{"title":"A Dynamic Three-Field Finite Element Model for Wave Propagation in Linear Elastic Porous Media","authors":"Bruna Campos, Robert Gracie","doi":"10.1002/nag.3916","DOIUrl":null,"url":null,"abstract":"<p>A three-field finite element (FE) model for dynamic porous media considering the de la Cruz and Spanos (dCS) theory is presented. Due to fluid viscous dissipation terms, wave propagation in the dCS theory yields an additional rotational wave compared to Biot (BT) theory. In addition, introducing porosity as a dynamic variable in the dCS model allows solid-fluid nonreciprocal interactions. Due to the volume-averaging technique, the dCS model further accounts for a macroscopic shear modulus and adds a new macroscopic constant. The porous media governing equations are formulated in terms of solid displacement, fluid pressure, and fluid displacement. Space and time convergence rates for the FE dCS model are demonstrated in a one-dimensional case. A dimensionless analysis performed in the dCS framework led to negligible differences between BT and dCS models except when assuming high fluid viscosity. Domains with small characteristic lengths resulted in BT and dCS damping terms in the same order of magnitude. One- and two-dimensional examples showed that dCS nonreciprocal interactions and the macroscopic shear modulus are responsible for modifying wave patterns. A two-dimensional injection well simulation with water and slickwater showed higher wave attenuation for the latter. High frequencies in dCS model were noticed to yield more significant changes in wave patterns. The numerical results highlight the contributions of the dCS porous media model and its importance in simulations of laboratory scale experiments, ultrasonic frequencies, and highly viscous fluids.</p>","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"49 4","pages":"1139-1157"},"PeriodicalIF":3.4000,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nag.3916","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical and Analytical Methods in Geomechanics","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/nag.3916","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, GEOLOGICAL","Score":null,"Total":0}
引用次数: 0
Abstract
A three-field finite element (FE) model for dynamic porous media considering the de la Cruz and Spanos (dCS) theory is presented. Due to fluid viscous dissipation terms, wave propagation in the dCS theory yields an additional rotational wave compared to Biot (BT) theory. In addition, introducing porosity as a dynamic variable in the dCS model allows solid-fluid nonreciprocal interactions. Due to the volume-averaging technique, the dCS model further accounts for a macroscopic shear modulus and adds a new macroscopic constant. The porous media governing equations are formulated in terms of solid displacement, fluid pressure, and fluid displacement. Space and time convergence rates for the FE dCS model are demonstrated in a one-dimensional case. A dimensionless analysis performed in the dCS framework led to negligible differences between BT and dCS models except when assuming high fluid viscosity. Domains with small characteristic lengths resulted in BT and dCS damping terms in the same order of magnitude. One- and two-dimensional examples showed that dCS nonreciprocal interactions and the macroscopic shear modulus are responsible for modifying wave patterns. A two-dimensional injection well simulation with water and slickwater showed higher wave attenuation for the latter. High frequencies in dCS model were noticed to yield more significant changes in wave patterns. The numerical results highlight the contributions of the dCS porous media model and its importance in simulations of laboratory scale experiments, ultrasonic frequencies, and highly viscous fluids.
提出了一种考虑de la Cruz和Spanos (dCS)理论的动态多孔介质三场有限元(FE)模型。由于流体黏性耗散项的存在,与Biot (BT)理论相比,dCS理论中的波传播产生了额外的旋转波。此外,在dCS模型中引入孔隙度作为一个动态变量,允许固-流非互反相互作用。由于采用体积平均技术,dCS模型进一步考虑了宏观剪切模量,并增加了一个新的宏观常数。多孔介质的控制方程是用固体位移、流体压力和流体位移来表示的。在一维情况下证明了有限元dCS模型的空间和时间收敛率。在dCS框架中进行的无量纲分析导致BT和dCS模型之间的差异可以忽略不计,除非假设流体粘度很高。具有较小特征长度的域导致了相同数量级的BT和dCS阻尼项。一维和二维的例子表明,dCS的非互反相互作用和宏观剪切模量是改变波型的原因。在含水和滑溜水的二维注水井模拟中,滑溜水的波衰减更高。在dCS模型中,高频会产生更显著的波形变化。数值结果突出了dCS多孔介质模型的贡献及其在实验室尺度实验、超声频率和高粘性流体模拟中的重要性。
期刊介绍:
The journal welcomes manuscripts that substantially contribute to the understanding of the complex mechanical behaviour of geomaterials (soils, rocks, concrete, ice, snow, and powders), through innovative experimental techniques, and/or through the development of novel numerical or hybrid experimental/numerical modelling concepts in geomechanics. Topics of interest include instabilities and localization, interface and surface phenomena, fracture and failure, multi-physics and other time-dependent phenomena, micromechanics and multi-scale methods, and inverse analysis and stochastic methods. Papers related to energy and environmental issues are particularly welcome. The illustration of the proposed methods and techniques to engineering problems is encouraged. However, manuscripts dealing with applications of existing methods, or proposing incremental improvements to existing methods – in particular marginal extensions of existing analytical solutions or numerical methods – will not be considered for review.