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1.
A numerical simulation is presented for three-dimensional three-phase fluid flow in a deforming saturated oil reservoir. The mathematical formulation describes a fully coupled governing equation systen which consists of the equilibrium and continuity equations for three immiscible fluids flowing in a porous medium. An elastoplastic soil model, based on a Mohr–Coulomb yield surface, is used. The finite element method is applied to obtain simultaneous solutions to the governing equations where displacement and fluid pressures are the primary unknowns. The final discretized equations are solved by a direct solver using fully implicit procedures. The developed model is used to investigate the problems of three-phase fluid flow in a deforming saturated oil reservoir.  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.
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   

4.
In the technology of oil recovery, oil production rate can be increased by generation of a vertical conductive fracture adjacent to the well-bore. In this paper the seepage flow and isothermal deformation in both the oil formation and the fracture are studied by modelling the formation as a two-dimensional infinite poroelastic medium and the conductive fracture as a one-dimensional poroelastic material, saturated by a one-phase compressible fluid. The plane strain condition is employed. Solutions for a growing conductive fracture and a stationary conductive fracture in the infinite medium are obtained by means of the finite element method based on a variational principle for the formation which can impose the governing equations of the fracture. Infinite elements are used outside the finite element domain. Numerical results indicate that the injection rate, the applied pressure and the crack mouth opening displacement at the well-bore oscillate during the propagation of the conductive fracture. The production rate of a well with the conductive fracture is compared with that of a well without the conductive fracture. Finally, a new definition of the conductivity coefficient for the conductive fracture is presented. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

5.
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   

6.
Aquifer contamination by organic chemicals in subsurface flow through soils due to leaking underground storage tanks filled with organic fluids is an important groundwater pollution problem. The problem involves transport of a chemical pollutant through soils via flow of three immiscible fluid phases: namely air, water and an organic fluid. In this paper, assuming the air phase is under constant atmospheric pressure, the flow field is described by two coupled equations for the water and the organic fluid flow taking interphase mass transfer into account. The transport equations for the contaminant in all the three phases are derived and assuming partition equilibrium coefficients, a single convective – dispersive mass transport equation is obtained. A finite element formulation corresponding to the coupled differential equations governing flow and mass transport in the three fluid phase porous medium system with constant air phase pressure is presented. Relevant constitutive relationships for fluid conductivities and saturations as function of fluid pressures lead to non-linear material coefficients in the formulation. A general time-integration scheme and iteration by a modified Picard method to handle the non-linear properties are used to solve the resulting finite element equations. Laboratory tests were conducted on a soil column initially saturated with water and displaced by p-cymene (a benzene-derivative hydrocarbon) under constant pressure. The same experimental procedure is simulated by the finite element programme to observe the numerical model behaviour and compare the results with those obtained in the tests. The numerical data agreed well with the observed outflow data, and thus validating the formulation. A hypothetical field case involving leakage of organic fluid in a buried underground storage tank and the subsequent transport of an organic compound (benzene) is analysed and the nature of the plume spread is discussed.  相似文献   

7.
An exact steady‐state closed‐form solution is presented for coupled flow and deformation of an axisymmetric isotropic homogeneous fluid‐saturated poroelastic layer with a finite radius due to a point sink. The hydromechanical behavior of the poroelastic layer is governed by Biot's consolidation theory. Boundary conditions on the lateral surface are specifically chosen to match the appropriate finite Hankel transforms and simplify the transforms of the governing equations. Ordinary differential equations in the transformed domain are solved, and then the analytical solutions in the physical space for the pore pressure and the displacements are finally obtained by using finite Hankel inversions. The analytical solutions at some special locations such as the top and bottom surfaces, lateral surface, and the symmetrical axis are given and analyzed. And a case study for the consolidation of a water‐saturated soft clay layer due to pumping is conducted. The analytical solution is verified against the finite element solution. Meanwhile, an analysis of coupled hydromechanical behavior is carried out herein. The presented analytical solution is an exact solution to the practical poroelastic problem within an axisymmetric finite layer. It can provide us a better understanding of the poroelastic behavior of the finite layer due to fluid extraction. Besides, it can be applied to calibrate numerical schemes of axisymmetric poroelasticity within finite domains. Copyright © 2017 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.
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   

10.
Unsaturated soils are three‐phase porous media consisting of a solid skeleton, pore liquid, and pore gas. The coupled mathematical equations representing the dynamics of unsaturated soils can be derived based on the theory of mixtures. Solution of these fully coupled governing equations for unsaturated soils requires tremendous computational resources because three individual phases and interactions between them have to be taken into account. The fully coupled equations governing the dynamics of unsaturated soils are first presented and then two finite element formulations of the governing equations are presented and implemented within a finite element framework. The finite element implementation of all the terms in the governing equations results in the complete formulation and is solved for the first time in this paper. A computationally efficient reduced formulation is obtained by neglecting the relative accelerations and velocities of liquid and gas in the governing equations to investigate the effects of fluid flow in the overall behavior. These two formulations are used to simulate the behavior of an unsaturated silty soil embankment subjected to base shaking and compared with the results from another commonly used partially reduced formulation that neglects the relative accelerations, but takes into account the relative velocities. The stress–strain response of the solid skeleton is modeled as both elastic and elastoplastic in all three analyses. In the elastic analyses no permanent deformations are predicted and the displacements of the partially reduced formulation are in between those of the reduced and complete formulations. The frequency of vibration of the complete formulation in the elastic analysis is closer to the predominant frequency of the base motion and smaller than the frequencies of vibration of the other two analyses. Proper consideration of damping due to fluid flows in the complete formulation is the likely reason for this difference. Permanent deformations are predicted by all three formulations for the elastoplastic analyses. The complete formulation, however, predicts reductions in pore fluid pressures following strong shaking resulting in somewhat smaller displacements than the reduced formulation. The results from complete and reduced formulations are otherwise comparable for elastoplastic analyses. For the elastoplastic analysis, the partially reduced formulation leads to stiffer response than the other two formulations. The likely reason for this stiffer response in the elastoplastic analysis is the interpolation scheme (linear displacement and linear pore fluid pressures) used in the finite element implementation of the partially reduced formulation. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

11.
This paper presents an algorithm and a fully coupled hydromechanical‐fracture formulation for the simulation of three‐dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3‐D fracture front at every fracture propagation step. A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time‐dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3‐D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented.  相似文献   

12.
The equations governing the dynamic behavior of saturated porous media as well as a finite element spatial discretization of these equations are summarized. A three-parameter time integration scheme called the Hilber–Hughes–Taylor α-method is used together with a predictor/multi-corrector algorithm, instead of the widely used Newmark's method, to integrate the spatially discrete finite element equations. The new time integration scheme possess quadratic accuracy and desirable numerical damping characteristics. The proposed numerical solution and bounding surface plasticity theory to describe the constitutive behaviour of soil have been implemented as the computer code DYSAC2. Predictions made by DYSAC2 code are verified using dynamic centrifuge test results for a clay embankment. Importance of initial state of a soil on its dynamic behaviour is demonstrated.  相似文献   

13.
The theoretical aspects of fully coupled thermohydromechanical behaviour of saturated porous media are presented. The non-linear behaviour of soil skeleton is assumed. A new concept called ‘thermal void ratio state surface’ is introduced to include thermal effects, and the stress state level influence on volume changes. The fluid phase flows according to Darcy's law and energy transport is assumed to follow Fourier's law classically. Variation of water permeability, water and solid unit weight due to thermal effects and pore pressure changes are included. A finite element package is developed based on final matrix form obtained from discretization of integral form of field equations by finite element method and integration in time. A very good agreement between the theoretical predictions and the experimental results was obtained for the several simple problems proposed by other authors. © 1997 by John Wiley & Sons, Ltd.  相似文献   

14.
We describe an algorithm for modeling saturated fractures in a poroelastic domain in which the reservoir simulator is coupled with a boundary element method. A fixed stress splitting is used on the underlying fractured Biot system to iteratively couple fluid and solid mechanics systems. The fluid system consists of Darcy’s law in the reservoir and is computed with a multipoint flux mixed finite element method, and a Reynolds’ lubrication equation in the fracture solved with a mimetic finite difference method. The mechanics system consists of linear elasticity in the reservoir and is computed with a continuous Galerkin method, and linear elasticity in the fracture is solved with a weakly singular symmetric Galerkin boundary element method. This algorithm is able to compute both unknown fracture width and unknown fluid leakage rate. An interesting numerical example is presented with an injection well inside of a circular fracture.  相似文献   

15.
储层流固耦合的数学模型和非线性有限元方程   总被引：2，自引：0，他引：2  
张广明  刘合  张劲  吴恒安  王秀喜 《岩土力学》2010,31(5):1657-1662
根据饱和多孔介质固体骨架的平衡方程和多孔介质中流体的连续性方程,建立了储层流固耦合数学模型。模型中引入了Jaumann应力速率公式描述多孔介质固体骨架的大变形效应,并考虑了地应力、初始孔隙压力、初始流体密度和初始孔隙度对耦合模型的影响。基于与微分方程等价的加权余量公式,在空间域采用有限元离散,对时间域进行隐式差分格式离散,导出了以单元节点位移和单元节点孔隙压力为未知量的储层流固耦合的非线性有限元增量方程。该模型在石油工程中有广泛的应用,为储层流固耦合的数值模拟奠定了理论基础。  相似文献   

16.
A finite element procedure is developed to accurately locate the free surface of unconfined seepage flow through porous media. The free surface is taken as the boundary between wet and dry soils, with flow in the saturated region characterized by Darcy's law. The method involves equations and meshing which are fully consistent with a general formulation for geotechnical engineering problems involving simultaneous solution of pore fluid pressures and soil skeleton displacements. Accuracy and versatility of the proposed procedure are demonstrated by solving various unconfined seepage flow problems through earth structures. Free surfaces and flownets are presented for the calculated flow fields.  相似文献   

17.
In our study, we develop a model for simulating fracturing processes in a poroelastic medium. The proposed approach combines the discrete fracture model enriched with contact plane mechanics. The model captures mechanical interactions of fractures and a deformable medium, fluid, and heat transfer in fractures and in a porous medium. Both effects of poroelasticity and thermoelasticity are accounted in our model. Mass and heat conservation equations are approximated by the finite volume method, and mechanical equilibrium equations are discretized by means of the Galerkin finite element approach. Two‐dimensional grid facets between 3‐dimensional finite elements are considered as possible fracture surfaces. Most of these facets are inactive from the beginning and are activated throughout the simulation. A fracture propagation criterion, based on Irwin's approach, is verified on each nonlinear iteration. When the criterion is satisfied, additional contact elements are added into finite element and discrete fracture model formulations respectively. The proposed approach allows modeling of existing natural and artificially created fractures within one framework. The model is tested on single‐ and multiple‐phase fluid flow examples for both isothermal and thermal conditions and verified against existing semianalytical solutions. The applicability of the approach is demonstrated on an example of practical interests where a sector model of an oil reservoir is simulated with different injection and production regimes.  相似文献   

18.
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   

19.
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   

20.
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   

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