Asiya Kudarova

Bending stiffness of a graphene sheet

The paper proposes a discrete mechanical model of monolayer graphene. A relation between parameters of the model and elastic characteristics of its equivalent continuum is derived by comparing the energy of small strains on micro- and macroscales. The relation allows one to determine the microscale interaction parameters from experimental data and, knowing the microscale parameters, to determine the mechanical properties of graphene. The main aim of the work is to estimate the bending stiffness of a graphene sheet. The proposed discrete model provides an analytical dependence of the graphene sheet bending stiffness on the microscale interaction parameters.

Higher-order homogenization for one-dimensional wave propagation in poroelastic composites

An effective model is derived for periodically layered poroelastic media, where layers represent mesoscopic-scale heterogeneities that are larger than the pore and grain sizes but smaller than the wavelength. Each layer is homogeneous, described by Biot’s equations of poroelasticity. The proposed model has only real-valued frequencyindependent effective coefficients determined analytically exclusively by the physical parameters of the layers. It serves as an alternative to the existing models with frequency-dependent effective elastic properties. Homogenization is based on asymptotic expansions with multiple spatial scales and results in equations of motion containing higher-order derivatives. It is valid for wavelengths much larger than the period of the system. This approach, being widely used in elasticity, is extended to poroelasticity in this work. The exact analytical solution, obtained by the application of Floquet’s theory to poroelastic composites, is used to validate the model.

Review Paper: A semi-empirical model of strain sensitivity for 4D seismic interpretation: Strain sensitivity model for 4D seismic

We reformulate the original model of Hatchell and Bourne and Roste, Stovas and Landro that couples fractional velocity change to subsurface strain via a fundamental constant R. The new model combines elastic compressibility of a dual-porosity system for a sand–shale mixture with horizontal planes of inter-granular weakness. The majority of observed R-factor magnitudes from post-stack 4D seismic data in both the reservoir and overburden can thus be explained. R is predicted to depend strongly on lithology and also initial strain state. The model is also extended to predict the observed angle-dependence of time-lapse time-shifts from pre-stack data. An expression for the gradient of time-shift with incidence angle is obtained in terms of the background VP/VS, and also the ratio of tangential to normal compliances BT/BN representing loss or creation of inter-granular coupling. If accurately estimated from data, this compliance ratio can be used as an additional parameter to assess the post-production state of the overburden. It is concluded that whilst R remains the over-arching parameter controlling the magnitude of time-shifts measured from 4D seismic data, BT/BN is a subtler parameter that may also prove of future value.

A Semi-Empirical Model for Interpreting Rock Strain Sensitivity in 4D Seismic Data

Several models have been recently proposed to connect observations of velocity change with strain deformation in and around reservoirs undergoing production and recovery. In this work we show that a simple compliance-based model combined with the original conceptual understanding of Hatchell and Bourne (2005) can adequately explain the magnitude of R factor values currently observed from calibrated field data in a variety of settings. The model is also used to determine an expression for the gradient of overburden time-shift variation with incidence angle. This gradient is predicted to be low but may vary according to the ratio of tangential to normal compliance at the intergranular contacts. This factor could perhaps be used as an additional parameter to assess the post-production state of the overburden.