Estimation Of Elastic Properties Research Articles

Estimating pore pressure in tight sandstone gas reservoirs: A comprehensive approach integrating rock physics models and deep neural networks

Pore pressure serves as an important driving power for subsurface fluid migration and therefore has a significant impact on gas accumulation and enrichment in tight sandstone reservoirs. Tight gas is typically produced in overpressure regions, where pressure coefficients are notably elevated. Thus, it is crucial to establish an effective methodology for precise pore pressure estimation. This study introduces an approach to improve pore pressure prediction by incorporating rock physical modeling and deep neural networks (DNNs) into the classical Eaton method. Compared to conventional techniques relying on empirical correlations between pressure coefficients and elastic properties, the proposed method considers the influence of porosity, fluids, and lithology, which could enhance reliability in pore pressure prediction. Meanwhile, a prediction model is developed using logging data and DNNs to estimate mineralogical volumetric fractions based on elastic properties. This prediction model allows improved estimation of rock matrix elastic properties using seismic-inverted data, which is crucial for estimating normal compaction velocity to extend pore pressure prediction from individual boreholes to the whole study area. Real data applications demonstrate that the predicted pressure coefficients derived from seismic data using the method presented in this paper align well with the gas enrichment estimated in previous studies for the tight sandstone reservoirs. Furthermore, regions with high values of pressure coefficients correspond to high gas content. These findings validate the effectiveness of the proposed methodology, which can provide valuable insights for identifying potential tight sandstone reservoirs.

Recent developments in modeling and analysis of rotating functionally graded panels: A review

This article presents a comprehensive review on recent developments in the techniques for modeling and exploration of rotating functionally graded material (FGM) panels carried out between periods 2000 to 2023. Special attention is given on literature pertaining to analysis of rotating FGM panels subjected to thermo-mechanical loading. This study scrutinizes the advancements made in analysis of panels such as beam, plate, shell and blades that includes effects like porosity, thermal stress, and piezo-electric in the mathematical model. The present article also highlights the importance and ease in implementation of rule of mixture for calculation of different temperature dependent material properties used in the analysis of rotating FGM panels. An in-depth review of literature clearly indicates the importance of taking thermal effect in the estimation of elastic properties for accurate analysis of rotating FGM panels. Further, a detailed analysis of temperature profile viz., linear/non-linear, is carried out. Finally, the article concludes with the future areas that need to be explored for the analysis of rotating FGM panels.

Machine Learning and Data Fusion Approach for Elastic Rock Properties Estimation and Fracturability Evaluation

Accurate rock elastic property determination is vital for effective hydraulic fracturing, particularly Young's modulus due to its link to rock brittleness. This study integrates interdisciplinary data for better predictions of elastic modulus, combining data mining, experiments, and calibrated synthetics. We used the microstructural insights extracted from rock images for geomechanical facies analysis. Additionally, the petrophysical data and well logs were correlated with shear wave velocity (Vs) and Young's modulus. We developed a machine-learning workflow to predict Young's modulus and assess rock fracturability, considering mineral composition, geomechanics, and microstructure. Our findings indicate that artificial neural networks effectively predict Young's modulus, while K-Means clustering and hierarchical support vector machines excel in identifying rock and geomechanical facies. Utilizing Microscale thin section analysis in conjunction with fracture modeling enhances our understanding of fracture geometries and facilitates fracturability assessment. Notably, fracturability is controlled by specific geomechanical facies during initiation and propagation and influenced by continuity of geomechanical facies in small depth intervals. In conclusion, this study demonstrates data mining and machine learning potential for predicting rock properties and assessing fracturability, aiding hydraulic fracturing design optimization through diverse data and advanced methods.

Particle Shape Complexity Reduction for Estimation of Effective Elastic Properties of the Composite

The material development is an expensive process, especially considering composite materials as their microstructure can be very complex. Particle reinforced composites in particular can consist of particles with complicated shapes. Traditionally ellipsoid approximations are used to reduce shape complexity, which comes at the drawback of neglecting the influence of the particles shape onto the composite mechanical properties. The computational method as proposed in this work employs particle swarm optimization in combination with the FE method to create spherical equivalents, which reduces the complexity but also stores the particle shape information. The proposed method can minimize the development cost of new particle reinforced composite materials, while increasing the spectrum of evaluated material features.

Estimation of directional single crystal elastic properties from nano-indentation by correlation with EBSD and first-principle calculations

In this study, a two-step optimisation process for the estimation of the single crystal stiffness tensor from the indentation modulus is presented. This was accomplished by using a 2-dimensional data correlation method for nano-indentation, EBSD and ab initio data, as well as EDS for phase separation in a multi-phase material. Here, a single-phase Fe-24Ni-0.4C austenitic steel and a two-phase Fe-9.5Ni-0.5Co Seymchan meteorite were used as example materials.In a first step, the combination of high-speed nano-indentation mapping data with elemental and orientation distribution maps allowed the estimation of indentation moduli along specific crystal surface planes normal directions, (001), (011) and (111) using a least squares optimisation based on starting values from DFT or experimentally determined stiffness tensors. A second global optimisation step to estimate the single crystal stiffness tensor using pre-solved solution parameters of the Vlassak-Nix equations yielded reasonable correspondence between the experimentally determined stiffness tensors from correlative nano-indentation data and other methods. The presented method demonstrates generally the possibility to derive directionally sensitive elastic properties from high-speed nano-indentation for cubic materials statistically.

Estimation of elastic properties and failure strength of layered rocks with a multi-scale damage approach

Layered rocks (LR) are composed of intact rock matrix (IRM) and various oriented rough weakness planes (e.g., fractures, bedding planes, and foliations). New microcracks can also be created and propagate in IRM during subsequent loading history. Effects of induced microcracks and pre-existing weakness planes on macroscopic mechanical behavior of LR are usually investigated separately. The novelty of the present work is to develop an original multi-scale damage approach to estimate the macroscopic anisotropic elastic properties and failure strength of LR. Two material scales are taken into consideration. At the macroscopic laboratory scale, a set of parallel rough weakness planes are embedded in the IRM, while at the microscopic scale, the IRM contains an elastic solid phase and randomly distributed microcracks. By means of a two-step homogenization technique, the effective elastic properties of LR is first determined. A multi-scale friction-damage model (MFDM) is further developed, by accounting for isotropic growth of closed microcracks and anisotropic evolution of rough weakness planes at two different scales. Subsequently, with the concept of critical damage, an analytical macroscopic strength criterion incorporating failure mechanisms of IRM and weakness planes is derived as an inherent result of the MFDM. Compared with experimental data, it shows that the macroscopic anisotropic elastic properties of LR are well estimated. However, the derived macroscopic strength criterion only provides a qualitative prediction of the anisotropic failure strength of LR for different orientations of weakness planes in conventional triaxial compression tests. By taking advantage of the fabric tensor approach, the strength criterion is further improved to take into account interaction between weakness planes and microcracks. The improved strength criterion is able to quantitatively capture the failure property of LR.

Phase-Resolved Optical Coherence Elastography: An Insight into Tissue Displacement Estimation.

Robust methods to compute tissue displacements in optical coherence elastography (OCE) data are paramount, as they play a significant role in the accuracy of tissue elastic properties estimation. In this study, the accuracy of different phase estimators was evaluated on simulated OCE data, where the displacements can be accurately set, and on real data. Displacement (∆d) estimates were computed from (i) the original interferogram data (Δφori) and two phase-invariant mathematical manipulations of the interferogram: (ii) its first-order derivative (Δφd) and (iii) its integral (Δφint). We observed a dependence of the phase difference estimation accuracy on the initial depth location of the scatterer and the magnitude of the tissue displacement. However, by combining the three phase-difference estimates (Δdav), the error in phase difference estimation could be minimized. By using Δdav, the median root-mean-square error associated with displacement prediction in simulated OCE data was reduced by 85% and 70% in data with and without noise, respectively, in relation to the traditional estimate. Furthermore, a modest improvement in the minimum detectable displacement in real OCE data was also observed, particularly in data with low signal-to-noise ratios. The feasibility of using Δdav to estimate agarose phantoms' Young's modulus is illustrated.

Multiscale framework for estimation of elastic properties of Poly ethylene terephthalate from the crystallization temperature

A 2D multiscale numerical strategy is presented in this paper. It allows to generate a representative elementary volume (REV) with a spherulitic microstructure used to predict the elastic properties of PET using a 2-scale numerical homogenization scheme. Because of the rapid crystallization kinetics of PET, DSC and optical microscopy were combined with empirical laws to estimate the crystallization kinetic parameters used to generate the REVs. Our framework allows estimating the elastic properties identified by tensile tests for several specimens crystallized at different temperatures. In addition, the comparison with mean-field models from the literature confirms that the Young's modulus of PET does not only depend on the crystallinity volume ratio but also on the crystal organization in the spherulites. The main advantage of this study is to provide a strategy for estimating the elastic properties that can be transposed to many semi-crystalline polymers with a spherulitic microstructure. Nevertheless, the numerical framework presented in the article is limited to semicrystalline polymers with a spherulitic microstructure, which crystallize under isothermal condition.

Uncertainty Quantification in the In Vivo Image-Based Estimation of Local Elastic Properties of Vascular Walls.

Patient-specific computational models are a powerful tool for planning cardiovascular interventions. However, the in vivo patient-specific mechanical properties of vessels represent a major source of uncertainty. In this study, we investigated the effect of uncertainty in the elastic module (E) on a Fluid-Structure Interaction (FSI) model of a patient-specific aorta. The image-based χ-method was used to compute the initial E value of the vascular wall. The uncertainty quantification was carried out using the generalized Polynomial Chaos (gPC) expansion technique. The stochastic analysis was based on four deterministic simulations considering four quadrature points. A deviation of about ±20% on the estimation of the E value was assumed. The influence of the uncertain E parameter was evaluated along the cardiac cycle on area and flow variations extracted from five cross-sections of the aortic FSI model. Results of stochastic analysis showed the impact of E in the ascending aorta while an insignificant effect was observed in the descending tract. This study demonstrated the importance of the image-based methodology for inferring E, highlighting the feasibility of retrieving useful additional data and enhancing the reliability of in silico models in clinical practice.

Experimental and numerical studies of a reinforced concrete component subjected to corrosion

In this study, an experimental study is first performed. Two complementary tests are realized on a typical reinforced concrete component sample composed of cement paste cylinders with inserted steel discs. In the first test, the deformation of sample due to the corrosion expansion of steel discs is measured. In the second test, the deformation is restricted while the reaction force due to steel corrosion expansion is identified. Based on the experimental data, a novel numerical approach is developed for the analysis of mechanical response and damage process of the tested samples. A simple but realistic homogenization scheme is proposed for the estimation of effective elastic properties of corroded steel. The evolution of corrosion-induced damage is described by using a phase-field method. The elastic properties of corroded steel are estimated. The predicted values of reaction force are compared with the experimental data. The amplitude of damage and the extent of damaged zone are evaluated and analyzed in terms of corrosion-related expansion ratio.

Study of effective elastic properties of heterogeneous materials with an artificial neural network model

This paper is devoted to the estimation of macroscopic elastic properties of composites containing inclusions and pores. Some representative analytical homogenization models are first recalled and their weaknesses are highlighted by comparisons with the reference numerical results obtained from direct simulations by a Fast Fourier Transform (FFT) method. A large data set is then constructed also based on numerical results obtained from FFT simulations for different types of micro-structures and for a large range of elastic properties of constituents. An artificial neural network (ANN)-based model containing two hidden layers is constructed and trained by using this data set. Different types of validation tests of the ANN model are presented. It is found that the ANN-based model can estimate the macroscopic elastic properties of strongly heterogeneous materials with a very good accuracy, for different types of micro-structures and a large range of porosity and inclusion volume fraction.

Risk-averse estimates of effective properties in heterogeneous elasticity

In this work, we propose a theoretical framework for computing pessimistic and optimistic estimates of effective properties in the case of heterogeneous elastic materials with uncertain microscopic elastic properties. We rely on a risk-averse measure widely used in finance called the conditional-value at risk (CVaR). The CVaR computes the conditional expectation of events occurring above a given risk level, thereby characterizing the extreme tails of the probability distribution of a random variable. In the context of elastic materials, we propose to use the CVaR on the elastic free energy to compute an optimistic estimate of the global stiffness for some confidence level α. Similarly, we also use the CVaR on the complementary elastic energy to compute a pessimistic estimate of the global stiffness. The obtained CVaR estimates benefit from a convex optimization formulation. The resulting material behavior is still elastic but not necessarily linear anymore. We discuss approximate formulations recovering a linear elastic behavior. We apply the proposed formulations to the micromechanical estimates of effective elastic properties of random heterogeneous materials.

Probabilistic inversion of seismic data for reservoir petrophysical characterization: Review and examples

The physics that describes the seismic response of an interval of saturated porous rocks with known petrophysical properties is relatively well understood and includes rock physics, petrophysics, and wave propagation models. The main goal of seismic reservoir characterization is to predict the rock and fluid properties given a set of seismic measurements by combining geophysical models and mathematical methods. This modeling challenge is generally formulated as an inverse problem. The most common geophysical inverse problem is the seismic (or elastic) inversion, i.e., the estimation of elastic properties, such as seismic velocities or impedances, from seismic amplitudes and traveltimes. The estimation of petrophysical properties, such as porosity, lithology, and fluid saturations, also can be formulated as an inverse problem and is generally referred to as rock-physics (or petrophysical) inversion. Several deterministic and probabilistic methods can be applied to solve seismic inversion problems. Deterministic algorithms predict a single solution, which is a “best” estimate or the most likely value of the model variables of interest. In probabilistic algorithms, on the other hand, the solution is the probability distribution of the model variables of interest, which can be expressed as a conditional probability density function or a set of model realizations conditioned on the data. The probabilistic approach provides a quantification of the uncertainty of the solution in addition to the most likely model. Our goal is to define the terminology, present an overview of probabilistic seismic and rock-physics inversion methods for the estimation of petrophysical properties, demonstrate the fundamental concepts with illustrative examples, and discuss the recent research developments.

Introduction of a Novel Image-Based and Non-Invasive Method for the Estimation of Local Elastic Properties of Great Vessels

Background: In the context of a growing demand for the use of in silico models to meet clinical requests, image-based methods play a crucial role. In this study, we present a parametric equation able to estimate the elasticity of vessel walls, non-invasively and indirectly, from information uniquely retrievable from imaging. Methods: A custom equation was iteratively refined and tuned from the simulations of a wide range of different vessel models, leading to the definition of an indirect method able to estimate the elastic modulus E of a vessel wall. To test the effectiveness of the predictive capability to infer the E value, two models with increasing complexity were used: a U-shaped vessel and a patient-specific aorta. Results: The original formulation was demonstrated to deviate from the ground truth, with a difference of 89.6%. However, the adoption of our proposed equation was found to significantly increase the reliability of the estimated E value for a vessel wall, with a mean percentage error of 9.3% with respect to the reference values. Conclusion: This study provides a strong basis for the definition of a method able to estimate local mechanical information of vessels from data easily retrievable from imaging, thus potentially increasing the reliability of in silico cardiovascular models.

Exploring the photovoltaic capabilities of Sc4C3 MXene using density functional theory

The purpose of this study is to explore the structural and optoelectronic properties of a two-dimensional MXene, Sc4C3 as a viable choice for charge transport layers and absorber layer additive in emerging photovoltaic technologies such as perovskite solar cells (PSCs), employing the principles of density functional theory (DFT) using the WIEN2k tool. The optimized lattice constant of the material and the volume for which the energy is minimum are estimated as 13.66 bohr and 2548.66 bohr3 respectively. The estimation of elastic properties, viz. the bulk modulus, shear modulus and Poisson’s ratio as 115 GPa, 71 GPa and 0.25 respectively, reveals that the material is resistant to deformation. The analysis of electronic properties and band structure indicates that Sc4C3 MXene has a direct bandgap of 0.747 eV at the Г point, and hence can be considered as a narrow bandgap semiconductor material. The study shows that the material possesses optimal light absorption properties with an absorption coefficient, dielectric permittivity and refractive index of 1.84 × 102 cm−1, 19.02 and 4.42 respectively, which are suitable for photovoltaic applications.

Generation of random microstructure in fiber reinforced composites and its comparison with carbon/carbon composite test samples through statistical analysis

ABSTRACT The elastic properties are important parameters for design of components using carbon/carbon composites. These elastic properties are required to be estimated with acceptable level of accuracy. These elastic properties are normally determined numerically. Estimation of elastic properties using numerical methods require accurate representation of microstructure of fibres in composite materials. Fibre arrangement is an important factor in the microstructure that shall be agree closely to the real composites. One of the method to compare the fibre arrangements in composites is through use of spatial statistics. In the present work the fibre arrangement in unidirectional composites is generated with volume fraction of 0.52–0.58 using an algorithm based on random removal of fibres. The fibre arrangements in carbon/carbon composite test samples are taken from microscopy images of unidirectional carbon/carbon composite, with same volume fraction of fibres. The simulated fibre arrangements are compared with carbon/carbon composites samples using statistical descriptors. The statistical descriptors are chosen from the spatial statistics. All the statistical descriptors show close agreement between the real and simulated microstructures.

Elastic properties and litho‐fluid facies estimation from pre‐stack seismic data through bidirectional long short‐term memory networks

ABSTRACTOne of the main goals of pre‐stack seismic inversion is the estimation of elastic properties (i.e. P‐, S‐ wave velocities and density) and litho‐fluid classes in the investigated area. To this end, many inversion strategies have been proposed, but the most popular is based on a two‐step inversion approach: First, elastic properties are inferred from pre‐stack data, and then a classification algorithm is used to convert the outcomes of the first stage into litho‐fluid facies. In this work, we propose an alternative approach based on recurrent neural networks. We train two bidirectional long short‐term memory networks to predict the inverse mappings from pre‐stack seismic data to elastic properties, and litho‐fluid classes. In the elastic inversion, we also use a Monte Carlo simulation approach to properly propagate onto the model space both the uncertainties related to noise contamination in the data and to the modelling error introduced by the network approximation. One crucial aspect of any machine‐learning inversion strategy is the definition of an appropriate training set. In this case, the models forming the training and validation examples are drawn according to a previously defined elastic and facies prior models derived from actual well log recordings. In particular, we assume a Gaussian‐mixture elastic prior, and we also take into account the uncertainties affecting the estimation of the transition probabilities of facies. We invert each seismic gather independently, and in this context, the generation of the training set, and the learning process can be accomplished with a very limited computational effort on a common notebook. Once trained, the networks estimate the elastic properties, the litho‐fluid facies and the related uncertainties from the pre‐stack data in near real‐time. Synthetic and field data inversions are used to validate the proposed method. The network predictions are also benchmarked against the outcomes of a more standard two‐step approach that combines a linear elastic inversion and a subsequent point‐wise Bayesian classification. Our results demonstrate that the implemented algorithm guarantees more accurate elastic property estimations and facies predictions than the standard inversion strategy. In particular, the predictions provided by the long short‐term memory network are less affected by erroneous assumptions on the noise statistics and prior model and by errors in the estimated source wavelet.

Target-Oriented Time-Lapse Elastic Full-Waveform Inversion Constrained by Deep Learning-Based Prior Model

Time-lapse (TL) seismic monitoring plays a vital role in reservoir characterization and management. Elastic full-waveform inversion (EFWI) has been applied to time-lapse seismic data to allow for a quantitative estimation of time-varying elastic properties. However, the high-resolution inversion can be computationally intense and ill-posed. To estimate the high-resolution time-lapse changes at a reasonable cost, we utilize two key techniques for the inversion: 1) we develop an elastic redatuming approach to retrieve the virtual elastic data for both base and monitor data at the target level using mainly a kinematically accurate velocity, thus, reducing the computational cost by focusing the high-resolution inversion on the target zone; 2) We integrate high-resolution well information and seismic data in the target-oriented inversion, where a high-resolution prior model is predicted by deep learning to regularize the inversion. A deep neural network (DNN) is capable of learning the mappings between the time-lapse seismic estimation and the facies interpreted from well information after the training process. Thus, we can derive a prior model for time-lapse changes by mapping the facies characterized by the property changes to the target inversion domain. We then implement the target-oriented TLEFWI regularized by the prior model, where the redatumed time-lapse elastic data and the prior model jointly contributes to the inversion result. The numerical examples validate that the proposed approach enables us to retrieve the time-lapse changes of elastic property in the target zone with improved resolution and well consistency.

Geotechnical and geophysical characterisations of construction waste-infilled quarry for housing and commercial developments: Case study of Tehran, Iran.

The fast population growth in the metropolitan areas of the province of Tehran has led to the scarcity of land and inevitable expansion of urban construction to non-engineered fills and construction/demolition waste disposal sites. An abandoned aggregate quarry, infilled with construction wastes over 16 years, has been recently selected for a new development project consisting of several multi-storey commercial and residential complexes (up to 7 storeys). This study was aimed at delineation of the waste materials, geophysical and field and laboratory geotechnical characterisations prior to foundation design, and the design of the excavation programme. Geo-electric resistivity test was used to delineate the waste materials from natural ground materials. Surface and downhole P- and S-wave velocity measurements were used for the estimation of dynamic elastic properties of the wastes. In total, 12 boreholes (15-30 m deep) along with 10 test pits (4-8.5 m deep) provided the opportunity for visual observations of the waste materials, necessary sampling for compositional analyses, laboratory shear strength tests and determination of waste deposit thickness in different regions of the site. Manual standard penetration test (SPT) was also used to evaluate in situ stiffness of the fine materials of the waste. Six field plate load tests were performed on the waste materials at their natural water content conditions and at saturated (flooded) ground conditions to determine their compressibility and the ground reaction modulus. Based on the results from extensive characterisation programme, it was concluded that the waste materials are in a metastable state and exhibit heterogeneity across the site. The findings of current case study can provide new insight into construction/demolition waste behaviour, using available geophysical and geotechnical tools and testing procedures for characterisation, and eventually helping in reliable design of foundations for new development projects.

Elastic Properties Estimation of Masonry Walls through the Propagation of Elastic Waves: An Experimental Investigation

Structural identification is one of the most important steps when dealing with historic buildings. Knowledge of the parameters, which define the mechanical properties of these kinds of structures, is fundamental in preparing interventions aimed at their restoration and strengthening, especially if they have suffered damage due to strong events. In particular, by using non-destructive techniques it is possible to estimate the mechanical characteristics of load-bearing structures without compromising the artistic value of the monumental buildings. In this paper, after recalling the main theoretical aspects, the use of elastic waves propagation through impact tests for the characterization of the masonry walls of a monumental building is described. The impact test allowed us to estimate the elastic characteristics of the homogeneous solid equivalent to masonry material. This confirms the great potential of the non-destructive diagnostics suitable for analyzing important structural parameters without affecting the preservation of historical masonry structures.