Development of a multi-continuum quadruple porosity model to estimate CO2 storage capacity and CO2 enhanced shale gas recovery

Geologic storage of CO2 in shale formation not only enhances natural gas recovery, but also sequestrates CO2 effectively. According to this technology, a multi-continuum quadruple porosity binary component gas model is developed to investigate carbon dioxide storage capacity and CO2 enhanced shale gas recovery, which is based on multiple flow mechanisms, including dissolution, adsorption/desorption, viscous flow, diffusion, slip flow and stress sensitivity of hydraulic fractures. This fully coupled model is divided into quadruple media, including organic matters, organic pore system, matrix system and natural fracture system. The matrix-fracture transfer flow is simulated by modified multiple interacting continua (MINC) method. Embedded discreate fracture model (EDFM) is introduced to describe the gas flow in hydraulic fractures and the transfer flow between hydraulic fractures and natural fractures. Finite difference method (FDM) and quasi-Newton iterative method are applied to solve this model. The reliability and practicability of this model is validated by matching the production history of a fractured horizontal well in shale gas reservoir. The effects of relevant parameters on production curves are analyzed, including adsorption parameters, dissolution parameters, well production pressure, injection pressure, volumetric fraction of kerogen and injection opportunity. The result shows that the model in this work is reliable and practicable, and the model presented here can be used to investigate the injectivity of CO2 and CO2 enhanced shale gas recovery

Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory

In this work, a new displacement-based Trefftz plate element is developed for size-dependent bending analysis of the thin plate structures in the context of the modified couple stress theory. This is achieved via two steps. First, the Trefftz functions, that are derived by introducing the thin plate bending assumptions into the three-dimensional governing equations of the modified couple stress elasticity, are adopted as the basis functions for designing the element's displacement interpolations. Second, the generalized conforming theory is employed to meet the interelement compatibility requirements in weak sense for ensuring the convergence property. The resulting 4-node displacement-based plate element performs like nonconforming models on coarse meshes and gradually converges into a conforming one with the mesh refinement. Numerical tests reveal that the new element can efficiently capture the size-dependent mechanical responses of thin microplates and exhibits satisfactory numerical accuracy and distortion tolerance. Moreover, as the element has only three degrees of freedom (DOF) per node, it can be easily incorporated into the commonly available finite element programs

Simulating Fractures with Bonded Discrete Element Method

Along with motion and deformation, fracture is a fundamental behaviour for solid materials, playing a critical role in physically-based animation. Many simulation methods including both continuum and discrete approaches have been used by the graphics community to animate fractures for various materials. However, compared with motion and deformation, fracture remains a challenging task for simulation, because the material's geometry, topology and mechanical states all undergo continuous (and sometimes chaotic) changes as fragmentation develops. Recognizing the discontinuous nature of fragmentation, we propose a discrete approach, namely the Bonded Discrete Element Method (BDEM), for fracture simulation. The research of BDEM in engineering has been growing rapidly in recent years, while its potential in graphics has not been explored. We also introduce several novel changes to BDEM to make it more suitable for animation design. Compared with other fracture simulation methods, the BDEM has some attractive benefits, e.g. efficient handling of multiple fractures, simple formulation and implementation, and good scaling consistency. But it also has some critical weaknesses, e.g. high computational cost, which demand further research. A number of examples are presented to demonstrate the pros and cons, which are then highlighted in the conclusion and discussion

A Divergence‐free Mixture Model for Multiphase Fluids

We present a novel divergence free mixture model for multiphase flows and the related fluid-solid coupling. The new mixture model is built upon a volume-weighted mixture velocity so that the divergence free condition is satisfied for miscible and immiscible multiphase fluids. The proposed mixture velocity can be solved efficiently by adapted single phase incompressible solvers, allowing for larger time steps and smaller volume deviations. Besides, the drift velocity formulation is corrected to ensure mass conservation during the simulation. The new approach increases the accuracy of multiphase fluid simulation by several orders. The capability of the new divergence-free mixture model is demonstrated by simulating different multiphase flow phenomena including mixing and unmixing of multiple fluids, fluid-solid coupling involving deformable solids and granular materials

A novel displacement-based Trefftz plate element with high distortion tolerance for orthotropic thick plates

In this work, a simple but robust 4-node displacement-based Trefftz plate element is proposed for efficiently analysis of orthotropic plate structures. This is achieved via two steps. First, the element's deflection and rotation fields are directly formulated at the base of the Trefftz functions of the orthotropic Mindlin–Reissner plate. Second, to ensure the convergence property and further enhance the element performance, the generalized conforming theory is employed to satisfy the requirement for interelement compatibility in weak sense. The resulting displacement-based element belongs to the nonconforming models on coarse meshes and gradually converges into a conforming one with the mesh refinement. Numerical benchmarks reveal that the new element can produce high precision results for both displacement and stress resultant. Moreover, it is free of shear locking and has good tolerances to mesh distortions

Hyperelastic finite deformation analysis with the unsymmetric finite element method containing homogeneous solutions of linear elasticity

A recent unsymmetric 4‐node, 8‐DOF plane finite element US‐ATFQ4 is generalized to hyperelastic finite deformation analysis. Since the trial functions of US‐ATFQ4 contain the homogenous closed analytical solutions of governing equations for linear elasticity, the key of the proposed strategy is how to deal with these linear analytical trial functions (ATFs) during the hyperelastic finite deformation analysis. Assuming that the ATFs can properly work in each increment, an algorithm for updating the deformation gradient interpolated by ATFs is designed. Furthermore, the update of the corresponding ATFs referred to current configuration is discussed with regard to the hyperelastic material model, and a specified model, neo‐Hookean model, is employed to verify the present formulation of US‐ATFQ4 for hyperelastic finite deformation analysis. Various examples show that the present formulation not only remain the high accuracy and mesh distortion tolerance in the geometrically nonlinear problems, but also possess excellent performance in the compressible or quasi‐incompressible hyperelastic finite deformation problems where the strain is large

Predicting the effective mechanical property of heterogeneous materials by image based modeling and deep learning

In contrast to the composition uniformity of homogeneous materials, heterogeneous materials are normally composed of two or more distinctive constituents. It is usually recognized that the effective material property of a heterogeneous material is related to the mechanical property and the distribution pattern of each forming constituent. However, to establish an explicit relationship between the macroscale mechanical property and the microstructure appears to be complicated. On the other hand, machine learning methods are broadly employed to excavate inherent rules and correlations based on a significant amount of data samples. Specifically, deep neural networks are established to deal with situations where input–output mappings are extensively complex. In this paper, a method is proposed to establish the implicit mapping between the effective mechanical property and the mesoscale structure of heterogeneous materials. Shale is employed in this paper as an example to illustrate the method. At the mesoscale, a shale sample is a complex heterogeneous composite that consists of multiple mineral constituents. The mechanical properties of each mineral constituent vary significantly, and mineral constituents are distributed in an utterly random manner within shale samples. Large quantities of shale samples are generated based on mesoscale scanning electron microscopy images using a stochastic reconstruction algorithm. Image processing techniques are employed to transform the shale sample images to finite element models. Finite element analysis is utilized to evaluate the effective mechanical properties of the shale samples. A convolutional neural network is trained based on the images of stochastic shale samples and their effective moduli. The trained network is validated to be able to predict the effective moduli of real shale samples accurately and efficiently. Not limited to shale, the proposed method can be further extended to predict effective mechanical properties of other heterogeneous materials

Incompressibility Enforcement for Multiple-fluid SPH Using Deformation Gradient

To maintain incompressibility in SPH fluid simulations is important for visual plausibility. However, it remains an outstanding challenge to enforce incompressibility in such recent multiple-fluid simulators as the mixture-model SPH framework. To tackle this problem, we propose a novel incompressible SPH solver, where the compressibility of fluid is directly measured by the deformation gradient. By disconnecting the incompressibility of fluid from the conditions of constant density and divergence-free velocity, the new incompressible SPH solver is applicable to both single- and multiple-fluid simulations. The proposed algorithm can be readily integrated into existing incompressible SPH frameworks developed for single-fluid, and is fully parallelizable on GPU. Applied to multiple-fluid simulations, the new incompressible SPH scheme significantly improves the visual effects of the mixture-model simulation, and it also allows exploitation for artistic controlling

Unified particle system for multiple-fluid flow and porous material

Porous materials are common in daily life. They include granular material (e.g. sand) that behaves like liquid flow when mixed with fluid and foam material (e.g. sponge) that deforms like solid when interacting with liquid. The underlying physics is further complicated when multiple fluids interact with porous materials involving coupling between rigid and fluid bodies, which may follow different physics models such as the Darcy's law and the multiple-fluid Navier-Stokes equations. We propose a unified particle framework for the simulation of multiple-fluid flows and porous materials. A novel virtual phase concept is introduced to avoid explicit particle state tracking and runtime particle deletion/insertion. Our unified model is flexible and stable to cope with multiple fluid interacting with porous materials, and it can ensure consistent mass and momentum transport over the whole simulation space