Consolidating rock-physics classics: A practical take on granular effective medium models

2019 ◽  
Vol 38 (5) ◽  
pp. 334-340 ◽  
Author(s):  
Fabien Allo
Keyword(s):  
Numerical Models ◽  
Quantitative Description ◽  
Rock Physics ◽  
Real Data ◽  
Analytical Form ◽  
Effective Medium ◽  
Seismic Exploration ◽  
Stiffness Index ◽  
Rock Composition ◽  
Rock Types

Granular effective medium (GEM) models rely on the physics of a random packing of spheres. Although the relative simplicity of these models contrasts with the complex texture of most grain-based sedimentary rocks, their analytical form makes them easier to apply than numerical models designed to simulate more complex rock structures. Also, unlike empirical models, they do not rely on data acquired under specific physical conditions and can therefore be used to extrapolate beyond available observations. In addition to these practical considerations, the appeal of GEM models lies in their parameterization, which is suited for a quantitative description of the rock texture. As a result, they have significantly helped promote the use of rock physics in the context of seismic exploration for hydrocarbon resources by providing geoscientists with tools to infer rock composition and microstructure from sonic velocities. Over the years, several classic GEM models have emerged to address modeling needs for different rock types such as unconsolidated, cemented, and clay-rich sandstones. We describe how these rock-physics models, pivotal links between geology and seismic data, can be combined into extended models through the introduction of a few additional parameters (matrix stiffness index, cement cohesion coefficient, contact-cement fraction, and laminated clays fraction), each associated with a compositional or textural property of the rock. A variety of real data sets are used to illustrate how these parameters expand the realm of seismic rock-physics diagnostics by increasing the versatility of the extended models and facilitating the simulation of plausible geologic variations away from the wells.

Using rock physics models to validate rock composition from multimineral log analysis

Geophysics ◽  
2021 ◽  
pp. 1-69
Author(s):  
Liwei Cheng ◽  
Manika Prasad ◽  
Reinaldo J. Michelena ◽  
Ali Tura ◽  
Shamima Akther ◽  
...  
Keyword(s):  
Quality Control ◽  
Reservoir Characterization ◽  
Rock Physics ◽  
Inequality Constraint ◽  
Effective Medium ◽  
Carbonate Reservoir ◽  
Log Analysis ◽  
Evaluation Tool ◽  
Rock Composition ◽  
Effective Medium Models

Multimineral log analysis is a quantitative formation evaluation tool for geological and petrophysical reservoir characterization. Rock composition can be estimated by solving equations that relate log measurements to the petrophysical endpoints of minerals and fluids. Due to errors in log data and uncertainties in petrophysical endpoints of constituents, we propose using effective medium models from rock physics as additional independent information to validate or constrain the results. In this paper, we examine the Voigt-Reuss (VR) bound model, self-consistent approximation (SCA), and differential effective medium (DEM). The VR bound model provides the first-order quality control of multimineral results. We first show a conventional carbonate reservoir study with intervals where the predicted effective medium models from multimineral results are inconsistent with the measured elastic properties. We use the VR bound model as an inequality constraint in multimineral analysis for plausible alternative solutions. SCA and DEM models provide good estimates in low porosity intervals and imply geological information for the porous intervals. Then, we show a field case of the Bakken and Three Forks formations. A linear interpolation of the VR bound model helps validate multimineral results and approximate the elastic moduli of clay. There are two major advantages to use our new method (a) rock physics effective medium models provide independent quality control of petrophysical multimineral results, and (b) multimineral information leads to realistic rock physics models.

QEMSCAN-Assisted Interpretation of Imbibition Capillary Pressure for Multiporosity Carbonate Rocks

SPE Journal ◽  
2020 ◽  
pp. 1-17
Author(s):  
Aymen Alramadhan ◽  
Yildiray Cinar
Keyword(s):  
Capillary Pressure ◽  
Numerical Models ◽  
Rock Composition ◽  
Rock Samples ◽  
Rock Types ◽  
Centrifuge Tests ◽  
Medium Permeability ◽  
Mercury Injection Capillary Pressure ◽  
The Impact ◽  
Selection Of

Summary In this paper, we present an experimental study that explores the potential links between the imbibition capillary pressure Pci and the pore systems and/or mineralogy for carbonate reservoirs undergoing waterflood. A systematic workflow has been formulated to ensure the data quality ofPci, minimize uncertainty in derivingPci from centrifuge tests, and analyze the data considering the pore-size distribution from mercury injection capillary pressure (MICP) and mineralogy from Quantitative Evaluation of Minerals by Scanning Electron Microscopy (QEMSCAN). The workflow starts with assessing the centrifuge production data for gravity-capillary equilibrium at each speed. Then, the quality-checked data are used to generate six differentPci curves using analytical and numerical models. The resulting curves provide a measure of the variability in solutions for various rock types and assist in the selection of the most-representativePci curve. Finally, the representative Pci curves of all rock samples are analyzed together with the MICP and QEMSCAN data to examine the change in Pci curves as a result of changes in the number and character of rock types, pore systems, dominant pore-throat radii, and mineralogy. Findings from this study shed light on the impact of mineralogy and pore systems on Pci. From the mineralogy perspective, the presence of dolomite, microporous calcite, or rutile and anatase (TiO2) within the rock composition is found to affect the Pci of the carbonate samples used in this study. The rock samples with these minerals should be separated from other bimodal samples before attempting to obtain a correlation between Pci and pore systems. The data analysis further reveals that some bimodal samples of medium permeability yield a better waterflood imbibition efficiency than those of the high-permeability samples. This observation is attributed to a better communication between the micropore and macropore systems, and a closer proximity of the peak radii of the micro- and macropore systems of the medium-permeability samples.

scholarly journals Chemical heterogeneities in the mantle: progress towards a general quantitative description

Solid Earth ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1409-1428 ◽  
Author(s):  
Massimiliano Tirone
Keyword(s):  
Mass Transfer ◽  
Chemical Equilibrium ◽  
Transport Model ◽  
Numerical Models ◽  
Quantitative Description ◽  
Transient State ◽  
Real Data ◽  
Initial State ◽  
Initial Size ◽  
Chemical Equilibration

Abstract. Chemical equilibration between two different assemblages (peridotite type and gabbro–eclogite type) has been determined using basic thermodynamic principles and certain constraints and assumptions regarding mass and reaction exchange. When the whole system (defined by the sum of the two subsystems) is in chemical equilibrium the two assemblages will not be homogenized, but they will preserve distinctive chemical and mineralogical differences. Furthermore, the mass transfer between the two subsystems defines two petrological assemblages that separately are also in local thermodynamic equilibrium. In addition, when two assemblages previously equilibrated as a whole in a certain initial mass ratio are held together assuming a different proportion, no mass transfer occurs and the two subsystems remain unmodified. By modeling the chemical equilibration results of several systems of variable initial size and different initial composition it is possible to provide a quantitative framework to determine the chemical and petrological evolution of two assemblages from an initial state, in which the two are separately in chemical equilibrium, to a state of equilibration of the whole system. Assuming that the local Gibbs energy variation follows a simple transport model with an energy source at the interface, a complete petrological description of the two systems can be determined over time and space. Since there are no data to constrain the kinetics of the processes involved, the temporal and spatial scale is arbitrary. The evolution model should be considered only a semiempirical tool that shows how the initial assemblages evolve while preserving distinct chemical and petrological features. Nevertheless, despite the necessary simplification, a 1-D model illustrates how chemical equilibration is controlled by the size of the two subsystems. By increasing the initial size of the first assemblage (peridotite like), the compositional differences between the initial and the final equilibrated stage become smaller, while on the eclogite-type side the differences tend to be larger. A simplified 2-D dynamic model in which one of the two subsystems is allowed to move with a prescribed velocity shows that after an initial transient state, the moving subsystem tends to preserve its original composition defined at the influx side. The composition of the static subsystem instead progressively diverges from the composition defining the starting assemblage. The observation appears to be consistent for various initial proportions of the two assemblages, which somehow simplify the development of potential tools for predicting the chemical equilibration process from real data and geodynamic applications. Four animation files and the data files of three 1-D and two 2-D numerical models are available following the instructions in the Supplement.

scholarly journals Chemical Heterogeneities in the Mantle: Progress Towards a General Quantitative Description

2018 ◽  
Author(s):  
Massimiliano Tirone
Keyword(s):  
Mass Transfer ◽  
Numerical Models ◽  
Quantitative Description ◽  
Transient State ◽  
Real Data ◽  
Initial State ◽  
Initial Size ◽  
Simple Diffusion ◽  
Chemical Equilibration ◽  
The Difference

Abstract. Chemical equilibration between two different assemblages (peridotite-type and gabbro/eclogite-type) of variable initial size assuming few different initial compositions has been determined using certain mass and reactions constraints and thermodynamic principles. The pattern that emerges suggests that mass transfer between the two sub-systems defines two petrological assemblages that separately are maintained in local thermodynamic equilibrium. In addition, when two assemblages previously equilibrated together in a certain mass ratio are rearranged assuming a different initial ratio, no mass transfer occurs and the two sub-systems remain unmodified. By modeling the chemical equilibration results of several systems it is possible to provide a quantitative framework to determine the chemical and petrological evolution of two assemblages from an initial state, in which the two are separately in chemical equilibrium, to a state of equilibration of the whole system (sum of the two sub-systems). Assuming that the local Gibbs energy variation follows a simple diffusion couple model, a complete petrological description of the two systems can be determined over time and space. Since there are no data to constrain the kinetic of the processes involved, the temporal and spatial scale is arbitrary. Nevertheless a 1-D static model shows how chemical equilibration is controlled by the size of the two sub-systems. As the initial size of the first assemblage (peridotite-like) increases, the differences between the initial and the final equilibrated stage becomes smaller, while on the opposite side the difference increases. A simplified 2-D dynamic model in which either one of the two sub-systems is allowed to move with a prescribed velocity, shows that after an initial transient state, the moving sub-system tends to preserve its original composition defined at the entry side. The other sub-system instead evolves towards a large compositional difference from the starting assemblage. The results appear to be the same varying the initial proportion of the two assemblages, which simplify somehow the development of potential tools for predicting the chemical equilibration process from real data and geodynamic applications. Four animations and data sets of three 1-D and two 2-D numerical models are available following the instructions in the supplementary material.

scholarly journals SAPHYR: Swiss Atlas of Physical Properties of Rocks: the continental crust in a database

2021 ◽  
Vol 114 (1) ◽  
Author(s):  
Alba Zappone ◽  
Eduard Kissling
Keyword(s):  
Physical Properties ◽  
Laboratory Data ◽  
Rock Physics ◽  
Resource Planning ◽  
Data Representation ◽  
Common People ◽  
Rock Types ◽  
Gis Tools ◽  
Porosity And Permeability ◽  
Thermal And Electrical Properties

AbstractThe Swiss Atlas of Physical Properties of Rocks (SAPHYR) project aims at centralize, uniform, and digitize dispersed and often hardly accessible laboratory data on physical properties of rocks from Switzerland and surrounding regions. The goal of SAPHYR is to make the quality-controlled and homogenized data digitally accessible to an open public, including industrial, engineering, land and resource planning companies as well as governmental and academic institutions, or simply common people interested in rock physics. The physical properties, derived from pre-existing literature or newly measured, are density, porosity and permeability as well as seismic, magnetic, thermal and electrical properties. The data were collected on samples either from outcrops or from tunnels and boreholes. At present, data from literature have been collected extensively for density, porosity, seismic and thermal properties. In the past years, effort has been placed especially on collecting samples and measuring the physical properties of rock types that were poorly documented in literature. A workflow for quality control on reliability and completeness of the data was established. We made the attempt to quantify the variability and the uncertainty of the data. The database has been recently transferred to the Federal Office of Topography swisstopo with the aim to develop the necessary tools to query the database and open it to the public. Laboratory measurements are continuously collected, therefore the database is ongoing and in continuous development. The spatial distribution of the physical properties can be visualized as maps using simple GIS tools. Here the distribution of bulk density and velocity at room conditions are presented as examples of data representation; the methodology to produce these maps is described in detail. Moreover we also present an exemplification of the use of specific datasets, for which pressure and temperatures derivatives are available, to develop crustal models.

Digital Rock Typing DRT Algorithm Formulation with Optimal Supervised Semantic Segmentation

2022 ◽  
Author(s):  
Omar Alfarisi ◽  
Djamel Ouzzane ◽  
Mohamed Sassi ◽  
TieJun Zhang
Keyword(s):  
Carbonate Rock ◽  
Chemical Properties ◽  
Rock Physics ◽  
Semantic Segmentation ◽  
Rock Properties ◽  
Digital Rock Physics ◽  
Digital Rock ◽  
Rock Types ◽  
Fluid Saturation ◽  
Rock Typing

<p><a></a>Each grid block in a 3D geological model requires a rock type that represents all physical and chemical properties of that block. The properties that classify rock types are lithology, permeability, and capillary pressure. Scientists and engineers determined these properties using conventional laboratory measurements, which embedded destructive methods to the sample or altered some of its properties (i.e., wettability, permeability, and porosity) because the measurements process includes sample crushing, fluid flow, or fluid saturation. Lately, Digital Rock Physics (DRT) has emerged to quantify these properties from micro-Computerized Tomography (uCT) and Magnetic Resonance Imaging (MRI) images. However, the literature did not attempt rock typing in a wholly digital context. We propose performing Digital Rock Typing (DRT) by: (1) integrating the latest DRP advances in a novel process that honors digital rock properties determination, while; (2) digitalizing the latest rock typing approaches in carbonate, and (3) introducing a novel carbonate rock typing process that utilizes computer vision capabilities to provide more insight about the heterogeneous carbonate rock texture.<br></p>

scholarly journals Stiffness Analysis to Predict the Spread Out of Fake Information

2021 ◽  
Vol 13 (9) ◽  
pp. 222
Author(s):  
Raffaele D'Ambrosio ◽  
Giuseppe Giordano ◽  
Serena Mottola ◽  
Beatrice Paternoster
Keyword(s):  
Numerical Experiments ◽  
Real Data ◽  
Sir Model ◽  
Stiffness Index ◽  
Fake News ◽  
Stiffness Analysis ◽  
Data Support

This work highlights how the stiffness index, which is often used as a measure of stiffness for differential problems, can be employed to model the spread of fake news. In particular, we show that the higher the stiffness index is, the more rapid the transit of fake news in a given population. The illustration of our idea is presented through the stiffness analysis of the classical SIR model, commonly used to model the spread of epidemics in a given population. Numerical experiments, performed on real data, support the effectiveness of the approach.

scholarly journals Bayesian rock physics inversion: application to CO2 storage monitoring

Geophysics ◽  
2021 ◽  
pp. 1-73
Author(s):  
Bastien Dupuy ◽  
Anouar Romdhane ◽  
Pierre-Louis Nordmann ◽  
Peder Eliasson ◽  
Joonsang Park
Keyword(s):  
Joint Inversion ◽  
Co2 Storage ◽  
Rock Physics ◽  
Model Space ◽  
Real Data ◽  
Sensitivity Study ◽  
Model Parameters ◽  
Reservoir Properties ◽  
Upward Migration ◽  
Before And After

Risk assessment of CO2 storage requires the use of geophysical monitoring techniques to quantify changes in selected reservoir properties such as CO2 saturation, pore pressure and porosity. Conformance monitoring and associated decision-making rest upon the quantified properties derived from geophysical data, with uncertainty assessment. A general framework combining seismic and controlled source electromagnetic inversions with rock physics inversion is proposed with fully Bayesian formulations for proper quantification of uncertainty. The Bayesian rock physics inversion rests upon two stages. First, a search stage consists in exploring the model space and deriving models with 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 like marginal probability densities. Both steps are based on the neighbourhood algorithm. The approach does not require any linearization of the rock physics model or assumption about the model parameters distribution. After describing the CO2 storage context, the available data at the Sleipner field before and after CO2 injection (baseline and monitor), and the rock physics models, we perform an extended sensitivity study. We show that prior information is crucial, especially in the monitor case. We demonstrate that joint inversion of seismic and CSEM data is also key to quantify CO2 saturations properly. We finally apply the full inversion strategy to real data from Sleipner. We obtain rock frame moduli, porosity, saturation and patchiness exponent distributions and associated uncertainties along a 1D profile before and after injection. The results are consistent with geology knowledge and reservoir simulations, i.e., that the CO2 saturations are larger under the caprock confirming the CO2 upward migration by buoyancy effect. The estimates of patchiness exponent have a larger uncertainty, suggesting semi-patchy mixing behaviour.

scholarly journals Stochastic reservoir characterization using prestack seismic data

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 978-993 ◽  
Author(s):  
Jo Eidsvik ◽  
Per Avseth ◽  
Henning Omre ◽  
Tapan Mukerji ◽  
Gary Mavko
Keyword(s):  
Reservoir Characterization ◽  
A Priori ◽  
Rock Physics ◽  
Real Data ◽  
Spatial Coupling ◽  
The North ◽  
Amplitude Versus Offset ◽  
Likelihood Model ◽  
Avo Attributes ◽  
The Impact

Reservoir characterization must be based on information from various sources. Well observations, seismic reflection times, and seismic amplitude versus offset (AVO) attributes are integrated in this study to predict the distribution of the reservoir variables, i.e., facies and fluid filling. The prediction problem is cast in a Bayesian setting. The a priori model includes spatial coupling through Markov random field assumptions and intervariable dependencies through nonlinear relations based on rock physics theory, including Gassmann's relation. The likelihood model relating observations to reservoir variables (including lithology facies and pore fluids) is based on approximations to Zoeppritz equations. The model assumptions are summarized in a Bayesian network illustrating the dependencies between the reservoir variables. The posterior model for the reservoir variables conditioned on the available observations is defined by the a priori and likelihood models. This posterior model is not analytically tractable but can be explored by Markov chain Monte Carlo (MCMC) sampling. Realizations of reservoir variables from the posterior model are used to predict the facies and fluid‐filling distribution in the reservoir. A maximum a posteriori (MAP) criterion is used in this study to predict facies and pore‐fluid distributions. The realizations are also used to present probability maps for the favorable (sand, oil) occurrence in the reservoir. Finally, the impact of seismic AVO attributes—AVO gradient, in particular—is studied. The approach is demonstrated on real data from a turbidite sedimentary system in the North Sea. AVO attributes on the interface between reservoir and cap rock are extracted from 3D seismic AVO data. The AVO gradient is shown to be valuable in reducing the ambiguity between facies and fluids in the prediction.

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