A fully coupled hydro‐thermo‐poro‐mechanical model for black oil reservoir simulation

A fully coupled formulation of a hydro‐thermo‐poro‐mechanical model for a three‐phase black oil reservoir model is presented. The model is based upon the approach proposed by one of the authors which fully couples geomechanical effects to multiphase flow. Their work is extended here to include non‐isothermal effects. The gas phase contribution to the energy equation has been neglected based on a set of assumptions. The coupled formulation given herein differs in several ways when compared to the earlier work and an attempt is made to link the flow based formulation and mixture theory. The Finite Element Method is employed for the numerical treatment and essential algorithmic implementation is discussed. Numerical examples are presented to provide further understanding of the current methodology. Copyright © 2001 John Wiley & Sons, Ltd.     

Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems

A new formulation of the element‐free Galerkin (EFG) method is developed for solving coupled hydro‐mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro‐mechanical problems. Examples are studied and compared with closed‐form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro‐mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd.     

A thermo‐hydro‐mechanical model for unsaturated soils based on the effective stress concept

A simple thermo‐hydro‐mechanical (THM) constitutive model for unsaturated soils is described. The effective stress concept is extended to unsaturated soils with the introduction of a capillary stress. This capillary stress is based on a microstructural model and calculated from attraction forces due to water menisci. The effect of desaturation and the thermal softening phenomenon are modelled with a minimal number of material parameters and based on existing models. THM process is qualitatively and quantitatively modelled by using experimental data and previous work to show the application of the model, including a drying path under mechanical stress with transition between saturated and unsaturated states, a heating path under constant suction and a deviatoric path with imposed suction and temperature. The results show that the present model can simulate the THM behaviour in unsaturated soils in a satisfactory way. Copyright © 2010 John Wiley & Sons, Ltd.     

Fast planar slides. A closed‐form thermo‐hydro‐mechanical solution

Heat‐induced excess pore pressures on the failure surface of a planar slide have been calculated by solving the mass and heat balance equations on the shear band. The set of differential equations and the equation of motion of the slide have been solved in closed form for the case of incompressible fluid and incompressible soil skeleton. The solution describes the accelerated motion of the slide. It has been compared with the numerical solution when soil and water stiffness terms are not disregarded. A case study, based on a well‐known translational slide (Cortes slide) has been solved. Numerical and analytical solutions are compared. Results of a sensitivity analysis indicate that the permeability of the shear band is the key parameter to control the onset of a rapid motion. For a band permeability above a threshold value, in the vicinity of 10^?15m² (10^?8m/s), fast accelerated motions are very unlikely. Copyright © 2009 John Wiley & Sons, Ltd.     

Damage identification using inverse analysis in coupled thermo‐hydro‐mechanical problems applied to masonry dams

In this paper, we propose a method to detect the damage and estimate the degree of damage by means of a multifield‐based inverse analysis. The fields being considered are displacement, temperature, and water pressure. Furthermore, the uncertainties due to the size of the damage, the errors in the measurement data, and the errors in the model parameters are also investigated. The uncertainty due to the measurements is quantified by assuming different sources of noise in the measurements. The inverse problem is solved repeatedly by a sampling process. The uncertainties in the inverse solutions can be quantified by their probability distributions. This method can be applied to identify damages in masonry dams using coupled nonlinear thermo‐hydro‐mechanical problems.     

A hierarchical thermo‐hydro‐plastic constitutive model for unsaturated soils and its numerical implementation

Unsaturated soils are highly heterogeneous 3‐phase porous media. Variations of temperature, the degree of saturation, and density have dramatic impacts on the hydro‐mechanical behavior of unsaturated soils. To model all these features, we present a thermo‐hydro‐plastic model in which the hydro‐mechanical hardening and thermal softening are incorporated in a hierarchical fashion for unsaturated soils. This novel constitutive model can capture heterogeneities in density, suction, the degree of saturation, and temperature. Specifically, this constitutive model has 2 ingredients: (1) it has a “mesoscale” mechanical state variable—porosity and 3 environmental state variables—suction, the degree of saturation, and temperature; (2) both temperature and mechanical effects on water retention properties are taken into account. The return mapping algorithm is applied to implement this model at Gauss point assuming an infinitesimal strain. At each time step, the return mapping is conducted only in principal elastic strain space, assuming no return mapping in suction and temperature. The numerical results obtained by this constitutive model are compared with the experimental results. It shows that the proposed model can simulate the thermo‐hydro‐mechanical behavior of unsaturated soils with satisfaction. We also conduct shear band analysis of an unsaturated soil specimen under plane strain condition to demonstrate the impact of temperature variation on shear banding triggered by initial material heterogeneities.     

基于敏感性分析的裂隙岩体渗流与应力静态全耦合参数反演

基于求解稳定渗流场与弹性位移场耦合问题的全耦合分析方法,应用提出的混合遗传算法作为优化算法,同时利用水头、位移等多类型量测资料,提出了裂隙岩体渗流与应力静态全耦合的参数反演方法。在目标函数建立中考虑了实测水头对渗流参数的敏感性,在待反演力学未知参数的选取中,依据提出的相对灵敏度概念,考虑了实测位移对力学参数的敏感性。针对某裂隙岸坡算例,研究了水库蓄水过程中位移场对力学参数敏感性,据此实现位移测点的优化布置,并以渗流场与位移场全耦合正分析计算结果作为假想实测值,进行该岩坡的全耦合参数反演分析,从而验证了所提出理论与研制程序的正确性和可行性。     

核废料处置概念库近场热-水-应力耦合模型及数值分析

特别考虑了缓冲层中温度梯度水分扩散、水蒸汽扩散对水连续性及能量守恒的影响,进一步完善了所建立的分析饱和-非饱和介质中热-水-应力耦合现象的控制方程,并针对试验资料,使用所开发的有限元程序对一个核废料处置概念库近场的热-水-应力耦合过程进行了数值模拟,考察了缓冲层及岩体中若干点的温度、饱和度、孔隙水压力及主应力的变化、分布情况,并将部分结果与国外类似软件的计算数据作了对比,结果显示,在定性和定量上二者的规律有某种一致性,从而得出了一定的认识。     

Thermo‐hydro‐mechanical modeling of damage in unsaturated porous media: Theoretical framework and numerical study of the EDZ

The damage model presented in this article (named ‘THHMD’ model) is dedicated to non‐isothermal unsaturated porous media. It is formulated by means of three independent strain state variables, which are the thermodynamic conjugates of net stress, suction and thermal stress. The damage variable is a second‐order tensor. Stress/strain relationships are derived from Helmholtz free energy, which is assumed to be the sum of damaged elastic potentials and ‘crack‐closure energies’. Damage is assumed to grow with tensile strains due to net stress, with pore shrinkage due to suction and with thermal dilatation. Specific conductivities are introduced to account for the effects of cracking on the intensification and on the orientation of liquid water and vapor flows. These conductivities depend on damage and internal length parameters. The mechanical aspects of the THHMD model are validated by comparing the results of a triaxial compression test with experimental measurements found in the literature. Parametric studies of damage are performed on three different heating problems related to nuclear waste disposals. Several types of loading and boundary conditions are investigated. The thermal damage potential is thoroughly studied. The THHMD model is expected to be a useful tool in the assessment of the Excavation Damaged Zone, especially in the vicinity of nuclear waste repositories. Copyright © 2011 John Wiley & Sons, Ltd.     

A fully coupled element‐free Galerkin model for hydro‐mechanical analysis of advancement of fluid‐driven fractures in porous media

Hydraulic fracturing (HF) of underground formations has widely been used in different fields of engineering. Despite the technological advances in techniques of in situ HF, the industry uses semi‐analytical tools to design HF treatment. This is due to the complex interaction among various mechanisms involved in this process, so that for thorough simulations of HF operations a fully coupled numerical model is required. In this study, using element‐free Galerkin (EFG) mesh‐less method, a new formulation for numerical modeling of hydraulic fracture propagation in porous media is developed. This numerical approach, which is based on the simultaneous solution of equilibrium and continuity equations, considers the hydro‐mechanical coupling between the crack and its surrounding porous medium. Therefore, the developed EFG model is capable of simulating fluid leak‐off and fluid lag phenomena. To create the discrete equation system, the Galerkin technique is applied, and the essential boundary conditions are imposed via penalty method. Then, the resultant constrained integral equations are discretized in space using EFG shape functions. For temporal discretization, a fully implicit scheme is employed. The final set of algebraic equations that forms a non‐linear equation system is solved using the direct iterative procedure. Modeling of cracks is performed on the basis of linear elastic fracture mechanics, and for this purpose, the so‐called diffraction method is employed. For verification of the model, a number of problems are solved. According to the obtained results, the developed EFG computer program can successfully be applied for simulating the complex process of hydraulic fracture propagation in porous media. Copyright © 2016 John Wiley & Sons, Ltd.     

A coupled chemo‐thermo‐hygro‐mechanical model of concrete at high temperature and failure analysis

A hierarchical mathematical model for analyses of coupled chemo‐thermo‐hygro‐mechanical behaviour in concretes at high temperature is presented. The concretes are modelled as unsaturated deforming reactive porous media filled with two immiscible pore fluids, i.e. the gas mixture and the liquid mixture, in immiscible–miscible levels. The thermo‐induced desalination process is particularly integrated into the model. The chemical effects of both the desalination and the dehydration processes on the material damage and the degradation of the material strength are taken into account. The mathematical model consists of a set of coupled, partial differential equations governing the mass balance of the dry air, the mass balance of the water species, the mass balance of the matrix components dissolved in the liquid phases, the enthalpy (energy) balance and momentum balance of the whole medium mixture. The governing equations, the state equations for the model and the constitutive laws used in the model are given. A mixed weak form for the finite element solution procedure is formulated for the numerical simulation of chemo‐thermo‐hygro‐mechanical behaviours. Special considerations are given to spatial discretization of hyperbolic equation with non‐self‐adjoint operator nature. Numerical results demonstrate the performance and the effectiveness of the proposed model and its numerical procedure in reproducing coupled chemo‐thermo‐hygro‐mechanical behaviour in concretes subjected to fire and thermal radiation. Copyright © 2005 John Wiley & Sons, Ltd.     

亥废料处置概念库近场热-水-应力耦合模型及数值分析

特别考虑了缓冲层中温度梯度水分扩散、水蒸汽扩散对水连续性及能量守恒的影响，进一步完善了所建立的分析饱和-非饱和介质中热-水-应力耦合现象的控制方程，并针对试验资料，使用所开发的有限元程序对一个核废料处置概念库近场的热-水-应力耦合过程进行了数值模拟，考察了缓冲层及岩体中若干点的温度、饱和度、孔隙水压力及主应力的变化、分布情况，并将部分结果与国外类似软件的计算数据作了对比，结果显示，在定性和定量上二者的规律有某种一致性，从而得出了一定的认识。     

孔隙气压对核废物地质处置热-流-固耦合影响的有限元分析

为考察孔隙气体压力对高放废物地质处置中的热-流-固耦合过程的影响,借用Leiws等建立的可变形孔隙介质中非等温空气流和水流模型,在其水连续性方程中加入了温度梯度引起的水分扩散项,研制出相应的热-水-气-应力耦合弹塑性二维有限元程序。针对一个假定的高放废物地质处置库模型,在相同的初始温度、孔隙水压力和岩体应力条件下,取3种缓冲层中的初始孔隙气体压力,通过数值模拟考察了处置库近场的主应力、饱和度、气和水的流速、温度和孔隙压力的分布与变化。结果显示,当缓冲层中的初始孔隙气压力较高时,其对围岩中应力影响较大。     

核废料地质处置概念库锚喷支护坑道热-水-应力耦合效应的二维离散元分析

假定一个核废料地质处置库位于具有一定水头的饱和节理岩体中,开挖完闭施作系统锚杆和喷混凝土支护。对坑道建造和一个50年期的热-水应力（T-H-M）耦合运营过程,使用UDEC程序进行数值模拟,分析无、有支护时近场围岩中的应力、变形、塑性区、温度、渗流的变化状态,以及不同场（温度、渗流、应力）耦合条件下的锚杆和喷混凝土中的承载情况。结果显示,喷混凝土和系统锚杆支护不仅具有常规的支护功能,并且可阻滞地下水从坑道表面的自由渗出,使得围岩中塑性区减小,裂隙水压力和温度升高;相比于应力单场作用的情况,在热-水-力耦合的条件下洞室围岩的稳定性下降,支护结构的受力状况变差。     

Numerical analysis of a one‐dimensional infiltration problem in unsaturated soil by a seepage–deformation coupled method

A multiphase coupled elasto‐viscoplastic finite element analysis formulation, based on the theory of porous media, is used to describe the rainfall infiltration process into a one‐dimensional soil column. Using this framework, we have numerically analyzed the generation of pore water pressure and deformations when rainfall is applied to the soil. A parametric study, including rainfall intensity, soil–water characteristic curves, and permeability, is carried out to observe their influence on the changes in pore water pressure and volumetric strain. From the numerical results, it is shown that the generation of pore water pressure and volumetric strain is mainly controlled by material parameters α and n′ that describe the soil–water characteristic curve. A comparison with the laboratory results shows that the proposed method can describe very well the characteristics observed during the experiments of one‐dimensional water infiltration into a layered unsaturated soil column. Copyright © 2010 John Wiley & Sons, Ltd.     

Experiment and validation of numerical simulation of coupled thermal,hydraulic and mechanical behaviour in the engineered buffer materials

Evaluation of the coupled heat transfer, water flow and stress changes in the engineered clay barrier is an important issue in the performance assessment of the high‐level radioactive waste disposal. To demonstrate the function of the engineered barrier system, the large‐scale experiment is conducted, which is called Big Bentonite facility (BIG‐BEN). The facility consists of an electric heater surrounded by glass beads, carbon steel overpack, buffer material and man‐made rock. The buffer is a mixture of bentonite and sand. The heater is operated at 0·8 kW. Water is injected from the interface between the buffer and the man‐made rocks at the pressure of 0·05 MPa. The duration of the experiment is 20 months. The change in temperature and swelling pressure are continuously monitored and gravimetric water content is measured by sampling. The coupled thermal, hydraulic and mechanical processes are simulated with a finite element code THAMES, which can simulate the fully coupled phenomena in the saturated and unsaturated clay under anisothermal condition. To examine the validity of the code, all the parameters used in the model are evaluated from the other laboratory tests. The simulated results are compared with the measured ones without calibration of the parameter values using the results from the BIG‐BEN experiment. It can be concluded that the changes in temperature and gravimetric water content within the buffer can be simulated reasonably well and that the mechanical effect such as swelling pressure is difficult to realize. Copyright © 2000 John Wiley & Sons, Ltd.     

核废料处置概念库开挖及封闭后近场热-水-应力耦合数值分析

考虑了缓冲层中温度梯度水分扩散、水蒸汽扩散对水连续性及能量守恒的影响,进一步完善了饱和-非饱和介质中热-水-应力耦合现象的控制方程。应用缓冲材料的实验资料,对核废料处置概念库开挖及封闭后近场的热-水-应力耦合过程进行了数值模拟,以考察围岩中的位移、塑性区、主应力、孔隙水压力和温度的分布及变化。认为开挖是引起洞室围岩中的变形及应力重新分布的主要原因,但坑道封闭后的热-水-应力耦合过程对变形及应力状态也产生了明显的影响。     

High‐order ADE scheme for solving the fluid diffusion equation in non‐uniform grids and its application in coupled hydro‐mechanical simulation

To improve the stability and efficiency of explicit technique, one proposed method is to use an unconditionally stable alternating direction explicit (ADE) scheme. However, the standard ADE scheme is only moderately accurate and restricted to uniform grids. This paper derives a novel high‐order ADE scheme capable of solving the fluid diffusion equation in non‐uniform grids. The new scheme is derived by performing a fourth‐order finite difference approximation to the spatial derivatives of the diffusion equation in non‐uniform grid. The implicit Crank‐Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps, giving rise to a new high‐order ADE scheme. Because the new scheme can be potentially applied in coupled hydro‐mechanical (H‐M) simulation, the pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer program Fast Lagrangian Analysis of Continua. This coupling procedure is called the sequentially explicit coupling technique based on the fourth‐order ADE scheme (SEA‐4). Verifications of well‐known consolidation problems showed that the new ADE scheme and SEA‐4 can reduce computer runtime by 46% to 75% to that of Fast Lagrangian Analysis of Continua's basic scheme. At the same time, the techniques still maintained average percentage error of 1.6% to 3.5% for pore pressure and 0.2% to 1.5% for displacement solutions and were still accurate under typical grid non‐uniformities. This result suggests that the new high‐order ADE scheme can provide an efficient explicit technique for solving the flow equation of a coupled H‐M problem, which will be beneficial for large‐scale and long‐term H‐M problems in geoengineering.     

Recent insights into analytical precision and modelling of DDA and NMM for practical problems

This paper discussed the analytical precision on equations of motion in some practical studies that use 2-D DDA, 2D-Coupled analysis of NMM & DDA, and 3D-DDA. We point out the main reason for numerical instability in DDA is loss of the effective digits when superposing the global stiffness matrix under the variable conditions of large and the small blocks. Categories of analyses are distributed in 2D-DDA static masonry structures such as the Great Pyramid and the Pont du Gard, 2D-DDA dynamic rock fall problems and the sensitivity of its analysis on the velocity ratio and the penalty, earthquake response analysis of rock slopes, 2D-NMM, 2D-coupled analysis of DDA and NMM and 3D-DDA rock fall problem. The selected examples on the Great Pyramid, Pont du Gard and Bayon Temple at Angkor Thom are located in Egypt, France and Cambodia respectively as UNESCO world heritages sites. The authors evaluated the applicability of the methods and the reliability of the results by comparing different methods and site observations from the practical problems.