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1.
The surface subsidence above a compacting saturated oil reservoir is the main topic of this paper. From a literature review, it is obvious that extensive efforts have been conducted for investigating this phenomenon in various situations. Herein, a numerical model, based on the finite element method, was used for simulating three-dimensional three-phase fluid flow in a deforming saturated oil reservoir. The mathematical formulation describes a fully coupled governing equation system which consists of the equilibrium and continuity equations for three immiscible fluids flowing in a porous media. An elastoplastic soil model, based on a Mohr Coulomb yield surface, was utilized. The finite element method was applied to obtain simultaneous solutions to the governing equations where the displacements and the fluid pressures are the primary unknowns. The final discretized equations are solved by a direct solver using fully implicit procedures. A linear analysis was used to study the stability conditions of the present model. Finally, a series of simulations were conducted to indicate the validity and the utility of the developed model. 相似文献
2.
An iterative method is presented for solving a fully coupled and implicit formulation of fluid flow in a porous medium. The mathematical model describes a set of fully coupled three-phase flow of compressible and immiscible fluids in a saturated oil reservoir. The finite element method is applied to obtain the simultaneous solution (SS) for the resulting highly non-linear partial differential equations where fluid pressures are the primary unknowns. The final discretized equations are solved iteratively by using a fully implicit numerical scheme. Several examples, illustrating the use of the present model, are described. The increased stability achieved with this scheme has permitted the use of larger time steps with smaller material balance errors. 相似文献
3.
Based on the theory of double-porosity, a novel mathematical model for multiphase fluid flow in a deforming fractured reservoir is developed. The present formulation, consisting of both the equilibrium and continuity equations, accounts for the significant influence of coupling between fluid flow and solid deformation, usually ignored in the reservoir simulation literature. A Galerkin-based finite element method is applied to discretize the governing equations both in the space and time domain. Throughout the derived set of equations the solid displacements as well as the fluid pressure values are considered as the primary unknowns and may be used to determine other reservoir parameters such as stresses, saturations, etc. The final set of equations represents a highly non-linear system as the elements of the coefficient matrices are updated during each iteration in terms of the independent variables. The model is employed to solve a field scale example where the results are compared to those of ten other uncoupled models. The results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered. © 1997 by John Wiley & Sons, Ltd. 相似文献
4.
用流固耦合方法研究油藏压裂后应力应变和孔渗特性变化 总被引：10，自引：1，他引：10
油藏压裂后将引起地应力场发生变化，使岩石变形，导致孔隙度和渗透率变化，进而影响产量，为研究这一问题，作者建立了油藏压裂后流－固耦合渗流模型，考虑了以下因素：油藏岩石变形，地应力，孔隙度和渗透率变化，人工裂缝，流体渗流与岩石应变耦合，储藏渗流与裂缝渗流耦合，非达西效应等。较详细地给出了耦合方程及推导过程，控制方程包括的未知变量有压力，饱和度及位移，11个变量，和11个方程，用有限差分方法将流体渗流和岩石应变方程离散成主对角占优的七对角矩阵，可在修改已有三维二相渗流和三维固体力学程序的基础上，采用隐式迭代方法求解，示例分析表明，用此模型可以研究储层应力变变，孔隙度和渗透率随时间和空间变化规律，为开发方案制定，整体压裂设计，压后生产管理等方面提供定量分析技术。 相似文献
5.
油井开采过程中油层变形的流固耦合分析 总被引：7，自引：0，他引：7
在油气开采过程中,随着油气的不断采出,必然造成孔隙流体压力的逐渐降低,由此导致储层岩石骨架的有效应力增大,使得油层产生变形或压实。当油层产生变莆或压实时,对油气生产将造成不利影响。比如：使得油藏的渗透率降低,继而使油井的产能降低,同时,油层的变形直接影响着油井和套管的变形与破坏等等。敢开采过程中油层的变形可以描述为三维变形与三维流体流动场的耦合问题,利用可变形多孔介质中流体渗流的流固耦合有限元数值 相似文献
6.
In this paper, a fully coupled numerical model is presented for the finite element analysis of the deforming porous medium interacting with the flow of two immiscible compressible wetting and non-wetting pore fluids. The governing equations involving coupled fluid flow and deformation processes in unsaturated soils are derived within the framework of the generalized Biot theory. The displacements of the solid phase, the pressure of the wetting phase and the capillary pressure are taken as the primary unknowns of the present formulation. The other variables are incorporated into the model using the experimentally determined functions that define the relationship between the hydraulic properties of the porous medium, i.e. saturation, relative permeability and capillary pressure. It is worth mentioning that the imposition of various boundary conditions is feasible notwithstanding the choice of the primary variables. The modified Pastor–Zienkiewicz generalized constitutive model is introduced into the mathematical formulation to simulate the mechanical behavior of the unsaturated soil. The accuracy of the proposed mathematical model for analyzing coupled fluid flows in porous media is verified by the resolution of several numerical examples for which previous solutions are known. Finally, the performance of the computational algorithm in modeling of large-scale porous media problems including the large elasto-plastic deformations is demonstrated through the fully coupled analysis of the failure of two earth and rockfill dams. Furthermore, the three-phase model is compared to its simplified one which simulates the unsaturated porous medium as a two-phase one with static air phase. The paper illustrates the shortcomings of the commonly used simplified approach in the context of seismic analysis of two earth and rockfill dams. It is shown that accounting the pore air as an independent phase significantly influences the unsaturated soil behavior. 相似文献
7.
A poroelastic numerical model is presented to evaluate three-dimensional consolidation due to groundwater withdrawal from desaturating anisotropic porous media. This numerical model is developed based on the fully coupled governing equations for groundwater flow in deforming variably saturated porous media and the Galerkin finite element method. Two different cases of unsaturated aquifers are simulated for the purpose of comparison: a cross-anisotropic soil aquifer, and a corresponding isotropic soil aquifer composed of a geometrically averaged equivalent material. The numerical simulation results show that the anisotropy has a significant effect on the shapes of three-dimensional hydraulic head distribution and displacement vector fields. Such an effect of anisotropy is caused by the uneven partitioning of the hydraulic pumping stress between the vertical and horizontal directions in both groundwater flow field and solid skeleton deformation field. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
8.
Reservoir depletion results in rock failure, wellbore instability, hydrocarbon production loss, oil sand production, and ground surface subsidence. Specifically, the compaction of carbonate reservoirs with soft rocks often induces large plastic deformation due to rock pore collapse. On the other hand, following the compaction of reservoirs and failure of rock formations, the porosity and permeability of formations will, in general, decrease. These bring a challenge for reservoir simulations because of high nonlinearity of coupled geomechanics and fluid flow fields. In this work, we present a fully implicit, fully coupled, and fully consistent finite element formulation for coupled geomechanics and fluid flow problems with finite deformation and nonlinear flow models. The Pelessone smooth cap plasticity model, an important material model to capture rock compaction behavior and a challenging material model for implicit numerical formulations, is incorporated in the proposed formulation. Furthermore, a stress-dependent permeability model is taken into account in the formulation. A co-rotational framework is adopted for finite deformation, and an implicit material integrator for cap plasticity models is consistently derived. Furthermore, the coupled field equations are consistently linearized including nonlinear flow models. The physical theories, nonlinear material and flow models, and numerical formulations are the focus of part I of this work. In part II, we verify the proposed numerical framework and demonstrate the performance of our numerical formulation using several numerical examples including a field reservoir with soft rocks undergoing serious compaction. 相似文献
9.
A three-dimensional, three-phase numerical model is presented for simulating the movement of immiscible fluids, including
nonaqueous-phase liquids (NAPLs), through porous media. The model is designed to simulate soil flume experiments and for practical
application to a wide variety of contamination scenarios involving light or dense NAPLs in heterogeneous subsurface systems.
The model is derived for the three-phase flow of water, NAPL, and air in porous media. The basic governing equations are based
upon the mass conservation of the constitutents within the phases. The descretization chosen to transform the governing equations
into the approximating equations, although logically regular, is very general. The approximating equations are a set of simultaneous
coupled nonlinear equations which are solved by the Newton-Raphson method. The linear system solutions needed for the Newton-Raphson
method are obtained using a matrix of preconditioner/accelerator iterative methods.
Because of the special way the governing equations are implemented, the model is capable of simulating many of the phenomena
considered necessary for the sucessful simulation of field problems including entry pressure phenomena, entrapment, and preferential
flow paths. The model is verified by comparing it with several exact analytic test solutions and three soil flume experiments
involving the introduction and movement of light nonaqueous-phase liquid (LNAPL) or dense nonaqueous-phase liquid (DNAPL)
in heterogeneous sand containing a watertable.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
10.
A fully coupled meshfree algorithm is proposed for numerical analysis of Biot’s formulation. Spatial discretization of the governing equations is presented using the Radial Point Interpolation Method (RPIM). Temporal discretization is achieved based on a novel three-point approximation technique with a variable time step, which has second order accuracy and avoids spurious ripple effects observed in the conventional two-point Crank Nicolson technique. Application of the model is demonstrated using several numerical examples with analytical or semi-analytical solutions. It is shown that the model proposed is effective in simulating the coupled flow deformation behaviour in fluid saturated porous media with good accuracy and stability irrespective of the magnitude of the time step adopted. 相似文献
11.
The details of the Element Free Galerkin (EFG) method are presented with the method being applied to a study on hydraulic fracturing initiation and propagation process in a saturated porous medium using coupled hydro-mechanical numerical modelling. In this EFG method, interpolation (approximation) is based on nodes without using elements and hence an arbitrary discrete fracture path can be modelled.The numerical approach is based upon solving two governing partial differential equations of equilibrium and continuity of pore water simultaneously. 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 of equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on the penalty method. In order to model discrete fractures, the so-called diffraction method is used.Examples are presented and the results are compared to some closed-form solutions and FEM approximations in order to demonstrate the validity of the developed model and its capabilities. The model is able to take the anisotropy and inhomogeneity of the material into account. The applicability of the model is examined by simulating hydraulic fracture initiation and propagation process from a borehole by injection of fluid. The maximum tensile strength criterion and Mohr–Coulomb shear criterion are used for modelling tensile and shear fracture, respectively. The model successfully simulates the leak-off of fluid from the fracture into the surrounding material. The results indicate the importance of pore fluid pressure in the initiation and propagation pattern of fracture in saturated soils. 相似文献
12.
13.
In this paper, a numerical model is developed for the fully coupled hydro‐mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non‐wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two‐phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three‐phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro‐mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non‐wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
14.
The problem of fully coupled consolidation and heat flow around a rigid cylindrical heat source buried in clay has been studied. The governing equations of the problem are summarized in the paper and a finite element time-marching scheme to obtain an approximate solution to the governing equations is described. The stress–strain behaviour of the skeleton of the saturated soil has been represented by both a linear elastic model and the modified Cam clay soil model. The results of a limited parametric study are presented with the aim of understanding the major mechanisms of soil behaviour close to buried canisters of hot radioactive waste. A range of soil properties has been included in the study, and the effects of soil disturbance during canister emplacement have also been considered. 相似文献
15.
用储层岩石抽提物的饱和烃色谱指纹识别油气层 总被引：12，自引：0，他引：12
利用储层岩石抽提物的饱和烃色 质总离子图的指纹特征判识储层的流体（油、气）类型。油层或油饱和的储层,饱和烃色 质总离子流图的特征是正构烷烃碳数分布宽,碳数分布在C15～C38之间,与原油样品的正构烷烃碳数分布相似;凝析气层的正构烷烃碳数分布略窄一些,碳数分布在C15～C35之间,低碳数（小于C21）的正构烷烃相对于油层富集,高碳数（大于C21）的正构烷烃丰度明显低于油层;干气层的正构烷烃碳数分布最窄,碳数分布在C15～ C28之间,只有低碳数的正构烷烃,高碳数的正构烷烃丰度极低。据此可用来识别油层、凝析气层和干气层,也可用于一些测井资料不全或测井质量差的老井的油气层复查、测井难以识别的火成岩油气层的识别,还可用于地层评价,为油气酸化层位的优选提供科学依据。 相似文献
16.
A three-dimensional solution is derived for the fluid flow in a deformable porous medium. It is assumed that the deformation of the medium is described by Hooke's law and the flow of the fluid by Darcy's law, i.e. the theory of poroelasticity applies. The governing equations are completed by suitable boundary conditions such that a compressed saturated cubic sponge is modelled. The solution is a three-dimensional generalisation of the one-dimensional solution of Terzaghi. A two-dimensional plane strain solution is derived also. Both solutions give excellent possibilities to test numerical codes. 相似文献
17.
Modeling of unsaturated granular flows by a two-layer approach 总被引：2，自引：1，他引：1
Flows of partially saturated grain-fluid mixtures over complex curved topography are commonly observed in nature. However, comprehensive understanding of the physics behind them is to date out of reach. To investigate their dynamic process, a two-layer approach is proposed, in which the fluid-saturated granular layer is overlaid by the pure granular material. More specifically, the lower layer is described by a two-phase mixture theory of density preserving solid and fluid constituents. For the upper layer, the single-phase granular mass is treated as a frictional Coulomb-like continuum, and the dilation effect and the influence of the interstitial air are ignored. The capillarity effects and grains-size segregation are not considered in both the layers. The lower and upper layers interact at an interface which is a material surface for the fluid phase, but across which the mass exchange for the granular phase may take place. The granular mass exchange across the layer interface is parameterized by an entrainment type postulate. In addition, the classical jump conditions are employed to connect both layers at the interface dynamically. Furthermore, we perform the depth-averaged technique for the saturated grain-fluid mixture lower layer and the pure granular upper layer, respectively, to simplify the governing equations established. It is demonstrated that the resulting model equations can be reduced to most of the existing single-layer pure granular flow models and saturated two-phase single-layer debris flow models. Numerical solutions demonstrate that the present two-layer model can describe flows of partially saturated grain-fluid mixtures and the transition process of a saturated grain-fluid mixture into an under-saturated state. 相似文献
18.
Eirik Keilegavlen Jeremy E. Kozdon Bradley T. Mallison 《Computational Geosciences》2012,16(4):1021-1042
The governing equations for multiphase flow in porous media have a mixed character, with both nearly elliptic and nearly hyperbolic variables. The flux for each phase can be decomposed into two parts: (1) a geometry- and rock-dependent term that resembles a single-phase flux; and (2) a mobility term representing fluid properties and rock–fluid interactions. The first term is commonly discretized by two- or multipoint flux approximations (TPFA and MPFA, respectively). The mobility is usually treated with single-point upstream weighting (SPU), also known as dimensional or donor cell upstream weighting. It is well known that when simulating processes with adverse mobility ratios, SPU suffers from grid orientation effects. An important example of this, which will be considered in this work, is the displacement of a heavy oil by water. For these adverse mobility ratio flows, the governing equations are unstable at the modeling scale, rendering a challenging numerical problem. These challenges must be addressed in order to avoid systematic biasing of simulation results. In this work, we present a framework for multidimensional upstream weighting for multiphase flow with buoyancy on general two-dimensional grids. The methodology is based on a dual grid, and the resulting transport methods are provably monotone. The multidimensional transport methods are coupled with MPFA methods to solve the pressure equation. Both explicit and fully implicit approaches are considered for time integration of the transport equations. The results show considerable reduction of grid orientation effects compared to SPU, and the explicit multidimensional approach allows larger time steps. For the implicit method, the total number of non-linear iterations is also reduced when multidimensional upstream weighting is used. 相似文献
19.
A. P. S. Selvadurai 《国际地质力学数值与分析法杂志》1978,2(2):189-197
The equations governing the undrained linear elastic behaviour of a saturated soil are formally similar to the equations governing slow of an incompressible Newtonian viscous fluid. This principle of equivalence can then be effectively employed to obtain the load-deflection reiationship for a deep rigid anchor with the shape of a solid of revolution which is embedded in bonded contact with an unbounded incompressible elastic medium. It is found that the load-deflection relationship for the deep rigid anchor can be directly recovered from the expression for the drag induced on an impermeable object with the same size and shape as the anchor, which is appropriately placed in a slow viscous flow region of uniform velocity. 相似文献
20.
Coupled formulation and algorithms for the simulation of non‐planar three‐dimensional hydraulic fractures using the generalized finite element method 
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下载免费PDF全文 This paper presents a coupled hydro‐mechanical formulation for the simulation of non‐planar three‐dimensional hydraulic fractures. Deformation in the rock is modeled using linear elasticity, and the lubrication theory is adopted for the fluid flow in the fracture. The governing equations of the fluid flow and elasticity and the subsequent discretization are fully coupled. A Generalized/eXtended Finite Element Method (G/XFEM) is adopted for the discretization of the coupled system of equations. A Newton–Raphson method is used to solve the resulting system of nonlinear equations. A discretization strategy for the fluid flow problem on non‐planar three‐dimensional surfaces and a computationally efficient strategy for handling time integration combined with mesh adaptivity are also presented. Several three‐dimensional numerical verification examples are solved. The examples illustrate the generality and accuracy of the proposed coupled formulation and discretization strategies. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献