油井开采过程中油层变形的流固耦合分析

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     

Time‐scale analysis in unsaturated porous media under external wave loads

Extreme waves caused by tsunamis and storm surges can lead to soil failures in the near‐shore region, which may have severe impact on coastal environments and communities. Multiphase flows in deformable porous media involve several coupled processes and multiple time scales, which are challenging for numerical simulations. The objective of this study is to investigate the roles of the various processes and their interactions in multiphase flows in unsaturated soils under external wave loading, via theoretical time‐scale analysis and numerical simulations. A coupled geomechanics–multiphase flow model based on conservation laws is used. Theoretical analysis based on coupled and decoupled models demonstrates that transient and steady‐state responses are governed by pore pressure diffusion and saturation front propagation, respectively, and that the two processes are essentially decoupled. Numerical simulations suggest that the compressibility of the pore fluids and the deformation of the soil skeleton are important when the transient responses of the media are of concern, while the steady‐state responses are not sensitive to these factors. The responses obtained from the fully coupled numerical simulations are explained by a simplified time‐scale analysis based on coupled and decoupled models. Copyright © 2010 John Wiley & Sons, Ltd.     

Pore to pore validation of pore network modelling against micromodel experiment results

Pore network modelling (PNM) has been widely used to study the multiphase flow and transport in porous media. Although a number of recent papers discussed the PNM validation on core-scale parameters such as permeability, relative permeability and capillary pressure; quantitative predictive potential of PNM on pore by pore basis has rarely been studied. The aim of this paper is to present a direct comparison between PNM simulations and corresponding micro-model experiments at the same scale and the same geometry. A number of well-defined and constrained two-phase flow in porous medium experimental scenarios were utilized to validate the physics solving part in PNM (filling rules, capillary and viscous pressure). This work validates that a dynamic pore network flow solver can predict two-phase flow displacements for these experiments for drainage situations at both pore and plug scales. A glass-etched micro-model is used to quantify the accuracy of a dynamic PNM solver on pore and core levels. Two-phase drainage micro fluidic experiments at different flow conditions are performed on micro-models. PNM simulations are performed on the same pattern and flow conditions as used in micro-model experiments. The two-phase distribution extracted from experiment images is registered onto rsults of PNM simulations for direct pore to pore comparison. Pore-scale matching level is found at around 75 % for all three test cases. The matching level of core-scale parameters such as S _{w c} and oil-phase permeability varies from case to case; the relative error to micro-model experiment measurements varies from 15 to 60 %. Possible reasons leading to discrepancies on core-scale parameters are discussed: missing considerations during validation of the combination of uncertainty in both simulator input parameters and experiments are seen as the principal factors.     

A FORMULATION OF FULLY COUPLED THERMAL–HYDRAULIC–MECHANICAL BEHAVIOUR OF SATURATED POROUS MEDIA—NUMERICAL APPROACH

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.     

Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method

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.     

一种适用于孔隙体积应变的有效应力方程

土力学奠基石Terzaghi有效应力原理被广泛应用于油藏孔隙和渗透率应力敏感研究中,然而其对于岩石孔隙体积应变的适用性存在争议。对颗粒不可压缩和颗粒可压缩的多孔介质分别进行了受力分析,推导了总体积、颗粒骨架、孔隙体积的有效应力表达式,与Biot、Skepmton有效应力方程对比,建立了适用于孔隙体积应变的新型有效应力方程,并进行了试验论证和应用举例。研究表明:在颗粒不可压缩多孔介质中,有效应力为超出平衡孔隙流压之外的颗粒间宏观等效应力;在颗粒可压缩变形多孔介质中,有效应力为其相同应变下的等效应力,有3种有效应力分别适用于总体积应变、颗粒体积应变、孔隙体积应变;新提出的孔隙体积有效应力方程与孔隙度、岩石总体积压缩系数、颗粒压缩系数、总应力和流压相关,4个理论计算式计算结果在3种多孔介质试验测试结果中的偏差均在5%以内;孔隙体积有效应力系数解决了如何定量增总应力来等效模拟储层降流压生产过程这一关键问题,3个压缩系数关系式理论计算准确方便。     

流固耦合问题及研究进展

传统的渗流理论一般假设流体流动的多孔介质骨架是完全刚性的,即在孔隙流体压力变化过程中,固体骨架不产生任何弹性或塑性变形,这时可将渗流作为非耦合问题来研究。这种简化虽然可以得到问题的近似解,但存在许多缺陷,而且也不切合生产实际。比如:在油田开采过程中,孔隙流体压力会逐渐降低,将导致储层内有效应力的变化,使储层产生变形。近年来,流固耦合问题越来越受到人们的重视,这方面的研究涉及许多领域。该文介绍了有关工程涉及到的流固耦合问题,重点针对油、气开采问题,介绍了储层流固耦合渗流的特点及研究方法和理论进展,包括单相、多相流体渗流的流固耦合数学模型及有限元数值模型。      

储层流固耦合的数学模型和非线性有限元方程

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。     

Modelling of fluid expulsion and deformation behaviour of dewatering sediments

A finite element model is developed for modelling coupled fluid expulsion/deformation behaviour of dewatering sediments subjected to external loadings under isothermal conditions. The non-linear deformation behaviour of the sediment (soil) skeleton is based on the force equilibrium equation in which the constitutive relationship of stress and strain is implemented by the modified Cam-Clay model in soil plasticity. The fluid flow behaviour in the model is described by the generalized porous media flow equation. The model allows temporal and spatial variations of porosity and permeability. The fluid viscosity and density are assumed to be temperature-dependent. The model also allows the development of single and multiple faults, depending upon the material (sediment and fluid) properties, loading and boundary conditions. Procedures are implemented for (1) updating the material properties such as porosity, permeability, fluid density and viscosity and (2) the development of faults which allow the formation of high-permeability conduits for fluid flow. The solution algorithm for displacements of the sediments and the excess pore (fluid) pressure is based on a residual load technique to handle the non-linear (elastic-plastic) deformation behaviour of the sediment skeleton. The model can be applied to one- and two-dimensional problems. Examples of a plane strain saturated sediment layer subjected to stepwise horizontal tractions versus time are given.     

A novel approach to eliminate error induced by cell to node projections

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.     

Multiphase lattice Boltzmann simulations for porous media applications

Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article, we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly report on multiphase flows containing solid particles, as well as implementation details and optimization issues.     

Modeling coupled THM processes of geological porous media with multiphase flow: Theory and validation against laboratory and field scale experiments

A FEM model for analysis of fully coupled multiphase flow, thermal transport and stress/deformation in geological porous media was developed based on the momentum, mass and energy conservation laws of the continuum mechanics and the averaging approach of the mixture theory over a three phase (solid–liquid–gas) system. Six processes (i.e. stress–strain, water flow, gas flow, vapor flow, heat transport and porosity evolution processes) and their coupling effects are considered, which not only makes the problem well-defined, but renders the governing PDEs closed, complete, compact and compatible. Displacements, pore water pressure, pore gas pressure, pore vapor pressure, temperature and porosity are selected as basic unknowns. The physical phenomena such as phase transition, gas solubility in liquid, thermo-osmosis, moisture transfer and moisture swelling are modeled. As a result, the relative humidity and other related variables in porous media can be evaluated on a sounder physical basis. A three dimensional computer code, THYME3D, was developed, with eight degrees of freedom at each node. The laboratory CEA Mock-up test and the field scale FEBEX benchmark test on bentonite performance assessment for underground nuclear waste repositories were used to validate the numerical model and the software. The coupled THM behaviors of the bentonite barriers were satisfactorily simulated, and the effects and impacts of the governing equations, constitutive relations and property parameters on the coupled THM processes were understood in terms of more straightforward interpretation of physical processes at microscopic scale of the porous media. The work developed enables further in-depth research on fully coupled THM or THMC processes in porous media.     

Numerical convergence study of iterative coupling for coupled flow and geomechanics

In this paper, we consider algorithms for modeling complex processes in porous media that include fluid and structure interactions. Numerous field applications would benefit from a better understanding and integration of porous flow and solid deformation. Important applications in environmental and petroleum engineering include carbon sequestration, surface subsidence, pore collapse, cavity generation, hydraulic fracturing, thermal fracturing, wellbore collapse, sand production, fault activation, and waste disposal, while similar issues arise in biosciences and chemical sciences as well. Here, we consider solving iteratively the coupling of flow and mechanics. We employ mixed finite element method for flow and a continuous Galerkin method for elasticity. For single-phase flow, we demonstrate the convergence and convergence rates for two widely used schemes, the undrained split and the fixed stress split. We discuss the extension of the fixed stress iterative coupling scheme to an equation of state compositional flow model coupled with elasticity and a single-phase poroelasticity model on general hexahedral grids. Computational results are presented.     

天然气水合物地层渗透率研究进展

天然气水合物开采涉及传热、水合物分解相变、多相渗流和地层变形4个物理过程。多相渗流过程伴随着对流传热,影响传热效率;多相渗流过程影响孔隙压力的消散速率,引起有效应力改变而影响地层变形;多相渗流过程影响传热的效率和孔隙压力的消散速率,使温度和压力条件发生变化,影响水合物的分解。多相渗流过程中,某相流体的有效渗透率不仅与该相流体的饱和度有关,还与地层绝对渗透率有关。地层绝对渗透率是多相渗流过程的关键参数之一。概述不同贮存状态水合物、地层孔隙率、水合物饱和度和地层有效应力对地层绝对渗透率影响的研究内容。以国内外天然气水合物地层绝对渗透率研究成果为基础,将来的研究重点主要包括粉细砂、黏土类地层和各向异性地层多相渗流研究,以及地层有效应力对绝对渗透率影响研究。     

Numerical modeling of multiphase fluid flow in deforming porous media: A comparison between two- and three-phase models for seismic analysis of earth and rockfill dams

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.     

相间相互作用原理与土壤水动力学基本方程

进一步阐明了多相介质力学分析的相间相互作用原理.应用相间相互作用原理重新推导了饱和土壤和非饱和土壤水分运动的控制方程,使两者具有统一的表达形式和理论基础.说明了达西定律的物理意义,在此基础上给出了非饱和土壤导水系数与饱和土壤渗透系数之间关系的表达式,该表达式在饱和条件下退化为饱和土的渗透系数.引用大连地区亚粘土和硅微粉在非饱和稳态渗流条件下的渗透试验结果验证了导水系数和饱和土的渗透系数之间的关系.     

A 2D mixed fracture–pore seepage model and hydromechanical coupling for fractured porous media

A novel two-dimensional mixed fracture–pore seepage model for fluid flow in fractured porous media is presented based on the computational framework of finite-discrete element method (FDEM). The model consists of a porous seepage model in triangular elements bonded by unbroken joint elements, as well as a fracture seepage model in broken joint elements. The principle for determining the fluid exchange coefficient of the unbroken joint element is provided to ensure numerical accuracy and efficiency. The mixed fracture–pore seepage model provides a simple but effective tool for solving fluid flow in fractured porous media. In this paper, examples of 1D and 2D seepage flow in porous media and porous media with a single fracture or multiple fractures are studied. The simulation results of the model match well with theoretical solutions or results obtained by commercial software, which verifies the correctness of the mixed fracture–pore seepage model. Furthermore, combining FDEM mechanical calculation and the mixed fracture–pore seepage model, a coupled hydromechanical model is built to simulate fluid-driven dynamic propagation of cracks in the porous media, as well as its influence on pore seepage and fracture seepage.

     

Thermal effects on fluid flow and hydraulic fracturing from wellbores and cavities in low-permeability formations

The coupled heat-fluid-stress problem of circular wellbore or spherical cavity subjected to a constant temperature change and a constant fluid flow rate is considered. Transient analytical solutions for temperature, pore pressure and stress are developed by coupling conductive heat transfer with Darcy fluid flow in a poroelastic medium. They are applicable to low permeability porous media suitable for liquid-waste disposal and also simulating reservoir for enhanced oil recovery, where conduction dominates the heat transfer process. A full range of solutions is presented showing separately the effects of temperature and fluid flow on pore pressure and stress development. It is shown that injection of warm fluid can be used to restrict fracture development around wellbores and cavities and generally to optimize a fluid injection operation. Both the limitations of the solutions and the convective flow effect are addressed. Copyright © 1999 John Wiley & Sons, Ltd.     

Visualizing complex pore structure and fluid flow in porous media using 3D printing technology and LBM simulation

Pore structures of porous media and properties of fluid flow are key factors for the study of non-Darcy groundwater flow. However, it is difficult to directly observe pore structures and flow properties, resulting in a “black box” problem of porous media. This problem has hindered the in-depth study of the groundwater flow mechanism at the pore scale. In recent years, 3D rapid prototyping technology has seen tremendous development. 3D printing provides digital models and printing models of porous media with clear internal structure. Thus, Lattice Boltzmann Method can be used to simulate the flow processes at the pore scale based on real pore structures. In this study, 3D printing cores and Lattice Boltzmann Method were coupled to conduct both laboratory and numerical experiments in spherical porous media with different sphere diameters and periodic arrays. The LBM simulation results show a good agreement with laboratory experimental results. With the advantages of LBM and 3D printing, this approach provides a visualization of the complex pore structure and fluid flow in pores, which is a promising method for studies of non-Darcy groundwater flow at the pore scale.     

Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method

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.