Numerical investigation of dual-porosity model with transient transfer function based on discrete-fracture model

Based on the characteristics of fractures in naturally fractured reservoir and a discrete-fracture model, a fracture network numerical well test model is developed.Bottom hole pressure response curves and the pressure field are obtained by solving the model equations with the finite-element method. By analyzing bottom hole pressure curves and the fluid flow in the pressure field, seven flow stages can be recognized on the curves. An upscaling method is developed to compare with the dual-porosity model(DPM). The comparisons results show that the DPM overestimates the inter-porosity coefficient λ and the storage factor ω. The analysis results show that fracture conductivity plays a leading role in the fluid flow. Matrix permeability influences the beginning time of flow from the matrix to fractures. Fractures density is another important parameter controlling the flow. The fracture linear flow is hidden under the large fracture density.The pressure propagation is slower in the direction of larger fracture density.     

考虑诱导缝多段压裂水平井非均质改造压力动态模型研究

为了准确模拟致密油藏水平井大规模压裂形成复杂裂缝网络系统和非均质储层井底压力变化,建立考虑诱导缝矩形非均质储层多段压裂水平井不稳定渗流数学模型,耦合裂缝模型与储层模型得到有限导流裂缝拉普拉斯空间井底压力解,对两种非均质储层模型分别利用数值解、边界元和已有模型验证其准确性.基于压力导数曲线特征进行流动阶段划分和参数敏感性分析,得到以下结果:和常规压裂水平井井底压力导数曲线相比较,理想模式下,考虑诱导缝影响时特有的流动阶段是综合线性流阶段、诱导缝向压裂裂缝“补充”阶段、储层线性流动阶段和拟边界控制流阶段.诱导缝条数的增加加剧了综合线性流阶段的持续时间,降低了流体渗流阻力,早期阶段压力曲线越低;当诱导缝与压裂裂缝导流能力一定时,裂缝导流能力越大,线性流持续时间越长;当所有压裂裂缝不在一个区域时,沿井筒方向两端区域低渗透率弱化了低渗区域诱导缝流体向压裂裂缝“补充”阶段,因此,沿井筒方向两端区域渗透率越低,早期阶段压力曲线越高;当所有压裂裂缝在一个区域时,渗透率变化只影响径向流阶段之后压力曲线形态,外区渗透率越低,早期径向流阶段之后压力曲线越高.通过实例验证,表明该模型和方法的实用性和准确性.     

基于离散裂缝的多段压裂水平井数值试井模型及应用

水平井压裂技术已经成为开发低渗透油气藏、页岩气藏和致密气场等非常规油气藏的关键技术。基于离散裂缝模型,对裂缝进行简化,建立了二维多段压裂水平井有限导流数值试井模型,利用有限元方法求解模型,获得多段压裂水平井试井理论曲线和压力场特征。分析表明:多段压裂水平井的试井理论曲线一共分为七个阶段:井筒储存段、裂缝线性流段、裂缝-地层双线性流段、裂缝干扰段、地层线性流段、系统径向流段和边界作用段,其中裂缝-地层双线性流段和裂缝干扰是其典型特征。分析了裂缝数量、裂缝间距、裂缝不对称、裂缝不等长和裂缝部分缺失等因素对试井理论曲线的影响,结果表明:裂缝数量和裂缝间距对试井理论曲线的影响最大。较多的裂缝、较大裂缝间距、对称的裂缝和等长的裂缝有利于降低压裂水平井井底的流动阻力,提高产能。将建立的数值试井模型应用于四川盆地一口多段压裂水平井的压力恢复测试的数值试井解释,结果表明:本文建立的模型可以较好的拟合压力恢复测试数据,可以获得裂缝的导流能力和裂缝长度,为压裂效果评价和压裂设计提供指导。      

考虑多重运移机制耦合页岩气藏压裂水平井数值模拟

页岩作为典型的微纳尺度多孔介质,游离气与吸附气共存,传统的达西定律已无法准确描述气体在页岩微纳尺度的运移规律.基于双重介质模型和离散裂缝模型构建页岩气藏分段压裂水平井模型,其中基岩中考虑气体的黏性流、Knudsen 扩散以及气体在基岩孔隙表面的吸附解吸,吸附采用Langmuir等温吸附方程;裂缝中考虑黏性流和Knudsen扩散,在此基础上建立基岩-裂缝双重介质压裂水平井数学模型并采用有限元方法对模型进行求解.结果表明,基岩固有渗透率越小,表面扩散和Knudsen扩散的影响越大,反之则越小;人工裂缝的性质包括条数、开度、半长以及间距,主要影响压裂水平井生产早期,随着人工裂缝参数值的增加,压裂水平井产能增加,累产气量也越大.其次,页岩气藏压裂诱导缝和天然裂缝的发育程度对页岩气藏的产能有很大的影响,水平井周围只有人工裂缝,周围天然裂缝不开启或不发育时,页岩气藏的水平井的产能较低.      

Numerical well test for well with finite conductivity vertical fracture in coalbed

A new well test model is developed for the hydraulic fractured well in coalbed by considering the following aspects： methane desorption phenomena, finite conductivity vertical fractures, and asymmetry of the fracture about the well. A new parameter is introduced to describe the storage of the fracture, which is named as a combined fracture storage. Another new concept called the fracture asymmetry coefficient is used to define the asymmetry of the fracture about the well. Finite element method （FEM） is used to solve the new mathematical model. The well test type curves and pressure fields are obtained and analyzed. The effects of the combined fracture storage, desorption factor, fracture conductivity, and fracture asymmetry coefficient on the well test type curves are discussed in detail. In order to verify the new model, a set of field well test data is analyzed.     

多尺度嵌入式离散裂缝模型模拟方法

天然裂缝性油藏和人工压裂油藏内裂缝形态多样,分布复杂,传统的离散裂缝模型将裂缝作为基岩网格的边界,采用非结构化网格进行网格划分,其划分过程复杂,计算量大。嵌入式离散裂缝模型划分网格时不需要考虑油藏内的裂缝形态,只需对基岩系统进行简单的网格剖分,可以大大降低网格划分的复杂度,从而提高计算效率。然而,在油藏级别的数值模拟和人工压裂裂缝下的产能分析中,仍然存在计算量巨大、模拟时间过长的问题。本文提出嵌入式离散裂缝模型的多尺度数值计算格式,使用多尺度模拟有限差分法研究嵌入式离散裂缝模型渗流问题。通过在粗网格上求解局部流动问题计算多尺度基函数,多尺度基函数可以捕捉裂缝与基岩间的相互关系,反映单元内的非均质性,因此该方法既有传统尺度升级法的计算效率,又可以保证计算精度,数值结果表明这是一种有效的裂缝性油藏数值模拟方法。     

两套节点格林元嵌入式离散裂缝模型数值模拟方法

对于原始嵌入式离散裂缝模型(EDFM), 在计算包含裂缝单元的基质网格内的压力分布时采用了线性分布假设, 这导致了油藏开发早期对非稳态窜流量的计算精度不足. 因此, 本文提出了一种两套节点格林元法的EDFM数值模拟方法. 两套节点格林元法的核心思想是将压力节点与流量节点区分开, 一套压力节点设置在单元顶点, 另一套流量节点设置在网格边的中点, 满足局部物质守恒、具有二阶精度的同时, 可适用于任意网格类型. 本文将两套节点格林元法与EDFM耦合, 采用了非稳态渗流控制方程的边界积分形式推导了基质网格与裂缝网格之间传质量的新格式, 代替了线性分布假设以提高模拟精度; 此外, 修正后的EDFM能适应任意形态的基质网格剖分, 拓展了原始EDFM仅适用于矩形基质网格、难以考虑复杂油藏边界的局限性. 研究表明: 通过对比商业模拟软件tNavigator? LGR模块与原始EDFM, 验证了本文模型具有较高的早期计算精度; 以复杂油藏边界?缝网?SRV分区模型为例, 通过对比SFEM-COMSOL商业模拟软件, 验证了本文模型处理复杂问题的适应性. 本文研究可用于裂缝性油藏开发动态的精确模拟.      

A new computation model of fractured horizontal well coupling with reservoir

Based on Green's functions and Newman's product principle, pressure drop formula was derived for considering simultaneous production of fractures and horizontal wellbore in unsteady state. A reservoir/fractured horizontal well coupling model is developed for finite conductivity condition that can be solved by the combination of quasi‐Newton method and PSO (Particle Swarm Optimization) algorithm. The solution of a practical example shows that lots of factors can affect the productivity of the fractured horizontal well. The number of the fractures has an optimizing range. Different fractures have different flow rates and the production in the central fracture is the lowest. The distribution of production rate in the wellbore has a wave‐like shape due to the influence of fractures. The closer fractures are the lower flow rate in well segments. Considering the horizontal wellbore production, the production rates in the fractures are asymmetric and the corresponding pressure drop curve is smoother. Copyright © 2010 John Wiley & Sons, Ltd.     

井筒气液两相流对致密气压裂水平井试井的影响

多段压裂水平井技术是目前开采致密气最常用的方法之一,在致密气压裂水平井试井测试中常常伴随着一定的产水量,井筒气液两相流会增加井筒流体的流动阻力,加大井筒流体流动对试井解释的影响.为了明确井筒气液两相流对致密气藏压裂水平井试井的影响,提高产水致密气压裂水平井的试井解释精度,建立了一种井筒气液两相流与地层渗流耦合的试井模型,采用数值方法对模型进行求解,获得了考虑井筒气液两相流的压裂水平井试井理论曲线、压力场分布及裂缝产量分布.研究结果表明:井筒气液两相流会增加试井理论曲线中压力和压力导数值,造成靠近入窗点的压力扩散要快于远离入窗点的压力扩散,引起靠近入窗点的裂缝产量要高于远离入窗点的裂缝产量.现场实例分析进一步说明,不考虑井筒两相流可能会对产水压裂水平井的试井解释结果产生很大误差,主要表现为水平井筒假设为无限大导流能力会使得拟合得到的表皮系数偏大,将测试点视为入窗点会使得拟合得到的原始地层压力偏小.所建立的考虑井筒两相流的压裂水平井试井模型为产水致密气井试井资料的正确解释提供了重要技术保障.      

Modeling of Two-Phase Flow in Fractured Porous Media on Unstructured Non-Uniformly Coarsened Grids

In this article, we investigate two strategies for coarsening fractured geological models. The first approach, which generates grids that resolve the fractures, is referred to as explicit fracture-matrix separation (EFMS). The second approach is based on a non-uniform coarsening strategy introduced in Aarnes et al. (Adv Water Resour 30(11):2177–2193, 2007a). A series of two-phase flow simulations where the saturation is modeled on the respective coarse grids are performed. The accuracy of the resulting solutions is examined, and the robustness of the two strategies is assessed with respect to number of fractures, degree of coarsening, well locations, phase viscosities, and fracture permeability. The numerical results show that saturation solutions obtained on the non-uniform coarse grids are consistently more accurate than the corresponding saturation solutions obtained on the EFMS grids. The numerical results also reveal that it is much easier to tune the upscaling factor with the non-uniform coarsening approach.     

Up-Scaling of Double Porosity Fractured Media Using Continuous-Time Random Walks Methods

We present a new application of continuous time random walks (CTRW) methods to model fluid flows in fractured rocks. The proposed method allows large scale equivalent permeability tensors and matrix/fractures exchange function to be computed from high resolution maps of fractured porous media. Knowing these parameters allows us to carry out large scale simulations of flows governed by the dual porosity equations of Warren and Root. A direct connection between the exchange function and the time correlation function of the presence in the fractures of a particle undergoing a suitable Brownian motion over the whole medium is derived. This connection allows us to develop an efficient numerical method to compute the transient exchange term within the complete range of time scales of interest. It also gives an alternative probabilistic interpretation of the Warren and Root model. For the sake of simplicity, in the present paper, the method will only be developed to Cartesian structured grids, although it can be adapted for unstructured grids highly suited to describing complex fracture networks.     

页岩气藏的双重介质-离散裂缝模型

考虑页岩气藏开发中渗流的多尺度效应,提出了一个基于裂缝-孔隙双重介质的离散裂缝模型．在该模型中,基质、天然裂缝和人工压裂裂缝采用各自控制方程独立计算,不同介质之间通过流量交换相互关联．为分析模型可靠性,分别和基于渗透率粗化及压裂裂缝导流能力无穷大的模型对比．数值算例显示,伴随着网格细分,该模型与精确渗透率粗化模型具有相同计算精度,两者收敛速度均较快,但该模型易推广到多相流动问题,而等压模型对产量将有所高估．研究了地质参数和工艺参数对气井产量的影响规律．计算结果表明天然裂缝渗透率及基质孔隙扩散系数对产气速率有着重要影响,产气速率伴随着人工压裂裂缝导流能力、长度以及数目的增加而增加,但是增加幅度会逐步趋缓．     

气藏压裂水平井非稳态流动分析

应用Green函数和Newman积原理,建立了压裂水平井与气藏耦合的非稳态流动模型,并给出求解方法。所建立的模型可应用多种约束条件,考虑了井筒压降和加速度的影响,并适用于各向异性气藏。实例计算表明：水平井在早期非稳态阶段的流量比拟稳态阶段大得多。早期非稳态流动阶段,各条裂缝之间未发生干扰,流量的大小与裂缝条数成正比例关...     

多层平行裂隙型多孔介质通道内流体流动传热特性

基于Brinkman-extended Darcy模型和局部热平衡模型, 对多层平行裂隙型多孔介质通道内的流动传热特性进行研究. 获得了多层平行裂隙型多孔介质通道内各区域的速度场、温度场、摩擦系数及努塞尔数解析解, 并分析了裂隙层数、达西数、空心率、有效热导率之比等对通道内流动传热特性的影响. 结果表明: 达西数较小时, 通道多孔介质层内会出现不随高度变化的达西速度, 此达西速度会随裂隙层数的增加而增大, 但却不受各裂隙层下多孔介质层位置变化的影响. 增加裂隙层数会减弱空心率对压降的影响, 会使通道内流体压降升高, 但升高程度会逐渐降低. 增大热导率之比或减小空心率会使多裂隙通道内出现阶梯式温度分布, 而在较小热导率之比或较大空心率时多裂隙情况下的温度分布曲线会趋于一致. 此外, 当热导率之比较小时, 多层裂隙通道内的传热效果在任何空心率下都要优于单裂隙情况, 当热导率之比较大时, 存在临界空心率使各裂隙层数通道内的传热效果相同, 且多裂隙通道内继续增加裂隙层数对传热强度影响不大.      

Modeling of Heat and Mass Transfer in a Fractured Porous Medium

While fractured formations are possibly the most important contributors to the production of oil worldwide, modeling fractured formations with rigorous treatments has eluded reservoir engineers in the past. To date, one of the most commonly used fractured reservoir models remains the one that was suggested by Warren and Root nearly four decades ago. In this paper, a new model for fractures embedded in a porous medium is proposed. The model considers the Navier-Stokes equation in the fracture (channel flow) while using the Brinkman equation for the porous medium. Unlike the previous approach, the proposed model does not require the assumption of orthogonality of the fractures (sugar cube assumption) nor does it impose incorrect boundary conditions for the interface between the fracture and the porous medium. Also, the transfer coefficient between the fracture and matrix interface does not need to be specified, unlike the cases for which Darcy's law is used. In order to demonstrate the usefulness of the approach, a two-dimensional model of a fractured formation is developed and numerical simulation runs conducted.

The proposed model is derived through a series of finite element modeling runs for various cases using the Navier-Stokes equation in the channel while maintaining the Brinkman equation in the porous medium. Various cases studied include different fracture orientations, fracture frequencies, and thermal and solutal constraints. The usefulness of the proposed model in modeling complex formations is discussed. Finally, a series of numerical runs also provided validity of the proposed model for the cases in which thermal and solutal effects are important. Such a study of double diffusive phenomena, coupled with forced convection, in the context of fractured formations has not been reported before.     

Extended finite element modeling of production from a reservoir embedded with an arbitrary fracture network

A numerical scheme based on the eXtended Finite Element Method (XFEM) is proposed to simulate complex fluid flow in a fractured porous reservoir. By enriching the elements fully cut by the fracture and the near‐tip region, the flow mechanism including the tip flux singularity can be exactly represented in the XFEM formulation. Fluid transfer between the matrix and the fractures can be easily coupled, and XFEM also overcomes the sensitivity to the mesh used in the traditional unstructured discretizations, regardless of the complexity of the fracture network. The method is validated for a simple case by the exact analytical solution. Results are compared between XFEM and FEM. Case studies are presented to illustrate the power, efficiency, accuracy, and flexibility of the proposed method for simulating transient productive flow in reservoirs with complex fracture networks.     

An efficient method for discretizing 3D fractured media for subsurface flow and transport simulations

We introduce a new method to discretize inclined non‐planar two‐dimensional (2D) fractures in three‐dimensional (3D) fractured media for subsurface flow and transport simulations. The 2D fractures are represented by ellipsoids. We first discretize the fractures and generate a 2D finite element mesh for each fracture. Then, the mesh of fractures is analyzed by searching and treating critical geometric configurations. Based on that search, the method generates a quality mesh and allows for including finer grids. A solute transport problem in fractured porous media is solved to test the method. The results show that the method (i) adequately represents the fractured domain by maintaining the geometric integrity of input surfaces and geologic data, (ii) provides accurate results for both simple and complex fractured domains, (iii) is insensitive to spatial discretization, and (iv) is computationally very efficient. For inclined and vertical fractures, analytical and numerical solutions are shown to be in good agreement. The method is therefore suitable to discretize fracture networks for flow and transport simulations in fractured porous media. Copyright © 2010 John Wiley & Sons, Ltd.     

基于XFEM-MBEM的嵌入式离散裂缝模型流固耦合数值模拟方法

离散缝网的表征与模拟是目前国内外研究的热点. 在非常规油气开发过程中, 由于地应力场的存在会对裂缝的流动属性产生显著影响, 若将裂缝视为静态对象, 与矿场数据会出现极大偏差, 因此要基于动态裂缝做更深入的研究. 本文针对致密油藏应力场?渗流场耦合力学问题, 提出了一种高效的混合数值离散化方法, 其中采用扩展有限元法 (XFEM) 求解岩石的弹性形变, 采用了混合边界元法 (MBEM) 精确计算基岩与裂缝间的非稳态窜流, 这两种数值格式是完全耦合的, 并对整体计算格式的时间项进行了全隐式求解, 可准确表征致密油藏开采过程中的裂缝变形及流体流动机理. 此外, 本文采用了嵌入式离散裂缝前处理算法显式表征大尺度水力压裂缝, 并考虑了支撑剂的作用; 采用了双孔有效应力原理和双重介质隐式裂缝表征方法, 可捕捉基质与小尺度天然裂缝的动态信息; 由此, 本文所提出的混合模型综合表征了基质?天然裂缝?水力压裂缝共同组成的致密油藏复杂渗流环境, 并通过几个实例论证了模型的准确性, 研究表明: 对致密油藏压裂水平井进行产能评价时, 应力场所引起渗流参数的改变及裂缝开度降低的影响不可忽略. 本文研究可为非常规油气资源的开发提供理论指导.      

缝洞型油藏三维离散缝洞数值试井模型

缝洞型碳酸盐岩油藏发育着大尺度的溶洞和裂缝,非均质性极强,缝洞型碳酸盐岩油藏问题的研究成为了世界级难题之一.由于大尺度溶洞和裂缝对储层的流体流动起主导作用,因此,基于连续介质理论的双重介质或三重介质模型已不适合其中流体流动的描述.根据大型缝洞分布地质特征,探索性地提出了一种板块组合的复合架构离散缝洞模型描述该类油藏中的流体流动,将三维空间大裂缝用板块描述,溶洞用高渗透率和高孔隙度不规则多面体团块描述.将裂缝面用二维三角形单元离散, 溶洞和基质用三维四面体离散, 利用三维混合单元有限元法对建立的不定常渗流模型进行求解,得到了三维渗流条件下的试井理论曲线及压力场分布.通过对试井理论曲线特征的分析, 获得了各敏感参数对试井曲线的影响规律.通过对1口井的实际测试资料解释结果的分析,并与实际地震反射资料及生产实际资料的对比,发现本文所建立的模型可以较好地反映裂缝和溶洞的地质动态状况,并与实际生产状况具有较好的一致性.这一结果说明了所建模型的正确性以及测试资料分析结果的可靠性.