A fast marching method for reservoir simulation

We present a fast marching level set method for reservoir simulation based on a fractional flow formulation of two-phase, incompressible, immiscible flow in two or three space dimensions. The method uses a fast marching approach and is therefore considerably faster than conventional finite difference methods. The fast marching approach compares favorably with a front tracking method as regards both efficiency and accuracy. In addition, it maintains the advantage of being able to handle changing topologies of the front structure. This revised version was published online in July 2006 with corrections to the Cover Date.     

Transient drainage volume characterization and flow simulation in reservoir models using the fast marching method

The Fast Marching Method (FMM) has been applied to characterize the transient drainage volume and to simulate flow as a function of time in porous media using the concept of the “diffusive time of flight” (DTOF). The DTOF (τ) provides a spatial coordinate which reduces the three dimensional pressure diffusivity equation to an equivalent one dimensional formulation. It is obtained from the solution to the Eikonal equation via the FMM. Previous applications of this approach have solved the flow equations numerically or by using an analytic asymptotic approximation. Both solution approaches rely upon three characteristics. (1) Accurate solution for the DTOF irrespective of the degree of heterogeneity within a reservoir model. (2) The approximation of the three dimensional pressure solution in terms of the τ coordinate. (3) Accurate representation and discretization of the drainage volume, on which the asymptotic and numerical flow simulations are based. The second and third of these characteristics are specific to reservoir engineering applications, and provide the focus of this study. Analysis of the drainage volume shows that the near well region requires special treatment, leading to a composite discretization for the drainage volume. This discretization has a direct impact upon the calculation of the well test pressure derivative when the asymptotic approximation is used for pressure transient interpretation. For flow simulation, the discretization directly impacts the calculation of the well index and the intercell transmissibility computed in the τ coordinate, and places additional constraints on the discretization of the drainage volume. These new results are validated by comparison with a commercial finite difference flow simulator, and are shown to be more accurate than earlier computational approaches.

     

Direct simulation of groundwater transit-time distributions using the reservoir theory

Groundwater transit times are of interest for the management of water resources, assessment of pollution from non-point sources, and quantitative dating of groundwaters by the use of environmental isotopes. The age of water is the time water has spent in an aquifer since it has entered the system, whereas the transit time is the age of water as it exits the system. Water at the outlet of an aquifer is a mixture of water elements with different transit times, as a consequence of the different flow-line lengths. In this paper, transit-time distributions are calculated by coupling two existing methods, the reservoir theory and a recent age-simulation method. Based on the derivation of the cumulative age distribution over the whole domain, the approach accounts for the whole hydrogeological framework. The method is tested using an analytical example and its applicability illustrated for a regional layered aquifer. Results show the asymmetry and multimodality of the transit-time distribution even in advection-only conditions, due to the aquifer geometry and to the velocity-field heterogeneity. Received, August 1998/Revised, May 1999, December 1999/Accepted, December 1999     

Decision-theoretic sensitivity analysis for reservoir development under uncertainty using multilevel quasi-Monte Carlo methods

At various stages of petroleum reservoir development, we encounter a large degree of geological uncertainty under which a rational decision has to be made. In order to identify which parameter or group of parameters significantly affects the output of a decision model, we investigate decision-theoretic sensitivity analysis and its computational issues in this paper. In particular, we employ the so-called expected value of partial perfect information (EVPPI) as a sensitivity index and apply multilevel Monte Carlo (MLMC) methods to efficient estimation of EVPPI. In a recent paper by Giles and Goda, an antithetic MLMC estimator for EVPPI is proposed and its variance analysis is conducted under some assumptions on a decision model. In this paper, for an improvement on the performance of the MLMC estimator, we incorporate randomized quasi-Monte Carlo methods within the inner sampling, which results in an multilevel quasi-Monte Carlo (MLQMC) estimator. We apply both the antithetic MLMC and MLQMC estimators to a simple waterflooding decision problem under uncertainty on absolute permeability and relative permeability curves. Through numerical experiments, we compare the performances of the MLMC and MLQMC estimators and confirm a significant advantage of the MLQMC estimator.     

Research on the environmental capacity of a reservoir by using the conceptual net method

The aquatic environment capacity possesses the largest tolerance to pollutants. We can improve the calculating precision using the conceptual net method. Its basic ways involved in calculation include the following aspects: first, to establish the flow continuity equation, flow motion equation, water quality equation and other mathematical models; at the same time, to conceptualize the reservoir studied, divide the reservoir into several functional areas, and use the one-dimensional section-beginning calculation model to calculate all cross-sections of each functional area; then, to superimpose the environmental capacity of each functional section to get the aquatic environment capacity of the entire two-dimensional space; and finally, to introduce how to make use of the conceptual net to calculate the aquatic environment capacity in terms of the actual reservoir’s situation.     

用区间有限元计算边坡荷载组合效应

边坡工程的稳定性受多种因素的影响,其荷载具有不确定性,可以用具有上、下限的区间数来表示,提出了用区间数学和有限元结合构成的区间有限元方法来求解边坡变形。以古树包边坡的变形为例,研究了该方法的可行性,并与常规有限元计算结果进行了比较,实例计算结果表明,该方法用于计算具有不确定性参数和荷载的工程问题的变形是有效的,与常规有限元的要考虑多种工况相比,计算工作量大大减少,使用简便,而计算结果却能满足工程需要,适合计算边坡工程。     

地下结构地震破坏静-动力耦合模拟研究

地下结构地震破坏过程模拟是研究地下结构抗震性能的有效手段,通过人工边界条件设置将围岩土体的自重应力作为动力响应模拟的初始状态,实现了地下结构地震响应静-动力耦合数值模拟。基于有限元分析软件ABAQUS,将极限剪应变作为破坏标准,采用生死单元法模拟了地下结构的地震破坏过程,通过结构埋深考虑了初始地应力对地下结构抗震性能的影响。模拟结果表明,地下结构的抗震性能存在一个最不利埋深,即最容易地震破坏的埋深,当结构的埋深超过最不利埋深时,结构的极限抗震能力增强,若结构产生地震破坏,则结构埋深越深即初始地应力越高其破坏程度也越强。     

Fully coupled hydraulic fracture simulation using the improved element partition method

The improved element partition method (IEPM) is a newly developed fracture simulation approach. IEPM allows a fracture to run across an element without introducing extra degrees of freedom. It can also simulate any number of fractures in a prescribed mesh without remeshing. In this study, the IEPM is extended to hydraulic fracture simulation. First, the seepage and volumetric storage matrix of a cracked element are derived using virtual nodes (the intersection points of a crack with element edges). Subsequently, the fully coupled hydromechanical equation is derived for this cracked element. To eliminate the extra degrees of freedom (virtual nodal quantities), the water pressure and displacement of the virtual nodes are associated with their adjacent nodes through least squares interpolation. Finally, the fully coupled equation in terms of nodal quantities is obtained. The verification cases validate the method. By using this method, the field-scale hydraulic fracturing process is well simulated. The proposed approach is simple and efficient for field-scale hydraulic fracture simulation.     

碳酸盐岩储集层模型数值模拟与分析

碳酸盐岩储层作为油气勘探领域中的重要研究目标,其波场特征变化极为复杂,为提高对该类储集层多波地震资料的认知度,高精度数值模拟是行之有效的方法之一。这里在各向同性弹性波方程基础上,推导了纵波、横波分离方程,运用高阶交错网格有限差分技术与PML边界吸收技术,高精度模拟地震波在碳酸盐岩储层中的传播,得到了该类储层模型中的弹性波全波场,也分离出纵波信息和转换波波场信息,并保留了各自能量信息。同时结合AVO技术分析了弹性波在碳酸盐岩储层中AVO响应特征,并通过对储层理论模型进行试算,分析研究该类储层中的波场响应特征及传播规律,为碳酸盐岩储层的识别与预测提供参考依据,更能满足复杂油气田勘探开发的实际需要。     

浅谈储层渗透率变异系数计算方法

储层的渗透率变异系数、极差、突进系数等是渗透率非均质程度的定量表征。文章探讨了渗透率变异系数的计算方法,认为:变异系数等计算方法与数据分布类型有关,变异系数等参数的计算需根据数据分布特征来选取适合的方法。劳伦兹系数与数据分布类型无关;劳伦兹系数是有界的,分布于0～1之间。尤其是在对数正态分布条件下,劳伦兹曲线、基尼系数完全由标准差σ决定,劳伦兹曲线、基尼系数以及σ这三者间存在着一一对应关系。劳伦兹系数可以用于储层非均质性定量评价。     

Numerical simulation of dynamic catastrophe of slope instability in three Gorges reservoir area based on FEM and SPH method

Natural Hazards - Affected by continuous heavy rainfall, a large number of landslide disasters occur every year in the Three Gorges Reservoir area, which causes serious property loss and...     

堆载诱发型土质滑坡运动特征物质点法模拟

坡顶堆载是人类工程活动诱发滑坡的主因之一。物质点法（MPM）属于一种无网格数值计算方法,它能够有效模拟滑坡大变形全过程物质行为与运动特征。文章基于线性形函数离散方法、MUSL求解格式及Drucker-Prager屈服准则,建立了可用于滑坡全过程模拟的单套单相物质点模型;通过对比干燥铝棒堆积物模拟砂堆失稳过程的基准试验结果,对模型有效性进行了验证。对堆载诱发型土质滑坡典型工况进行了物质点法全过程模拟,获得了滑坡全过程中典型时刻坡体形态、塑性应变分布以及控制点滑速演化趋势。结果表明:算例堆载诱发型土质滑坡属推移型滑坡,具有渐进性破坏特征,可分为坡顶压缩、局部蠕滑、加速滑动与减速滑动等四个阶段。参数分析结果亦表明,堆载诱发型土质滑坡前缘物质运动特征量均与堆载量间存在强正相关性、而与土体黏聚力及内摩擦角存在强负相关性。统计29种典型工况,分别建立了峰值滑动加速度、最大滑速、最大滑距及坡体最大动能等运动特征量与堆载量、土体黏聚力及内摩擦角之间的线性回归方程,可用于堆载诱发型土质滑坡致灾行为预测。     

基于UDEC的隧道掘进机滚刀破岩数值模拟研究

现今全断面隧道掘进机（TBM）施工方法在长大深埋隧道工程中已被广泛采用,对滚刀破岩关键技术的进一步认识具有重要的工程价值。为了研究滚刀破岩机制,分析刀圈断面形态、岩石强度和节理角度对其的影响,运用UDEC方法建立了滚刀贯切岩石的二维数值系列模型,对TBM滚刀破岩过程进行了仿真。分析表明：滚刀破岩是滚刀下岩石拉破坏和剪破坏的综合反映,拉破坏是裂纹萌生与扩展的主要驱动机制;刃宽较大的平刀与刃角较大的楔刀破岩效果较好;平刀与楔刀在软岩中破岩效果相近,平刀在硬岩施工中比楔刀的破岩效果好;滚刀对节理角度为30°～60°的岩石破坏效果较好,由于楔刀的“劈裂”作用,楔刀比平刀更适合用于贯切含有节理的岩石。     

Interpretation of well-cell pressures on hexagonal grids in numerical reservoir simulation

Peaceman’s equivalent well-cell radius for 2D square grids has been generalized to 2D grids consisting of regular hexagons. The development consists of the following steps. Firstly, the analytical solution for the pressure drop between injector and producer for wells in a seven-spot pattern is determined. Secondly, this solution is compared with the numerical solution on hexagonal grids for a sixth of a seven-spot pattern. Finally, the equivalent well-cell radius is calculated, and its asymptotic behavior for infinitely fine grids is derived. The results are valid for both steady-state and unsteady-state conditions.     

基于颗粒流模型的TBM滚刀破岩过程数值模拟研究

为了研究全断面岩石掘进机（TBM）盘型滚刀的破岩机制及其影响因素,采用颗粒流方法建立了岩石与滚刀的二维数值模型,实现了对TBM滚刀破岩过程的模拟。分析表明,滚刀的破岩过程可分为冲击挤压破碎、大量微裂纹生成、张拉性主裂纹扩展3个阶段,证实了滚刀破岩的挤压-张拉破坏理论。在滚刀侵入深度相同的前提下,随着刀圈刃角以及刃宽的增加,滚刀下的压碎区也相应增大,张拉性主裂纹数目增多,滚刀的破岩能力提高;与平刃刀圈相比,楔刃刀圈的“楔块劈裂”作用更加显著,使径向裂纹扩展得更快且更深入岩石内部。TBM滚刀对强度较高或较低岩石的破坏损伤较小,而对中等强度的岩石破坏损伤最为显著。     

基于波浪理论的水库地质灾害涌浪数值分析方法

有别于国内现行广泛应用Navie-Stokes方程进行地质灾害涌浪的数值模拟技术,本文采用波浪理论对地质灾害涌浪波进行了分析。地质灾害涌浪波是非周期性波,并且有强烈的非线性,介于中等水波至浅水波之间;可用浅水波模型和Boussinesq模型进行数学描述。本文采用有限差分法的Boussinesq模型,以三峡库区龚家方崩滑体涌浪为例,模拟了涌浪波的传播和爬高问题。该模型能够计算形成涌浪瞬时河面、河面最大波高图、最大流速矢量图、最大爬坡和预警分布图。模拟计算结果与调查结果吻合非常好。这说明基于波浪理论的地质灾害涌浪分析方法精度较高,为涌浪的预测研究提供了一种新的研究方法。     

颗粒破碎的三维离散元模拟研究

采用PFC等离散元方法研究岩土材料的颗粒破碎已经成为热点。采用考虑局部应力集中的点荷载破碎准则,利用阿波罗填充和膨胀法保证破碎前、后颗粒之间的种群平衡,并引入尺寸因子来表征不同粒径的颗粒强度。在此基础上,开展了石英砂、钙质砂和萨克拉门托河砂3种不同破碎难易程度材料的数值试验,并与室内试验结果进行对比。结果表明:建立的三维颗粒破碎模型能够很好地描述破碎难易程度不同的颗粒材料的压缩特性;考虑应力集中效应的点荷载破碎准则比基于平均应力Mohr-Coulomb理论的颗粒破碎准则更能真实地反应颗粒材料的破碎现象。同时,所建立的模型能够揭示破碎对颗粒材料各向异性消散和级配曲线演化的影响规律。     

Melting of corundum using conventional and two-phase molecular dynamic simulation method

The melting curve of corundum is calculated by using two approaches: the first one is conventional and the second one is two-phase molecular dynamics method both utilizing the same pairwise interatomic potential developed earlier on. The melting curve obtained by the two-phase simulation method is in agreement with the existing experimental data up to 25 GPa. A comparison of melting curves obtained by a two-phase simulation method and a conventional molecular dynamic method in NPT ensemble demonstrates a substantial overestimation of melting temperatures when applying conventional molecular dynamic technique. The inaccuracy of the conventional method increases with increasing pressure and, in the case of corundum, changes from about 300 K at 1 bar to about 1000 K at 1 Mbar. Received: 25 November 1996 / Revised, accepted: 11 March 1997     

近井储层改造对天然气水合物藏降压开采特性影响的数值模拟研究

本文基于我国第一轮海域天然气水合物试采地质模型,利用Tough+Hydrate对近井储层改造后的水合物藏进行降压开采模拟研究。探究了多孔骨架渗流通道对气/水输送、压降传播、水合物分解等的影响机制,评估了近井储层改造在不同开采层位和整个开采过程中对产能提高的贡献大小。模拟结果表明：多孔骨架渗流通道内气/水流速高,可以起到导流、防砂的作用;近井储层改造可促进压降传播,加快水合物分解,但骨架通道的增产作用随开采时间增加逐渐减弱;近井储层改造在不同开采层位起到的增产效果不同,三相层中的增产效果最明显,但由于模拟改造范围较小、形成的多孔骨架渗流通道渗透性较低,增产效果不明显,多孔骨架渗流通道高度为50 cm时,2年产气量仅提高11.7%。