稠油油藏蒸汽驱中后期剩余油分布特征及提高采收率方式研究

针对中国浅层及中深层稠油油藏,利用数值模拟研究方法,研究了不同稠油油藏的蒸汽驱开发规律和蒸汽驱中后期的剩余油分布特征,明确了稠油油藏蒸汽驱中后期的提高采收率方式。研究结果表明:浅层稠油油藏与中深层稠油油藏蒸汽驱的开发规律基本一致。驱替阶段生产效果好、产量高且稳定、油汽比高、含水率低;蒸汽突破后的开发阶段也是蒸汽驱开发的重要阶段,但是该阶段油汽比明显低于驱替阶段,表明该阶段蒸汽热效率明显降低。不同稠油油藏的剩余油分布特征类似,均表现出明显的垂向动用差异特征,即油层上部动用程度高,剩余油饱和度低,油层下部动用程度低,剩余油饱和度高,下部油层是剩余油挖潜的主要对象。从下到上逐层上返开发和多介质辅助是提高蒸汽驱中后期采收率的有效方式。研究结果对同类油藏开发具有重要意义。     

Traveling waves in a finite condensation rate model for steam injection

Steam drive recovery of oil is an economical way of producing oil even in times of low oil prices and is used worldwide. This paper focuses on the one-dimensional setting, where steam is injected into a core initially containing oil and connate water while oil and water are produced at the other end. A three-phase (oil, water, steam) hot zone develops, which is abruptly separated from the two-phase (oil + water) cold zone by the steam condensation front. The oil, water and energy balance equations (Rankine–Hugoniot conditions) cannot uniquely solve the system of equations at the steam condensation front. In a previous study, we showed that two additional constraints follow from an analysis of the traveling wave equation representing the shock; however, within the shock, we assumed local thermodynamic equilibrium. Here we extend the previous study and include finite condensation rates; using that appropriate scaling requires that the Peclet number and the Damkohler number are of the same order of magnitude. We give a numerical proof, using a color-coding technique, that, given the capillary diffusion behavior and the rate equation, a unique solution can be obtained. It is proven analytically that the solution for large condensation rates tends to the solution obtained assuming local thermodynamic equilibrium. Computations with realistic values to describe the viscous and capillary effects show that the condensation rate can have a significant effect on the global saturation profile, e.g. the oil saturation just upstream of the steam condensation front.     

运用半离散中心迎风格式计算二维浅水方程的研究

以三阶中心加权本质无振荡重构为基础,采用一维一维进行计算的方法,给出了求解二维浅水方程的高分辨率三阶半离散中心迎风格式.引入的重构方法既提高了格式的精度,又保证格式是无振荡的.时间的离散用最优的三阶SSP(Strong Stability Preserving)Runge-Kutta方法.源项的离散用辛普森公式.计算方法保持了中心差分格式简单的优点,即不需用黎曼解算器和进行特征分解过程.数值模拟结果与其它方法所得结果一致,表明了方法的有效性和稳定性.     

Shallow-water simulations by a well-balanced WAF finite volume method: a case study to the great flood in 2011, Thailand

A well-balanced finite volume method for solving two-dimensional shallow water equations with weighted average flux (WAF) is developed in this work to simulate flooding. Friction source terms are estimated with a semi-implicit scheme resulting in an efficient numerical method for simulating shallow water flows over irregular domains, for both wet and dry beds. A wet/dry cell tracking technique is also presented for reducing computational time. The accuracy of these methods are investigated by application to well-studied cases. For practical purposes, the developed scheme is applied to simulate the flooding of the Chao Phraya river from Chai Nat to Sing Buri provinces in Thailand during October 13–17, 2011. The numerical simulations yield results that agree with the existing data obtained from the satellite images.     

Uniqueness conditions in a hyperbolic model for oil recovery by steamdrive

In this paper we study a one-dimensional model for oil recovery by steamdrive. This model consists of two parts: a (global) interface model and a (local) steam condensation/capillary diffusion model. In the interface model a steam condensation front (SCF) is present as an internal boundary between the hot steam zone (containing water, oil and steam) and the cold liquid zone (containing only water and oil). Disregarding capillary pressure away from the SCF, a 2× 2 hyperbolic system arises for the water and steam saturation. This system cannot be solved uniquely without additional conditions at the SCF. To find such conditions we blow up the SCF and consider a parabolic transition model, including capillary diffusion. We study in detail the existence conditions for traveling wave solutions. These conditions provide the missing matching conditions at the SCF in the hyperbolic limit. We show that different transition models yield different matching conditions, and thus different solutions of the interface model. We also give a relatively straightforward approximation and investigate its validity for certain ranges of model parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

求解对流占优地下水水质模型的有限元高精度广义迎风单元均衡格式及应用

根据水质模型的具体特点，对不同的方程采用不同方法，水流问题用有限元法；对流弥散方程先用算子分裂的方法分解为两个方程，即对流方程和弥散方程，前者用高精度广义迎风格式求解，对弥散方程则采用多单元均衡格式法求解，最后合成为高精度广义迎风均衡格式求出溶质浓度。通过对数值实验例子的计算和实验溶质迁移的模拟，可以看出在求解对流弥散定解问题时，广义迎风均衡格式克服了有限元数值波动和浓度出现负值的问题，与有限元相比有较大改进。     

Isogeometric analysis for unsaturated flow problems

Unsaturated flow problems in porous media often described by Richards’ equation are of great importance in many engineering applications. In this contribution, we propose a new numerical flow approach based on isogeometric analysis (IGA) for modeling the unsaturated flow problems. The non-uniform rational B-spline (NURBS) basis is utilized for spatial discretization whereas the stable implicit backward Euler method for time discretization. The nonlinear Richards’ equation is iteratively solved with the aid of the Newton–Raphson scheme. Owing to some desirable features of an efficient numerical flow approach, major advantages of the present formulation involve: (a) numerical oscillation at the wetting front can be avoided or facilitated, simply by using either an h-refinement or a lumped mass matrix technique; (b) higher-order exactness can be obtained due to the nature of the IGA features; (c) the approach is straightforward to implement and it does not need any transformation, e.g., Kirchhoff transformation or filter algorithm; and (d) in contrast to the Picard iteration scheme, which forms linear convergences, the proposed approach can however yield quadratic convergences by using the Newton–Raphson method for solving resultant nonlinear equations. Numerical model validation is analyzed by solving a three-dimensional unsaturated flow problem in soil, and its derived results are verified against analytical solutions. Numerical applications are then studied by considering three extensive examples with simple and complex configurations to further show the accuracy and applicability of the present IGA.     

非结构网格上的三维浅水流动数值模型

针对当前复杂环境水流模拟的需求,建立了新型的基于特征型高分辨率数值算法的三维非结构网格浅水动力模型。模型采用有限体积法离散sigma坐标下的三维浅水方程,运用Roe黎曼近似解评估水平界面通量。模型网格拟合边界能力强,可根据需要局部加密;格式数值性能优良,具有守恒性、单调迎风性、高数值分辨率等特性。同时,应用干湿判别法处理动边界,以适应浅滩地形漫/露过程模拟的需要。封闭水池内部风生环流、干河床上溃坝过程和长江口实际潮流场的模拟从不同侧面展示了模型的特点,结果表明它能够准确地预测水流的三维流动结构,而且计算简单高效,具有良好的数值稳定性。     

A finite element solution of a fully coupled implicit formulation for reservoir simulation

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.     

非饱和渗流问题的自适应欠松弛变量变换方法

在使用有限元方法求解非饱和土渗流问题时,土-水特征曲线和渗透率函数的强烈非线性经常会造成计算中出现迭代不收敛、计算误差大等问题。基于变量变换的思想,结合时间步长自适应技术提出了一种求解非饱和渗流问题的新方法--欠松弛RFT变换方法（ATUR1）。ATUR1方法通过变量变换,大大降低了Richards方程中未知数在空间和时间上的非线性程度,从而改善这种非线性所带来的计算收敛困难和精度差等问题。欠松弛技术的引入减少了迭代过程中的振荡现象,进一步提高了非线性迭代计算的效率。时间步长自适应技术则有效地控制整个计算过程的误差。数值算例结果说明,ATUR1可以有效地提高计算效率和精度,是一种准确有效的计算方法。     

三维三相渗流数模在提高非均质油藏注水开发采收率中的应用

强非均质油藏注水开发过程中随着水洗程度的加深．高渗层水淹严重，低渗层无法动用或动用程度较低，油层平面及纵向动用差异日益增大，严重影响注水开发效果．以强非均质油藏板9断块为例，针对油藏本身的流体特性及注水开发特点，从油、气、水三相渗流达西运动方程和物质守恒角度出发，建立了该断块油藏三维三相渗流数学模型．优化设计合理的网格系统以及算法组合对该断块进行了数值模拟研究，准确描述剩余潜力分布．有针对性的提出综合治理措施．使开发效果得到明显改善，为同类断块油藏的开发提供指导和借鉴。     

Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems

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.     

An edge-based strain smoothing particle finite element method for large deformation problems in geotechnical engineering

To solve large deformation geotechnical problems, a novel strain-smoothed particle finite element method (SPFEM) is proposed that incorporates a simple and effective edge-based strain smoothing method within the framework of original PFEM. Compared with the original PFEM, the proposed novel SPFEM can solve the volumetric locking problem like previously developed node-based smoothed PFEM when lower-order triangular element is used. Compared with the node-based smoothed PFEM known as “overly soft” or underestimation property, the proposed SPFEM offers super-convergent and very accurate solutions due to the implementation of edge-based strain smoothing method. To guarantee the computational stability, the proposed SPFEM uses an explicit time integration scheme and adopts an adaptive updating time step. Performance of the proposed SPFEM for geotechnical problems is first examined by four benchmark numerical examples: (a) bar vibrations, (b) large settlement of strip footing, (c) collapse of aluminium bars column, and (d) failure of a homogeneous soil slope. Finally, the progressive failure of slope of sensitive clay is simulated using the proposed SPFEM to show its outstanding performance in solving large deformation geotechnical problems. All results demonstrate that the novel SPFEM is a powerful and easily extensible numerical method for analysing large deformation problems in geotechnical engineering.     

Water Curtain System Pre-design for Crude Oil Storage URCs: A Numerical Modeling and Genetic Programming Approach

In this paper the main criteria of the water curtain system for unlined rock caverns (URCs) is described. By the application of numerical modeling and genetic programming (GP), a method for water curtain system pre-design for Iranian crude oil storage URCs (common dimension worldwide) is presented. A comprehensive set of numerical simulations is performed using the finite element based commercial software (COMSOL 5.1) where the results are used as database for genetic programming. Describing equations of water inflow to the filled and empty caverns and water production rate of water curtain boreholes are generated using GP. By equating the proposed equations to each other, water curtain system can be pre-designed. Relative error of the generated GP equations shows their ability and accuracy. Applying a standard regression coefficient method, sensitivity analysis of parameters related to water curtain performance and water inflow to the caverns is performed as well. The results help the design of the water curtain system for crude oil storage caverns worldwide.     

A micromechanical-based elasto-viscoplastic model for the Callovo-Oxfordian argillite: Algorithms,validations, and applications

For a potential geological barrier of high-level radioactive waste repositories in France, the long-term mechanical behavior of the Callovo-Oxfordian (COx) argillite is the most concern for engineers. In this paper, a micromechanical-based elasto-viscoplastic model is proposed, and its numerical realization is our main object. The COx argillite is considered as a three-phase composite consists of porous clay, quartz, and calcite. By assigning appropriate constitutive laws to those constituents, the macroscopic elasto-viscoplastic behavior of the COx argillite is determined with an extended Hill's incremental approach. The numerical aspects includes (a) a new formulation is proposed for the plastic multiplier when adopting the overstress (Perzyna) model to define the viscoplastic strain. Meanwhile, a new formulation is also proposed to solve it within the framework of an implicit returning mapping scheme. (b) The corresponding consistent tangent moduli are strictly derived by extending the method proposed for solving plastic problems; (c) the efficiency of the proposed integration algorithms for the local constitutive equations and the homogenization procedure are validated, receptively, by a built-in porous plasticity model of a commercial finite element (FE) program ABAQUS and by FE computations of a two-phase unit cell; and (d) the proposed micromechanical model is finally applied to simulate experiment data in short-term triaxial compression tests and long-term triaxial creep tests. And the numerical results show that it is able to reflect the variation of the mechanical behavior with respect to the varied mineralogical compositions.     

特超稠油油藏水平井蒸汽驱油物理模拟实验

以胜利油田A区块特超稠油油藏为目标区块,自主研发了高温高压二维比例物理模型,研究了不同开发阶段水平井蒸汽驱油机理,开展了油藏压力、井底干 度、注汽强度对水平井蒸汽驱的效果影响的研究。物模实验结果显示,蒸汽驱整个过程分为三个阶段：存水回采期、汽驱受效期、蒸汽突破期。存水回采期蒸汽腔向水平方向扩展,以水平驱替方式为主 ;汽驱受效期蒸汽腔向垂向和水平方向扩展,以水平驱替方式为主,纵向泄油为辅;后期蒸汽突破,蒸汽腔继续向上方扩展,以纵向泄油为主,实现油层整体动用。5 MPa时转蒸汽驱的采出程度高于7 MPa时转蒸汽驱的采出程度;蒸汽驱的井底蒸汽干度应不低于0.4,蒸汽干度越高,水平井蒸汽驱的开发效果越好;注汽强度为1.9 t/(d·ha·m)时温度场最为发育。同时,在高压下提高干度可实现水 平井蒸汽驱的有效开发。以上的实验结果较好地指导了胜利油田A区块特超稠油油藏水平井蒸汽驱开发,取得了明显的开发效果,该研究对于类似稠油和超稠油油藏水平井蒸汽驱开发具有重要的指导意义 。     

A new locally conservative numerical method for two-phase flow in heterogeneous poroelastic media

We construct a new class of locally conservative numerical methods for two-phase immiscible flow in heterogeneous poroelastic media. Within the framework of the so-called iteratively coupled methods and fixed-stress split algorithm we develop mixed finite element methods for the flow and geomechanics subsystems which furnish locally conservative Darcy velocity and transient porosity input fields for the transport problem for the water saturation. Such hyperbolic equation is decomposed within an operator splitting technique based on a predictor–corrector scheme with the predictor step discretized by a higher-order non-oscillatory finite volume central scheme. The proposed scheme adopts an inhomogeneous dual mesh with variable cell size ruled by the local wave speed of propagation to compute numerical fluxes at cell edges. In the limit of small time steps the central scheme gives rise to a semidiscrete formulation for the water saturation capable of incorporating heterogeneous porosity fields and generalized flux functions including the water transport due to the solid phase velocity. Numerical simulations of a water-flooding problem in secondary oil recovery are presented for different realizations of the input random fields (permeability, Young modulus and initial porosity). Comparison between the accuracies of the proposed approach and the traditional one-way coupled hydro-geomechanical formulation are presented. The effects of the cross-correlation between the input random fields and compaction drive mechanism upon finger growth and breakthrough curves are also analyzed. A notable feature of the formulation proposed herein is the accurate prediction of the influence of geomechanical effects upon the unstable movement of the water front, whose evolution is dictated by rock heterogeneity and unfavorable viscosity ratio, without deteriorating the local conservative character of the numerical schemes.     

台兰河地下水库辐射井抽水过程的非稳定渗流场的有限元分析

针对台兰河地下水库大口径辐射井抽水效果的数值模拟问题,在分析了大口径辐射井渗流行为基础上,提出了应用辐射井子结构法和子结构开关器等辐射井精细模拟技术,并联用改进的截止负压法、迭代增量法和求解大型稀疏矩阵的预处理共轭梯度算法进行有辐射井影响的地下水非稳定渗流场的有限元分析。应用自主研发的三维可视化渗流有限元计算软件GWSS对台兰河地下水库辐射井抽水试验过程中的非稳定渗流场进行了数值模拟研究。研究结果表明：所有观测井计算水位的平均绝对误差为0.22 m,单井水位的平均误差最大值为 0.40 m,最小值为0.02 m,各观测井地下水位的模拟值与实测值的变化趋势吻合较好。经验证算法的合理性和程序的可靠性较好。提出的辐射井子结构法可以精细模拟辐射井的渗流行为和局部精细渗流场,可用于分析辐射井抽水过程中的地下水非稳定渗流变化及取水效率评价。     

极浅层稠油油藏油砂特征及潜力评价

油砂和浅层稠油是具有超低开发成本的两类非常规资源,非常规与历次油价下跌密切相关,使得这类资源成为了全球瞩目的焦点.春风油田兼具地表油砂和浅层稠油两类非常规,但岩心在地表会呈现极松散的不成型油砂,使得一些基础常规实验无法测定,影响到进一步分析评估.因此,需要针对这类非常规资源进行一系列新实验,即在常规实验的基础上,增加热物性、高温相渗、核磁共振等专项实验,并与常规实验结果进行比较.热物性实验发现,储层内部灰质、泥质夹层导热性良好,反映热波及效率会较高.相渗实验发现,油砂的油水相渗Kro和Krw的终点间距较大,两相覆盖范围宽,束缚水饱和度低,且孔隙越均匀,油相相对渗透率就越大.实验还发现,热物性、相渗、阵列感应实验得到的不同参数,相互之间存在一定相关性.利用新的核磁共振方法,可直接得到束缚水饱和度,获取原始含油饱和度,进而求取驱油效率,大大简化实验步骤和测试项目.最后,通过驱油效率计算和潜力评价发现,虽然经过多轮次吞吐,油砂目前的平均含油饱和度仍然很高,反映了稠油储量动用程度低,仍有很大的开发潜力.     

交错网格下的浅水方程高分辨Gauss型格式

在交错网格上,基于高精度的Gauss积分公式,针对浅水波方程设计了对模拟涌波具有高分辨率的完全二阶精度的数值计算格式。由于采用了交错网格,差分格式不需要解Riemann问题,因此本文格式具有计算简单、工作量少、编程简便等特点。另外,在一维单个方程时,本文格式在CFL(Courant Friedrich Lewy)条件限制下为TVD(Total Variation Diminishing)格式,在二维和三维情况下格式具有MmB(Maximum and Minimum Bounds Preserving)性质。利用国家高性能计算中心(合肥)的曙光1000型分布存储大规模并行机,对在交错网格下所构造的求解浅水方程的高分辨差分格式进行了并行实现,几个算例的计算结果令人满意。