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1.
Mansoureh Jesmani Mathias C. Bellout Remus Hanea Bjarne Foss 《Computational Geosciences》2016,20(6):1185-1209
This work considers the well placement problem in reservoir management and field development optimization. In particular, it emphasizes embedding realistic and practical constraints into a mathematical optimization formulation. Such constraints are a prerequisite for the wider use of mathematical optimization techniques in well placement problems, since constraints are a way to incorporate reservoir engineering knowledge into the problem formulation. There are important design limitations that are used by the field development team when treating the well placement problem, and these limitations need to be articulated and eventually formalized within the problem before conducting the search for optimal well placements. In addition, these design limitations may be explicit or implicit. In this work, various design limitations pertaining to well locations have been developed in close collaboration with a field operator on the Norwegian Continental Shelf. Moreover, this work focuses on developing constraint-handling capability to enforce these various considerations during optimization. In particular, the Particle Swarm Optimization (PSO) algorithm is applied to optimize for the well locations, and various practical well placement constraints are incorporated into the PSO algorithm using two different constraint-handling techniques: a decoder procedure and the penalty method. The decoder procedure maps the feasible search space onto a cube and has the advantage of not requiring parameter tuning. The penalty method converts the constrained optimization problem into an unconstrained one by introducing an additional term, which is called a penalty function, to the objective function. In contrast to the penalty method, only feasible solutions are evaluated in the decoder method. Through numerical simulations, a comparison between the penalty method and the decoder technique is performed for two cases. We show that the decoder technique can easily be implemented for the well placement problem, and furthermore, that it performs better than the penalty method in most of the cases. 相似文献
2.
This work presents the coupling of two locally conservative methods for elliptic problems: namely, the discontinuous Galerkin method and the mixed finite element method. The couplings can be defined with or without interface Lagrange multipliers. The formulations are shown to be equivalent. Optimal error estimates are given; penalty terms may or may not be included. In addition, the analysis for non-conforming grids is also discussed. 相似文献
3.
《Geomechanics and Geoengineering》2013,8(3):221-236
This paper presents a new point-to-face contact algorithm for contacts between two polyhedrons with planar boundaries. A new discrete numerical method called three-dimensional discontinuous deformation analysis (3-D DDA) is used and formulations of normal contact submatrices based on the proposed algorithm are derived. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. This approach does not need to use an iterative algorithm in each time step to obtain the contact plane, unlike the ‘Common-Plane’ method applied in the existing 3-D DDA. In the present 3-D DDA method, block contact constraints are enforced using the penalty method. This approach is quite simple, but may lead to inaccuracies that may be large for small values of the penalty number. The penalty method also creates block contact overlap, which violates the physical constraints of the problem. These limitations are overcome by using the augmented Lagrangian method that is used for normal contacts in this research. This point-to-face contact model has been programmed and some illustrative examples are provided to demonstrate the new contact rule between two blocks. A comparison between results obtained by using the augmented Lagrangian method and the penalty method is presented as well. 相似文献
4.
This paper presents the relationships between some numerical methods suitable for a heterogeneous elliptic equation with application to reservoir simulation. The methods discussed are the classical mixed finite element method (MFEM), the control-volume mixed finite element method (CVMFEM), the support operators method (SOM), the enhanced cell-centered finite difference method (ECCFDM), and the multi-point flux-approximation (MPFA) control-volume method. These methods are all locally mass conservative, and handle general irregular grids with anisotropic and heterogeneous discontinuous permeability. In addition to this, the methods have a common weak continuity in the pressure across the edges, which in some cases corresponds to Lagrange multipliers. It seems that this last property is an essential common quality for these methods.
T.F. Russell: Partially supported by the National Science Foundation Grant Nos. DMS-0084438 and DMS-0222300. 相似文献
5.
采用剖开算子法,把二维输运问题剖分为两个子初值问题(对流分步、扩散分步)。在任意三角形网格中,分别对不同性质的算子采用各自适合的算法,即采用特征线法求解对流分步,采用半隐式有限元法求解扩散分步。重点探讨了对流插值问题,给出了一种完全对称三次插值模式,有效地减少了数值阻尼。为了克服高阶插值数值震荡问题,计算中保证了函数及其一阶偏导数连续。算例表明,数值方法模拟结果与精确解吻合较好。该算法在求解输运方程(包括纯对流输运方程)时,既能有效减少数值阻尼,也能保证计算中不出现数值震荡。 相似文献
6.
Some major challenges for geophysicists and structural geologists using three-dimensional boundary element method codes (3D-BEM)
are: (1) reducing the amount of memory required to solve large and dense systems and (2) incorporation of inequality constraints
such as traction inequality constraints (TIC) and displacement inequality constraints (DIC). The latter serves two purposes.
First, for example, inequality constraints can be used to simulate frictional slip (using TIC). Second, these constraints
can prevent element interpenetration while allowing opening mode (using DIC). We have developed a method that simultaneously
incorporates both types of functionality of the inequality constraints. We show that the use of an appropriate iterative solver
not only avoids the allocation of significant memory for solving the system (allowing very large model computation and simplifying
parallelization on multi-core processors), but also admits interesting features such as natural incorporation of TICs and
DICs. Compared to other techniques of contact management (e.g., Lagrange multipliers, penalty method, or complementarity problem),
this new simple methodology, which does not use any incremental trial-and-error procedures, brings more flexibility, while
making the system more stable and less subject to round-off errors without any computational overhead. We provide validations
and comparisons of the inequality constraints implementation using 2D analytical and numerical solutions. 相似文献
7.
Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method 
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下载免费PDF全文 A finite element algorithm for frictionless contact problems in a two‐phase saturated porous medium, considering finite deformation and inertia effects, has been formulated and implemented in a finite element programme. The mechanical behaviour of the saturated porous medium is predicted using mixture theory, which models the dynamic advection of fluids through a fully saturated porous solid matrix. The resulting mixed formulation predicts all field variables including the solid displacement, pore fluid pressure and Darcy velocity of the pore fluid. The contact constraints arising from the requirement for continuity of the contact traction, as well as the fluid flow across the contact interface, are enforced using a penalty approach that is regularised with an augmented Lagrangian method. The contact formulation is based on a mortar segment‐to‐segment scheme that allows the interpolation functions of the contact elements to be of order N. The main thrust of this paper is therefore how to deal with contact interfaces in problems that involve both dynamics and consolidation and possibly large deformations of porous media. The numerical algorithm is first verified using several illustrative examples. This algorithm is then employed to solve a pipe‐seabed interaction problem, involving large deformations and dynamic effects, and the results of the analysis are also compared with those obtained using a node‐to‐segment contact algorithm. The results of this study indicate that the proposed method is able to solve the highly nonlinear problem of dynamic soil–structure interaction when coupled with pore water pressures and Darcy velocity. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
8.
Alternative assignment of invariant point stabilities in a possible P – T phase diagram is given by a family of grids that derives from a form of the Euler equation. Invariant points are represented by great circles that divide the surface of a sphere (the Euler sphere) into polygonal regions that correspond to the number of potential solutions or grids in n -component systems with n +3 non-degenerate phases. A particular invariant point is stable in all grids on one side of the great circle and metastable on the other. The advantage of this representation is the ease and efficiency by which all grids consistent with experimental and theoretical constraints can be identified. The method is well suited for systems of n +3 phases in which the thermochemical data necessary for direct calculation of the phase diagram is either uncertain or non-existent for one or more of the phases. The mass balance equations among the n +3 phases of interest define the Euler sphere for any particular system. There is a unique Euler sphere for unary systems, and another for binary systems. Ternary and quaternary systems have four and 11 different types of Euler spheres, respectively. In the ternary case with six phases, the 16 non-degenerate chemographies belong to four groups that are associated with the four Euler spheres. An analysis of those groups shows a close relationship between the topologies of the chemographies and the topologies of the grids represented on the Euler sphere. Euler spheres for degenerate chemographies are characterized by a smaller number of spherical polygons. A useful application of the Euler sphere concept is the systematic derivation of possible FMAS petrogenetic grids from subsystem constraints. Assumption of just one stable invariant point in each of MAS and FAS systems is consistent with seven FMAS grids involving cordierite, garnet, hypersthene, quartz, sapphirine, sillimanite and spinel. 相似文献
9.
This paper extends the multipoint flux-approximation (MPFA) control-volume method to quadrilateral grids for which the adjacent cells do not necessarily share corners. Examples are grids with faults and locally refined grids. This paper gives a derivation of the method for such grids. The difference between two-point flux-approximation (TPFA) results and MPFA results for faults and local grid refinements is demonstrated for synthetic problems. Further, the results are compared with results from uniform fine-grid simulations. The effect of repeated fault patterns as well as anisotropy is investigated. Large errors may be found for the TPFA method for flow through a series of faults in an anisotropic medium. Finally, a comparison is done for a reservoir field application. 相似文献
10.
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. 相似文献
11.
In this paper, we study the use of virtual element method (VEM) for geomechanics. Our emphasis is on applications to reservoir simulations. The physical processes behind the formation of the reservoirs, such as sedimentation, erosion, and faulting, lead to complex geometrical structures. A minimal representation, with respect to the physical parameters of the system, then naturally leads to general polyhedral grids. Numerical methods which can directly handle this representation will be highly favorable, in particular in the setting of advanced work-flows. The virtual element method is a promising candidate to solve the linear elasticity equations on such models. In this paper, we investigate some of the limits of the VEM method when used on reservoir models. First, we demonstrate that care must be taken to make the method robust for highly elongated cells, which is common in these applications, and show the importance of calculating forces in terms of traction on the boundary of the elements for elongated distorted cells. Second, we study the effect of triangulations on the surfaces of curved faces, which also naturally occur in subsurface models. We also demonstrate how a more stable stabilization term for reservoir application can be derived. 相似文献
12.
We develop an ELLAM-MFEM approximation to the strongly coupled systems of time-dependent nonlinear partial differential equations (PDEs) and constraining equations, which describe fully miscible, highly compressible, multicomponent flows through heterogeneous and compressible porous media with singular sources and sinks. An Eulerian–Lagrangian localized adjoint method (ELLAM) is presented to solve the transport equations for concentrations. A mixed finite element method (MFEM) is used to solve the pressure PDE for the pressure and Darcy velocity simultaneously, which generates accurate fluid velocities and minimizes the numerical difficulties occurring in standard methods caused by differentiation of the pressure and then multiplication by rough coefficients. The ELLAM-MFEM solution technique symmetrizes and stabilizes the governing transport PDEs and greatly reduces nonphysical oscillation and/or excessive numerical dispersion present in many large-scale simulators. Computational experiments show that the ELLAM-MFEM solution technique can generate stable and physically reasonable numerical simulations even if coarse spatial grids and very large time steps are used. 相似文献
13.
非连续变形分析(DDA)方法是一种新的用来分析块体系统运动和变形的非连续介质数值计算方法。研究的核心工作是致力于对现有DDA接触问题处理方法的改进。DDA主要采用罚函数法和Lagrange乘子法处理接触问题,合理设定罚参数很困难,此外,因开闭迭代而引起的刚度矩阵的不连续变化也会导致收敛方面的困难。为避免引入罚参数及传统意义上的开闭迭代,用混合线性互补模型(LCDDA)对DDA方法进行了重新描述。在此基础上,综合基于非光滑分析的Newton法的局部平方收敛和最速下降法的全局线性收敛的优势,提出求解LCDDA模型的有效算法。根据上述思想及理论研究成果编制了完整的计算程序,算例计算结果证明了方法的精度及可行性。 相似文献
14.
The paper presents Cauchy stress tensor computation over parallel grids of message passing interface (MPI) parallel three-dimensional (3D) discrete element method (DEM) simulations of granular materials, considering spherical and nonspherical particles. The stress tensor computation is studied for quasi-static and dynamic conditions, and its resulting symmetry or asymmetry is discussed within the context of classical continuum mechanics (CCM), granular materials mechanics (GMM), and micropolar continuum mechanics (MCM). The average Cauchy stress tensor computation follows Bagi's and Nicot's formulations and is verified within MPI parallel 3D DEM simulations involving dynamically adaptive compute grids. These grids allow calculation of temporal and spatial distributions of stress across granular materials under static and dynamic conditions. The vertical stress component in gravitationally deposited particle assemblies exhibits nonuniform spatial distributions under static equilibrium, and its zone of maximum value changes during the process of gravitational pluviation and collapse. These phenomena reveal a microstructural effect on stress distribution within granular materials that is attributed to their discrete particulate nature (particle size, shape, gradation, boundary conditions, etc). 相似文献
15.
与 Cosserat 理论相比,偶应力理论在一定程度上可以降低数值框架的复杂度,已逐渐应用于岩土体应变局部化分析中。然而,一般的偶应力有限元法需要满足 C1连续性,即单元内部和单元交界面上的应变都需要具有连续性。为了避免开发较为复杂的C1型偶应力单元,在 Cosserat 连续体理论框架下,通过借助罚函数方法对 C1连续性进行松弛来获得偶应力理论的逼近解,建立了基于罚函数的偶应力有限元方法 PCS-FEM。通过平面应变条件下的弹性圆孔应力集中问题对 PCS-FEM 方法的有效性进行了验证,并应用于土体应变局部化分析中。通过对Ottawa砂的平面应变试验进行数值模拟,发现 PCS-FEM 方法获得的应力−应变曲线及剪切带破坏形态与试验结果基本一致,且能够克服经典连续体理论病态的网格敏感性问题,保证应变局部化问题的适定性;通过对承受偏心荷载作用下的土坡应变局部化经典算例进行分析,发现 PCS-FEM 方法同样可以克服土坡应变软化阶段的网格敏感性问题,展现土体的渐进破坏过程。 相似文献
16.
The present study pertains to the finding of the lower bound solution, formulating it as a non-linear programming problem using the generalized method developed by Lysmer with certain variations to incorporate the non-linear no-yield condition constraints directly in the analysis. The method considers the family of plane stress fields having the property that all stresses vary linearly within each triangular element of some mesh which covers the soil mass under study. For this type of stress field it is possible to express all equilibrium conditions as a set of linear constraints and the no-yield as a set of non-linear constraints. The boundary condition constraints may be of linear equality or inequality type. By expressing some of the design variables in terms of the remaining variables the linear equality constraints are implicity satisfied. Such a technique minimizes the complexity of the problem by eliminating the equality constraints and reduces the dimensionality of the problem, saving much, computational effort. The optimal lower bound is isolated by formulating it as a non-linear programming (NLP) problem subjected to both linear and non-linear inequality constraints. The sequential unconstrained minimization technique using the extended penalty function method as suggested by Kavlie has been used to isolate the optimal lower bound. The method has successfully been applied to the passive earth pressure and bearing capacity problem. Numerical results are obtained and compared with Lysmer's solution to show the effectiveness of the present approach. 相似文献
17.
Michael G. Edwards 《Computational Geosciences》2002,6(3-4):433-452
Locally conservative flux-continuous, full-tensor, discretization schemes are presented for general unstructured grids. The schemes are control-volume distributed, where flow variables and rock properties are assigned to the polygonal control-volumes derived from the primal grid. A relationship between these finite volume schemes and the mixed finite element method is established. An extension for unstructured grids is described that leads to a general symmetric positive definite discretization matrix for both quadrilateral and triangular grids. A novel flow based gridding approach for unstructured mesh generation is also proposed for heterogeneous reservoir domains. Results computed with the flux continuous schemes on unstructured flow-based grids demonstrate the advantages of the methods. 相似文献
18.
Flow in a porous medium can be described by a set of non-linear partial differential equations. The pressure variable satisfies
a maximum principle, which guarantees that the solution will have no oscillations. A discretisation of the pressure equation
should preserve this monotonicity property. Whether a numerical method is monotone will depend both on the medium and on the
grid. We study monotonicity of Multi-point Flux Approximation methods on triangular grids. We derive necessary conditions
for monotonicity on uniform grids. Further, we study the robustness of the methods on rough grids, and quantify the violations
of the maximum principle. These investigations are done for single phase flow, however, they are supported by two-phase simulations. 相似文献
19.
A fully coupled element‐free Galerkin model for hydro‐mechanical analysis of advancement of fluid‐driven fractures in porous media 下载免费PDF全文
下载免费PDF全文 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. 相似文献
20.
Simulation of fracturing processes in porous rocks can be divided into two main branches: (i) modeling the rock as a continuum enhanced with special features to account for fractures or (ii) modeling the rock by a discrete (or discontinuous) approach that describes the material directly as a collection of separate blocks or particles, e.g., as in the discrete element method (DEM). In the modified discrete element (MDEM) method, the effective forces between virtual particles are modified so that they reproduce the discretization of a first-order finite element method (FEM) for linear elasticity. This provides an expression of the virtual forces in terms of general Hook’s macro-parameters. Previously, MDEM has been formulated through an analogy with linear elements for FEM. We show the connection between MDEM and the virtual element method (VEM), which is a generalization of FEM to polyhedral grids. Unlike standard FEM, which computes strain-states in a reference space, MDEM and VEM compute stress-states directly in real space. This connection leads us to a new derivation of the MDEM method. Moreover, it enables a direct coupling between (M)DEM and domains modeled by a grid made of polyhedral cells. Thus, this approach makes it possible to combine fine-scale (M)DEM behavior near the fracturing region with linear elasticity on complex reservoir grids in the far-field region without regridding. To demonstrate the simulation of hydraulic fracturing, the coupled (M)DEM-VEM method is implemented using the Matlab Reservoir Simulation Toolbox (MRST) and linked to an industry-standard reservoir simulator. Similar approaches have been presented previously using standard FEM, but due to the similarities in the approaches of VEM and MDEM, our work provides a more uniform approach and extends these previous works to general polyhedral grids for the non-fracturing domain. 相似文献