheme. This model accounts for intrinsic anisotropy of rock matrix and heterogeneities and shape-induced anisotropy arising because the dimensions of kerogen inclusions and pores are larger parallel to the bedding plane than perpendicular to this plane. The model relates the results of seismic amplitude variation with offset inversion, such as P- and S-impedance, to the composition of the rock and enables identification of rock classes such as calcareous, argillaceous, siliceous, and mixed shales. This allows the choice of locations with the best potential for economic production of hydrocarbons. While this can be done using well data, prestack inversion of seismic P-wave data allows identification of the best locations before the wells are drilled. The results clearly show the ambiguity in rock classification obtained using poststack inversion of P-wave seismic data and demonstrate the need for prestack seismic inversion. The model provides estimates of formation anisotropy, as required for accurate determination of P- and S-impedance, and shows that anisotropy is a function not only of clay content but also other components of the rock as well as the aspect ratio of kerogen and pores. Estimates of minimum horizontal stress based on the model demonstrate the need to identify rock class and estimate anisotropy to determine the location of any stress barriers that may inhibit hydraulic fracture growth.
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Johansen, Tor Arne, Erling Hugo Jensen, Gary Mavko, and Jack Dvorkin. "Inverse rock physics modeling for reservoir quality prediction." GEOPHYSICS 78, no. 2 (March 1, 2013): M1—M18. http://dx.doi.org/10.1190/geo2012-0215.1.
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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.
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Li, Changping, Longchen Duan, Songcheng Tan, Victor Chikhotkin, and Xiaohui Wang. "An Electro Breakdown Damage Model for Granite and Simulation of Deep Drilling by High-Voltage Electropulse Boring." Shock and Vibration 2019 (November 29, 2019): 1–12. http://dx.doi.org/10.1155/2019/7149680.
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Electropulse rock breaking has wide application prospects in hard rock drilling and ore breaking. At present, there are no suitable physical mathematical models that describe electropulse boring (EPB) processes under confining pressures. In this paper, a high-voltage electropulse breakdown damage model is established for granite, which includes three submodels. It considers electric field distortions inside the rock, and an electric field distribution coefficient is introduced in the electro-breakdown model. A shock-wave model is also constructed and solved. To simulate the heterogeneity of rocks, EPB rock breaking in deep environments is simulated using the two-dimensional Particle Flow Code (PFC2D) program. The solved shock wave is loaded into the model, and confining pressure is applied by the particle servo method. An artificial viscous boundary is used in the numerical simulation model. Using this approach, a complete numerical simulation of electropulse granite breaking is achieved. Breakdown strength and the influences of physical and mechanical parameters on it are also obtained. Time-varying waveforms of electrical parameters are obtained, and the effect of confining pressure on EPB is also described.
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Dalvand, Mohammad, and Reza Falahat. "A new rock physics model to estimate shear velocity log." Journal of Petroleum Science and Engineering 196 (January 2021): 107697. http://dx.doi.org/10.1016/j.petrol.2020.107697.
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Gallop, Jeremy, Olena Babak, and Kun Liu. "A rock physics model to map gross lithology using compaction." Geophysical Prospecting 68, no. 2 (October 21, 2019): 615–30. http://dx.doi.org/10.1111/1365-2478.12860.
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Liu, Yangjun (Kevin), Nader Chand Dutta, Denes Vigh, Jerry Kapoor, Cara Hunter, Emmanuel Saragoussi, Laura Jones, Sherman Yang, and Mohamed Abdelmonem Eissa. "Basin-scale integrated earth-model building using rock-physics constraints." Leading Edge 35, no. 2 (February 2016): 141–45. http://dx.doi.org/10.1190/tle35020141.1.
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Pradhan, Anshuman, Nader C. Dutta, Huy Q. Le, Biondo Biondi, and Tapan Mukerji. "Approximate Bayesian inference of seismic velocity and pore-pressure uncertainty with basin modeling, rock physics, and imaging constraints." GEOPHYSICS 85, no. 5 (June 26, 2020): ID19—ID34. http://dx.doi.org/10.1190/geo2019-0767.1.
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We have introduced a methodology for quantifying seismic velocity and pore-pressure uncertainty that incorporates information regarding the geologic history of a basin, rock physics, well log, drilling, and seismic data. In particular, our approach relies on linking velocity models to the basin modeling outputs of porosity, mineral volume fractions, and pore pressure through rock-physics models. We account for geologic uncertainty by defining prior probability distributions on lithology-specific porosity compaction model parameters, permeability-porosity model parameters, and heat-flow boundary condition. Monte Carlo basin simulations are performed by sampling the prior uncertainty space. We perform probabilistic calibration of the basin model outputs by defining data likelihood distributions to represent well data uncertainty. Rock physics modeling transforms the basin modeling outputs to give us multiple velocity realizations used to perform multiple depth migrations. We have developed an approximate Bayesian inference framework that uses migration velocity analysis in conjunction with well data for updating velocity and basin modeling uncertainty. We apply our methodology in 2D to a real field case from the Gulf of Mexico; our methodology allows for building a geologic and physical model space for velocity and pore-pressure prediction with reduced uncertainty.
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Dupuy, Bastien, Anouar Romdhane, Pierre-Louis Nordmann, Peder Eliasson, and Joonsang Park. "Bayesian rock-physics inversion: Application to CO2 storage monitoring." GEOPHYSICS 86, no. 4 (June 30, 2021): M101—M122. http://dx.doi.org/10.1190/geo2020-0218.1.
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Risk assessment of [Formula: see text] storage requires the use of geophysical monitoring techniques to quantify changes in selected reservoir properties such as [Formula: see text] saturation, pore pressure, and porosity. Conformance monitoring and the associated decision making rest upon the quantified properties derived from geophysical data, with uncertainty assessment. We have developed a general framework combining seismic and controlled-source electromagnetic (CSEM) inversions with rock-physics inversion with fully Bayesian formulations for proper quantification of uncertainty. The Bayesian rock-physics inversion rests upon two stages. First, a search stage consists of exploring the model space and deriving models with the associated probability density function (PDF). Second, an appraisal or importance sampling stage is used as a “correction” step to ensure that the full model space is explored and that the estimated posterior PDF can be used to derive quantities such as marginal probability densities. Both steps are based on the neighborhood algorithm. The approach does not require any linearization of the rock-physics model or assumption about the model parameters’ distribution. After describing the [Formula: see text] storage context, the available data at the Sleipner field before and after [Formula: see text] injection (baseline and monitor), and the rock-physics models, we perform an extended sensitivity study. We find that prior information is crucial, especially in the monitor case. We determine that joint inversion of seismic and CSEM data is also key to properly quantifying [Formula: see text] saturations. Finally, we apply the full inversion strategy to real data from Sleipner. We obtain rock frame moduli, porosity, saturation, and patchiness exponent distributions and the associated uncertainties along a 1D profile before and after injection. The results are consistent with geology knowledge and reservoir simulations, i.e., that the [Formula: see text] saturations are larger under the caprock confirming the [Formula: see text] upward migration by buoyancy effect. The estimates of the patchiness exponent have a larger uncertainty, suggesting semipatchy mixing behavior.
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Xie, Wei, and Kyle T. Spikes. "Reservoir facies design and modeling using probabilistic rock-physics templates." GEOPHYSICS 86, no. 1 (January 1, 2021): M17—M28. http://dx.doi.org/10.1190/geo2020-0044.1.
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We have developed a technique to design and optimize reservoir lithofluid facies based on probabilistic rock-physics templates. Subjectivity is promoted to design possible facies scenarios with different pore-fluid conditions, and quantitative simulations and evaluations are conducted in facies model selection. This method aims to provide guidelines for reservoir-facies modeling in an exploration setting in which limited data exist. The work includes two parts: facies-model simulations and uncertainty evaluations. We have first derived scenarios with all possible fluid types using Gassmann fluid substitution. We designed models with different numbers of facies and pore-fluid conditions using site-specific rock-physics templates. Detailed facies simulations were conducted in the petroelastic, elastic, and seismic domains in a step-by-step framework to preserve the geologic interpretability. The use of probabilistic rock-physics templates allowed for multiple realizations of each facies model to account for different types and magnitudes of errors and to infer facies probability and uncertainty. For each realization, we used Bayesian classification to assign facies labels. Comparisons between the predicted and true labels provided the success rates and entropy indices to quantify the prediction errors and confidence degrees, respectively. This workflow was tested with well-log data from a clastic reservoir in the Gulf of Mexico. We simulated models with five to seven facies with different pore-fluid parameters. From the petroelastic, elastic, and seismic domains, the uncertainty of facies models significantly increased due to well-log measurement errors, data-model mismatch, and resolution differences. The facies model consisting of oil sand, gas sand, and shale was the optimal set based on the high success rates and low entropy indices. Facies profiles estimated from this optimal model presented significant consistency with well-log interpretations. The techniques and results demonstrated here could be applied to different types of clastic reservoirs, and they provide useful constraints for reservoir facies modeling during early oilfield exploration stages.
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Shen, Yi, Jack Dvorkin, and Yunyue Li. "Improving seismic QP estimation using rock-physics constraints." GEOPHYSICS 83, no. 3 (May 1, 2018): MR187—MR198. http://dx.doi.org/10.1190/geo2016-0665.1.
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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 [Formula: see text] to [Formula: see text]. We derive an approximate closed-form solution relating [Formula: see text] to [Formula: see text] using rock-physics modeling. This relation is tested on well data from a clean clastic gas reservoir, of which the [Formula: see text] values are computed from the log data. Next, we create a 2D synthetic gas-reservoir section populated with [Formula: see text] and [Formula: see text] and generate respective synthetic seismograms. Now, the goal is to invert this synthetic seismic section for [Formula: see text]. If we use standard seismic inversion based solely on seismic data, the inverted attenuation model has low resolution and incorrect positioning, and it is distorted. However, adding our relation between velocity and attenuation, we obtain an attenuation model very close to the original section. This method is tested on a 2D field seismic data set from Gulf of Mexico. The resulting [Formula: see text] model matches the geologic shape of an absorption body interpreted from the seismic section. Using this [Formula: see text] model in seismic migration, we make the seismic events below the high-absorption layer clearly visible, with improved frequency content and coherency of the events.
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CHEN, HONGJIE, WEIYA XU, WEI WANG, RUBIN WANG, and CHONG SHI. "A NONLINEAR VISCOELASTIC-PLASTIC RHEOLOGICAL MODEL FOR ROCKS BASED ON FRACTIONAL DERIVATIVE THEORY." International Journal of Modern Physics B 27, no. 25 (September 12, 2013): 1350149. http://dx.doi.org/10.1142/s021797921350149x.
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The soft-matter element between the ideal solid and the ideal liquid is established and is described based on the definition of the fractional derivatives. By replacing a component in the generalized Kelvin model with the soft-matter component and connecting it in series with a nonlinear visco-plastic body, a nonlinear viscoelasto-plastic rheological model is proposed based on the fractional derivatives in order to describe the rheological behaviors of rocks. The data obtained from the triaxial creep tests of a typical rock are simulated with this model and the fitting result is good. The model can describe well three rheological stages of the rock during the triaxial creep tests. The validity of this model is then discussed. In this model, the fractional order β controls creep strain rate in the stable creep stage under the condition of low stress; while the creep index n controls creep rate of the accelerated rheological stage under the condition of high stress. Few parameters and good simulation results manifest the outstanding performance of the model. The model also adopts the damage theory to describe the progressive deterioration of rock viscous coefficient of the accelerated creep stage. The model can also give an excellent description of the three rheological stages of rocks, especially the accelerated creep stage.
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Khalid, Perveiz, Daniel Broseta, Dan Vladimir Nichita, and Jacques Blanco. "A modified rock physics model for analysis of seismic signatures of low gas-saturated rocks." Arabian Journal of Geosciences 7, no. 8 (July 9, 2013): 3281–95. http://dx.doi.org/10.1007/s12517-013-1024-0.
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Abbas Babasafari, Amir, Deva Ghosh, Ahmed M. A. Salim, and S. Y. Moussavi Alashloo. "Rock Physics Modeling Assisted Reservoir Properties Prediction: Case Study in Malay Basin." International Journal of Engineering & Technology 7, no. 3.32 (August 26, 2018): 24. http://dx.doi.org/10.14419/ijet.v7i3.32.18385.
Full textAbstract:
Shear velocity log is not measured at all wells in oil and gas fields, thus rock physics modeling plays an important role to predict this type of log. Therefore, seismic pre stack inversion is performed and elastic properties are estimated more accurately. Subsequently, a robust Petro-Elastic relationship arising from rock physics model leads to far more precise prediction of petrophysical properties. The more accurate rock physics modeling results in less uncertainty of reservoir modeling. Therefore, a valid rock physics model is intended to be built. For a better understanding of reservoir properties prediction, first of all rock physics modeling for each identified litho-facies classes should be performed separately through well log analysis.
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Prioul, Romain, Andrey Bakulin, and Victor Bakulin. "Nonlinear rock physics model for estimation of 3D subsurface stress in anisotropic formations: Theory and laboratory verification." GEOPHYSICS 69, no. 2 (March 2004): 415–25. http://dx.doi.org/10.1190/1.1707061.
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We develop a rock physics model based on nonlinear elasticity that describes the dependence of the effective stiffness tensor as a function of a 3D stress field in intrinsically anisotropic formations. This model predicts the seismic velocity of both P‐ and S‐waves in any direction for an arbitrary 3D stress state. Therefore, the model overcomes the limitations of existing empirical velocity‐stress models that link P‐wave velocity in isotropic rocks to uniaxial or hydrostatic stress. To validate this model, we analyze ultrasonic velocity measurements on stressed anisotropic samples of shale and sandstone. With only three nonlinear constants, we are able to predict the stress dependence of all five elastic medium parameters comprising the transversely isotropic stiffness tensor. We also show that the horizontal stress affects vertical S‐wave velocity with the same order of magnitude as vertical stress does. We develop a weak‐anisotropy approximation that directly links commonly measured anisotropic Thomsen parameters to the principal stresses. Each Thomsen parameter is simply a sum of corresponding background intrinsic anisotropy and stress‐induced contribution. The stress‐induced part is controlled by the difference between horizontal and vertical stresses and coefficients depending on nonlinear constants. Thus, isotropic rock stays isotropic under varying but hydrostatic load, whereas transversely isotropic rock retains the same values of dimensionless Thomsen parameters. Only unequal horizontal and vertical stresses alter anisotropy. Since Thomsen parameters conveniently describe seismic signatures, such as normal‐moveout velocities and amplitude‐variation‐with‐offset gradients, this approximation is suitable for designing new methods for the estimation of 3D subsurface stress from multicomponent seismic data.
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Denny, M. "Curling rock dynamics: Towards a realistic model." Canadian Journal of Physics 80, no. 9 (September 1, 2002): 1005–14. http://dx.doi.org/10.1139/p02-072.
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We present a model of curling rock motion, which yields realistic dependence upon the dynamical parameters. The underlying assumptions are motivated by physical arguments. We make clear which of the model predictions depend upon the assumptions made about frictional asymmetry and which are independent of these assumptions. PACS Nos.: 45.20
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ZHANG, CHENGYUAN, XIAOYAN LIU, DAOYING XI, and QUANSHENG LIU. "AN ROCK-PHYSICS-BASED COMPLEX PORE-FLUID-DISTRIBUTION MODEL TO SEISMIC DYNAMICAL RESPONSE." International Journal of Modern Physics B 22, no. 09n11 (April 30, 2008): 1437–42. http://dx.doi.org/10.1142/s021797920804689x.
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It is very important to know how the reservoir rock and its fluid properties are linked to seismic dynamic response. Literatures show that there are a variety of rock-physics models such as the most famous Biot-Gassmann equation aimed at the relationship between seismic velocity and liquid saturation. Most of these models make a fundamental assumption of one fluid phase or homogeneous phase within the pore volume. In this paper, we discuss possible seismic velocities change in a two immiscible pore fluids (i.e. water-gas) saturated reservoir with patchy saturation distribution. It is found that P-wave velocity of a reservoir rock with the same saturation but different pore fluid distribution exhibits noticeable variation and deviate overall from Gassmann's results. We use DEM theory to explain this phenomenon. It belongs to hybrid approach in rock-physics modeling and can handle complex pore-fluid-distribution cases. Based on the modeling study, we found that various fluid-distribution models may significantly affect the modulus and P-wave velocity. The seismic reflection time, amplitude and phase characteristics may change with the choice of pore-fluid-distribution models. Relevant rock mechanical experiments indicate the same trend of seismic responses. It also be proven by seismic reservoir monitoring experiment (time lapse study) that incorrect conclusion may be drawn about the strong seismic reflection in pure Utsira Sand if the microscopic pore-fluid-distribution effects are not taken into account.
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Naftaly, U., M. Schwartz, A. Aharony, and D. Stauffer. "The granular fracture model for rock fragmentation." Journal of Physics A: Mathematical and General 24, no. 19 (October 7, 1991): L1175—L1184. http://dx.doi.org/10.1088/0305-4470/24/19/009.
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Hu, Qi, Scott Keating, Kristopher A. Innanen, and Huaizhen Chen. "Direct updating of rock-physics properties using elastic full-waveform inversion." GEOPHYSICS 86, no. 3 (April 8, 2021): MR117—MR132. http://dx.doi.org/10.1190/geo2020-0199.1.
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Quantitative estimation of rock-physics properties is an important part of reservoir characterization. Most current seismic workflows in this field are based on amplitude variation with offset. Building on recent work on high-resolution multiparameter inversion for reservoir characterization, we have constructed a rock-physics parameterized elastic full-waveform inversion (EFWI) scheme. Within a suitably formed multiparameter EFWI, in this case a 2D frequency-domain isotropic-elastic full-waveform inversion with a truncated Gauss-Newton optimization, any rock-physics model with a well-defined mapping between its parameters and seismic velocity/density can be examined. We select a three-parameter porosity, clay content, and water saturation (PCS) parameterization, and we link them to elastic properties using three representative rock-physics models: the Han empirical model, the Voigt-Reuss-Hill boundary model, and the Kuster and Toksöz inclusion model. Numerical examples suggest that conditioning issues, which make a sequential inversion (in which velocities and density are first determined through EFWI, followed by PCS parameters) unstable, are avoided in this direct approach. Significant variability in inversion fidelity is visible from one rock-physics model to another. However, the response of the inversion to the range of possible numerical optimization and frequency selections, as well as acquisition geometries, varies widely. Water saturation tends to be the most difficult property to recover in all situations examined. This can be explained with radiation pattern analysis, in which very low relative scattering amplitudes from saturation perturbations are observed. An investigation performed with a Bayesian approach illustrates that the introduction of prior information may increase the inversion sensitivity to water saturation.
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Dvorkin, Jack, and Uri Wollner. "Rock-physics transforms and scale of investigation." GEOPHYSICS 82, no. 3 (May 1, 2017): MR75—MR88. http://dx.doi.org/10.1190/geo2016-0422.1.
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Rock-physics “velocity-porosity” transforms are usually established on sets of laboratory and/or well data with the latter data source being dominant in recent practice. The purpose of establishing such transforms is to (1) conduct forward modeling of the seismic response for various geologically plausible “what if” scenarios in the subsurface and (2) interpret seismic data for petrophysical properties and conditions, such as porosity, clay content, and pore fluid. Because the scale of investigation in the well is considerably smaller than that in reflection seismology, an important question is whether the rock-physics model established in the well can be used at the seismic scale. We use synthetic examples and well data to show that a rock-physics model established at the well approximately holds at the seismic scale, suggest a reason for this scale independence, and explore where it may be violated. The same question can be addressed as an inverse problem: Assume that we have a rock-physics transform and know that it works at the scale of investigation at which the elastic properties are seismically measured. What are the upscaled (smeared) petrophysical properties and conditions that these elastic properties point to? It appears that they are approximately the arithmetically volume-averaged porosity and clay content (in a simple quartz/clay setting) and are close to the arithmetically volume-averaged bulk modulus of the pore fluid (rather than averaged saturation).
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Xue, Yang, Xiaohui Liu, Rui Zhao, Yu Zheng, and Xin Gui. "Investigation on Triaxial Dynamic Model Based on the Energy Theory of Bedding Coal Rock under Triaxial Impact Compression." Shock and Vibration 2021 (July 30, 2021): 1–15. http://dx.doi.org/10.1155/2021/5537341.
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To investigate the dynamic failure characteristics of bedding rocks in depth, a series of dynamic impact compression tests on parallel and vertical bedding coal rocks were conducted by the split Hopkinson pressure bar test system at 10–103 s−1 strain rates and 0, 4, 8, and 12 MPa confining pressures. According to the experiments, the mechanical properties and energy characteristics of bedding coal rock under different confining pressures and strain rates were obtained, and a triaxial dynamic constitutive model of bedding coal rock was established based on the energy theory of rock failure. The results show that the compressive strength, peak strain, incident energy, dissipated energy, and dynamic strength increase factor gradually increase with increase in strain rate, but the increase in peak strain weakens as confining pressure rises. The influence of bedding structure on strength and energy is not obvious in the uniaxial state, while it gradually enhances as confining pressure increases. The obvious difference in DIF and the energy dissipation ratio of bedding coal rocks gets obvious in SHPB tests. Considering the influence of confining pressure, strain rate, and bedding on the dynamic failure characteristics, the dynamic constitutive model of bedding coal rock was established by introducing the comprehensive influence factor K and the DIF. Comparing with test results, the model parameters are almost confirmed, and the correctness of the model is further verified by analysing the law of K value. Meanwhile, the stress-softening characteristics of coal rock in postpeak are well simulated by the dynamic constitutive model. The results can provide reference value for dynamic issues such as high-efficiency rock breaking, prevention of rock burst, and surrounding rock support in deep rock masses.