Vertical Permeability Distribution of Reservoirs with Impermeable Barriers

The presence of impermeable horizontal barriers (such as shales) in a reservoir is known to have a significant effect on its vertical permeability. Since calculation of an effective vertical permeability of such a reservoir is important, approximation of the distribution of vertical permeability may also be useful for analysis of the two-phase vertical flow of buoyant fluid, such as may occur in the subsurface injection of carbon dioxide into saline formations. In this situation, the maximum likely vertical permeability of a reservoir with impermeable barriers, which could be estimated from the probability distribution of the vertical permeability, is a more useful metric than an overall effective value for the vertical permeability due to its presumed relationship to breakthrough time. In this article, we derive expressions for the mean and variance of the vertical permeability of both two and three-dimensional reservoirs using the statistical streamline method of Begg and King (Paper No. 13529, 1985), and calculate the probability distribution of the vertical permeability of a reservoir with impermeable barriers. In addition, we also provide a simple statistical analysis of the presence of high vertical permeability regions in the reservoir, which may be of importance in coarse-scale simulations of vertical migration.     

裂缝性低渗透油藏流-固耦合理论与数值模拟

根据裂缝性低渗油藏的储层特征,建立适合裂缝性砂岩油藏渗流的等效连续介质模型。将渗流力学与弹塑性力学相结合,建立裂缝性低渗透油藏的流-固耦合渗流数学模型,并给出其数值解.通过数值模拟对一实际井网开发过程中孔隙度、渗透率的变化以及开发指标进行计算,并和刚性模型以及双重介质模型的计算结果进行了分析比较.     

Asymptotics,Saturation Fronts,and High Resolution Reservoir Characterization

Using an asymptotic methodology we formulate a fast, accurate algorithm for the inversion of multi-phase flow data. The approach is appropriate for many common reservoir production strategies such as CO₂ and water flooding. The technique compares well to a purely numerical method with a significant reduction in computation time. In an application to fractional flow data from the North Robertson field in West Texas, 100,000 permeability and porosity parameters are determined on a workstation. Generally, higher permeability, approaching 1milli-Darcy, is found in the eastern portion of the reservoir. The permeability estimates agree with type curve analysis for material and volumetric balances and a previous numerical pilot-point inversion.     

Analytical three-dimensional renormalization for calculating effective permeabilities

The ability to calculate an effective permeability of a heterogeneous reservoir based on knowledge of its small-scale permeability is fundamental to practical numerical reservoir characterization. One elegant technique that forms the basis of this process is renormalization (King, P.R.: Transport Porous Med. 4, 37–58 (1989)). In two dimensions, renormalization can be implemented using a simple analytical formula. In three dimensions, however, no such analytical result exists, and renormalization must be performed using a numerical implementation. In this article, we present a simple analytical approximation to the method of renormalization in three dimensions. A detailed comparison with numerical results demonstrates its accuracy and highlights the significant reduction in computational cost achieved.     

低渗岩心驱替过程中的压力分布特征研究

考虑低渗岩心的应力敏感性,通过实验和数值计算,研究了一维水驱油过程中,压力的分布及变化规律,并对其影响因素进行了分析. 结果表明：压力分布由于受到应力敏感性的影响而显示出明显的非线性特征,在前缘面处存在一个明显的分界点;应力敏感性程度、黏度比对压力分布的影响较大.     

天然气水合物降压开采沉积物压缩效应数值模拟研究

深海天然气水合物降压开采过程中,沉积物的压缩会改变储层的物理力学特性,进而对天然气的开采效果产生显著影响.为揭示沉积物压缩效应下井周围储层物理力学特性演化规律,本文建立了考虑沉积物压缩效应的理论模型,通过COMSOL模拟研究了不同初始固有渗透率、初始水合物饱和度和井底压力条件下的降压开采中生产井周围储层的物理力学特性演化规律以及开采效果.结果表明:受沉积物压缩的影响,水合物分解区的渗透率随着与井筒距离的增加先增加后减少;产气与产水速率由零立即上升至峰值,然后迅速下降,并且考虑沉积物压缩时的产气与产水速率比不考虑时低;在水合物完全分解区,渗透率的大小与有效应力成负相关关系,未分解区渗透率的大小与水合物饱和度成负相关关系;井底压力越小,有效应力越大,生产井周围储层的渗透率下降越明显;初始水合物饱和度对产气与产水的影响存在拐点,饱和度拐点位于0.25与0.35之间,高水合物饱和度并不代表储层开采效果好,产气速率的高低还与储层的渗透率有关,高水合物饱和度储层的渗透率较低,产气速率较低;储层初始固有渗透率较高时显著促进了开采效果,但储层变形量较大增加了储层的不稳定性.     

Wormhole Propagation Behavior Under Reservoir Condition in Carbonate Acidizing

In carbonate reservoirs, acid is injected into the formation under breakdown pressure to react with the rock to remove the contaminations caused by drilling and production, which is called carbonate acidizing in reservoir development. In carbonate acidizing, acid flows selectively through large pores to create wormholes. Wormhole propagation under experimental condition has been studied by many experts. In this paper, a model which couples a two-scale continuum model simulating wormholing in the invaded zone and a reservoir flow model for the compressed zone was used to study the wormhole propagation behavior under reservoir condition. In this model, the porosity values which are uniformly distributed used in former literature follow the normal law. Based on the model, we first compared the results of the two porosity generation methods, and then studied the wormhole propagation behavior under reservoir condition, and finally simulated a two-layer formation to study the effects of distance and permeability ratio between the two layers. The results show that the normally distributed porosities simulate wormholing better. The effect of compressed zone on wormhole propagation increases with the decrease of compressibility factor and wormhole has a maximal value in length. The effect of distance between the two layers on wormhole lengths and acid distributions can be divided into three zones based on the wormhole length in the lower layer. A critical value of permeability ratio between the two layers exists, below and above which the wormhole length in the low permeability layer decreases sharply and almost keeps constant, respectively.     

三维非均匀不稳定渗流方程的二维不均匀粗化算法

在无源汇条件下,根据流过某一个横截面的流体流量等于流过这一横截面内所有精细网格的流体流量之和这一特点提出了粗化网格等效渗透率的计算方法。在粗化区内,利用直接解法求解二维渗流方程,再用这些解合成粗化网格的三维合成解,并由合成解计算粗化网格的等效渗透率。根据精度的要求采用了不均匀网格粗化,在流体流速大的区域采用精细网格。利用所得等效渗透率计算了粗化网格的某三维非均匀不稳定渗流场的压降解,结果表明三维非均匀不稳定渗流方程的二维不均匀粗化解非常逼近采用精细网格的解,但计算的速度比采用精细网格提高了80倍。     

Transient Pressure Behavior of Reservoirs with Discrete Conductive Faults and Fractures

Fractures and faults are common features of many well-known reservoirs. They create traps, serve as conduits to oil and gas migration, and can behave as barriers or baffles to fluid flow. Naturally fractured reservoirs consist of fractures in igneous, metamorphic, sedimentary rocks (matrix), and formations. In most sedimentary formations both fractures and matrix contribute to flow and storage, but in igneous and metamorphic rocks only fractures contribute to flow and storage, and the matrix has almost zero permeability and porosity. In this study, we present a mesh-free semianalytical solution for pressure transient behavior in a 2D infinite reservoir containing a network of discrete and/or connected finite- and infinite-conductivity fractures. The proposed solution methodology is based on an analytical-element method and thus can be easily extended to incorporate other reservoir features such as sealing or leaky faults, domains with altered petrophysical properties (for example, fluid permeability or reservoir porosity), and complicated reservoir boundaries. It is shown that the pressure behavior of discretely fractured reservoirs is considerably different from the well-known Warren and Root dual-porosity reservoir model behavior. The pressure behavior of discretely fractured reservoirs shows many different flow regimes depending on fracture distribution, its intensity and conductivity. In some cases, they also exhibit a dual-porosity reservoir model behavior.     

On the Initiation of a Hydrothermal Eruption Using the Shock-Tube Model

In this work, the authors introduce the shock-tube model for a hydrothermal eruption in a geothermal reservoir. The governing equations, based on the multiphase Euler equations and a Darcy-type law, are solved using a three-phase weighted sub-system numerical solver. Results are then presented which show the importance of the geometry of the geothermal reservoir in predicting the initiation of a hydrothermal eruption. In particular, the porosity, permeability, and cohesion of the reservoir are shown to significantly affect the pressure difference required to initiate an eruption. Finally, the authors show the importance of the initial liquid water/water vapour volume fractions in determining the size of an eruption, and further show boiling to be of major importance.     

A Simple Model of a Two-Layered High-Temperature Liquid-Dominated Geothermal Reservoir as a Part of a Large-Scale Hydrothermal Convection System

The Kakkonda geothermal reservoir, Japan, is a typical high-temperature liquid-dominated geothermal reservoir, except for its distinctive two-layered temperature structure. It has a shallow permeable reservoir of 230–260°, and a deep less permeable reservoir of 350–360°. Geology and hydrology indicate that the shallow reservoir is one to two orders of magnitude more permeable than the deep reservoir, but that the two reservoirs communicate. It has been widely assumed in engineering and scientific circles that the connection between the two reservoirs is a zero or low permeability barrier to fluid flow. We show that this hypothesis is untenable, based on both physical evidence and numerical simulation. We numerically model the evolution of the geothermal system as it heats after emplacement of an intrusion. The two-layered temperature structure is found to be a consequence of the permeability difference, i.e. the two-layered permeability structure.     

Integration of genetic algorithm and a coactive neuro-fuzzy inference system for permeability prediction from well logs data

Permeability is one of the reservoir fundamental properties, which relate to the amount of fluid contained in a reservoir and its ability to flow. These properties have a significant impact on petroleum fields operations and reservoir management. The most reliable data of local permeability are taken from laboratory analysis of cores. Extensive coring is very expensive and this expense becomes reasonable in very limited cases. Thus, the proper determination of the permeability is of paramount importance because it affects the economy of the whole venture of development and operation of a field. In this study, we introduce a new hybrid network based on Coactive Neuro-Fuzzy Inference System (CANFIS). CANFIS is a dependable and robust network that developed to identify a non-linear relationship and mapping between petrophysical data and core samples. Then to improve the system performance, genetic algorithm (GA) was integrated in order to search of optimal network parameters and decrease of noisy data in training samples. An Iranian offshore gas field is located in the Persian Gulf, has been selected as the study area in this paper. Well log data are available on substantial number of wells. Core samples are also available from a few wells. It was shown that the new proposed strategy is an effective method in predicting permeability from well logs.     

Lattice Boltzmann Simulation of Fluid Flow in Synthetic Fractures

Fractures play an important role in reservoir engineering as they dominate the fluid flow in the reservoir. All evidence suggests that rarely can one model flow and transport in a fractured rock consistently by treating it as a uniform or mildly nonuniform isotropic continuum. Instead, one must generally account for the highly erratic heterogeneity, directional dependence, dual or multicomponent nature and multiscale behavior of fractured rocks. As experimental methods are expensive and time consuming most of the time numerical methods are used to study flow and transport in a fractured rock. In this work, we present results of the numerical computations for single phase flow simulations through two-dimensional synthetically created fracture apertures. These synthetic rock fractures are created using different fractal dimensions, anisotropy factors, and mismatch lengths. Lattice Boltzmann method (LBM), which is a new computational approach suitable to simulate fluid flow especially in complex geometries, was then used to determine the permeability for different fractures. Regions of high velocity and low velocity flow were identified. The resulting permeability values were less than the ones obtained with the cubic law estimates. It has been found that as the mean aperture–fractal dimension ratio increased permeability increased. Moreover as the anisotropy factor increased permeability decreased. Neural network simulations were used to generalize the results.     

砂砾岩油藏渗透系数研究

为了掌握砂砾岩油藏渗流规律,基于砂砾岩中砾和砂含量及其排列方式不同,开展了理论和实验研究。把砂砾岩孔隙度和渗透率设为砾、砂含量的函数,再基于Kozeny-Carman方程建立渗透率与孔隙度和颗粒粒径的函数关系。研究表明,砂砾岩组成及颗粒排列方式是控制砂砾岩渗透系数的主要因素,砂砾岩渗透率与孔隙度为一种线性关系。水驱油实验进一步表明,束缚水饱和度依赖于砂、砾含量,含水上升快,揭示了砂砾岩油藏特有的渗流特点。     

考虑二次梯度项及动边界的双重介质低渗透油藏流动分析

在传统试井模型的非线性偏微分方程中根据弱可压缩流体的假设,忽略了二次梯度项,对于低渗透油藏这种方法是有疑问的.低渗透问题一个显著的特点就是流体的流动边界随着时间不断向外扩展.为了更好地研究双重介质低渗透油藏中流体的流动问题,考虑了二次梯度项及活动边界的影响,同时考虑了低渗透油藏的非达西渗流特征,建立了双重介质低渗透油藏流动模型.采用Douglas-Jones预估-校正差分方法获得了无限大地层定产量生产时模型的数值解,分别讨论了不同参数变化时压力的变化规律及活动边界随时间的传播规律,还分析了考虑和忽略二次梯度项影响时模型数值解之间的差异随时间的变化规律,做出了典型压力曲线图版,这些结果可用于实际试井分析.     

An Experimental Method for One Dimensional Permeability Characterization of Heterogeneous Porous Media at the Core Scale

Many reservoir simulator inputs are derived from laboratory experiments. Special core analysis techniques generally assume that core samples are homogeneous. This assumption does not hold for porous media with significant heterogeneities. This paper presents a new method to characterize core scale permeability heterogeneity. The method is validated by both numerical and experimental results. The leading idea consists in injecting a high viscosity miscible fluid into a core sample saturated with a low viscosity fluid. In such conditions, the fluid displacement is expected to be piston-like. We investigate the evolution of the pressure drop as a function of time. A continuous permeability profile is estimated along flow direction from the pressure drop assuming that the core sample is a stack of infinitely thin cross sections perpendicular to flow direction. Thus, we determine a permeability value for each cross section. Numerical and laboratory experiments are carried out to validate the method. Flow simulations are performed for numerical models representing core samples to estimate the pressure drop. The selected models are sequences of plugs with constant permeabilities. In addition, laboratory displacements are conducted for both low permeability and high permeability core samples. To investigate whether there is dispersion inside the porous medium, CT scan measurements are performed during fluid displacement: the location of the front is observed at successive time intervals. The results validate the methodology developed in this paper as long as heterogeneity is one dimensional.     

A Computational Approach to Determine Average Reservoir Pressure in a Coalbed Methane (CBM) Well Flowing Under Dominant Matrix Shrinkage Effect

Desorption of gas from coal matrix alters the pore volume of fracture network. Consequently, cleat porosity and permeability of reservoir changes as pressure depletes. The method of standard pressure analysis calculations produces incorrect results in the case of coalbed methane reservoirs producing under dominant matrix shrinkage effect. The change in cleat porosity and permeability due to shrinkage of coal matrix following gas desorption with pressure depletion invalidates the underlying assumptions made in the derivation of diffusivity equation. Consequently, equations of pseudo-steady state commonly used in conventional reservoirs no longer remain valid as the porosity and permeability values change with pressure depletion. In this paper, effort has been made to describe pseudo-steady-state flow in coalbed methane reservoirs in the form of a new equation that accounts for pressure dependency of cleat porosity and permeability due to shrinkage of coal matrix. The concept of Al-Hussainy et al. (1966) has been extended to define a new pseudo-pressure function which assimilates within itself the pressure dependence of porosity and permeability Palmer and Mansoori (1998). Equation has been used to relate the cleat porosity with pressure. The equation-based computational method suggested in this paper finds its usefulness in estimating average reservoir pressure for any known flowing bottom hole pressure and thus reducing the frequency of future pressure buildup tests. The new equation is also useful in predicting reservoir pressure under the situation when coal matrix shrinks below desorption pressure. The equation used in the computational method has been validated with the help of numerical simulator CMG-GEM.     

含泥质夹层油藏蒸汽注采过程的自适应网格算法研究

根据泥质夹层的低渗特性及空间分布，本文提出了一种含泥质夹层油藏网格渗透率的粗化计算方法，并在此基础上，将自适应网格算法应用于含泥质夹层油藏的数值模拟，提升其计算效率．在计算过程中，网格的动态划分仅依据流体物理量的变化，泥质夹层区域不全部采用细网格，仅针对流动锋面处的泥质夹层采用细网格，其余泥质夹层处采用不同程度的粗网格．相较于传统算法，网格数大幅下降．数值算例表明，自适应网格算法的计算结果精度与全精细网格一致，能够准确模拟出泥质夹层对于流体的阻碍作用，同时计算效率得到大幅提升，约为全精细网格算法的3~7 倍．     

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.     

河道砂油藏的自适应非均匀网格粗化算法

以河道砂的观测深度为确定性数据，由贝叶斯理论通过随机楚模的方法楚立横截面为抛物线形状的河道砂油藏边界面，并将渗透率自适应网格技术应用于河道砂油藏的网格粗化算法中。在渗透率或孔隙度交化异常区域自动采用精细网格，用直接解法求解渗透率或孔隙度交化异常区域的压强分布，而在其他区域采用不均匀网格粗化方法计算，印在流体流速大的区域采用精细网格。用本文方法计算了河道砂油藏的压强分布，结果表明河道砂油藏的三维不均匀自适应网格粗化算法的解在渗透率或孔隙度异常区的压强分布规律更逼近采用精细网格的解，在其他区域压强分布规律非常逼近粗化算法的解，但计算的速度比采用精细网格提高了100多倍。