Yong Sheng

Microscopic modelling of the hydraulic fracturing process

A microscopic perspective is introduced in this study which offers a detailed insight at the inter-particle level to the geo-mechanical responses caused by fluid injection and the resulting pressure build-up. This was achieved by employing the Discrete Element Method (DEM) to model the pressure development and the subsequent fracturing and/or cavity propagation. This technique represents the formation material as an assembly of discrete particles linked to each other through contacts. Numerical experiments were carried out on two sample materials. For the first instance, tests were carried out on a bulk material, representative of a generic intact rock, with the breakage of inter-particle bonds indicating the formation of cracks. The second series of tests was carried out on granular type materials such as sand, where particle separation signified cavity initiation and separation. It was observed from the DEM modelling results that the intact rock material showed a predominance of mode II fracturing at high fluid velocities. However, when the fluid velocity is reduced considerably the fracturing behaviour tended towards more of mode I. Also, records of the pressure development were taken from the numerical results and were used to monitor the fracturing events. The outcome of this study highlights important aspects of the hydraulic fracturing process especially at the particle–particle scale, and thus provides a strong basis for more exhaustive studies involving larger scale reservoir modelling and more complex fracturing scenarios.

Carbon dioxide injection and associated hydraulic fracturing of reservoir formations

The storage potential of subsurface geological systems makes them viable candidates for long-term disposal of significant quantities of CO2. The geo-mechanical responses of these systems as a result of injection processes as well as the protracted storage of CO2 are aspects that require sufficient understanding. A hypothetical model has been developed that conceptualises a typical well-reservoir system comprising an injection well where the fluid (CO2) is introduced and a production/abandoned well sited at a distant location. This was accomplished by adopting a numerical methodology (discrete element method), specifically designed to investigate the geo-mechanical phenomena whereby the various processes are monitored at the inter-particle scale. Fracturing events were simulated. In addition, the influence of certain operating variables such as injection flow rate and fluid pressure was studied with particular interest in the nature of occurring fractures and trend of propagation, the pattern and magnitude of pressure build-up at the well vicinity, pressure distribution between well regions and pore velocity distribution between well regions. Modelling results generally show an initiation of fracturing caused by tensile failure of the rock material at the region of fluid injection; however, fracturing caused by shear failure becomes more dominant at the later stage of injection. Furthermore, isolated fracturing events were observed to occur at the production/abandoned wells that were not propagated from the injection point. This highlights the potential of CO2 introduced through an injection well, which could be used to enhance oil/gas recovery at a distant production well. The rate and magnitude of fracture development are directly influenced by the fluid injection rate. Likewise, the magnitude of pressure build-up is greatly affected by the fluid injection rate and the distance from the point of injection. The DEM modelling technique illustrated provides an effective procedure that allows for more specific investigations of geo-mechanical mechanisms occurring at subsurface systems. The application of this methodology to the injection and storage of CO2 facilitates the understanding of the fracturing phenomenon as well as the various factors governing the process.

Influence of rock failure behaviour on predictions in sand production problems

The mechanical strength of rock in terms of shear or compressive failure has been previously adopted as a criterion for sand production and when used solely has been proven to overestimate the process. On the other hand, ignoring the mechanical strength behaviour of the material increases the tendency for inaccurate estimations of the erosion process. In this work, an equally proportionated inclusion of the mechanical strength and erosion-based criteria in sanding predictions is proposed and assessed by numerical models. Several rock failure models and their influences on the sanding process have been analysed, including models such as the Drucker–Prager (DP), the Drucker–Prager hardening (DP hardening), the Mohr–Coulomb (MC) and the Mohr–Coulomb softening (MC softening). Modelling outcomes show distinct differences in rock response to operating and boundary conditions (e.g. flow rate and drawdown), and predictions of sand production. It was confirmed by modelling results that despite the low magnitude of stresses and strains developed at the well face and perforation regions, post-yield hardening behaviour increases the estimation of the amount and intensity of sand production. Also, incorporating a post-yield softening behaviour increases the magnitude of stresses and strains; however, this effect is observed to have a negligible impact on sand production. The role of void ratio has been recognised as a dominant factor, as its evolution significantly determines the pattern and intensity of sand production. A more cautious selection and rigorous coupling of rock strength models in sand production modelling is therefore essential if accuracy of predictions is to be improved.

A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method

Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM). In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca2+ concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissues corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart.

Inter-relationship between joint dilatancy and frictional resistance: impact on fracture behaviour

Rock joints possess features that alter both the characteristics of rock formations and the fracturing process. Two important properties that govern the shear behaviour and dilatancy behaviour of discontinuities have been analysed in this paper by the discrete element method (DEM). The ability of a frictional joint to suppress fracture growth decreases as the frictional resistance increases; however, the rate and extent of fracturing increases with joint dilatancy. The influence of joint frictional resistance is more dominant at high values and in this range effects of small magnitudes of dilatancy are correspondingly insignificant. At low joint friction the occurrence of even a small amount of dilation increases the severity of the fracturing process. This study highlights the interactions between two main joint properties with the anticipation that the concepts derived here will be useful for predicting fracture behaviour at the subsurface.

The performance of stochastic designs in wellbore drilling operations

Wellbore drilling operations frequently entail the combination of a wide range of variables. This is underpinned by the numerous factors that must be considered in order to ensure safety and productivity. The heterogeneity and sometimes unpredictable behaviour of underground systems increases the sensitivity of drilling activities. Quite often the operating parameters are set to certify effective and efficient working processes. However, failings in the management of drilling and operating conditions sometimes result in catastrophes such as well collapse or fluid loss. This study investigates the hypothesis that optimising drilling parameters, for instance mud pressure, is crucial if the margin of safe operating conditions is to be properly defined. This was conducted via two main stages: first a deterministic analysis—where the operating conditions are predicted by conventional modelling procedures—and then a probabilistic analysis via stochastic simulations—where a window of optimised operation conditions can be obtained. The outcome of additional stochastic analyses can be used to improve results derived from deterministic models. The incorporation of stochastic techniques in the evaluation of wellbore instability indicates that margins of the safe mud weight window are adjustable and can be extended considerably beyond the limits of deterministic predictions. The safe mud window is influenced and hence can also be amended based on the degree of uncertainty and the permissible level of confidence. The refinement of results from deterministic analyses by additional stochastic simulations is vital if a more accurate and reliable representation of safe in situ and operating conditions is to be obtained during wellbore operations.

Effects of friction conditions on the formation of dead metal zone in orthogonal cutting – a finite element study

Abstract A numerical study of the effects of friction conditions on the formation of dead metal zone (DMZ) is presented. The friction conditions are classified as three different cases in the form of coefficient: (1) constant coefficient of friction, (2) “smooth” and “sharp” change of the friction coefficient and (3) time-dependent friction coefficient. These friction cases are numerically investigated using the finite element (FE) code ABAQUS/Explicit. A FE model based on the arbitrary-Lagrangian–Eulerian approach is developed to simulate the cutting process and investigate the influences of the friction conditions. The simulated results, for a wide range of friction conditions, are obtained, analyzed and compared with previously published experimental/numerical data. It has been found that the friction coefficient has a direct effect on the amount and shape of DMZ, the sharp change of coefficient has a larger effect on the DMZ formation than the smooth one and the formation of DMZ is more determined by the value of the friction coefficient than its duration.

Multi-scale modeling of the progressive damage in cross-ply laminates under thermal and mechanical loading

The progressive damage in cross-ply laminates was modeled by discrete element method (DEM). A particle radius expansion method was used to account for thermal loading applied to cross-ply laminates in which nominal fibers were introduced in the 0° plies so as to achieve the anisotropic thermal expansion behaviors. A series of convergence and validation tests of both mechanical and thermal properties of the 0° plies with nominal fibers have been carried out in order to validate the method. The DEM results of interfacial stress distribution of cross-ply laminates under pure thermal loading and under coupled thermal/mechanical loading were compared with other theoretical predictions. Microstructure of 90° plies was also studied by the DEM model. Transverse cracking which was formed by the coalescence of micro cracks in matrix and at fiber/matrix interface has been observed in the modeling results together with the ply-ply delaminations. It was found that the DEM model can predict not only the stress distribution but also the progressive damage initialized from the constituent failure due to its multi scale nature.

Numerical Modelling of Damage Progression in Single-Fiber Composite under Axial Tension

Damage and failure of the fiber reinforced composites remain as a challenging research subject in the area of material science and engineering. In this study a novel particle assembly model is developed using two dimensional Discrete Element Method (DEM) for the purpose of simulating the damage and failure process of the single-fiber composite (SFC) under axial tension. Fiber (SiC) and matrix (Epoxy) are represented by particles bonded together through elastic parallel bonds which are calibrated by a series of numerical tests. The contacts between the fiber particles and matrix particles are directly accounted for the fiber/matrix interface which is represented by the contact softening model similar to the cohesive zone model (CZM) in the continuum mechanics. The single-fiber composite tensile test is carried out using the developed DEM model in order to evaluate the interactions between fiber breakage, interfacial debonding and matrix cracking. The numerical results have demonstrated the capability of the developed DEM model in simulating the entire failure process of each individual constituent of the single fiber composite. This study has also confirmed that the DEM model has unique advantages over the conventionally numerical models in terms of dealing with the evolution of microscopic damages in composite materials.