Poromechanics Response of Inclined Wellbore Geometry in Fractured Porous Media

This paper presents the poromechanics/poroelastic analytical solution for stress and pore pressure fields induced by the action of drilling and/or the pressurization of an inclined/horizontal wellbore in fractured fluid-saturated porous media, or naturally fractured fluid-saturated rock formations. The model which is developed within the framework of the coupled processes in the dual-porosity/dual-permeability approach accounts for coupled isothermal fluid flow and rock/fractures deformation. The solution to the inclined/horizontal wellbore problem is derived for a wellbore drilled in an infinite naturally fractured poroelastic medium, subjected to three-dimensional in situ state of stress and pore pressure. The dual-porosity analytical solution is first reduced to the limiting single-porosity case and verified against an existing single-porosity solution. A comparison between single-porosity and dual-porosity poroelastic results is conducted and displayed in this work. Finally, wellbore stability analyses have been carried out to demonstrate possible applications of the solution.     

Finite element formulation and application of poroelastic generalized plane strain problems

A generalized plane strain finite element is developed for the analysis of poroelasticity problems. The validity and accuracy of the special element is demonstrated by analyzing inclined borehole problems in isotropic and transversely isotropic poroelastic materials. For the former, comparison is made with an analytical solution and the latter, with a three-dimensional finite element solution. A substantial reduction in computational effort is realized for the generalized plane strain finite element, as compared to the three-dimensional finite element. This is achieved without sacrificing the accuracy and the ability to account for the three-dimensional material anisotropy and far field stress components.     

Modeling Fully Coupled Oil–Gas Flow in a Dual-Porosity Medium

A finite element model has been developed to simulate two-phase, (i.e., oil and gas) flow and solid deformation in a dual-porosity medium. The model accounts for coupling between solid deformations and fluid flow in both the primary medium (representing the matrix pores and solid) and the secondary medium (used to represent fractures in the present study). The model is verified against relevant analytical solutions and then applied to the problem of an inclined wellbore under generalized plane strain conditions, subjected to a three-dimensional in situ state of stress in a fractured formation saturated with oil and gas. A parametric study has been carried out to demonstrate the effect of dual-porosity parameters, phase saturations, and interaction between the two media. The implementation of double effective stress laws in the present study is a significant deviation from some classical dual-porosity models and helps to incorporate the effect of deformation of the secondary medium (representing the fractures).     

Porochemothermoelastic Solution for an Inclined Borehole in a Transversely Isotropic Formation

A generalized anisotropic poromechanics formulation for chemically active poroelastic media under nonisothermal conditions, termed as porochemothermoelastic, is presented. The pore fluid is modeled as a two-species constituent comprised of the solute and the solvent. Governing equations are developed and applied to obtain the analytical solution for an inclined borehole in chemically active transversely isotropic formation subjected to a three-dimensional state of stress and nonisothermal conditions. Numerical examples are presented to demonstrate the thermochemical effects on stress and pore pressure distributions in the vicinity of the borehole and their potential impacts on borehole stability.     

带有柔性齿圈和行星架的直齿和斜齿行星传动的模拟

本文提供可以仿真具有变形零件的直齿和斜齿行星齿轮周转齿轮的三维静态和动态性能的模型。通过三维有限元方法得出的结构求出齿圈和行星架的变形分布。根据模型的转化技术,通过考虑到轮齿接触弹性原则,由连接齿圈结构和行星轮分块参数模型限定内齿轮元件。沿接触线导出离散的啮合刚度和当量法面偏差,并把啮合齿面位置作为随时间变化再计算它们的数值。采用约束基础技术仿真一个连接行星轮中心的行星架,用组合板块参数太阳轮／行星齿轮和沿轴装零件集成刚度,质量和惯量完善行星齿轮／周转齿轮模型。对整个啮合仿真用综合时间一分级积分框图和接触算法解相应的运动方程式。得出的一些准静态和动态的结果表明所推荐的混合模型的趋向和考虑齿圈和行星架变形的重要性。     

Mechanical characterization of small shale samples subjected to fluid exposure using the inclined direct shear testing device

The mechanical strength, elastic moduli, and other properties of shale are known to be highly sensitive to any variation in pore fluid content and pore fluid chemical composition. To date, all existing rock mechanics testing procedures and studies attempting to quantitatively quantify these changes employ standard methods and techniques, i.e., shale testing under hydrostatic confinement, triaxial tests, or direct shear tests, which require very long fluid circulation time due to the intrinsic low hydraulic permeability and low solute diffusivity of shale rocks and large sample size recommended by these conventional methods. Moreover, standard-size samples for conventional rock testing methods are not always available, and the use of non-conventional size samples is sometimes required. In this work, shale testing and results on rock sample the size and shape of a stack of a few pennies are presented. The inclined direct shear test, an innovative patent-pending testing method for small and thin rock specimens, has been developed to facilitate mechanical strength characterization under variable confining pressure, with tested material exposed to different fluids at any desired exposure time, while dynamic elastic moduli can be simultaneously monitored as functions of applied stress state. This device has been compared to standard triaxial test with excellent results. Practical applications using the inclined direct shear testing device (IDSTD^TM) for three shale rocks of different natures are also presented herein.     

Poroviscoelastic Two-Dimensional Anisotropic Solution with Application to Articular Cartilage Testing

The transverse anisotropic poromechanics solution for the two-dimensional Mandel-type problem geometry is extended in this paper to account for the orthotropic nature of the porous media, thus mimicking the response of articular cartilage samples when subjected to load perturbation. The anisotropic solution presented takes into account the viscoelastic and anisotropic nature of the fluid-saturated cartilage specimen sandwiched between two impermeable rigid plates and subjected to quasi-static step loading conditions; thus simulating the unconfined compressive test responses of cartilage samples in biomechanics laboratory setups. The solution addresses the stress, fluid pressure, and displacement results due to load application through exact modeling of the intrinsic nature of the orthotropic viscoelastic matrix structure as well as the compressible interstitial fluid flow responses. Poromechanical parameter characterization and modeling of biological tissues, such as cartilage, will find this analytical solution to the two-dimensional anisotropic poroviscoelastic geometry very useful. This problem will not only serve as a benchmark for validating numerical schemes and simulations but also assist in calibrating laboratory results on biological tissues, including cyclic loadings.     

Poromechanics Response of Inclined Wellbore Geometry in Chemically Active Fractured Porous Media

The porochemoelastic analytical models and solutions have been used to describe the response of chemically active saturated porous media such as clays, shales, and biological tissues. To date, all existing solutions are only applicable to single-porosity and single-permeability model, which could fall short when the porous material exhibits multiporosity and/or multipermeability characteristics, such as secondary porosity or fractures. This work summarizes the general linear dual-porosity and dual-permeability porochemoelastic formulation and presents the solution of an inclined wellbore drilled in a fluid-saturated chemically active fractured formation, such as fractured shale, subjected to a three-dimensional in situ state of stress. The analytical solution to this geometry incorporates coupled matrix-fracture deformation, simultaneous fluid flows, solute transports and interporosity exchanges induced by the combined influences of stress variation, fluid pressure and solute chemical salinity gradients under isothermal conditions. The fracture system is modeled as a secondary porosity porous continuum following Biot’s formulation while using mixture theory and the pore fluid is a binary solution comprised of a solvent and a solute. Results for the transient stresses and dual pore pressure distributions due to the coupled fracture and hydrochemical effects are plotted in the vicinity of the inclined wellbore and compared with the classical porochemoelastic and poroelastic counterparts. Finally, wellbore stability analyses are carried out to demonstrate applications of the solutions to field drilling operations.     

Time-Dependent Poromechanical Responses of Saturated Cylinders

The uniaxial, hydrostatic, and triaxial tests of saturated cylindrical rock samples are very common in a rock mechanics laboratory. The conventional solution for the mechanical responses of the sample under such testing conditions (an axial load and a confining pressure) is trivial within the elastic range. For saturated samples, however, these elastic solutions can only be applied to the drained or undrained cases, and there has been a lack of transient analyses of cylindrical samples under such tests, taking into account the pore fluid pressure buildup and the coupling effects, especially for samples with low permeability. In this paper, poroelasticity is employed to develop the solution for saturated cylindrical samples subjected to an axial load and a confining pressure. Significant poroelastic effects on the tests were observed through the analyses of a uniaxial test and a triaxial test based on the proposed poroelastic solution. Without consideration of the poroelastic effects, erroneous interpretations of the testing results can be expected.