共查询到20条相似文献，搜索用时 7 毫秒
1.
One proposed geothermal heat extraction scheme relies on water circulation in a large vertical crack created by hydraulic fracturing in a hot dry impermeable rock mass. Water flow, heat convection and crack opening widths are analysed by finite elements. Governing field equations of the problem are first set up rigorously and then various small terms are identified and neglected, retaining the effects of pressure gradient, buoyancy, velocity head (kinetic energy) and head loss due to viscous friction in the water flow equation, and the effects of heat convection in water and heat conduction in rock in the heat transfer equation. The finite element scheme for water flow is based on a variational principle that is typical for diffusion problems, and for heat transfer it is based on the method of least-square residuals. The system of differential equations is highly non-linear. The non-linear terms and coefficients are treated in the fiaite element analysis as constant; the finite element analysisof, the steady-state pressures, fluxes and temperatures is then iterated, evaluating all non-linear terms and coefficients on the basis of the solution obtained in the previous iteration. Numerically calculated fields at various times after the start ofcooling are presented. They indicate some features favourable for the geothermal scheme, such as formation of eddy currents, and downward flux of water toward hotter rock. However, other important questions would have to be solved to gain full understanding, of this proposed geothermal scheme. 相似文献
2.
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
3.
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
4.
Nadia Laredj Hanifi Missoum Karim Bendani Mustapha Maliki 《Arabian Journal of Geosciences》2011,5(5):935-942
Knowledge of transport processes of heat and moisture in soils of arid zones is vital to understanding the environmental and economic impacts of many activities: agriculture, waste disposal, geoenvironmental practices and earth sciences. Through extensive review and study on the different aspects of coupled transfer processes in swelling porous media, a general mathematical model for coupled heat, moisture, air flow and deformation problems in clayey soils is proposed in a consistent and unified manner. The model is characterized by the presence of a deformable solid matrix filled with two fluid phases (liquid water and air). In the proposed model, both pore water and air transfers are assumed to be governed by the generalized Darcy’s law. Fully coupled, non-linear partial differential equations are established and then solved by using a Galerkin weighted residual approach in space domain and an implicit integrating scheme in time domain. The obtained model has been finally validated by means of some case tests for the prediction of the thermo-hydro-mechanical behaviour of unsaturated swelling soils. The calculated relative errors between experimental and numerical results are 3% for temperature and 7% for stresses. Consequently, the developed numerical model predicts satisfactory results, compared to experimental test measures. The model is applicable to two-dimensional problems with various initial and boundary conditions; non-linear soil parameters can be easily included in this model. 相似文献
5.
将液化流动的土体视为流体,运用流体力学原理,基于矢量符号运算法进行液化场地的动力场分析,求解出动力场解析解。采用ABAQUS/CFD进行液化场地流体动力学有限元分析,根据流动基本控制方程,计算出动力场的数值解。分析结果表明,液化土体横向流动时,隧道结构周围的应力场既包括由表面压力引起的压力阻力,也包括由剪应力引起的摩擦阻力;隧道结构周围的液化土体流动速度很小,但在隧道结构下方存在流动速度加强区;理论计算的动力场解析解大于有限元计算的数值解,但总体的分布变化趋势基本一致;隧道结构附近的应力场变化较为密集,所受到的应力主要分布在液化土体流动的迎面位置。 相似文献
6.
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
7.
In this paper, a fully coupled thermo-hydro-mechanical model is presented for two-phase fluid flow and heat transfer in fractured/fracturing porous media using the extended finite element method. In the fractured porous medium, the traction, heat, and mass transfer between the fracture space and the surrounding media are coupled. The wetting and nonwetting fluid phases are water and gas, which are assumed to be immiscible, and no phase-change is considered. The system of coupled equations consists of the linear momentum balance of solid phase, wetting and nonwetting fluid continuities, and thermal energy conservation. The main variables used to solve the system of equations are solid phase displacement, wetting fluid pressure, capillary pressure, and temperature. The fracture is assumed to impose the strong discontinuity in the displacement field and weak discontinuities in the fluid pressure, capillary pressure, and temperature fields. The mode I fracture propagation is employed using a cohesive fracture model. Finally, several numerical examples are solved to illustrate the capability of the proposed computational algorithm. It is shown that the effect of thermal expansion on the effective stress can influence the rate of fracture propagation and the injection pressure in hydraulic fracturing process. Moreover, the effect of thermal loading is investigated properly on fracture opening and fluids flow in unsaturated porous media, and the convective heat transfer within the fracture is captured successfully. It is shown how the proposed computational model is capable of modeling the fully coupled thermal fracture propagation in unsaturated porous media. 相似文献
8.
This paper presents a fully coupled finite element formulation for partially saturated soil as a triphasic porous material, which has been developed for the simulation of shield tunnelling with heading face support using compressed air. While for many numerical simulations in geotechnics use of a two‐phase soil model is sufficient, the simulation of compressed air support demands the use of a three‐phase model with the consideration of air as a separate phase. A multiphase model for soft soils is developed, in which the individual constituents of the soil—the soil skeleton, the fluid and the gaseous phase—and their interactions are considered. The triphasic model is formulated within the framework of the theory of porous media, based upon balance equations and constitutive relations for the soil constituents and their mixture. An elasto‐plastic, cam–clay type model is extended to partially saturated soil conditions by incorporating capillary pressure according to the Barcelona basic model. The hydraulic properties of the soil are described via DARCY 's law and the soil–water characteristic curve after VAN GENUCHTEN . Water is modelled as an incompressible and air as a compressible phase. The model is validated by means of selected benchmark problems. The applicability of the model to geotechnical problems is demonstrated by results from the simulation of a compressed air intervention in shield tunnelling. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
9.
In this paper, we present a numerical model for simulating two-phase (oil–water and air–water) incompressible and immiscible flow in porous media. The mathematical model which is based on a fractional flow formulation is formed of two nonlinear partial differential equations: a mean pressure equation and a water saturation equation. These two equations can be solved in a sequential manner. Two numerical methods are used to discretize the equations of the two-phase flow model: mixed hybrid finite elements are used to treat the pressure equation, h-based Richards' equation and the diffusion term in the saturation equation, the advection term in the saturation equation is treated with the discontinuous finite elements. We propose a better way to calculate the nonlinear coefficients contained in our equations on each element of the discretized domain. In heterogeneous porous media, the saturation becomes discontinuous at the interface between two porous media. We show in this paper how to use the capillary pressure–saturation relationship in order to handle the saturation jump in the mixed hybrid finite element method. The two-phase flow simulator is verified against analytical solutions for some flow problems treated by other authors. 相似文献
10.
A micro‐hydromechanical model for granular materials is presented. It combines the discrete element method for the modeling of the solid phase and a pore‐scale finite volume formulation for the flow of an incompressible pore fluid. The coupling equations are derived and contrasted against the equations of conventional poroelasticity. An analogy is found between the discrete element method pore‐scale finite volume coupling and Biot's theory in the limit case of incompressible phases. The simulation of an oedometer test validates the coupling scheme and demonstrates the ability of the model to capture strong poromechanical effects. A detailed analysis of microscale strain and stress confirms the analogy with poroelasticity. An immersed deposition problem is finally simulated and shows the potential of the method to handle phase transitions. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
11.
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
12.
Magnus Wangen 《Computational Geosciences》2013,17(4):647-659
A procedure based on the finite element method is suggested for modeling of 3D hydraulic fracturing in the subsurface. The proposed formulation partitions the stress field into the initial stress state and an additional stress state caused by pressure buildup. The additional stress is obtained as a solution of the Biot equations for coupled fluid flow and deformations in the rock. The fluid flow in the fracture is represented on a regular finite element grid by means of “fracture” porosity, which is the volume fraction of the fracture. The use of the fracture porosity allows for a uniform finite element formulation for the fracture and the rock, both with respect to fluid pressure and displacement. It is demonstrated how the fracture aperture is obtained from the displacement field. The model has a fracture criterion by means of a strain limit in each element. It is shown how this criterion scales with the element size. Fracturing becomes an intermittent process, and each event is followed by a pressure drop. A procedure is suggested for the computation of the pressure drop. Two examples of hydraulic fracturing are given, when the pressure buildup is from fluid injection by a well. One case is of a homogeneous rock, and the other case is an inhomogeneous rock. The fracture geometry, well pressure, new fracture area, and elastic energy released in each event are computed. The fracture geometry is three orthogonal fracture planes in the homogeneous case, and it is a branched fracture in the inhomogeneous case. 相似文献
13.
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
14.
Mathematical simulation of non‐isothermal multiphase flow in deformable unsaturated porous media is a complicated issue because of the need to employ multiple partial differential equations, the need to take into account mass and energy transfer between phases and because of the non‐linear nature of the governing partial differential equations. In this paper, an analytical solution for analyzing a fully coupled problem is presented for the one‐dimensional case where the coefficients of the system of equations are assumed to be constant for the entire domain. A major issue is the non‐linearity of the governing equations, which is not considered in the analytical solution. In order to introduce the non‐linearity of the equations, an iterative discretized procedure is used. The domain of the problem is divided into identical time–space elements that cover the time–space domain. A separate system of equations is defined for each element in the local coordinate system, the initial and boundary conditions for each element are obtained from the adjacent elements and the coefficients of the system of equations are considered to be constant in each step. There are seven governing differential equations that should be solved simultaneously: the equilibrium of the solid skeleton, mass conservation of fluids (water, water vapor and gas) and energy conservation of phases (solid, liquid and gas). The water vapor is not in equilibrium with water and different phases do not have the same temperature. The governing equations that have been solved seem to be the most comprehensive in this field. Three examples are presented for analyzing heat and mass transfer in a semi‐infinite column of unsaturated soil. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
15.
Magnus Wangen 《国际地质力学数值与分析法杂志》1993,17(6):401-432
This article presents a numerical model of heat and fluid flow in compacting sedimentary basins formulated in Lagrangian co-ordinates. The Lagrangian co-ordinates are the sediment particle positions of the completely compacted basin. A finite element formulation of excess water pressure and temperature in these Lagrangian co-ordinates is presented, in addition to an equivalent formulation in the real co-ordinates. The later formulation is also Lagrangian of nature, since the elements of the grid in the real co-ordinates always frame the same sediment particles. In other words, it is the Lagrangian grid mapped to the real space. This is done in an iterative loop which solves for excess water pressure, and then updates the real co-ordinates of the sediment particles. By comparing the two finite element formulations it is concluded that the one in real space is the simplest, most efficient and most precise. The model is validated by comparison with two dimensionless one-dimensional solutions, one analytical for the linear case, and one numerical for the non-linear case. Both these one-dimensional solutions are obtained on the unit interval, where the moving top boundary caused by continuous sedimentation is incorporated. 相似文献
16.
Rigoberto G. Sanabria Castro Sandra M. C. Malta Abimael F. D. Loula Luiz Landau 《Computational Geosciences》2001,5(4):301-330
A finite element formulation is proposed to approximate a nonlinear system of partial differential equations, composed by an elliptic subsystem for the pressure–velocity and a transport equation (convection–diffusion) for the concentration, which models the incompressible miscible displacement of one fluid by another in a rigid porous media. The pressure is approximated by the classical Galerkin method and the velocity is calculated by a post-processing technique. Then, the concentration is obtained by a Galerkin/least-squares space–time (GLS/ST) finite element method. A numerical analysis is developed for the concentration approximation. Then, stability, convergence and numerical results are presented confirming the a priori error estimates. 相似文献
17.
A thermodynamically consistent extension of the constitutive equations of saturated soils to unsaturated conditions is often worked out through the use of a unique ‘effective’ interstitial pressure, accounting equivalently for the pressures of the saturating fluids acting separately on the internal solid walls of the pore network. The natural candidate for this effective interstitial pressure is the space averaged interstitial pressure. In contrast experimental observations have revealed that, at least, a pair of stress state variables was needed for a suitable framework to describe stress–strain–strength behaviour of unsaturated soils. The thermodynamics analysis presented here shows that the most general approach to the behaviour of unsaturated soils actually requires three stress state variables: the suction, which is required to describe the invasion of the soil by the liquid water phase through the retention curve; two effective stresses, which are required to describe the soil deformation at water saturation held constant. However a simple assumption related to the plastic flow rule leads to the final need of only a Bishop-like effective stress to formulate the stress–strain constitutive equation describing the soil deformation, while the retention properties still involve the suction and possibly the deformation. Commonly accepted models for unsaturated soils, that is the Barcelona Basic Model and any approach based on the use of an effective averaged interstitial pressure, appear as special extreme cases of the thermodynamic formulation proposed here. 相似文献
18.
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
19.
Johannes Korsawe Eugen Perau Susanne Potthoff Gerhard Starke 《Computers and Geotechnics》2003,30(8):695-705
A new model for two-phase flow of water and air in soil is presented. This leads to a system of two mass balance equations and two equations representing conservation of momentum of fluid and gas, respectively. This paper is concerned with the verification of this model for the special case of a rigid soil skeleton by computational experiments. Its numerical treatment is based on the Raviart–Thomas mixed finite element method combined with an implicit Euler time discretization. The feasibility of the method is illustrated for some test examples of one- and two-dimensional two-phase flow problems. 相似文献
20.
考虑气相影响的降雨入渗过程分析研究 总被引：4，自引：1，他引：3
降雨入渗过程是水在下渗的过程中驱替空气的水-气二相流过程,对这一过程的精确模拟一直是渗流计算的难点,目前的处理方法通常是忽略孔隙气压力变化的影响。根据多相流理论,结合质量守恒定律和达西定律,建立了水-气二相流模型,模型的求解采用积分有限差分法和Newton-Raphson迭代方法,通过变换主要变量来表达相态的变化,实现了水相、气相边界条件及降雨入渗边界的精确模拟。利用上述模型对一土柱试验进行模拟,从而验证了模型的正确性,研究了一均质土层的降雨入渗过程,得到了孔隙水压力、孔隙气压力和毛细压力及含水率的变化过程。根据入渗率与地表孔隙气压力的变化关系,验证了孔隙气压力的增大对入渗水流产生阻滞作用。在求解非稳定渗流问题中,考虑空气压力变化的影响是值得研究的。 相似文献