DEM Approach for Quartz-Water Mixture

Soft porosity = Fracture porosity in Rock Physics modelling Hard porosity = Porosity associated with isometric voids Differential Effective Medium approach = Incorporating inclusions in small steps to estimate effective elastic properties Eshelby method = Estimating effective elastic parameters at small concentration increments

Slope of elastic moduli-concentration relationship = Determined by aspect ratio of inclusions Non-linear behavior of effective moduli = Result of interactions between inclusions and evolving microstructure Incremental approach in estimating effective properties = Adding small portions of inclusions step by step Effective properties dependency on construction path taken = Different properties obtained based on host material selection

Aspect ratio deviation from 1 in ellipsoidal inclusions = May result in more pronounced slope of elastic moduli-concentration relationship Increasing amount of inclusions = Leads to non-linear behavior of effective elastic moduli Preferred host material selection impact on effective moduli = Properties vary based on construction path taken Combining fractures with isometric pores in a model = Allows for dual porosity representation

<p>Ellipsoidal inclusions model = Slope determined by aspect ratio Incremental inclusion model = Estimating effective properties at each small concentration step Coupled system of ODEs model = Corresponds to very small Δx incremental scheme Numerical approach model = Used for finding solutions to the system of equations</p> Signup and view all the answers

<p>Empirical methods = Statistical relationships calibrated on real data measurements Inclusion-based models = Rock composed of effective matrix and isolated pores approximated by simple shapes Granular media models = Rock framework composed of contacting grains with interactions between individual grains playing a crucial role Critical porosity = Porosity value at which there is a significant change in the mechanical and elastic properties of a rock</p> Signup and view all the answers

<p>Empirical methods = Based on statistical relationships calibrated on real data measurements Inclusion-based models = Assumption of rock composed of effective matrix and isolated pores approximated by geometrically simple shapes Granular media models = Implies rock’s framework is composed of contacting grains with interactions between individual grains determining elastic behavior Critical porosity = Refers to porosity value at which there is a significant change in mechanical and elastic properties of a rock</p> Signup and view all the answers

<p>Empirical methods = Statistical relationships calibrated using real data measurements Inclusion-based models = Rock effectively composed of some effective matrix and isolated pores approximated by geometrically simple shapes Granular media models = Rock’s framework composed of contacting grains, with crucial role played by interactions between individual grains Critical porosity = Porosity value where mechanical and elastic properties significantly change in a rock</p> Signup and view all the answers

<p>Empirical methods = Based on statistical relationships that can be calibrated using real data measurements Inclusion-based models = Assumes rock is effectively composed of some effective matrix and isolated pores that can be approximated by geometrically simple shapes Granular media models = Implies rock’s framework is composed of contacting grains; behavior determined by interactions between individual grains Critical porosity = Refers to porosity value at which there is a significant change in the mechanical and elastic properties of a rock</p> Signup and view all the answers

<p>Critical porosity = Porosity value where the Bulk and Shear modulus of rocks vanish Inclusion-based models = Approaches in rock physics to describe the elastic behavior of rocks with heterogeneities Effective bulk modulus = Parameter describing the linear decrease of elastic modules with concentrations of inclusions Empirical models = Models capturing overall trends but lacking physical basis for specific contributions</p> Signup and view all the answers

<p>a and b = Define decreasing rates of elastic modules with porosity A = Determines the slope of linear decrease in Effective bulk modulus with inclusion concentration K_m and G_m = Correspond to mineral part properties at zero porosity x = Represents concentration of inclusions in the Effective bulk modulus expression</p> Signup and view all the answers

<p>Needles = One of the shapes used to estimate influence in inclusion-based models Disks = Geometry type used to estimate influence of inclusions in rocks Penny-shaped cracks = Inclusion shape considered in more generalized forms for estimating influence Matrix properties = Elastic properties that influence parameter A in inclusion-based models</p> Signup and view all the answers

<p>Trendlines intersect at 35-40% = Observation from classical paper by Dvorkin and Nur Different stiffnesses = Characteristics used to describe rocks using critical porosity model Static approximation vs. wave scattering theory = Classical approaches in inclusion-based models with equivalent results for small amounts of inclusions Simple empirical model = Model describing elastic behavior based on parameters a, b, K_m, G_m</p> Signup and view all the answers

<p>Linear decrease with concentrations of inclusions = Effective Shear modulus behavior Approximation by straight lines on crossplots = Data points behavior observed by Dvorkin and Nur Small amount of inclusions result in equivalent results = Findings from both static approximation and wave scattering theory approaches Dependence on internal structure of rock = Critical porosity model's variability based on rock types</p> Signup and view all the answers

<p>DEM = Method for modelling effective elastic properties of rocks Voight-Reuss and Hashin-Shtrikman bounds = Theoretical models added for comparison in DEM approach Granular media models = Approach considering material as assembly of individual particles interacting with each other Soft-sand model = Model for calculating bulk and shear modules of dry sand</p> Signup and view all the answers

<p>Ellipsoids with different aspect ratios = Inclusions in Quartz-water mixture Spheres = Idealized representations of grains in granular media models Regular sphere packs and random packings of spheres = Configurations considered in Hertz-Mindlin model Sorting deterioration but not cementation at grain contacts = Relation to porosity changes in soft-sand model</p> Signup and view all the answers

<p>Incremental additions order = Affects effective modules in multiple inclusion shapes Elongated ellipsoids = Lead to faster decrease in P-wave velocity with porosity Initial compaction state = Significantly influences stiffness at grain contacts in granular media models Effective pressure = Influences effective elastic moduli according to Hertz-Mindlin model</p> Signup and view all the answers

<p>Granular rocks = Not well represented by pack of identical spheres Collective response of individual particles = Derives macroscopic behavior of granular material Two contacting spheres under stress = Origin of Hertz-Mindlin model Geological materials = Have complex and heterogeneous nature</p> Signup and view all the answers

<p>Effective elastic properties depend on effective pressure = Outcome of models based on Hertz-Mindlin model Precompacted granular media = Assumption made by many effective models building upon Hertz-Mindlin model End-members defining a model = Characteristic of soft-sand model Packing and sorting quantification using spheres = Feature of granular media models</p> Signup and view all the answers

<p>Lower Hashin-Shtrikman boundary = Used to obtain effective elastic properties of porous rock with intermediate porosity Upper Hashin-Shtrikman boundary = Connects the end-members in the porosity-elastic-modulus plane for 'soft-sand' model Dvorkin-Nur model = Theoretical model explaining elastic parameters influenced by cementation Rock-Physics diagnostics = Using sorting and cementation trends to analyze variations in elastic properties</p> Signup and view all the answers

<p>Sorting = Results in small variations in elastic properties Cementation = Leads to abrupt changes in elastic parameters Porosity = Changed significantly by sorting but may change little due to cementation Burial histories = Influences degree of cementations in sandstones</p> Signup and view all the answers

<p>Stiff-sandstone model or modified Upper Hashin-Shtrikman bound = Estimating contribution of sorting deterioration effect Soft-sand model = Estimating elastic properties of uncemented well-sorted sandstone Lower Hashin-Shtrikman boundary = Mixing properties of two end-members for porous rock with intermediate porosity Dvorkin-Nur model = Explaining and predicting elastic parameters of rocks influenced by cementation</p> Signup and view all the answers

<p>Point A (initial step) = Estimate elastic properties of reference uncemented well-sorted sandstone Point B (second step) = Take into account the cementation at grain contacts using Dvorkin-Nur model or modified Upper Hashin-Shtrikman bound Point C (final step) = Estimate contribution of sorting deterioration effect using 'soft-sand' model</p> Signup and view all the answers

<p>Voight-Reuss-Hill approximation = Estimating effective elastic properties of the averaged mineral part of the rock DEM approach = Method used for analyzing internal rock's structure and creating an elastic model for the drained rock Gassmann equations = Defining elastic parameters of the fluid-saturated reservoir Rock-Physics Templates approach = Visual tool for understanding and interpreting interdependencies between different rock parameters</p> Signup and view all the answers

<p>Inclusion-based models = Models for 'dry' rock elastic properties Granular media models = Models for 'dry' rock elastic properties Linear elasticity theory = Based on Hooke's law and proportionality between stress and strain Multivariate Rock Physics Model = Describes the influence of geological factors on elastic parameters of rocks</p> Signup and view all the answers

<p>Acoustic Impedance = Main elastic parameter for seismic amplitudes interpretation P-Impedance = Used as one of the main axes in Rock Physics Templates approach Vp/Vs ratio = Main elastic parameter for seismic amplitudes interpretation Elastic modules = Proportionality coefficients in linear elasticity equations</p> Signup and view all the answers

<p>Compressional deformation = One of the fundamental types of deformation of continuous media Shear deformation = One of the fundamental types of deformation of continuous media Amplitudes of reflected waves = Depend on contrasts of elastic properties and density on the reflection interface Rock physics diagnostics = Using Rock Physics Templates for interpreting elastic properties obtained from well logs or seismic inversion</p> Signup and view all the answers

<p>Self-Consistent approach = Can be applied for estimating effective elastic properties of mineral part of rocks Calibrated Rock Physics Model = Prerequisite for Rock Physics Template analysis Inclusion-based models = 'Dry' rock elastic properties modeling method Fluid-saturated reservoir analysis = Estimating elastic properties of fluids at reservoir conditions</p> Signup and view all the answers