CO2地质封存力学问题的数值模拟方法综述

随着社会的发展,人类对化石能源的依赖导致大量的CO2排入大气层,从而引起全球变暖、海平面上升等一系列全球性气候问题。CO2地质封存是当前CO2减排最有前景的技术,但大量的CO2注入地层易诱发相应的力学问题：地表隆起变形、盖层完整性受损、断层活化等。因此,为了降低CO2地质封存带来的安全风险,理论分析、数值模拟和响应面方法等手段被应用于此类力学问题的分析中。由于数值模拟方法能够解决大尺度范围内复杂几何模型的多场耦合问题,数值模拟成为当前在CO2地质封存力学领域中应用最广泛的方法。因此,对CO2地质封存若干力学问题的数值模拟方法进行了全面的综述。首先,简要介绍了多孔介质的温度-渗流-力学-化学（THMC）多场耦合原理,并对数值模拟解决多场耦合问题的方法进行了归类。然后,详细总结了数值模拟在解决CO2地质封存力学问题方面的国内研究进展。最后,讨论了数值模拟方法在此类力学问题方面的应用缺陷,并提出了若干建议。     

3D geomechanical modeling and estimating the compaction and subsidence of Fahlian reservoir formation (X-field in SW of Iran)

A geomechanical model can reveal the mechanical behavior of rocks and be used to manage the reservoir programs in a better mode. Fluid pressure will be reduced during hydrocarbon production from a reservoir. This reduction of pressure will increase the effective stress due to overburden sediments and will cause porous media compaction and surface subsidence. In some oil fields, the compacting reservoir can support oil and gas production. However, the phenomena can also cause the loss of wells and reduced production and also cause irreparable damage to the surface structures and affect the surrounding environment. For a detailed study of the geomechanical behavior of a hydrocarbon field, a 3D numerical model to describe the reservoir geomechanical characteristics is essential. During this study, using available data and information, a coupled fluid flow-geomechanic model of Fahlian reservoir formation in X-field in SW of Iran was constructed to estimate the amount of land subsidence. According to the prepared model, in this field, the maximum amount of the vertical stress is 110 MPa and the maximum amount of the horizontal stress is 94 MPa. At last, this model is used for the prediction of reservoir compaction and subsidence of the surface. The maximum value of estimated ground subsidence in the study equals to 29 mm. It is considered that according to the obtained values of horizontal and vertical movement in the wall of different wells, those movements are not problematic for casing and well production and also the surrounding environment.     

Large‐scale poroelastic fractured reservoirs modeling using the fast multipole displacement discontinuity method

An effective approach to modeling the geomechanical behavior of the network and its permeability variation is to use a poroelastic displacement discontinuity method (DDM). However, the approach becomes rather computationally intensive for an extensive system of cracks, particularly when considering coupled diffusion/deformation processes. This is because of additional unknowns and the need for time‐marching schemes for the numerical integration. The Fast Multipole Method (FMM) is a technique that can accelerate the solution of large fracture problems with linear complexity with the number of unknowns both in memory and CPU time. Previous works combining DDM and FMM for large‐scale problems have accounted only for elastic rocks, neglecting the fluid leak‐off from the fractures into the matrix and its influence on pore pressure and stress field. In this work we develop an efficient geomechanical model for large‐scale natural fracture networks in poroelastic reservoirs with fracture flow in response to injection and production operations. Accuracy and computational performance of the proposed method with those of conventional poroelastic DDM are compared through several case studies involving up to several tens of thousands of boundary elements. The results show the effectiveness of the FMM approach to successfully evaluate field‐scale problems for the design of exploitation strategies in unconventional geothermal and petroleum reservoirs. An example considering faults reveals the impact of reservoir compartmentalization because of sealing faults for both geomechanical and flow variables under elastic and poroelastic rocks. Copyright © 2015 John Wiley & Sons, Ltd.     

Dynamic stress analysis of a class of geomechanics problems by the boundary element method

This paper presents the application of an advanced BEM for periodic and transient dynamic stress analyses of a class of geomechanics problems. For transient dynamic analysis, the problem is first solved in the Laplace transform space, which happens to be similar to the periodic dynamic analysis, and then the time domain solution is obtained by numerical inversion of transform domain solutions. The numerical implementation of the BEM used to present the results in this paper is complete and most general available to date. It is capable of treating very large, multi-layered problems by substructuring and satisfying the equilibrium and compatibilities at the interfaces. With the help of this substructuring, capability problems related to layered media and soil–structure interaction have been analysed. A number of examples are presented and through comparisons with available analytical and numerical results, the applicability and usefulness of the present analysis to real geomechanical problems are established.     

Numerical modelling of seismic slope failure using MPM

The Finite Element Method (FEM) is widely used in the simulation of geotechnical applications. Owing to the limitations of FEM to model problems involving large deformations, many efforts have been made to develop methods free of mesh entanglement. One of these methods is the Material Point Method (MPM) which models the material as Lagrangian particles capable of moving through a background computational mesh in Eulerian manner. Although MPM represents the continuum by material points, solution is performed on the computational mesh. Thus, imposing boundary conditions is not aligned with the material representation. In this paper, a non-zero kinematic condition is introduced where an additional set of particles is incorporated to track the moving boundary. This approach is then applied to simulate the seismic motion resulting in failure of slopes. To validate this simulation procedure, two geotechnical applications are modelled using MPM. The first is to reproduce a shaking table experiment where the results of another numerical method are available. After validating the present numerical scheme for relatively large deformation problem, it is applied to simulate progression of a large-scale landslide during the Chi-Chi earthquake of Taiwan in which excessive material deformation and transportation is taking place.     

Three-dimensional numerical modeling of land subsidence in Shanghai,China

Shanghai, in China, has experienced two periods of rapid land subsidence mainly caused by groundwater exploitation related to economic and population growth. The first period occurred during 1956–1965 and was characterized by an average land subsidence rate of 83 mm/yr, and the second period occurred during 1990–1998 with an average subsidence rate of 16 mm/yr. Owing to the establishment of monitoring networks for groundwater levels and land subsidence, a valuable dataset has been collected since the 1960s and used to develop regional land subsidence models applied to manage groundwater resources and mitigate land subsidence. The previous geomechanical modeling approaches to simulate land subsidence were based on one-dimensional (1D) vertical stress and deformation. In this study, a numerical model of land subsidence is developed to simulate explicitly coupled three-dimensional (3D) groundwater flow and 3D aquifer-system displacements in downtown Shanghai from 30 December 1979 to 30 December 1995. The model is calibrated using piezometric, geodetic-leveling, and borehole extensometer measurements made during the 16-year simulation period. The 3D model satisfactorily reproduces the measured piezometric and deformation observations. For the first time, the capability exists to provide some preliminary estimations on the horizontal displacement field associated with the well-known land subsidence in Shanghai and for which no measurements are available. The simulated horizontal displacements peak at 11 mm, i.e. less than 10 % of the simulated maximum land subsidence, and seems too small to seriously damage infrastructure such as the subways (metro lines) in the center area of Shanghai.     

A Functional Data Analysis Approach to Surrogate Modeling in Reservoir and Geomechanics Uncertainty Quantification

Uncertainty quantification for geomechanical and reservoir predictions is in general a computationally intensive problem, especially if a direct Monte Carlo approach with large numbers of full-physics simulations is used. A common solution to this problem, well-known for the fluid flow simulations, is the adoption of surrogate modeling approximating the physical behavior with respect to variations in uncertain parameters. The objective of this work is the quantification of such uncertainty both within geomechanical predictions and fluid-flow predictions using a specific surrogate modeling technique, which is based on a functional approach. The methodology realizes an approximation of full-physics simulated outputs that are varying in time and space when uncertainty parameters are changed, particularly important for the prediction of uncertainty in vertical displacement resulting from geomechanical modeling. The developed methodology has been applied both to a subsidence uncertainty quantification example and to a real reservoir forecast risk assessment. The surrogate quality obtained with these applications confirms that the proposed method makes it possible to perform reliable time–space varying dependent risk assessment with a low computational cost, provided the uncertainty space is low-dimensional.     

Multiscale modeling of large deformation in geomechanics

Large deformation soil behavior underpins the operation and performance for a wide range of key geotechnical structures and needs to be properly considered in their modeling, analysis, and design. The material point method (MPM) has gained increasing popularity recently over conventional numerical methods such as finite element method (FEM) in tackling large deformation problems. In this study, we present a novel hierarchical coupling scheme to integrate MPM with discrete element method (DEM) for multiscale modeling of large deformation in geomechanics. The MPM is employed to treat a typical boundary value problem that may experience large deformation, and the DEM is used to derive the nonlinear material response from small strain to finite strain required by MPM for each of its material points. The proposed coupling framework not only inherits the advantages of MPM in tackling large deformation engineering problems over the use of FEM (eg, no need for remeshing to avoid mesh distortion in FEM), but also helps avoid the need for complicated, phenomenological assumptions on constitutive material models for soil exhibiting high nonlinearity at finite strain. The proposed framework lends great convenience for us to relate rich grain-scale information and key micromechanical mechanisms to macroscopic observations of granular soils over all deformation levels, from initial small-strain stage en route to large deformation regime before failure. Several classic geomechanics examples are used to demonstrate the key features the new MPM/DEM framework can offer on large deformation simulations, including biaxial compression test, rigid footing, soil-pipe interaction, and soil column collapse.     

土质滑坡运动全过程物质点法模拟及其应用

物质点法（MPM）属于一种无网格数值计算方法,它可导入各种土体本构模型,考虑土体流固耦合行为,能够有效模拟土质滑坡大变形及超大变形。本文介绍了物质点法基本原理、控制方程与求解格式;基于5种物质点法的多孔介质表征模型,简要回顾了土质滑坡运动全过程物质点法模拟的最新研究进展。采用单套单相物质点模型,对深圳“12·20”人工堆填土滑坡全过程进行了物质点法模拟,使用了线性加载方式确定初始应力场,并使用了Drucker-Prager屈服准则弹塑性本构模型、GIMP算法与MUSL求解格式。模拟结果表明,该边坡发生失稳后,最大滑距达510m,滑坡范围纵向间距为1050m,最小滑坡角5.95°,均与观测结果相吻合。土体内部等效塑性应变区的演化趋势显示,滑坡机制为渐进式破坏,具体表现为:坡趾土体首先沿基岩界面发生剪切破坏,随后坡顶出现拉张裂隙,坡趾与坡顶塑性区分别沿基岩界面向坡体内部发育,形成贯通滑动面后滑动加速,超大变形出现。物质点法模拟滑坡运动全过程有助于理解滑坡致灾行为,可为滑坡防治提供参考。     

城市垃圾填埋场振动台试验的数值模拟研究

对填埋场振动台模型试验进行非线性数值分析,并与试验结果相互补充、印证,进一步考察填埋场的地震响应规律。研究表明,特殊的夹层结构形式导致水平地震作用下城市垃圾填埋场存在两个主要的响应频率,在这两个主要频率附近模型顶部取得峰值加速度响应;不考虑其他因素的影响,填埋场防渗层的地震永久位移与输入地震动的水平位移振幅近似呈正比关系;坡比是影响填埋场覆盖层和衬垫层永久位移最主要的因素。     

岩土力学参数空间变异性的集合卡尔曼滤波估值

岩土参数具有结构性和随机性的空间变异特征,该特征导致岩土参数具有不确定性。以地质统计学作为岩土参数空间变异性分析的理论基础,将分布于研究区的岩土参数视为区域化变量,变异函数既描述了岩土参数整体的空间结构性变化,又描述了其局部的随机性变化,用变异函数理论模型作为描述岩土参数空间变异规律的数学模型。引入集合卡尔曼滤波（EnKF）分析方法,利用时空分布的观测数据,对岩土参数空间变异性进行估值。数值算例表明,EnKF能够有效地融合观测数据,较好地提供岩土参数空间变异性的估值。     

岩土力学参数空间变异性的集合卡尔曼滤波佶值

岩土参数具有结构性和随机性的空间变异特征，该特征导致岩土参数具有不确定性。以地质统计学作为岩土参数空间变异性分析的理论基础，将分布于研究区的岩土参数视为区域化变量，变异函数既描述了岩土参数整体的空间结构性变化，又描述了其局部的随机性变化，用变异函数理论模型作为描述岩土参数空间变异规律的数学模型。引入集合卡尔曼滤波（EnKF）分析方法，利用时空分布的观测数据，对岩土参数空间变异性进行估值。数值算例表明，EnKF能够有效地融合观测数据，较好地提供岩土参数空间变异性的估值。     

Parallel solution to ill‐conditioned FE geomechanical problems

Parallel computers are potentially very attractive for the implementation of large size geomechanical models. One of the main difficulties of parallelization, however, relies on the efficient solution of the frequently ill‐conditioned algebraic system arising from the linearization of the discretized equilibrium equations. While very efficient preconditioners have been developed for sequential computers, not much work has been devoted to parallel solution algorithms in geomechanics. The present study investigates the state‐of‐the‐art performance of the factorized sparse approximate inverse (FSAI) as a preconditioner for the iterative solution of ill‐conditioned geomechanical problems. Pre‐and post‐filtration strategies are experimented with to increase the FSAI efficiency. Numerical results show that FSAI exhibits a promising potential for parallel geomechanical models mainly because of its almost ideal scalability. With the present formulation, however, at least 4 or 8 processors are required in the selected test cases to outperform one of the most efficient sequential algorithms available for FE geomechanics, i.e. the multilevel incomplete factorization (MIF). Further research is needed to improve the FSAI efficiency with a more effective selection of the preconditioner non‐zero pattern. Copyright © 2011 John Wiley & Sons, Ltd.     

Hydrogeological studies on the mechanical behavior of landfill gases and leachate of the Nanjido Landfill in Seoul, Korea

 The Nanjido Landfill is the largest uncontrolled landfill in Korea and it causes various kinds of environmental problems. Landfill gases and leachate are recognized as the most serious environmental problems associated with the landfill. This study employs a series of numerical models and uses test data to interpret the distribution and flow of landfill gases and leachate. Leachate seepage appears about 40–60 m higher than the estimated basal groundwater table. Thus, seepage data indicate that perched or floating leachate layers are formed in the unsaturated zone of the landfill. The leachate production rate is estimated using infiltration test data and a model for unsaturated groundwater flow. Geochemical data indicate that the landfill leachate degrades the basal groundwater quality along the downgradient zone. The environmental impact of the leachate on river water is estimated. Received: 17 June 1996 · Accepted: 2 October 1996     

Zoned finite strip method and its applications in geomechanics

The technique of Finite Strip method has been extended for zoned strips. One strip can have several different materials in horizontal direction including dummy materials. The new developed zoned Finite Strip (Z.F.S.) method has many engineering applications, particularly in geomechanical problems. The formulation is presented and three different geotechnical problems have been solved using the new Z.F.S. method, which could not be solved by the original Finite Strip method. The results are compared with the solution for the same problems obtained by analytical and/or numerical (Finite Element) methods. The reduced input and output for the Z.F.S. method compared to the Finite Element method makes this method attractive particularly for practising engineers. However the results can be as good as the well known Finite Element method.     

Modelling of contaminant transport through landfill liners using EFGM

Modelling of contaminant transport through landfill liners and natural soil deposits is an important area of research activity in geoenvironmental engineering. Conventional mesh‐based numerical methods depend on mesh/grid size and element connectivity and possess some difficulties when dealing with advection‐dominant transport problems. In the present investigation, an attempt has been made to provide a simple but sufficiently accurate methodology for numerical simulation of the two‐dimensional contaminant transport through the saturated homogeneous porous media and landfill liners using element‐free Galerkin method (EFGM). In the EFGM, an approximate solution is constructed entirely in terms of a set of nodes and no characterization of the interrelationship of the nodes is needed. The EFGM employs moving least‐square approximants to approximate the function and uses the Lagrange multiplier method for imposing essential boundary conditions. The results of the EFGM are validated using experimental results. Analytical and finite element solutions are also used to compare the results of the EFGM. In order to test the practical applicability and performance of the EFGM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the EFGM and the field investigation data. Copyright © 2009 John Wiley & Sons, Ltd.     

The modelling of anchors using the material point method

The ultimate capacity of anchors is determined using the material point method (MPM). MPM is a so‐called meshless method capable of modelling large displacements, deformations and contact between different bodies. A short introduction to MPM is given and the derivation of the discrete governing equations. The analysis of a vertically loaded anchor and one loaded at 45° is presented. The load–displacement curves are compared to that obtained from experiments and the effect of soil stiffness and anchor roughness is investigated. The results of the vertically loaded anchor are also compared to an analytical solution. The displacement of the soil surface above the anchor was measured and compared to the numerical predictions. Convergence with mesh refinement is demonstrated and the effect of mesh size and dilatancy angle on the shear band width and orientation is indicated. The results show that MPM can model anchor pull out successfully. No special interface elements are needed to model the anchor–soil interface and the predicted ultimate capacities were within 10% of the measured values. Copyright © 2005 John Wiley & Sons, Ltd.     

Reservoir geomechanical parameters identification based on ground surface movements

Determination of geomechanical parameters of petroleum reservoir and surrounding rock is important for coupled reservoir–geomechanical modeling, borehole stability analysis and hydraulic fracturing design. A displacement back analysis technique based on artificial neural network (ANN) and genetic algorithm (GA) combination is investigated in this paper to identify reservoir geomechanical parameters based on ground surface displacements. An ANN is used to map the nonlinear relationship between Young’s modulus, E, Poisson’s ratio, v, internal friction angle, Φ, cohesion, c and ground surface displacements. The necessary training and testing samples for ANN are created by using numerical analysis. GA is used to search the set of unknown reservoir geomechanical parameters. Results of the numerical experiment show that the displacement back analysis technique based on ANN–GA combination can effectively identify reservoir geomechanical parameters based on ground surface movements as a result of oil and gas production.     

Preconditioners in computational geomechanics: A survey

The finite element (FE) solution of geomechanical problems in realistic settings raises a few numerical issues depending on the actual process addressed by the analysis. There are two basic problems where the linear solver efficiency may play a crucial role: 1. fully coupled consolidation and 2. faulted uncoupled consolidation. A class of general solvers becoming increasingly popular relies on the Krylov subspace (or Conjugate Gradient‐like) methods, provided that an efficient preconditioner is available. For both problems mentioned above, the possible preconditioners include the diagonal scaling (DS), the Incomplete LU decomposition (ILU), the mixed constraint preconditioning (MCP) and the multilevel incomplete factorization (MIF). The development and the performance of these algorithms have been the topic of several recent works. The present paper aims at providing a survey of the preconditioners available to date in computational geomechanics. In particular, a review and a critical discussion of DS, ILU, MCP and MIF are given along with some comparative numerical results. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical modelling of regional faults in land subsidence prediction above gas/oil reservoirs

The stress variation induced by gas/oil production may activate pre‐existing regional faults. This may enhance the expected land subsidence due to the generation of mechanically weak points close to the producing field. A class of elasto‐plastic interface elements (IE), specifically designed to address the mechanical behaviour of faults over a regional scale, is integrated into a finite element (FE) geomechanical model and used to investigate the role exerted by active faults in anthropogenic land subsidence. The importance of regional faults depends on a variety of factors including depth of the depleted reservoir, fault number, orientation and size, geomechanical properties of porous medium, pore pressure drawdown induced by fluid production, etc. With the aid of some representative examples, a useful indication is provided as to where and how fault activation may influence both magnitude and extent of the land subsidence bowl above producing gas/oil reservoirs, pointing to a generally limited impact on the ground surface. The simulation of a real faulted gas reservoir in a complex 3‐D setting shows that the proposed IE can be simply and efficiently incorporated into a FE geomechanical model, thus improving the quality of the stress and displacement prediction. Copyright © 2007 John Wiley & Sons, Ltd.