Master of Science

thesisTight shale reservoirs have recently emerged as potential game changers in oil and gas and energy sectors worldwide. Consequently, exploration and exploitation of unconventional reservoirs has significantly increased over the last decade. Currently used stimulation designs are based on conventional planar fracture models that cannot realistically simulate the geometry and the extent of hydraulically induced fractures. For that reason, developing models that can thoroughly and accurately describe fracture network initiation and propagation plays a significant role in evaluating well production. The main goal of this work is to evaluate the utility of the peridynamic theory (PD) in modeling the process of hydraulic fracturing. Peridynamics is a nonlocal theory of continuum media that can facilitate a direct coupling between classical continuum mechanics and molecular dynamics. A linear-viscoelastic PD model was applied to a three-dimensional domain that was discretized with cubic lattices of particles. Damage in the model is represented by the bond breakage; as the stretch between two lattices reaches its critical limit, s_0, the bond breaks. The validity of the peridynamic simulation was tested by comparing results obtained in this project against the results obtained in a study performed by Zhou et al. Therefore, six sets of experimental tests were conducted to simulate hydraulic fracturing based on the peridynamic method. Five sets of the simulation results produced in this work were in good agreement with the experimental results. The investigation examined the influences of the differential horizontal stress and preexisting fracture, along with different approach angles, on the geometry of the hydraulic fracture. Different injection rates were applied to the model in order to compare the fractured area that resulted from different injection rates. The simulation showed that the maximum dilatation and fractured zone occurred at the injection rate of 0.61 m3?min. The 0.61 m3/min injection rate caused the highest complete damage (0.9-1) with 5.24 % of the total number of atoms. As a result, the peridynamic approach presents promising results in predicting fracture propagation and damage area

Anisotropic Continuum-Molecular Models: A Unified Framework Based on Pair Potentials for Elasticity, Fracture and Diffusion-Type Problems

This paper presents a unified framework for continuum-molecular modeling of anisotropic elasticity, fracture and diffusion-based problems within a generalized two-dimensional peridynamic theory. A variational procedure is proposed to derive the governing equations of the model, that postulates oriented material points interacting through pair potentials from which pairwise generalized actions are computed as energy conjugates to properly defined pairwise measures of primary field variables. While mass is considered as continuous function of volume, we define constitutive laws for long-range interactions such that the overall anisotropic behavior of the material is the result of the assigned elastic, conductive and failure micro-interaction properties. The non-central force assumption in elasticity, together with the definition of specific orientation-dependent micromoduli functions respecting material symmetries, allow to obtain a fully anisotropic non-local continuum using a purely pairwise description of deformation and constitutive properties. A general and consistent micro-macro moduli correspondence principle is also established, based on the formal analogy with the classic elastic and conductivity tensors. The main concepts presented in this work can be used for further developments of anisotropic continuum-molecular formulations to include other mechanical behaviors and coupled phenomena involving different physics

A non-local vector calculus,non-local volume-constrained problems,and non-local balance laws

A vector calculus for nonlocal operators is developed, including the definition of nonlocal divergence, gradient, and curl operators and the derivation of the corresponding adjoints operators. Nonlocal analogs of several theorems and identities of the vector calculus for differential operators are also presented. Relationships between the nonlocal operators and their differential counterparts are established, first in a distributional sense and then in a weak sense by considering weighted integrals of the nonlocal adjoint operators. The nonlocal calculus gives rise to volume-constrained problems that are analogous to elliptic boundary-value problems for differential operators; this is demonstrated via some examples. Another application is posing abstract nonlocal balance laws and deriving the corresponding nonlocal field equations

Thermomechanical analysis of composites under shock load using peridynamics

Composite structures have been increasingly used in marine industries because of their high performance. During their service time, they may be exposed to extreme loading conditions such as underwater explosions. Both thermal loading effects on deformation and deformation effects on temperature need to be taken into consideration in the numerical simulations. Therefore, a thermomechanical analysis is conducted in a fully coupled manner, in order to investigate the thermal and mechanical responses of composite materials under explosion loads. In this study, the peridynamics theory is used for failure analyses of composite structure

Peridynamic-based multiscale frameworks for continuous and discontinuous material response

This PhD thesis aimed to develop two broad classes of multiscale frameworks for peridynamic theory to address two pressing needs: first is increased computational efficiency and the second is characterisation of heterogeneous media. To achieve these goals, two multiscale frameworks were proposed: model order reduction methodologies and homogenization frameworks. The model order reduction schemes were designed to improve computational efficiency, while the homogenization methodology aimed to provide frameworks for characterisation of heterogeneous materials within the peridynamic theory. Two specific model order reduction schemes were proposed, including a coarsening methodology and a model order reduction method based on static condensation. These schemes were applied to benchmark problems and shown to be effective in reducing the computational requirement of peridynamic models without compromising the fidelity of the simulation results. Additionally, a first-order nonlocal computational homogenization framework was proposed to characterise heterogeneous systems in the framework of peridynamics. This framework was utilised to characterise the behaviour of elastic and viscoelastic materials and materials with evolving microstructures. The results from these studies agreed with published results. The thesis achieved the goal of contributing to the development of efficient and accurate multiscale frameworks for peridynamic theory, which have potential applications in a wide range of fields, including materials science and engineering.This PhD thesis aimed to develop two broad classes of multiscale frameworks for peridynamic theory to address two pressing needs: first is increased computational efficiency and the second is characterisation of heterogeneous media. To achieve these goals, two multiscale frameworks were proposed: model order reduction methodologies and homogenization frameworks. The model order reduction schemes were designed to improve computational efficiency, while the homogenization methodology aimed to provide frameworks for characterisation of heterogeneous materials within the peridynamic theory. Two specific model order reduction schemes were proposed, including a coarsening methodology and a model order reduction method based on static condensation. These schemes were applied to benchmark problems and shown to be effective in reducing the computational requirement of peridynamic models without compromising the fidelity of the simulation results. Additionally, a first-order nonlocal computational homogenization framework was proposed to characterise heterogeneous systems in the framework of peridynamics. This framework was utilised to characterise the behaviour of elastic and viscoelastic materials and materials with evolving microstructures. The results from these studies agreed with published results. The thesis achieved the goal of contributing to the development of efficient and accurate multiscale frameworks for peridynamic theory, which have potential applications in a wide range of fields, including materials science and engineering

Modelling artificial ground freezing subjected to high velocity seepage

Artificial ground freezing (AGF) is a ground improvement technique for en- suring the safety of underground construction works in water-bearing soils. High velocity water transport in coarse-grain soils can prevent the ice wall formation in brine-based ground freezing methods. This can be overcome by using expendable refrigerants such as solid carbon dioxide and liquid nitro- gen, which provide much lower temperatures. Presented here is a model for analysis and design of ground freezing by expendable refrigerants under high velocity seepage conditions. Non-local mathematical formulations of heat transfer and water flow in soils are developed within the framework of the Peridynamics theory. Their computational implementation uses an adaptive multi-grid peridynamic approach to analyse large domains efficiently. The simulations are tested successfully against several benchmarks. The devel- oped model enables reliable analyses of the effects of main geological and technological parameters on the ice-wall delivery in the presence of ground- water flow

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized