裂缝性孔隙介质储层参数全波形反演的高效计算

基于BISQ机制的裂缝孔隙介质储层参数(孔隙度、固相密度和流相密度)全波形反演对于BISQ理论的推广应用以解决油气勘探和开发的实际问题具有重要意义.然而,庞大的计算量将限制其发展和应用.本文提出了将小生境主从式并行遗传算法与多震源混合激发采集技术相结合的方法来改善这一问题.最后,以双层的基于BISQ机制的二维裂缝孔隙介质模型为例,进行了储层参数反演的数值分析.数值反演算例结果表明:基于小生境主从式并行遗传算法和多震源混合激发采集技术的储层参数反演方法极大地提高了原小生境遗传算法储层参数反演的计算效率,为利用孔隙介质储层参数反演进行油气预测和油藏监测奠定了理论基础.     

含气介质临界点、流体和骨架弹性参数的数值计算方法

目前临界孔隙度及孔隙介质的研究主要为测试分析的实验方法,如何运用数值计算方法求取孔隙流体介质临界点和组分弹性参数一直是备受关注的课题.本文提出了求取孔隙介质临界点、孔隙内流体和骨架弹性参数的数值计算公式及方法,并结合含气样品测试数据实现了这种数值计算.文章首先给出了3个包含孔隙度的线性方程,通过有机组合每个线性方程中的两个系数得到求取有关弹性参数的数值计算公式.然后,详细阐述了计算的方法和步骤以及需要注意的问题,把室内含气砂岩样品实测的综合介质密度、纵波速度和横波速度作为数值计算的输入数据,求得了临界点和流体及骨架等相关弹性参数的具体数值.通过比较分析本文数学方法求得的计算数据与实验方法测得的实测数据,表明了该数值计算公式的正确性和数值实现方法的有效性.     

利用走时反演二维多孔介质渗透率

综合利用直接方法和优化方法研究二维多孔介质渗透率反演问题. 问题的提法与前人不同,是由区域内各点流体渗透的走时来反演渗透率. 该反问题的求解可分成两步进行,归结为两个相应的子问题进行研究. 首先由流体走时反演二维多孔介质速度场的数值算法,然后由二维多孔介质速度场反演二维多孔介质渗透率的数值算法,最后给出数值例子. 数值结果表明了所用数值方法的正确性和有效性.     

频率域有限差分数值模拟地震波衰减和震电效应特征

地震波在地下含流体孔隙介质中传播时,会引起中观尺度的"局域流",进而产生地震波震电效应.基于Biot(1941)固结理论的准静态方程,在频率域中采用空间有限差分方法,正演模拟虚岩石物理岩样的地震波衰减和震电效应.与时间域虚岩石物理方法相比,该方法既可以直接求取任一频率下的地震波衰减和电势,便于应用于实际岩样的预测分析,也避免了讨论岩样外表面施加的力源函数表达式及时间剖分稳定性条件等问题.首先利用周期性层状介质模型验证了本文所描述方法的有效性,并进一步求取分析了周期性层状介质两种不同特征单元的渗流电流密度及电势,数值模拟结果表明由中观尺度"局域流"引起的震电效应电势振幅数量级在实验室测量范围之内,随后,分析研究了四种不同高渗介质占比值的地震衰减及震电效应特征.最后,将本文提出的震电效应数值计算方法推广至二维,并求取了二维斑块饱和模型的地震波衰减、速度频散、电势的振幅和相位角数值结果.     

流体饱和多孔隙介质二维弹性波方程正演模拟的小波有限元法

本文将小波有限元法引入到流体饱和多孔隙介质二维波动方程的正演模拟中,以二维Daubechies小波的尺度函数代替多项式函数作为插值函数,构造二维张量积小波单元.引入一类特征函数解决了Daubechies小波没有显式解析表达式所带来的基函数积分值计算问题,并推导出计算分数节点上Daubechies小波函数值的递推公式,从而构造出由小波系数空间到波场位移空间的快速小波变换.数值模拟结果表明该方法是有效的.     

层析成像技术在多相流中的研究动态

在多相流检测中,层析成像技术可获取多相流体二维/三维的时空局部的、微观的分布信息,是目前多相流参数检测技术研究发展的前沿和趋势之一.本文较系统阐述了国内外应用电阻层析、电容层析、射线层析、超声层析技术进行多相流检测的原理、研究现状以及层析成像技术在多相流应用方面的发展.     

裂缝-孔隙介质储层渗透率表征及其影响因素分析

含裂缝多孔介质渗透率预测是非常规油气资源勘探开发的一个紧迫问题.现有多孔介质岩石物理模型通常利用圆形孔管模拟宏观岩石孔隙空间,难以定量描述软孔隙/裂缝在压力作用下的闭合情况,缺乏裂缝/孔隙间流量交换的连通机制.本文提出含三维裂缝/软孔隙网络多孔介质模型,将储层岩石裂缝/软孔隙表示为椭圆截面微管,建立了周期性压力作用下微观裂缝流量表达式,通过网络模型和流量守恒条件,得到含有三维裂缝/软孔隙网络的多孔介质渗透率计算方法.数值算例表明,预测结果与实验数据分布范围吻合很好,能够给出不同类型岩心对应孔隙纵横比的分布图.三维裂缝/软孔隙网络模型建立了宏观可观测量与裂缝参数之间关系,能够定量分析岩石渗透率随裂缝体密度、纵横比、孔隙流体类型和围压等因素的变化规律,为复杂条件下储层渗透率预测提供了一种有效方法.     

二维介质的射线追踪模拟

本文讨论了射线追踪的一般问题,提出了二维介质射线追踪模拟的具体方法。物理模型的数值计算表明本文的方法是有效的。     

一种求解井间2.5维逆散射问题的迭代算法的研究

从二维非均匀介质中的声波方程出发,采用三维点源作为震源,提出了一种求解井间2.5维逆散射问题的迭代算法.其中,入射场与格林函数皆采用Maslov渐近理论予以计算,以避免非均匀介质中出现的焦散现象.数值模拟结果表明,本文提出的算法是有效的.     

带地形的可控源电磁法2.5维各向异性介质正演研究

目前,对于可控源电磁法各向异性介质2.5维问题,主要采用一次场、二次场分离的方法消除场源奇异性并降低截断边界对计算区域的影响.该方法数值计算精度高,但是很难适用于复杂地形条件下的数值模拟.针对复杂地形问题,基于总场的有限元方法表现出一定的优越性,然而,这种方法存在场源奇异性问题和截断边界问题.本文采用基于总场计算的方法对带地形的可控源电磁法2.5维各向异性介质进行模拟研究,推导了考虑电导率和介电常数各向异性的2.5维控制方程;引入网格加密-收缩算法降低场源奇异性的影响范围,提升数值计算效率;引入行波分解边界条件降低截断边界的影响;提出任意采样反傅里叶变换方法,快速、高精度地计算出空间域电磁场分量.理论模型数值算例中:首先,验证了本文算法的有效性;其次,对任意各向异性倾角产生的可控源电磁响应规律进行研究;最后,采用山丘模型对各向异性介质电磁场的响应规律进行了模拟和分析.     

A numerical method for two-phase flow in fractured porous media with non-matching grids

We propose a novel computational method for the efficient simulation of two-phase flow in fractured porous media. Instead of refining the grid to capture the flow along the faults or fractures, we represent the latter as immersed interfaces, using a reduced model for the flow and suitable coupling conditions. We allow for non matching grids between the porous matrix and the fractures to increase the flexibility of the method in realistic cases. We employ the extended finite element method for the Darcy problem and a finite volume method that is able to handle cut cells and matrix-fracture interactions for the saturation equation. Moreover, we address through numerical experiments the problem of the choice of a suitable numerical flux in the case of a discontinuous flux function at the interface between the fracture and the porous matrix. A wrong approximate solution of the Riemann problem can yield unphysical solutions even in simple cases.     

平面S波在饱和多孔热弹性介质边界的反射问题研究

针对饱和多孔介质中热弹性波的传播特性问题,基于多孔介质理论和广义的热弹性模型,研究平面S波在饱和多孔热弹性介质边界上的反射问题。以考虑流-固耦合的饱和多孔介质波动方程和热-弹耦合的广义热弹性基本方程出发,建立饱和多孔介质的热-流-固耦合弹性波动模型。通过引入势函数并考虑自由透水和绝热的边界条件,经过理论推导最终给出在饱和多孔热弹性介质边界上的四种反射波的振幅反射率的理论表达式。在此基础上进行数值计算,分别讨论平面S波的入射频率、入射角和热膨胀系数等参数对四种反射波的振幅反射率的影响情况。结果表明:各反射波的振幅反射率分别随频率和热膨胀系数的增大而增大,同时也受到平面S波入射角变化的影响。该结论对于土动力学的理论研究及其相关的工程勘探具有一定的指导意义。     

基于Comsol的饱和多孔介质动力方程的数值模拟及应用

两相饱和多孔介质的动力响应问题在地震工程领域具有重要的研究意义,由于涉及到固相和液相的动力耦合,使得该问题的求解尤为复杂。本文利用Comsol在求解多场耦合问题上的优点,针对Biot饱和多孔介质u-U耦合形式下的波动方程特征,经过一系列微分算子运算和矩阵变换得到导数形式下的波动方程,基于Comsol Multiphysics提供的广义偏微分方程模式对变形后的波动方程进行求解,并把改进后的无限元边界应用到无限域动力问题的模拟中。通过与饱和多孔介质动力响应的解析解进行对比,验证模型求解技术的可行性和正确性,并在此基础上讨论饱和土地基中空沟隔振效果与饱和土体参数孔隙率、泊松比的关系。通过研究分析,可以为饱和土地基中空沟隔振设计提供一些有价值的参考。     

The dynamic response of fluid-saturated porous materials with application to seismically induced soil liquefaction

The numerical simulation of liquefaction phenomena in fluid-saturated porous materials within a continuum-mechanical framework is the aim of this contribution. This is achieved by exploiting the Theory of Porous Media (TPM) together with thermodynamically consistent elasto-viscoplastic constitutive laws. Additionally, the Finite Element Method (FEM) besides monolithic time-stepping schemes is used for the numerical treatment of the arising coupled multi-field problem. Within an isothermal and geometrically linear framework, the focus is on fully saturated biphasic materials with incompressible and immiscible phases. Thus, one is concerned with the class of volumetrically coupled problems involving a potentially strong coupling of the solid and fluid momentum balance equations and the algebraic incompressibility constraint. Applying the suggested material model, two important liquefaction-related incidents in porous media dynamics, namely the flow liquefaction and the cyclic mobility, are addressed, and a seismic soil–structure interaction problem to reveal the aforementioned two behaviors in saturated soils is introduced.     

Effects of chemical reactions on density-dependent fluid flow: on the numerical formulation and the development of instabilities

A three-dimensional, reactive numerical flow model is developed that couples chemical reactions with density-dependent mass transport and fluid flow. The model includes equilibrium reactions for the aqueous species, kinetic reactions between the solid and aqueous phases, and full coupling of porosity and permeability changes that result from precipitation and dissolution reactions in porous media. A one-step, global implicit approach is used to solve the coupled flow, transport and reaction equations with a fully implicit upstream-weighted control volume discretization. The Newton–Raphson method is applied to the discretized non-linear equations and a block ILU-preconditioned CGSTAB method is used to solve the resulting Jacobian matrix equations. This approach permits the solution of the complete set of governing equations for both concentration and pressure simultaneously affected by chemical and physical processes. A series of chemical transport simulations are conducted to investigate coupled processes of reactive chemical transport and density-dependent flow and their subsequent impact on the development of preferential flow paths in porous media. The coupled effects of the processes driving flow and the chemical reactions occurring during solute transport is studied using a carbonate system in fully saturated porous media. Results demonstrate that instability development is sensitive to the initial perturbation caused by density differences between the solute plume and the ambient groundwater. If the initial perturbation is large, then it acts as a “trigger” in the flow system that causes instabilities to develop in a planar reaction front. When permeability changes occur due to dissolution reactions occurring in the porous media, a reactive feedback loop is created by calcite dissolution and the mixed convective transport of the system. Although the feedback loop does not have a significant impact on plume shape, complex concentration distributions develop as a result of the instabilities generated in the flow system.     

A new scheme for numerical modelling of flow and transport processes in 3D fractured porous media

The objective of this work is to develop a new numerical approach for the three-dimensional modelling of flow and transient solute transport in fractured porous media which would provide an accurate and efficient treatment of 3D complex geometries and inhomogeneities. For this reason, and in order to eliminate as much as possible the number of degrees of freedom, the fracture network, fractures and their intersections, are solved with a coupled 2D–1D model while the porous matrix is solved independently with a 3D model. The interaction between both models is accounted for by a coupling iterative technique. In this way it is possible to improve efficiency and reduce CPU usage by avoiding 3D mesh refinements of the fractures. The approach is based on the discrete-fracture model in which the exact geometry and location of each fracture in the network must be provided as an input. The formulation is based on a multidimensional coupling of the boundary element method-multidomain (BEM-MD) scheme for the flow and boundary element dual reciprocity method-multidomain (BE-DRM-MD) scheme for the transport. Accurate results and high efficiency have been obtained and are reported in this paper.     

耦合有限单元法扩边的直流电阻率勘探无单元Galerkin法正演

本文分析了目前直流电阻率正演模拟中的无单元Galerkin法（EFGM）和有限单元法（FEM）的优缺点,针对采用第一类边界条件需要足够大的计算域时EFGM计算成本高的问题,在计算域外围区域采用FEM扩边,提出了直流电阻率的无单元Galerkin-有限单元耦合法（EFG-FE）.采用具有Kronecker delta函数性质的径向基点插值法（RPIM）构造EFGM形函数,在外围区域将EFGM与FEM直接耦合,无需其他处理手段,消除了传统EFGM与FEM耦合中存在的界面耦合困难.EFG-FE将模型计算域分割为EFGM区域和FEM区域,模型核心区域采用EFGM计算,发挥EFGM灵活性、适应性强和高精度的优点,使得模型建立简单方便,对任意复杂地电模型适应性强,同时获得高精度模拟结果.在模型计算域外围采用快速扩展的FEM单元网格进行剖分,利用其数值稳定性和高效性,使用少量FEM节点和单元网格将计算域大范围扩大满足第一类边界条件,同时不大幅增加计算成本,进而提高计算效率.最后,通过不同正演方法的模型算例的模拟结果对比,验证了本文提出的EFG-FE有效可行,其模拟结果具有很高的模拟精度,且相比于采用第三类边界条件的EFGM提高了计算效率,具有更好的模拟性能.     

饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法

本文基于Biot的饱和多孔介质本构方程,考察具有辐射阻尼的外行球面波,推导了饱和多孔介质三维黏弹性人工边界的法向和切向边界方程;在已有的饱和多孔介质二维显式有限元数值计算方法基础上,提出该理论的三维方法,并开发了实现该三维方法的有限元程序.算例表明饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法具有较好的精度和稳定性.     

Coupling multiscale finite element method for consolidation analysis of heterogeneous saturated porous media

The multiscale finite element method is developed for solving the coupling problems of consolidation of heterogeneous saturated porous media under external loading conditions. Two sets of multiscale base functions are constructed, respectively, for the pressure field of fluid flow and the displacement field of solid skeleton. The coupling problems are then solved with a multiscale numerical procedure in space and time domain. The heterogeneities induced by permeabilities and mechanical parameters of the saturated porous media are both taken into account. Numerical experiments are carried out for different cases in comparison with the standard finite element method. The numerical results show that the coupling multiscale finite element method can be successfully used for solving the complicated coupling problems. It reduces greatly the computing effort in both memory and time for transient problems.     

Numerical modelling of multiphase flow in porous media

The simultaneous flow of immiscible fluids in porous media occurs in a wide variety of applications. The equations governing these flows are inherently nonlinear, and the geometries and material properties characterizing many problems in petroleum and groundwater engineering can be quite irregular. As a result, numerical simulation often offers the only viable approach to the mathematical modelling of multiphase flows. This paper provides an overview of the types of models that are used in this field and highlights some of the numerical techniques that have appeared recently. The exposition includes discussions of multiphase, multispecies flows in which chemical transport and interphase mass transfers play important roles. The paper also examines some of the outstanding physical and mathematical problems in multiphase flow simulation. The scope of the paper is limited to isothermal flows in natural porous media; however, many of the special techniques and difficulties discussed also arise in artificial porous media and multiphase flows with thermal effects.