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1.
Discrete fracture model for simulating waterflooding processes under fracturing conditions 
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下载免费PDF全文 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
2.
In engineering practices, different numerical methods for fluid flow simulation and solid deformation/stress simulation are adopted to model fluid–structure interaction problems in porous media. Cell‐centered finite volume method is widely used in fluid flow simulation, while the solid deformation/stress simulation is usually accomplished by using the Galerkin vertex‐centered finite element method, which leads to the incompatibility between cell variables with nodal variables. Therefore, the data transfer between cell variables and nodal variables is inevitable. Consequently, this kind of transfer will lead to extra artificial error. Hence, the major concern is how to minimize the error due to cell to node projections. In this paper, a problem of pore pressure diffusion within a one‐dimensional heterogeneous porous medium is investigated. We present a new projection scheme and corresponding error formula, where the error control factor is introduced. The new projection scheme is based on piecewise linear interpolations. Results demonstrate that if the error control factor is chosen properly, the error due to the projection from cell to node can be controlled effectively, and the most desired zero error can be achieved. Finally, we analyze some practical cases in consideration of permeability contrast and mesh uniformity. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
3.
Richard E. Ewing Raytcho D. Lazarov Steve L. Lyons Dimitrios V. Papavassiliou Joseph Pasciak Guan Qin 《Computational Geosciences》1999,3(3-4):185-204
Numerical simulation of fluid flow in a hydrocarbon reservoir has to account for the presence of wells. The pressure of a grid cell containing a well is different from the average pressure in that cell and different from the bottom-hole pressure for the well [17]. This paper presents a study of grid pressures obtained from the simulation of single phase flow through an isotropic porous medium using different numerical methods. Well equations are proposed for Darcy flow with Galerkin finite elements and mixed finite elements. Furthermore, high velocity (non-Darcy) flow well equations are developed for cell-centered finite difference, Galerkin finite element and mixed finite element techniques. 相似文献
4.
Joachim Berdal Haga Harald Osnes Hans Petter Langtangen 《Computational Geosciences》2012,16(3):723-734
Large-scale simulations of coupled flow in deformable porous media require iterative methods for solving the systems of linear
algebraic equations. Construction of efficient iterative methods is particularly challenging in problems with large jumps
in material properties, which is often the case in realistic geological applications, such as basin evolution at regional
scales. The success of iterative methods for such problems depends strongly on finding effective preconditioners with good
parallel scaling properties, which is the topic of the present paper. We present a parallel preconditioner for Biot’s equations
of coupled elasticity and fluid flow in porous media. The preconditioner is based on an approximation of the exact inverse
of the two-by-two block system arising from a finite element discretisation. The approximation relies on a highly scalable
approximation of the global Schur complement of the coefficient matrix, combined with generally available state-of-the-art
multilevel preconditioners for the individual blocks. This preconditioner is shown to be robust on problems with highly heterogeneous
material parameters. We investigate the weak and strong parallel scaling of this preconditioner on up to 512 processors and
demonstrate its ability on a realistic basin-scale problem in poroelasticity with over eight million tetrahedral elements. 相似文献
5.
This paper investigates the two‐dimensional flow problem through an anisotropic porous medium containing several intersecting curved fractures. First, the governing equations of steady‐state fluid flow in a fractured porous body are summarized. The flow follows Darcy's law in matrix and Poiseuille's law in fractures. An infinite transversal permeability is considered for the fractures. A multi‐region boundary element method is used to derive a general pressure solution as a function of discharge through the fractures and the pressure and the normal flux on the domain boundary. The obtained solution fully accounts for the interaction and the intersection between fractures. A numerical procedure based on collocation method is presented to compute the unknowns on the boundaries and on the fractures. The numerical solution is validated by comparing with finite element solution or the results obtained for an infinite matrix. Pressure fields in the matrix are illustrated for domains containing several interconnected fractures, and mass balance at the intersection points is also checked. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
6.
A four‐node plane parametric element based on quadrilateral area coordinate and its application to coupled solid‐deformation/fluid‐flow simulation for porous geomaterials 下载免费PDF全文
下载免费PDF全文 Gen Li 《国际地质力学数值与分析法杂志》2015,39(3):251-276
A four‐node plane parametric element AQGβ6‐I is constructed on the basis of the quadrilateral area coordinate, the generalized conforming principle and the projection technique with a penalty factor β within an interval of 0–1. When β = 0, the element has excellent bending performance. When β = 1, the element can pass patch test strictly; its performance is as good as many famous elements. When β value is between 0 and 1, such as β = 0.5, the element can arrive at a compromise between (relatively) low sensitivity to mesh distortion and perfect convergence. The work provides an illuminating method to alleviate a difficult problem in finite element modelling using the four‐node quadrilateral element, which can pass the strict patch test, but has poor performance in bending dominated problem; on the contrary, it has excellent performance in bending dominated problem but cannot pass the strong patch test. The AQGβ6‐I with the convergence formulation (β = 1) is then applied to coupled solid‐deformation/fluid‐flow simulation for porous geomaterials. The computational examples are carried out to demonstrate that the AQGβ6‐I (β = 1) element is not only stable, reliable and efficient but also of high accuracy. The present study provides a good applicable element for finite element simulations of solid‐deformation/fluid‐flow for porous geomaterials. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
7.
Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method 下载免费PDF全文
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.
The focus of this work is efficient solution methods for mixed finite element models of variably saturated fluid flow through
deformable porous media. In particular, we examine preconditioning techniques to accelerate the convergence of implicit Newton–Krylov
solvers. We highlight an approach in which preconditioners are built from block-factorizations of the coupled system. The
key result of the work is the identification of effective preconditioners for the various sub-problems that appear within
the block decomposition. We use numerical examples drawn from both linear and nonlinear hydromechanical models to test the
robustness and scalability of the proposed methods. Results demonstrate that an algebraic multigrid variant of the block preconditioner
leads to mesh-independent convergence, good parallel efficiency, and insensitivity to the material parameters of the medium. 相似文献
9.
This paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM‐XFEM is its ability to model discontinuities in the domain independently of the computational mesh. The proposed FM approach is a continuum‐based approach that is used to model the flow interaction between the porous matrix and existing fractures via a transfer function. Fracture geometry is defined using the level set method. Therefore, in contrast to the discrete fracture flow model, the fracture representation is not meshed along with the computational domain. Consequently, the method is able to determine the influence of fractures on fluid flow within a fractured domain without the complexity of meshing the fractures within the domain. The XFEM component of the scheme addresses the discontinuous displacement field within elements that are intersected by existing fractures. In XFEM, enrichment functions are added to the standard finite element approximation to adequately resolve discontinuous fields within the simulation domain. Numerical tests illustrate the ability of the method to adequately describe the displacement and fluid pressure fields within a fractured domain at significantly less computational expense than explicitly resolving the fracture within the finite element mesh. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
10.
11.
A formulation has been derived for the flow of non-Newtonian (power-law) fluids in deformable, fractured porous media. The formulation is enhanced with a subgrid scale model to accurately represent the flow of the power-law fluids inside the cracks. The resulting equations have been discretised using standard (Lagrangian) finite element shape functions and with non-uniform rational B-splines (NURBS), which have been cast into a standard finite element datastructure using Bézier extraction. The effect of the power-law index on the velocity inside the fracture and on the total fluid flow through the porous medium has been analysed for a typical boundary-value problem. It is shown that large differences between non-Newtonian and linearised Newtonian fluids can occur for the fluid velocity inside the fracture. This can significantly influence the total fluid transport through the domain. A mesh sensitivity study has been carried out as well and shows that markedly smaller element sizes are required in order to obtain accurate results for the local flow inside the fracture, compared with the element sizes necessary for obtaining accurate results inside the porous medium away from the fracture. Moreover, a comparison has been made between the results obtained using standard Lagrange polynomials and those obtained using NURBS. It is shown that while both discretisation methods are able to accurately simulate the deformations and pressures in the porous medium, the higher interelement continuity of NURBS is mandatory for obtaining correct values of the fluid velocities inside the fracture, especially near the tips. 相似文献
12.
A three-phase hydro-mechanical model for hydraulic fracturing is proposed. Three phases include: porous solid, fracturing fluid and host fluid. Discontinuity is handled using extended finite element method (XFEM) while cohesive crack model is used as fracturing criterion. Flow through fracture is defined as one-dimensional laminar flow, and flow through porous medium (host reservoir) is defined as two-dimensional Darcy flow. Coupling between two fluids in each space, fracture and pore, is captured through capillary pressure–saturation relationship, while the identical fluids in fracture and pore are coupled through a so-called leak-off mass transfer term. Coupling between fluids and deformation is captured through compatibility of volumetric strain of fluids within fracture and pore, and volumetric strain of the matrix. Spatial and temporal discretisation is achieved using the standard Galerkin method and the finite difference technique, respectively. The model is verified against analytical solutions available from literature. The leaking of fracturing fluid into the medium and suction of porous fluid into the fracture around the tip, are investigated. Sensitivity analyses are carried out for cases with slow and fast injection rates. It is shown that the results by single-phase flow may underestimate the leak-off. 相似文献
13.
This paper identifies imbalanced columns (or rows) as a significant source of ill‐conditioning in the preconditioned coefficient matrix using the standard Jacobi preconditioner, for finite element solution of Biot's consolidation equations. A simple and heuristic preconditioner is proposed to reduce this source of ill‐conditioning. The proposed preconditioner modifies the standard Jacobi preconditioner by scaling the excess pore pressure degree‐of‐freedoms in the standard Jacobi preconditioner with appropriate factors. The performance of such preconditioner is examined using the symmetric quasi‐minimal residual method. To alleviate storage requirements, element‐by‐element iterative strategies are implemented. Numerical experiment results show that the proposed preconditioner reduces both the number of iteration and CPU execution time significantly as compared with the standard Jacobi preconditioner. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
14.
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
15.
An analytical solution is proposed for transient flow and deformation coupling of a fluid‐saturated poroelastic medium within a finite two‐dimensional (2‐D) rectangular domain. In this study, the porous medium is assumed to be isotropic, homogeneous, and compressible. In addition, the point sink can be located at an arbitrary position in the porous medium. The fluid–solid interaction in porous media is governed by the general Biot's consolidation theory. The method of integral transforms is applied in the analytical formulation of closed‐form solutions. The proposed analytical solution is then verified against both exact and numerical results. The analytical solution is first simplified and validated by comparison with an existing exact solution for the uncoupled problem. Then, a case study for pumping from a confined aquifer is performed. The consistency between the numerical solution and the analytical solution confirms the accuracy and reliability of the analytical solution presented in this paper. The proposed analytical solution can help us to obtain in‐depth insights into time‐dependent mechanical behavior due to fluid withdrawal within finite 2‐D porous media. Moreover, it can also be of great significance to calibrate numerical solutions in plane strain poroelasticity and to formulate relevant industry norms and standards. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
16.
Constitutive equations for the mechanical and hydraulic behaviour of saturated porous rock with joint sets of specified orientations are developed by superposing continuum representations for the mechanical and hydraulic properties of the intact rock and each of the joint sets. The resulting continuum theory allows for fluid diffusion through and between interconnected rock pores and joint sets of specified orientation, and also accounts for the anisotropy of the mechanical properties due to joint stiffnesses. The accuracy and reliability of this model are verified by finite element simulation of example problems. The first example considers joint orientation-dependent rock deformation in a hypothetical porous medium with one joint set of different dip angles. More realistic examples related to rock slope stability and reservoir-induced seismicity are also considered in which the constitutive law's utility for modelling time-dependent fluid pressures is illustrated. 相似文献
17.
含软夹层的层状沉积河谷场地的地震动力响应分析 总被引：1，自引：0，他引：1
把层状沉积河谷场地中的软夹层模拟为流体饱和多孔介质,结合已有的对单相弹性固体介质、流体饱和多孔介质进行动力反应分析的显式有限元方法,建立了既能描述沉积河谷谷底的软土场地（用流体饱和多孔介质描述）,又能描述河谷周边山体（用单相弹性介质描述）的计算模型,并利用该方法分析了研究在P波入射下软夹层厚度以及软夹层的刚度等因素对层状沉积谷场地地震动力响应的影响。 相似文献
18.
An important part of our global wealth depends on the extraction of fluids from porous media. More recently, sequestration of carbon dioxide (rmCO2) into deep geological layers as a possible measure to mitigate climate change has increased interest in fluid injection into porous media. Sophisticated numerical models play an important role in managing the uncertainties related to the subsurface, and finite element methods are the most versatile tool allowing the coupling of fluid flow, geomechanics and other physical processes. This paper gives insight into two important aspects of fluid injection/extraction in porous media: the correct modeling of the bore hole through specification of initial stresses, which together with a fully coupled strategy allows simulation of nonlinear poromechanics, and the imposition of appropriate boundary conditions that allow the controlled injection/extraction of a total specified amount of fluid in an anisotropic porous medium, without exceeding a safe operating pressure. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
19.
The purpose of this paper is to simulate the coupled dynamic deformation and water flow that occur in saturated soils when subjected to traffic loads, which is a problem with several practical applications. The wave propagation causes vibrations leading to discomfort for passengers and people in the surroundings and increase wear on both the vehicle and road structure. The water flow may cause internal erosion and material transport in the soil. Further, the increased pore water pressure could reduce the bearing capacity of embankments. The saturated soil is modelled as a water‐saturated porous medium. The traffic is modelled as a number of moving wheel contact loads. Dynamic effects are accounted for, which lead to a coupled problem with solid displacements, water velocity and pressure as primary unknowns. A finite element program has been developed to perform simulations. The simulations clearly demonstrate the induced wave propagation and water flow in the soil. The simulation technique is applicable to railway as well as road traffic. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
20.
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